Taycan Turbo S analysis.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## The Taycan Turbo S: what Porsche doesn't want you to know! ##\n",
    "### Or, what you can do with public vehicle data ###"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![2020-porsche-taycan.jpg](img/2020-porsche-taycan.jpg)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First, a mantra: all models are wrong, some models are useful"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "using Unitful\n",
    "using Interpolations\n",
    "using DelimitedFiles\n",
    "using Plots\n",
    "using Polynomials\n",
    "using DifferentialEquations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "mass_veh = 2_358.7; #kg\n",
    "A_frontal = 2.331866; #m^2\n",
    "Cd = 0.25;\n",
    "max_spd = 257.5; #kph\n",
    "tire_r_front = 0.3595; #in m, 21\" rims, 265/35 tires\n",
    "tire_r_rear = 0.358; # in m, 21\" rims, 305/30 tires\n",
    "boost_time = 2.5; #s"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "#The stuff I had to guess\n",
    "ϕ_p = 0.95;\n",
    "slip_ratio = 1.15;\n",
    "rr = 0.01;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Physical constants\n",
    "ρ=1.225; #kg/m^3\n",
    "gn = ustrip(Unitful.gn);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Calculated constants\n",
    "f_traction_max = ϕ_p * mass_veh * gn;\n",
    "traction_limit_tq= f_traction_max * ((tire_r_front+tire_r_rear)/2)\n",
    "f_rr = rr*mass_veh*gn;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Handy values to have around\n",
    "spd_range = range(0,max_spd,length=1001);"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![taycan_pt_tq.png](img/taycan_pt_tq.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We'll call the blue line `pt_max_tq` and load the [DataThief](https://datathief.org/) output into Julia"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "pt_max_tq = readdlm(\n",
    "    \"taycan_pt_tq.txt\",\n",
    "    ',',\n",
    "    Float64,\n",
    "    '\\n',\n",
    "    skipstart=1);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Similarly, we'll call the max torque for the rear axle in first gear `ra1_max_tq`. We'll also set the first speed point equal to zero since DataThief doesn't trace out."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "ra1_max_tq = readdlm(\n",
    "    \"taycan_pt_tq_ra1.txt\",\n",
    "    ',',\n",
    "    Float64,\n",
    "    '\\n',\n",
    "    skipstart=1)\n",
    "ra1_max_tq[1,1]=0.0;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And for second gear on the rear axle, we'll use `ra2_max_tq`. There's no shifting to zero like in first gear since the DataThief data doesn't fully reach the torque limited regime for the motor"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "ra2_max_tq = readdlm(\n",
    "    \"taycan_pt_tq_ra2.txt\",\n",
    "    ',',\n",
    "    Float64,\n",
    "    '\\n',\n",
    "    skipstart=1);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally, we'll call the front motor torque `fa_max_tq`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "fa_max_tq = readdlm(\n",
    "    \"taycan_pt_tq_fa.txt\",\n",
    "    ',',\n",
    "    Float64,\n",
    "    '\\n',\n",
    "    skipstart=1);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Julia also provides some convenient interpolation functions, so we'll turn this data into something we can put into a simulation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "max_tq_itp = LinearInterpolation(\n",
    "    pt_max_tq[:,1], \n",
    "    pt_max_tq[:,2], \n",
    "    extrapolation_bc=Line()\n",
    ");\n",
    "\n",
    "ra1_max_itp = LinearInterpolation(\n",
    "    ra1_max_tq[:,1],\n",
    "    ra1_max_tq[:,2],\n",
    "    extrapolation_bc = Line()\n",
    ");\n",
    "\n",
    "ra2_max_itp = LinearInterpolation(\n",
    "    ra2_max_tq[:,1],\n",
    "    ra2_max_tq[:,2],\n",
    "    extrapolation_bc = Line()\n",
    ");\n",
    "\n",
    "fa_max_itp = LinearInterpolation(\n",
    "    fa_max_tq[:,1],\n",
    "    fa_max_tq[:,2],\n",
    "    extrapolation_bc = Flat()\n",
    ");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Interestingly, because the interpolations are functions, we can splice the two rear gears together pretty elegantly"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "ra_max_itp (generic function with 1 method)"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ra_max_itp(spd) = max(ra1_max_itp(spd), ra2_max_itp(spd))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Porsche has also said that the can boost the rear motor to 610 Nm and 370 kW for 2.5 seconds, but again we can use the functional nature of the interpolation data to scale what Porsche has provided. It's not perfect, but it should be approximately correct. I've also previously estimated the gear ratio for first gear on the rear axle to be about 15.33"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "boosted_ra_max_itp (generic function with 1 method)"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "boosted_ra_max_itp(spd) = min(ra_max_itp(spd)*370/335, 610*15.33)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
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       "  671.313,222.869 673.291,222.865 675.269,222.861 677.247,225.259 679.226,226.865 681.204,226.861 683.182,226.857 685.16,226.853 687.138,226.894 689.116,230.421 \n",
       "  691.095,230.852 693.073,230.848 695.051,233 697.029,236.527 699.007,240.054 700.985,247.58 702.964,255.107 704.942,258.634 706.92,262.161 708.898,269.689 \n",
       "  710.876,273.215 712.854,276.741 714.833,284.268 716.811,287.795 718.789,303.322 720.767,306.849 722.745,310.375 724.723,313.902 726.702,321.429 728.68,324.956 \n",
       "  730.658,332.483 732.636,336.01 734.614,343.536 736.592,347.063 738.571,350.59 740.549,358.117 742.527,361.644 744.505,365.171 746.483,372.697 748.461,380.224 \n",
       "  750.44,383.751 752.418,391.278 754.396,394.805 756.374,398.331 758.352,405.859 760.33,409.386 762.309,412.912 764.287,420.439 766.265,427.298 768.243,427.494 \n",
       "  770.221,431.019 772.199,438.546 774.178,446.073 776.156,449.6 778.134,453.126 780.112,456.652 782.09,464.179 784.069,471.706 786.047,475.234 788.025,478.76 \n",
       "  790.003,482.286 791.981,489.813 793.959,493.341 795.938,496.868 797.916,504.394 799.894,507.92 801.872,511.447 803.85,518.974 805.828,522.501 807.807,526.028 \n",
       "  809.785,533.555 811.763,537.081 813.741,540.608 815.719,548.135 817.697,555.662 819.676,559.189 821.654,562.716 823.632,566.242 825.61,569.769 827.588,573.297 \n",
       "  829.566,576.824 831.545,580.35 833.523,583.877 835.501,587.402 837.479,594.93 839.457,598.456 841.435,601.983 843.414,605.51 845.392,609.036 847.37,612.563 \n",
       "  849.348,616.09 851.326,619.617 853.304,623.144 855.283,630.671 857.261,631.735 859.239,633.724 861.217,641.251 863.195,644.778 865.173,648.306 867.152,651.832 \n",
       "  869.13,655.359 871.108,658.885 873.086,662.412 875.064,665.939 877.042,669.466 879.021,676.992 880.999,680.518 882.977,684.045 884.955,687.572 886.933,691.1 \n",
       "  888.911,694.626 890.89,695.861 892.868,695.857 894.846,699.865 896.824,703.873 898.802,703.869 900.78,703.865 902.759,707.314 904.737,710.841 906.715,714.367 \n",
       "  908.693,717.894 910.671,721.421 912.649,724.947 914.628,728.473 916.606,731.918 918.584,731.914 920.562,739.054 922.54,739.93 924.518,742.108 926.497,745.635 \n",
       "  928.475,749.161 930.453,752.688 932.431,756.215 934.409,759.742 936.387,759.963 938.366,762.794 940.344,770.321 942.322,771.987 944.3,773.375 946.278,776.902 \n",
       "  948.256,780.429 950.235,783.955 952.213,784.003 954.191,787.01 956.169,790.536 958.147,794.063 960.125,796.024 962.104,797.117 964.082,800.643 966.06,804.169 \n",
       "  968.038,807.696 970.016,808.04 971.994,810.75 973.973,814.276 975.951,816.052 977.929,817.33 979.907,820.857 981.885,824.384 983.863,827.911 985.842,828.068 \n",
       "  987.82,830.964 989.798,834.491 991.776,838.017 993.754,840.089 995.733,841.071 997.711,844.597 999.689,848.101 1001.67,848.097 1003.65,855.178 1005.62,856.113 \n",
       "  1007.6,858.232 1009.58,864.129 1011.56,865.286 1013.54,868.813 1015.51,872.339 1017.49,875.866 1019.47,879.393 1021.45,880.154 1023.43,882.445 1025.41,884.158 \n",
       "  1027.38,885.499 1029.36,888.162 1031.34,892.553 1033.32,896.079 1035.3,896.174 1037.27,899.134 1039.25,902.66 1041.23,904.186 1043.21,904.182 1045.19,904.178 \n",
       "  1047.16,904.174 1049.14,904.17 1051.12,904.166 1053.1,904.161 1055.08,904.157 1057.06,904.153 1059.03,904.149 1061.01,904.145 1062.99,904.141 1064.97,904.137 \n",
       "  1066.95,904.133 1068.92,904.128 1070.9,904.124 1072.88,906.615 1074.86,908.128 1076.84,909.668 1078.82,913.195 1080.79,916.14 1082.77,916.247 1084.75,919.774 \n",
       "  1086.73,920.14 1088.71,922.828 1090.68,924.144 1092.66,925.882 1094.64,928.148 1096.62,928.144 1098.6,928.14 1100.58,928.136 1102.55,931.515 1104.53,932.14 \n",
       "  1106.51,932.136 1108.49,932.132 1110.47,933.623 1112.44,936.136 1114.42,936.676 1116.4,940.14 1118.38,940.136 1120.36,943.255 1122.34,944.14 1124.31,946.309 \n",
       "  1126.29,948.144 1128.27,949.363 1130.25,952.148 1132.23,952.417 1134.2,955.943 1136.18,956.148 1138.16,958.997 1140.14,960.152 1142.12,962.05 1144.1,964.156 \n",
       "  1146.07,965.103 1148.05,968.16 1150.03,968.156 1152.01,968.152 1153.99,971.211 1155.96,972.156 1157.94,974.265 1159.92,976.16 1161.9,977.318 1163.88,980.164 \n",
       "  1165.85,980.371 1167.83,983.897 1169.81,984.163 1171.79,984.159 1173.77,986.478 1175.75,988.163 1177.72,989.532 1179.7,992.167 1181.68,992.585 1183.66,996.111 \n",
       "  1185.64,996.167 1187.61,996.163 1189.59,998.692 1191.57,1000.17 1193.55,1001.75 1195.53,1004.17 1197.51,1004.8 1199.48,1008.18 1201.46,1008.17 1203.44,1008.17 \n",
       "  1205.42,1010.91 1207.4,1012.17 1209.37,1013.96 1211.35,1016.18 1213.33,1016.17 1215.31,1016.54 1217.29,1020.07 1219.27,1020.17 1221.24,1020.17 1223.22,1022.65 \n",
       "  1225.2,1024.17 1227.18,1024.17 1229.16,1025.23 1231.13,1028.17 1233.11,1028.17 1235.09,1028.16 1237.07,1031.33 1239.05,1032.17 1241.03,1032.16 1243,1033.91 \n",
       "  1244.98,1036.17 1246.96,1036.16 1248.94,1036.5 1250.92,1040.02 1252.89,1040.16 1254.87,1040.16 1256.85,1042.6 1258.83,1044.16 1260.81,1045.66 1262.79,1048.17 \n",
       "  1264.76,1048.16 1266.74,1048.23 1268.72,1051.76 1270.7,1052.16 1272.68,1052.16 1274.65,1054.34 1276.63,1056.16 1278.61,1056.16 1280.59,1056.92 1282.57,1060.16 \n",
       "  1284.55,1060.16 1286.52,1060.15 1288.5,1063.03 1290.48,1064.16 1292.46,1064.15 1294.44,1065.61 1296.41,1068.16 1298.39,1068.15 1300.37,1068.19 1302.35,1071.72 \n",
       "  1304.33,1072.15 1306.3,1072.15 1308.28,1074.3 1310.26,1076.15 1312.24,1077.35 1314.22,1080.16 1316.2,1080.15 1318.17,1080.15 1320.15,1083.46 1322.13,1084.15 \n",
       "  1324.11,1084.15 1326.09,1086.04 1328.06,1088.15 1330.04,1088.15 1332.02,1088.62 1334,1092.14 1335.98,1092.15 1337.96,1092.14 1339.93,1092.14 1341.91,1094.25 \n",
       "  1343.89,1096.14 1345.87,1096.14 1347.85,1096.83 1349.82,1100.14 1351.8,1100.14 1353.78,1100.14 1355.76,1100.13 1357.74,1102.46 1359.72,1104.14 1361.69,1104.13 \n",
       "  1363.67,1104.13 1365.65,1104.57 1367.63,1108.1 1369.61,1108.13 1371.58,1108.12 1373.56,1110.68 1375.54,1112.13 1377.52,1112.12 1379.5,1112.12 1381.48,1112.79 \n",
       "  1383.45,1116.12 1385.43,1116.12 1387.41,1116.11 1389.39,1116.11 1391.37,1118.42 1393.34,1120.11 1395.32,1120.11 1397.3,1121 1399.28,1124.11 1401.26,1124.11 \n",
       "  1403.24,1124.11 1405.21,1124.1 1407.19,1126.63 1409.17,1128.11 1411.15,1128.1 1413.13,1129.21 1415.1,1132.11 1417.08,1132.1 1419.06,1132.1 1421.04,1132.09 \n",
       "  1423.02,1134.85 1425,1136.1 1426.97,1136.09 1428.95,1136.09 1430.93,1136.95 1432.91,1140.09 1434.89,1140.09 1436.86,1140.09 1438.84,1143.06 1440.82,1144.09 \n",
       "  1442.8,1144.08 1444.78,1144.08 1446.75,1145.17 1448.73,1148.08 1450.71,1148.08 1452.69,1148.08 1454.67,1148.07 1456.65,1150.8 1458.62,1152.08 1460.6,1152.07 \n",
       "  1462.58,1152.07 1464.56,1152.91 1466.54,1156.07 1468.51,1156.07 1470.49,1156.06 1472.47,1156.06 1474.45,1158.54 1476.43,1160.06 1478.41,1160.06 1480.38,1160.06 \n",
       "  1482.36,1160.05 1484.34,1160.18 1486.32,1163.7 1488.3,1164.05 1490.27,1164.05 1492.25,1164.04 1494.23,1164.04 1496.21,1165.34 1498.19,1168.04 1500.17,1168.04 \n",
       "  1502.14,1168.03 1504.12,1168.03 1506.1,1170.97 1508.08,1172.03 1510.06,1172.03 1512.03,1172.03 1514.01,1173.08 1515.99,1176.03 1517.97,1176.03 1519.95,1176.02 \n",
       "  1521.93,1176.02 1523.9,1176.01 1525.88,1178.24 1527.86,1180.02 1529.84,1180.01 1531.82,1180.01 1533.79,1180.34 1535.77,1183.87 1537.75,1184.01 1539.73,1184.01 \n",
       "  1541.71,1184 1543.69,1184 1545.66,1185.5 1547.64,1188 1549.62,1188 1551.6,1187.99 1553.58,1187.99 1555.55,1191.14 1557.53,1191.99 1559.51,1191.99 \n",
       "  1561.49,1191.98 1563.47,1191.98 1565.44,1192.77 1567.42,1195.98 1569.4,1195.98 1571.38,1195.98 1573.36,1195.97 1575.34,1198.41 1577.31,1199.98 1579.29,1199.97 \n",
       "  1581.27,1199.97 1583.25,1199.96 1585.23,1200.04 1587.2,1203.57 1589.18,1203.96 1591.16,1203.96 1593.14,1203.96 1595.12,1203.95 1597.1,1205.2 1599.07,1207.96 \n",
       "  1601.05,1207.95 1603.03,1207.95 1605.01,1207.94 1606.99,1207.94 1608.96,1210.36 1610.94,1211.94 1612.92,1211.94 1614.9,1211.93 1616.88,1211.93 1618.86,1211.93 \n",
       "  1620.83,1211.92 1622.81,1215.05 1624.79,1215.93 1626.77,1215.92 1628.75,1215.92 1630.72,1215.91 1632.7,1216.68 1634.68,1219.92 1636.66,1219.91 1638.64,1219.91 \n",
       "  1640.62,1219.91 1642.59,1219.9 1644.57,1221.84 1646.55,1223.91 1648.53,1223.9 1650.51,1223.9 1652.48,1223.89 1654.46,1223.89 1656.44,1223.88 1658.42,1226.53 \n",
       "  1660.4,1227.89 1662.38,1227.88 1664.35,1227.88 1666.33,1227.88 1668.31,1227.87 1670.29,1227.87 1672.27,1231.22 1674.24,1231.87 1676.22,1231.87 1678.2,1231.86 \n",
       "  1680.18,1231.86 1682.16,1232.85 1684.14,1235.86 1686.11,1235.86 1688.09,1235.86 1690.07,1235.85 1692.05,1235.85 1694.03,1238.01 1696,1239.85 1697.98,1239.85 \n",
       "  1699.96,1239.84 1701.94,1239.84 1703.92,1239.83 1705.89,1239.83 1707.87,1242.7 1709.85,1243.83 1711.83,1243.83 1713.81,1243.83 1715.79,1243.82 1717.76,1243.82 \n",
       "  1719.74,1243.86 1721.72,1247.38 1723.7,1247.82 1725.68,1247.81 1727.65,1247.81 1729.63,1247.81 1731.61,1247.8 1733.59,1248.54 1735.57,1251.81 1737.55,1251.8 \n",
       "  1739.52,1251.8 1741.5,1251.79 1743.48,1251.79 1745.46,1251.78 1747.44,1253.23 1749.41,1255.79 1751.39,1255.78 1753.37,1255.78 1755.35,1255.78 1757.33,1255.77 \n",
       "  1759.31,1255.77 1761.28,1255.76 1763.26,1257.44 1765.24,1259.77 1767.22,1259.76 1769.2,1259.76 1771.17,1259.76 1773.15,1259.75 1775.13,1259.75 1777.11,1262.13 \n",
       "  1779.09,1263.75 1781.07,1263.75 1783.04,1263.74 1785.02,1263.74 1787,1263.73 1788.98,1263.73 1790.96,1263.73 1792.93,1266.35 1794.91,1267.73 1796.89,1267.73 \n",
       "  1798.87,1267.72 1800.85,1267.72 1802.83,1267.71 1804.8,1267.71 1806.78,1271.03 1808.76,1271.71 1810.74,1271.71 1812.72,1271.71 1814.69,1271.7 1816.67,1271.7 \n",
       "  1818.65,1272.19 1820.63,1275.7 1822.61,1275.7 1824.58,1275.69 1826.56,1275.69 1828.54,1275.68 1830.52,1275.68 1832.5,1276.88 1834.48,1279.68 1836.45,1279.68 \n",
       "  1838.43,1279.68 1840.41,1279.67 1842.39,1279.67 1844.37,1279.66 1846.34,1279.66 1848.32,1279.66 1850.3,1280.62 1852.28,1283.66 1854.26,1283.66 1856.24,1283.65 \n",
       "  1858.21,1283.65 1860.19,1283.64 1862.17,1283.64 1864.15,1283.63 1866.13,1284.83 1868.1,1287.64 1870.08,1287.63 1872.06,1287.63 1874.04,1287.63 1876.02,1287.62 \n",
       "  1878,1287.62 1879.97,1287.61 1881.95,1287.61 1883.93,1288.58 1885.91,1291.61 1887.89,1291.61 1889.86,1291.61 1891.84,1291.6 1893.82,1291.6 1895.8,1291.59 \n",
       "  1897.78,1291.59 1899.76,1291.59 1901.73,1292.32 1903.71,1295.59 1905.69,1295.58 1907.67,1295.58 1909.65,1295.58 1911.62,1295.57 1913.6,1295.57 1915.58,1295.56 \n",
       "  1917.56,1295.56 1919.54,1296.06 1921.52,1299.56 1923.49,1299.56 1925.47,1299.56 1927.45,1299.55 1929.43,1299.55 1931.41,1299.54 1933.38,1299.54 1935.36,1300.27 \n",
       "  1937.34,1303.54 1939.32,1303.54 1941.3,1303.54 1943.28,1303.53 1945.25,1303.53 1947.23,1303.52 1949.21,1303.52 1951.19,1303.51 1953.17,1304.01 1955.14,1307.52 \n",
       "  1957.12,1307.51 1959.1,1307.51 1961.08,1307.51 1963.06,1307.5 1965.03,1307.5 1967.01,1307.49 1968.99,1308.22 1970.97,1311.5 1972.95,1311.49 1974.93,1311.49 \n",
       "  1976.9,1311.49 1978.88,1311.48 1980.86,1311.48 1982.84,1311.47 1984.82,1311.47 1986.79,1311.97 1988.77,1315.47 1990.75,1315.47 1992.73,1315.46 1994.71,1315.46 \n",
       "  1996.69,1315.46 1998.66,1315.45 2000.64,1315.45 2002.62,1315.44 2004.6,1315.44 2006.58,1315.44 2008.55,1318.76 2010.53,1319.44 2012.51,1319.44 2014.49,1319.43 \n",
       "  2016.47,1319.43 2018.45,1319.42 2020.42,1319.42 2022.4,1319.41 2024.38,1319.41 2026.36,1322.5 2028.34,1323.41 2030.31,1323.41 2032.29,1323.41 2034.27,1323.4 \n",
       "  2036.25,1323.4 2038.23,1323.39 2040.21,1323.39 2042.18,1323.39 2044.16,1323.38 2046.14,1325.77 2048.12,1327.39 2050.1,1327.38 2052.07,1327.38 2054.05,1327.37 \n",
       "  2056.03,1327.37 2058.01,1327.37 2059.99,1327.36 2061.97,1327.36 2063.94,1329.51 2065.92,1331.36 2067.9,1331.36 2069.88,1331.35 2071.86,1331.35 2073.83,1331.34 \n",
       "  2075.81,1331.34 2077.79,1331.34 2079.77,1331.33 2081.75,1333.25 2083.73,1335.34 2085.7,1335.33 2087.68,1335.33 2089.66,1335.32 2091.64,1335.32 2093.62,1335.32 \n",
       "  2095.59,1335.31 2097.57,1335.31 2099.55,1335.3 2101.53,1335.3 2103.51,1336.04 2105.48,1339.3 2107.46,1339.3 2109.44,1339.29 2111.42,1339.29 2113.4,1339.29 \n",
       "  2115.38,1339.28 2117.35,1339.28 2119.33,1339.27 2121.31,1339.27 2123.29,1339.31 2125.27,1342.84 2127.24,1343.27 2129.22,1343.27 2131.2,1343.26 2133.18,1343.26 \n",
       "  2135.16,1343.25 2137.14,1343.25 2139.11,1343.24 2141.09,1343.24 2143.07,1346.58 2145.05,1347.24 2147.03,1347.24 2149,1347.24 2150.98,1347.23 2152.96,1347.23 \n",
       "  2154.94,1347.22 2156.92,1347.22 2158.9,1347.22 2160.87,1347.21 2162.85,1347.21 2164.83,1349.37 2166.81,1351.21 2168.79,1351.21 2170.76,1351.2 2172.74,1351.2 \n",
       "  2174.72,1351.2 2176.7,1351.19 2178.68,1351.19 2180.66,1351.18 2182.63,1351.18 2184.61,1352.64 2186.59,1355.18 2188.57,1355.18 2190.55,1355.17 2192.52,1355.17 \n",
       "  2194.5,1355.17 2196.48,1355.16 2198.46,1355.16 2200.44,1355.15 2202.42,1355.15 2204.39,1355.91 2206.37,1359.15 2208.35,1359.15 2210.33,1359.15 2212.31,1359.14 \n",
       "  2214.28,1359.14 2216.26,1359.13 2218.24,1359.13 2220.22,1359.12 2222.2,1359.12 2224.17,1359.17 2226.15,1362.7 2228.13,1363.12 2230.11,1363.12 2232.09,1363.11 \n",
       "  2234.07,1363.11 2236.04,1363.1 2238.02,1363.1 2240,1363.1 2241.98,1363.09 2243.96,1363.09 2245.93,1363.08 2247.91,1363.08 2249.89,1365.02 2251.87,1367.08 \n",
       "  2253.85,1367.08 2255.83,1367.07 2257.8,1367.07 2259.78,1367.07 2261.76,1367.06 2263.74,1367.06 2265.72,1367.05 2267.69,1367.05 2269.67,1367.05 2271.65,1367.81 \n",
       "  2273.63,1371.05 2275.61,1371.05 2277.59,1371.04 2279.56,1371.04 2281.54,1371.03 2283.52,1372.97 2285.5,1375.04 2287.48,1376.03 2289.45,1379.55 2291.43,1383.08 \n",
       "  2293.41,1386.61 \n",
       "  \"/>\n",
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       "  315.243,86.2547 317.221,86.2547 319.199,86.2547 321.177,86.2547 323.155,86.2547 325.133,86.2547 327.112,86.2547 329.09,86.2547 331.068,86.2547 333.046,86.2547 \n",
       "  335.024,86.2547 337.002,86.2547 338.981,86.2547 340.959,86.2547 342.937,86.2547 344.915,86.2547 346.893,86.2547 348.872,86.2547 350.85,86.2547 352.828,86.2547 \n",
       "  354.806,86.2547 356.784,86.2547 358.762,86.2547 360.741,86.2547 362.719,86.2547 364.697,86.2547 366.675,86.2547 368.653,86.2547 370.631,86.2547 372.61,86.2547 \n",
       "  374.588,86.2547 376.566,86.2547 378.544,86.2547 380.522,86.2547 382.5,86.2547 384.479,86.2547 386.457,86.2547 388.435,86.2547 390.413,86.2547 392.391,86.2547 \n",
       "  394.369,86.2547 396.348,86.2547 398.326,86.2547 400.304,86.2547 402.282,86.2547 404.26,86.2547 406.238,86.2547 408.217,86.2547 410.195,86.2547 412.173,86.2547 \n",
       "  414.151,86.2547 416.129,86.2547 418.107,86.2547 420.086,86.2547 422.064,86.2547 424.042,86.2547 426.02,86.2547 427.998,86.2547 429.976,86.2547 431.955,86.2547 \n",
       "  433.933,86.2547 435.911,86.2547 437.889,86.2547 439.867,86.2547 441.845,86.2547 443.824,86.2547 445.802,86.2547 447.78,86.2547 449.758,86.2547 451.736,86.2547 \n",
       "  453.714,86.2547 455.693,86.2547 457.671,86.2547 459.649,86.2547 461.627,86.2547 463.605,86.2547 465.583,86.2547 467.562,86.2547 469.54,86.2547 471.518,86.2547 \n",
       "  473.496,86.2547 475.474,86.2547 477.452,86.2547 479.431,86.2547 481.409,86.2547 483.387,86.2547 485.365,86.2547 487.343,86.2547 489.321,86.2547 491.3,86.2547 \n",
       "  493.278,86.2547 495.256,86.2547 497.234,86.2547 499.212,86.2547 501.19,86.2547 503.169,86.2547 505.147,86.2547 507.125,86.2547 509.103,86.2547 511.081,86.2547 \n",
       "  513.059,86.2547 515.038,86.2547 517.016,86.2547 518.994,86.2547 520.972,86.2547 522.95,86.2547 524.928,86.2547 526.907,86.2547 528.885,86.2547 530.863,86.2547 \n",
       "  532.841,86.2547 534.819,86.2547 536.797,86.2547 538.776,86.2547 540.754,86.2547 542.732,86.2547 544.71,86.2547 546.688,86.2547 548.666,86.2547 550.645,86.2547 \n",
       "  552.623,86.2547 554.601,86.2547 556.579,86.2547 558.557,86.2547 560.536,86.2547 562.514,86.2547 564.492,86.2547 566.47,86.2547 568.448,86.2547 570.426,86.2547 \n",
       "  572.405,86.2547 574.383,86.2547 576.361,86.2547 578.339,86.2547 580.317,86.2547 582.295,86.2547 584.274,86.2547 586.252,86.2547 588.23,86.2547 590.208,86.2547 \n",
       "  592.186,86.2547 594.164,86.2547 596.143,86.2547 598.121,86.2547 600.099,86.2547 602.077,86.2547 604.055,86.2547 606.033,86.2547 608.012,86.2547 609.99,86.2547 \n",
       "  611.968,86.2547 613.946,86.2547 615.924,86.2547 617.902,86.2547 619.881,86.2547 621.859,86.2547 623.837,86.2547 625.815,86.2547 627.793,86.2547 629.771,86.2547 \n",
       "  631.75,86.2547 633.728,86.2547 635.706,86.2547 637.684,86.2547 639.662,86.2547 641.64,86.2547 643.619,86.2547 645.597,86.2547 647.575,86.2547 649.553,86.2547 \n",
       "  651.531,86.2547 653.509,86.2547 655.488,86.2547 657.466,86.2547 659.444,86.2547 661.422,86.2547 663.4,86.2547 665.378,86.2547 667.357,86.2547 669.335,86.2547 \n",
       "  671.313,86.2547 673.291,86.2547 675.269,86.2547 677.247,86.2547 679.226,86.2547 681.204,86.2547 683.182,86.2547 685.16,86.2547 687.138,86.2547 689.116,86.2547 \n",
       "  691.095,86.2547 693.073,86.2547 695.051,88.1007 697.029,91.9967 699.007,95.8924 700.985,104.205 702.964,112.518 704.942,116.413 706.92,120.308 708.898,128.623 \n",
       "  710.876,132.518 712.854,136.412 714.833,144.725 716.811,148.621 718.789,165.77 720.767,169.665 722.745,173.56 724.723,177.456 726.702,185.769 728.68,189.664 \n",
       "  730.658,197.977 732.636,201.873 734.614,210.186 736.592,214.081 738.571,217.976 740.549,226.29 742.527,230.185 744.505,234.08 746.483,242.394 748.461,250.707 \n",
       "  750.44,254.602 752.418,262.915 754.396,266.811 756.374,270.706 758.352,279.02 760.33,282.915 762.309,286.81 764.287,295.123 766.265,302.699 768.243,302.915 \n",
       "  770.221,306.809 772.199,315.122 774.178,323.435 776.156,327.331 778.134,331.225 780.112,335.12 782.09,343.433 784.069,351.746 786.047,355.643 788.025,359.537 \n",
       "  790.003,363.432 791.981,371.745 793.959,375.641 795.938,379.537 797.916,387.849 799.894,391.744 801.872,395.64 803.85,403.953 805.828,407.848 807.807,411.744 \n",
       "  809.785,420.057 811.763,423.952 813.741,427.847 815.719,436.161 817.697,444.474 819.676,448.369 821.654,452.264 823.632,456.16 825.61,460.055 827.588,463.951 \n",
       "  829.566,467.847 831.545,471.741 833.523,475.636 835.501,479.53 837.479,487.845 839.457,491.739 841.435,495.634 843.414,499.529 845.392,503.425 847.37,507.32 \n",
       "  849.348,511.215 851.326,515.111 853.304,519.006 855.283,527.319 857.261,528.494 859.239,530.692 861.217,539.005 863.195,542.901 865.173,546.797 867.152,550.691 \n",
       "  869.13,554.586 871.108,558.482 873.086,562.377 875.064,566.272 877.042,570.168 879.021,578.481 880.999,582.375 882.977,586.27 884.955,590.165 886.933,594.062 \n",
       "  888.911,597.957 890.89,599.321 892.868,599.316 894.846,603.743 896.824,608.17 898.802,608.165 900.78,608.161 902.759,611.97 904.737,615.865 906.715,619.759 \n",
       "  908.693,623.655 910.671,627.551 912.649,631.445 914.628,635.34 916.606,639.145 918.584,639.14 920.562,647.026 922.54,647.994 924.518,650.399 926.497,654.294 \n",
       "  928.475,658.19 930.453,662.085 932.431,665.98 934.409,669.876 936.387,670.119 938.366,673.247 940.344,681.56 942.322,683.4 944.3,684.933 946.278,688.828 \n",
       "  948.256,692.724 950.235,696.619 952.213,696.672 954.191,699.992 956.169,703.887 958.147,707.782 960.125,709.948 962.104,711.155 964.082,715.05 966.06,718.944 \n",
       "  968.038,722.84 970.016,723.22 971.994,726.212 973.973,730.108 975.951,732.069 977.929,733.481 979.907,737.376 981.885,741.271 983.863,745.166 985.842,745.341 \n",
       "  987.82,748.539 989.798,752.435 991.776,756.329 993.754,758.617 995.733,759.701 997.711,763.597 999.689,767.466 1001.67,767.462 1003.65,775.283 1005.62,776.315 \n",
       "  1007.6,778.655 1009.58,785.169 1011.56,786.446 1013.54,790.343 1015.51,794.237 1017.49,798.132 1019.47,802.027 1021.45,802.868 1023.43,805.399 1025.41,807.29 \n",
       "  1027.38,808.772 1029.36,811.713 1031.34,816.562 1033.32,820.457 1035.3,820.562 1037.27,823.831 1039.25,827.725 1041.23,829.411 1043.21,829.406 1045.19,829.402 \n",
       "  1047.16,829.397 1049.14,829.393 1051.12,829.388 1053.1,829.384 1055.08,829.379 1057.06,829.375 1059.03,829.37 1061.01,829.365 1062.99,829.361 1064.97,829.356 \n",
       "  1066.95,829.352 1068.92,829.347 1070.9,829.343 1072.88,832.094 1074.86,833.765 1076.84,835.466 1078.82,839.361 1080.79,842.614 1082.77,842.732 1084.75,846.628 \n",
       "  1086.73,847.032 1088.71,850.001 1090.68,851.454 1092.66,853.373 1094.64,855.877 1096.62,855.872 1098.6,855.868 1100.58,855.863 1102.55,859.595 1104.53,860.285 \n",
       "  1106.51,860.281 1108.49,860.276 1110.47,861.923 1112.44,864.699 1114.42,865.295 1116.4,869.121 1118.38,869.116 1120.36,872.562 1122.34,873.539 1124.31,875.935 \n",
       "  1126.29,877.961 1128.27,879.308 1130.25,882.384 1132.23,882.68 1134.2,886.576 1136.18,886.801 1138.16,889.949 1140.14,891.224 1142.12,893.32 1144.1,895.646 \n",
       "  1146.07,896.693 1148.05,900.068 1150.03,900.064 1152.01,900.059 1153.99,903.438 1155.96,904.482 1157.94,906.811 1159.92,908.904 1161.9,910.183 1163.88,913.326 \n",
       "  1165.85,913.555 1167.83,917.45 1169.81,917.744 1171.79,917.74 1173.77,920.301 1175.75,922.162 1177.72,923.673 1179.7,926.584 1181.68,927.046 1183.66,930.94 \n",
       "  1185.64,931.002 1187.61,930.998 1189.59,933.79 1191.57,935.42 1193.55,937.163 1195.53,939.842 1197.51,940.536 1199.48,944.265 1201.46,944.26 1203.44,944.256 \n",
       "  1205.42,947.28 1207.4,948.678 1209.37,950.653 1211.35,953.1 1213.33,953.096 1215.31,953.503 1217.29,957.398 1219.27,957.513 1221.24,957.509 1223.22,960.248 \n",
       "  1225.2,961.931 1227.18,961.927 1229.16,963.097 1231.13,966.349 1233.11,966.344 1235.09,966.34 1237.07,969.843 1239.05,970.762 1241.03,970.758 1243,972.692 \n",
       "  1244.98,975.18 1246.96,975.176 1248.94,975.543 1250.92,979.437 1252.89,979.593 1254.87,979.589 1256.85,982.288 1258.83,984.011 1260.81,985.66 1262.79,988.433 \n",
       "  1264.76,988.429 1266.74,988.509 1268.72,992.404 1270.7,992.847 1272.68,992.842 1274.65,995.255 1276.63,997.264 1278.61,997.26 1280.59,998.106 1282.57,1001.68 \n",
       "  1284.55,1001.68 1286.52,1001.67 1288.5,1004.85 1290.48,1006.1 1292.46,1006.09 1294.44,1007.7 1296.41,1010.51 1298.39,1010.51 1300.37,1010.55 1302.35,1014.44 \n",
       "  1304.33,1014.93 1306.3,1014.92 1308.28,1017.29 1310.26,1019.34 1312.24,1020.67 1314.22,1023.77 1316.2,1023.76 1318.17,1023.76 1320.15,1027.41 1322.13,1028.18 \n",
       "  1324.11,1028.18 1326.09,1030.26 1328.06,1032.6 1330.04,1032.59 1332.02,1033.11 1334,1037.01 1335.98,1037.01 1337.96,1037.01 1339.93,1037 1341.91,1039.33 \n",
       "  1343.89,1041.42 1345.87,1041.42 1347.85,1042.18 1349.82,1045.84 1351.8,1045.84 1353.78,1045.83 1355.76,1045.83 1357.74,1048.41 1359.72,1050.25 1361.69,1050.25 \n",
       "  1363.67,1050.24 1365.65,1050.73 1367.63,1054.63 1369.61,1054.66 1371.58,1054.65 1373.56,1057.48 1375.54,1059.08 1377.52,1059.07 1379.5,1059.07 1381.48,1059.8 \n",
       "  1383.45,1063.49 1385.43,1063.49 1387.41,1063.48 1389.39,1063.48 1391.37,1066.03 1393.34,1067.9 1395.32,1067.89 1397.3,1068.88 1399.28,1072.32 1401.26,1072.31 \n",
       "  1403.24,1072.31 1405.21,1072.3 1407.19,1075.1 1409.17,1076.73 1411.15,1076.72 1413.13,1077.95 1415.1,1081.14 1417.08,1081.14 1419.06,1081.13 1421.04,1081.13 \n",
       "  1423.02,1084.17 1425,1085.55 1426.97,1085.55 1428.95,1085.54 1430.93,1086.5 1432.91,1089.97 1434.89,1089.96 1436.86,1089.96 1438.84,1093.24 1440.82,1094.38 \n",
       "  1442.8,1094.37 1444.78,1094.37 1446.75,1095.57 1448.73,1098.79 1450.71,1098.79 1452.69,1098.78 1454.67,1098.78 1456.65,1101.79 1458.62,1103.2 1460.6,1103.2 \n",
       "  1462.58,1103.19 1464.56,1104.12 1466.54,1107.61 1468.51,1107.61 1470.49,1107.6 1472.47,1107.6 1474.45,1110.34 1476.43,1112.02 1478.41,1112.02 1480.38,1112.01 \n",
       "  1482.36,1112.01 1484.34,1112.15 1486.32,1116.04 1488.3,1116.43 1490.27,1116.42 1492.25,1116.42 1494.23,1116.41 1496.21,1117.85 1498.19,1120.83 1500.17,1120.83 \n",
       "  1502.14,1120.83 1504.12,1120.82 1506.1,1124.07 1508.08,1125.24 1510.06,1125.24 1512.03,1125.23 1514.01,1126.39 1515.99,1129.66 1517.97,1129.65 1519.95,1129.65 \n",
       "  1521.93,1129.64 1523.9,1129.64 1525.88,1132.09 1527.86,1134.06 1529.84,1134.06 1531.82,1134.05 1533.79,1134.42 1535.77,1138.32 1537.75,1138.47 1539.73,1138.47 \n",
       "  1541.71,1138.46 1543.69,1138.46 1545.66,1140.12 1547.64,1142.88 1549.62,1142.87 1551.6,1142.87 1553.58,1142.86 1555.55,1146.34 1557.53,1147.29 1559.51,1147.28 \n",
       "  1561.49,1147.28 1563.47,1147.27 1565.44,1148.15 1567.42,1151.7 1569.4,1151.69 1571.38,1151.69 1573.36,1151.68 1575.34,1154.37 1577.31,1156.1 1579.29,1156.1 \n",
       "  1581.27,1156.1 1583.25,1156.09 1585.23,1156.17 1587.2,1160.07 1589.18,1160.51 1591.16,1160.5 1593.14,1160.5 1595.12,1160.49 1597.1,1161.87 1599.07,1164.92 \n",
       "  1601.05,1164.91 1603.03,1164.91 1605.01,1164.9 1606.99,1164.9 1608.96,1167.57 1610.94,1169.32 1612.92,1169.32 1614.9,1169.31 1616.88,1169.31 1618.86,1169.3 \n",
       "  1620.83,1169.3 1622.81,1172.75 1624.79,1173.72 1626.77,1173.72 1628.75,1173.71 1630.72,1173.71 1632.7,1174.55 1634.68,1178.13 1636.66,1178.12 1638.64,1178.12 \n",
       "  1640.62,1178.12 1642.59,1178.11 1644.57,1180.25 1646.55,1182.53 1648.53,1182.53 1650.51,1182.52 1652.48,1182.52 1654.46,1182.52 1656.44,1182.51 1658.42,1185.43 \n",
       "  1660.4,1186.93 1662.38,1186.93 1664.35,1186.92 1666.33,1186.92 1668.31,1186.91 1670.29,1186.91 1672.27,1190.61 1674.24,1191.33 1676.22,1191.33 1678.2,1191.32 \n",
       "  1680.18,1191.32 1682.16,1192.41 1684.14,1195.74 1686.11,1195.74 1688.09,1195.73 1690.07,1195.73 1692.05,1195.72 1694.03,1198.11 1696,1200.15 1697.98,1200.14 \n",
       "  1699.96,1200.14 1701.94,1200.13 1703.92,1200.13 1705.89,1200.12 1707.87,1203.29 1709.85,1204.54 1711.83,1204.54 1713.81,1204.54 1715.79,1204.53 1717.76,1204.53 \n",
       "  1719.74,1204.57 1721.72,1208.46 1723.7,1208.94 1725.68,1208.94 1727.65,1208.94 1729.63,1208.93 1731.61,1208.93 1733.59,1209.75 1735.57,1213.35 1737.55,1213.34 \n",
       "  1739.52,1213.34 1741.5,1213.33 1743.48,1213.33 1745.46,1213.33 1747.44,1214.92 1749.41,1217.75 1751.39,1217.74 1753.37,1217.74 1755.35,1217.73 1757.33,1217.73 \n",
       "  1759.31,1217.73 1761.28,1217.72 1763.26,1219.58 1765.24,1222.14 1767.22,1222.14 1769.2,1222.13 1771.17,1222.13 1773.15,1222.12 1775.13,1222.12 1777.11,1224.75 \n",
       "  1779.09,1226.54 1781.07,1226.54 1783.04,1226.53 1785.02,1226.53 1787,1226.52 1788.98,1226.52 1790.96,1226.52 1792.93,1229.41 1794.91,1230.94 1796.89,1230.93 \n",
       "  1798.87,1230.93 1800.85,1230.92 1802.83,1230.92 1804.8,1230.91 1806.78,1234.58 1808.76,1235.34 1810.74,1235.33 1812.72,1235.33 1814.69,1235.32 1816.67,1235.32 \n",
       "  1818.65,1235.87 1820.63,1239.74 1822.61,1239.74 1824.58,1239.73 1826.56,1239.73 1828.54,1239.72 1830.52,1239.72 1832.5,1241.04 1834.48,1244.14 1836.45,1244.14 \n",
       "  1838.43,1244.13 1840.41,1244.13 1842.39,1244.12 1844.37,1244.12 1846.34,1244.11 1848.32,1244.11 1850.3,1245.18 1852.28,1248.53 1854.26,1248.53 1856.24,1248.52 \n",
       "  1858.21,1248.52 1860.19,1248.51 1862.17,1248.51 1864.15,1248.5 1866.13,1249.83 1868.1,1252.93 1870.08,1252.92 1872.06,1252.92 1874.04,1252.91 1876.02,1252.91 \n",
       "  1878,1252.9 1879.97,1252.9 1881.95,1252.89 1883.93,1253.96 1885.91,1257.32 1887.89,1257.31 1889.86,1257.31 1891.84,1257.3 1893.82,1257.3 1895.8,1257.29 \n",
       "  1897.78,1257.29 1899.76,1257.28 1901.73,1258.09 1903.71,1261.71 1905.69,1261.7 1907.67,1261.7 1909.65,1261.69 1911.62,1261.69 1913.6,1261.68 1915.58,1261.68 \n",
       "  1917.56,1261.67 1919.54,1262.22 1921.52,1266.1 1923.49,1266.09 1925.47,1266.09 1927.45,1266.08 1929.43,1266.08 1931.41,1266.07 1933.38,1266.07 1935.36,1266.88 \n",
       "  1937.34,1270.49 1939.32,1270.49 1941.3,1270.48 1943.28,1270.48 1945.25,1270.47 1947.23,1270.47 1949.21,1270.46 1951.19,1270.46 1953.17,1271.01 1955.14,1274.88 \n",
       "  1957.12,1274.88 1959.1,1274.87 1961.08,1274.87 1963.06,1274.86 1965.03,1274.86 1967.01,1274.86 1968.99,1275.66 1970.97,1279.28 1972.95,1279.27 1974.93,1279.27 \n",
       "  1976.9,1279.26 1978.88,1279.26 1980.86,1279.25 1982.84,1279.25 1984.82,1279.25 1986.79,1279.79 1988.77,1283.67 1990.75,1283.66 1992.73,1283.66 1994.71,1283.65 \n",
       "  1996.69,1283.65 1998.66,1283.65 2000.64,1283.64 2002.62,1283.64 2004.6,1283.63 2006.58,1283.63 2008.55,1287.3 2010.53,1288.05 2012.51,1288.04 2014.49,1288.04 \n",
       "  2016.47,1288.04 2018.45,1288.03 2020.42,1288.03 2022.4,1288.02 2024.38,1288.02 2026.36,1291.43 2028.34,1292.44 2030.31,1292.44 2032.29,1292.43 2034.27,1292.43 \n",
       "  2036.25,1292.42 2038.23,1292.42 2040.21,1292.41 2042.18,1292.41 2044.16,1292.4 2046.14,1295.04 2048.12,1296.83 2050.1,1296.82 2052.07,1296.82 2054.05,1296.81 \n",
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      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plot(\n",
    "    spd_range,\n",
    "    ra_max_itp.(spd_range),\n",
    "    label = \"Base rear axle torque\",\n",
    "    legend = :topright,\n",
    "    xlabel = \"Speed (kph)\",\n",
    "    ylabel = \"Wheel torque (Nm)\"\n",
    ")\n",
    "plot!(\n",
    "    spd_range,\n",
    "    boosted_ra_max_itp.(spd_range),\n",
    "    label=\"Boosted rear axle torque\"\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Porsche has also said that the front motor can be boosted 440 Nm, but I believe the power is constant, so we need to do some more sophisticated extrapolation in order to estimate the higher torque performance. The `polyfit` below fits the power limited section of the motor performance and estimates the torque performance between the current max torque and the boosted value.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "pwr_idx = findfirst(x->x<3100, fa_max_tq[:,2]);\n",
    "pwr_poly = polyfit(fa_max_tq[pwr_idx:end,1], fa_max_tq[pwr_idx:end,2],4);\n",
    "boosted_fa_max_itp(spd) = min(440*8.05, pwr_poly(spd));"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's do another plot comparison to make sure the resulting trends look correct."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
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       "  572.405,233.394 574.383,233.382 576.361,233.37 578.339,233.358 580.317,233.346 582.295,233.334 584.274,233.322 586.252,233.31 588.23,233.298 590.208,233.286 \n",
       "  592.186,233.274 594.164,233.262 596.143,233.25 598.121,233.238 600.099,233.226 602.077,233.214 604.055,233.202 606.033,233.19 608.012,233.178 609.99,233.166 \n",
       "  611.968,233.154 613.946,233.142 615.924,233.13 617.902,233.118 619.881,233.106 621.859,233.094 623.837,233.082 625.815,233.07 627.793,233.058 629.771,233.046 \n",
       "  631.75,233.034 633.728,233.022 635.706,233.01 637.684,232.998 639.662,232.986 641.64,232.974 643.619,232.962 645.597,232.95 647.575,232.938 649.553,232.926 \n",
       "  651.531,232.914 653.509,232.902 655.488,232.89 657.466,232.878 659.444,232.866 661.422,232.854 663.4,232.842 665.378,232.83 667.357,232.818 669.335,232.806 \n",
       "  671.313,232.794 673.291,232.782 675.269,232.77 677.247,232.758 679.226,232.746 681.204,232.734 683.182,232.722 685.16,232.71 687.138,232.698 689.116,232.687 \n",
       "  691.095,232.675 693.073,232.663 695.051,232.651 697.029,232.639 699.007,232.627 700.985,232.615 702.964,232.603 704.942,232.591 706.92,232.579 708.898,232.567 \n",
       "  710.876,232.555 712.854,232.543 714.833,232.531 716.811,232.519 718.789,232.507 720.767,232.495 722.745,232.483 724.723,232.471 726.702,232.459 728.68,232.447 \n",
       "  730.658,232.435 732.636,232.423 734.614,232.411 736.592,232.399 738.571,232.387 740.549,232.375 742.527,232.363 744.505,232.351 746.483,232.339 748.461,232.327 \n",
       "  750.44,232.315 752.418,232.303 754.396,232.291 756.374,232.279 758.352,232.267 760.33,232.255 762.309,232.243 764.287,232.231 766.265,232.219 768.243,232.207 \n",
       "  770.221,232.195 772.199,232.183 774.178,232.171 776.156,232.159 778.134,232.147 780.112,232.135 782.09,232.123 784.069,232.111 786.047,232.099 788.025,232.087 \n",
       "  790.003,232.075 791.981,232.063 793.959,232.051 795.938,232.039 797.916,232.027 799.894,232.015 801.872,232.003 803.85,231.991 805.828,231.979 807.807,231.967 \n",
       "  809.785,231.955 811.763,231.943 813.741,231.931 815.719,231.919 817.697,231.908 819.676,231.896 821.654,231.884 823.632,231.872 825.61,231.86 827.588,231.848 \n",
       "  829.566,231.836 831.545,231.824 833.523,231.812 835.501,231.8 837.479,231.788 839.457,231.776 841.435,231.764 843.414,231.752 845.392,231.74 847.37,231.728 \n",
       "  849.348,231.716 851.326,231.704 853.304,231.692 855.283,231.68 857.261,231.668 859.239,231.656 861.217,231.644 863.195,231.632 865.173,231.62 867.152,231.608 \n",
       "  869.13,231.596 871.108,231.584 873.086,231.572 875.064,231.56 877.042,231.548 879.021,231.536 880.999,231.524 882.977,231.512 884.955,231.5 886.933,231.488 \n",
       "  888.911,231.476 890.89,231.464 892.868,231.452 894.846,231.44 896.824,231.428 898.802,231.416 900.78,231.404 902.759,231.392 904.737,231.38 906.715,231.368 \n",
       "  908.693,231.356 910.671,231.344 912.649,231.332 914.628,231.32 916.606,231.308 918.584,231.296 920.562,231.284 922.54,231.272 924.518,231.26 926.497,231.248 \n",
       "  928.475,231.236 930.453,231.224 932.431,231.212 934.409,231.2 936.387,231.188 938.366,231.176 940.344,231.164 942.322,231.152 944.3,231.14 946.278,231.128 \n",
       "  948.256,231.116 950.235,231.105 952.213,231.093 954.191,237.113 956.169,242.704 958.147,242.692 960.125,242.68 962.104,242.668 964.082,242.656 966.06,242.644 \n",
       "  968.038,250.705 970.016,254.256 971.994,254.244 973.973,254.232 975.951,254.22 977.929,255.445 979.907,265.669 981.885,265.82 983.863,265.808 985.842,265.796 \n",
       "  987.82,265.784 989.798,270.409 991.776,277.396 993.754,277.384 995.733,277.372 997.711,277.36 999.689,277.348 1001.67,277.336 1003.65,277.324 1005.62,282.629 \n",
       "  1007.6,288.936 1009.58,288.924 1011.56,288.912 1013.54,288.9 1015.51,298.966 1017.49,300.512 1019.47,307.821 1021.45,312.124 1023.43,316.677 1025.41,323.736 \n",
       "  1027.38,325.533 1029.36,335.761 1031.34,345.989 1033.32,346.959 1035.3,354.848 1037.27,358.571 1039.25,363.699 1041.23,370.183 1043.21,372.553 1045.19,382.781 \n",
       "  1047.16,393.013 1049.14,393.407 1051.12,401.865 1053.1,405.019 1055.08,410.721 1057.06,416.63 1059.03,419.576 1061.01,429.801 1062.99,439.866 1064.97,439.854 \n",
       "  1066.95,448.885 1068.92,451.466 1070.9,457.741 1072.88,463.078 1074.86,466.597 1076.84,474.69 1078.82,475.453 1080.79,485.681 1082.77,486.289 1084.75,494.533 \n",
       "  1086.73,497.901 1088.71,497.889 1090.68,502.017 1092.66,509.501 1094.64,510.873 1096.62,521.101 1098.6,521.101 1100.58,529.957 1102.55,532.713 1104.53,538.809 \n",
       "  1106.51,544.325 1108.49,544.313 1110.47,546.294 1112.44,555.925 1114.42,555.913 1116.4,555.901 1118.38,564.005 1120.36,567.512 1122.34,572.861 1124.31,579.124 \n",
       "  1126.29,581.713 1128.27,590.736 1130.25,590.724 1132.23,600.797 1134.2,602.336 1136.18,602.324 1138.16,608.281 1140.14,613.936 1142.12,617.137 1144.1,625.548 \n",
       "  1146.07,625.536 1148.05,625.524 1150.03,634.845 1152.01,637.136 1153.99,637.124 1155.96,642.329 1157.94,648.735 1159.92,648.723 1161.9,648.711 1163.88,648.699 \n",
       "  1165.85,658.665 1167.83,660.311 1169.81,667.521 1171.79,671.923 1173.77,671.911 1175.75,675.005 1177.72,683.523 1179.7,683.511 1181.68,683.499 1183.66,683.487 \n",
       "  1185.64,691.341 1187.61,695.099 1189.59,695.087 1191.57,695.075 1193.55,697.453 1195.53,706.687 1197.51,706.675 1199.48,716.537 1201.46,718.287 1203.44,718.275 \n",
       "  1205.42,724.017 1207.4,729.886 1209.37,729.874 1211.35,729.862 1213.33,729.85 1215.31,729.839 1217.29,738.985 1219.27,741.45 1221.24,741.438 1223.22,741.426 \n",
       "  1225.2,741.414 1227.18,743.721 1229.16,753.026 1231.13,753.014 1233.11,762.805 1235.09,764.626 1237.07,764.614 1239.05,764.602 1241.03,764.59 1243,767.541 \n",
       "  1244.98,776.202 1246.96,776.19 1248.94,776.178 1250.92,785.253 1252.89,787.79 1254.87,787.778 1256.85,787.766 1258.83,787.754 1260.81,787.742 1262.79,788.617 \n",
       "  1264.76,798.845 1266.74,799.342 1268.72,807.701 1270.7,810.954 1272.68,810.942 1274.65,810.93 1276.63,813.809 1278.61,822.542 1280.59,822.53 1282.57,822.518 \n",
       "  1284.55,822.506 1286.52,822.494 1288.5,828.779 1290.48,834.105 1292.46,834.093 1294.44,834.081 1296.41,834.069 1298.39,834.057 1300.37,843.741 1302.35,845.669 \n",
       "  1304.33,852.597 1306.3,857.281 1308.28,857.269 1310.26,857.257 1312.24,857.245 1314.22,857.333 1316.2,867.561 1318.17,868.845 1320.15,868.833 1322.13,875.045 \n",
       "  1324.11,880.445 1326.09,880.433 1328.06,880.421 1330.04,880.409 1332.02,880.397 1334,880.385 1335.98,888.637 1337.96,891.997 1339.93,897.493 1341.91,903.609 \n",
       "  1343.89,903.597 1345.87,903.585 1347.85,903.573 1349.82,903.561 1351.8,903.549 1353.78,903.537 1355.76,903.525 1357.74,908.341 1359.72,915.137 1361.69,915.125 \n",
       "  1363.67,915.113 1365.65,915.101 1367.63,924.676 1369.61,926.713 1371.58,926.701 1373.56,926.689 1375.54,926.677 1377.52,926.665 1379.5,926.653 1381.48,926.672 \n",
       "  1383.45,936.897 1385.43,938.252 1387.41,938.24 1389.39,944.38 1391.37,949.852 1393.34,949.84 1395.32,949.828 1397.3,949.816 1399.28,949.804 1401.26,949.792 \n",
       "  1403.24,957.972 1405.21,961.404 1407.19,961.392 1409.17,961.38 1411.15,961.368 1413.13,961.356 1415.1,961.344 1417.08,971.568 1419.06,972.956 1421.04,972.944 \n",
       "  1423.02,972.932 1425,972.92 1426.97,976.304 1428.95,984.532 1430.93,984.52 1432.91,984.508 1434.89,984.496 1436.86,992.64 1438.84,996.108 1440.82,996.096 \n",
       "  1442.8,996.084 1444.78,996.072 1446.75,996.06 1448.73,996.048 1450.71,1006.24 1452.69,1007.66 1454.67,1007.65 1456.65,1007.64 1458.62,1007.62 1460.6,1007.61 \n",
       "  1462.58,1007.6 1464.56,1008.23 1466.54,1018.46 1468.51,1019.2 1470.49,1019.19 1472.47,1019.18 1474.45,1019.16 1476.43,1019.15 1478.41,1019.14 1480.38,1020.45 \n",
       "  1482.36,1030.68 1484.34,1030.74 1486.32,1030.73 1488.3,1030.72 1490.27,1036.78 1492.25,1042.33 1494.23,1042.32 1496.21,1042.3 1498.19,1042.29 1500.17,1042.28 \n",
       "  1502.14,1042.27 1504.12,1042.26 1506.1,1049 1508.08,1053.87 1510.06,1053.86 1512.03,1053.84 1514.01,1053.83 1515.99,1053.82 1517.97,1053.81 1519.95,1053.8 \n",
       "  1521.93,1053.78 1523.9,1059.85 1525.88,1065.4 1527.86,1065.38 1529.84,1065.37 1531.82,1065.36 1533.79,1065.35 1535.77,1074.82 1537.75,1076.96 1539.73,1076.95 \n",
       "  1541.71,1076.94 1543.69,1076.92 1545.66,1076.91 1547.64,1078.18 1549.62,1088.42 1551.6,1088.51 1553.58,1088.5 1555.55,1088.49 1557.53,1088.48 1559.51,1088.46 \n",
       "  1561.49,1088.45 1563.47,1088.44 1565.44,1089.03 1567.42,1099.26 1569.4,1100.04 1571.38,1100.03 1573.36,1100.02 1575.34,1100 1577.31,1099.99 1579.29,1099.98 \n",
       "  1581.27,1099.97 1583.25,1099.96 1585.23,1110.11 1587.2,1111.57 1589.18,1111.56 1591.16,1111.54 1593.14,1111.53 1595.12,1111.52 1597.1,1113.47 1599.07,1123.13 \n",
       "  1601.05,1123.12 1603.03,1123.11 1605.01,1123.1 1606.99,1123.08 1608.96,1123.07 1610.94,1123.06 1612.92,1123.05 1614.9,1123.04 1616.88,1123.02 1618.86,1123.01 \n",
       "  1620.83,1131.8 1622.81,1134.62 1624.79,1134.61 1626.77,1134.6 1628.75,1134.59 1630.72,1134.58 1632.7,1134.56 1634.68,1134.55 1636.66,1134.54 1638.64,1134.53 \n",
       "  1640.62,1134.52 1642.59,1134.5 1644.57,1134.49 1646.55,1137.16 1648.53,1146.1 1650.51,1146.09 1652.48,1146.08 1654.46,1146.07 1656.44,1146.06 1658.42,1146.04 \n",
       "  1660.4,1146.03 1662.38,1146.02 1664.35,1146.01 1666.33,1146 1668.31,1145.98 1670.29,1145.97 1672.27,1145.96 1674.24,1152.74 1676.22,1157.57 1678.2,1157.56 \n",
       "  1680.18,1157.55 1682.16,1157.54 1684.14,1157.52 1686.11,1157.51 1688.09,1166.34 1690.07,1169.12 1692.05,1169.11 1694.03,1169.1 1696,1169.09 1697.98,1169.08 \n",
       "  1699.96,1169.06 1701.94,1169.05 1703.92,1169.04 1705.89,1169.03 1707.87,1169.02 1709.85,1174.44 1711.83,1180.63 1713.81,1180.62 1715.79,1180.6 1717.76,1180.59 \n",
       "  1719.74,1180.58 1721.72,1180.57 1723.7,1180.56 1725.68,1180.54 1727.65,1180.53 1729.63,1180.52 1731.61,1180.51 1733.59,1180.5 1735.57,1180.48 1737.55,1180.47 \n",
       "  1739.52,1188.66 1741.5,1192.08 1743.48,1192.07 1745.46,1192.06 1747.44,1192.05 1749.41,1192.04 1751.39,1192.02 1753.37,1192.01 1755.35,1192 1757.33,1191.99 \n",
       "  1759.31,1191.98 1761.28,1191.96 1763.26,1191.95 1765.24,1194.01 1767.22,1203.56 1769.2,1203.55 1771.17,1203.54 1773.15,1203.53 1775.13,1203.52 1777.11,1203.5 \n",
       "  1779.09,1207.6 1781.07,1215.11 1783.04,1215.1 1785.02,1215.09 1787,1215.08 1788.98,1215.07 1790.96,1215.06 1792.93,1215.04 1794.91,1215.03 1796.89,1215.02 \n",
       "  1798.87,1215.01 1800.85,1215 1802.83,1214.98 1804.8,1224.56 1806.78,1226.6 1808.76,1226.58 1810.74,1226.57 1812.72,1226.56 1814.69,1226.55 1816.67,1226.54 \n",
       "  1818.65,1226.52 1820.63,1226.51 1822.61,1226.5 1824.58,1226.49 1826.56,1226.48 1828.54,1226.46 1830.52,1226.45 1832.5,1228.55 1834.48,1238.06 1836.45,1238.05 \n",
       "  1838.43,1238.04 1840.41,1238.03 1842.39,1238.02 1844.37,1238 1846.34,1237.99 1848.32,1237.98 1850.3,1237.97 1852.28,1237.96 1854.26,1237.94 1856.24,1237.93 \n",
       "  1858.21,1237.92 1860.19,1237.91 1862.17,1237.9 1864.15,1237.88 1866.13,1240.02 1868.1,1249.5 1870.08,1249.48 1872.06,1249.47 1874.04,1249.46 1876.02,1249.45 \n",
       "  1878,1249.44 1879.97,1249.42 1881.95,1252.23 1883.93,1261.04 1885.91,1261.02 1887.89,1261.01 1889.86,1261 1891.84,1260.99 1893.82,1260.98 1895.8,1260.96 \n",
       "  1897.78,1260.95 1899.76,1260.94 1901.73,1260.93 1903.71,1260.92 1905.69,1260.9 1907.67,1260.89 1909.65,1260.88 1911.62,1260.87 1913.6,1265.07 1915.58,1272.48 \n",
       "  1917.56,1272.47 1919.54,1272.46 1921.52,1272.44 1923.49,1272.43 1925.47,1272.42 1927.45,1272.41 1929.43,1272.4 1931.41,1272.38 1933.38,1272.37 1935.36,1272.36 \n",
       "  1937.34,1272.35 1939.32,1272.34 1941.3,1272.32 1943.28,1272.31 1945.25,1272.3 1947.23,1272.29 1949.21,1275.17 1951.19,1283.9 1953.17,1283.89 1955.14,1283.88 \n",
       "  1957.12,1283.86 1959.1,1283.85 1961.08,1283.84 1963.06,1283.83 1965.03,1283.82 1967.01,1283.8 1968.99,1283.79 1970.97,1283.78 1972.95,1283.77 1974.93,1283.76 \n",
       "  1976.9,1283.74 1978.88,1283.73 1980.86,1283.72 1982.84,1283.71 1984.82,1283.7 1986.79,1283.89 1988.77,1294.12 1990.75,1295.3 1992.73,1295.28 1994.71,1295.27 \n",
       "  1996.69,1295.26 1998.66,1295.25 2000.64,1295.24 2002.62,1295.22 2004.6,1295.21 2006.58,1304.97 2008.55,1306.82 2010.53,1306.81 2012.51,1306.8 2014.49,1306.79 \n",
       "  2016.47,1306.78 2018.45,1306.76 2020.42,1306.75 2022.4,1306.74 2024.38,1306.73 2026.36,1306.72 2028.34,1306.7 2030.31,1306.69 2032.29,1306.68 2034.27,1306.67 \n",
       "  2036.25,1306.66 2038.23,1306.64 2040.21,1306.63 2042.18,1306.62 2044.16,1313.69 2046.14,1318.23 2048.12,1318.22 2050.1,1318.21 2052.07,1318.2 2054.05,1318.18 \n",
       "  2056.03,1318.17 2058.01,1318.16 2059.99,1318.15 2061.97,1318.14 2063.94,1318.12 2065.92,1318.11 2067.9,1318.1 2069.88,1318.09 2071.86,1318.08 2073.83,1318.06 \n",
       "  2075.81,1318.05 2077.79,1318.04 2079.77,1318.03 2081.75,1318.02 2083.73,1321.04 2085.7,1329.63 2087.68,1329.62 2089.66,1329.6 2091.64,1329.59 2093.62,1329.58 \n",
       "  2095.59,1329.57 2097.57,1329.56 2099.55,1329.54 2101.53,1329.53 2103.51,1329.52 2105.48,1329.51 2107.46,1329.5 2109.44,1329.48 2111.42,1329.47 2113.4,1329.46 \n",
       "  2115.38,1329.45 2117.35,1329.44 2119.33,1329.42 2121.31,1329.41 2123.29,1329.4 2125.27,1338.62 2127.24,1341.01 2129.22,1341 2131.2,1340.99 2133.18,1340.98 \n",
       "  2135.16,1340.96 2137.14,1340.95 2139.11,1340.94 2141.09,1340.93 2143.07,1340.92 2145.05,1348.09 2147.03,1352.53 2149,1352.52 2150.98,1352.5 2152.96,1352.49 \n",
       "  2154.94,1352.48 2156.92,1352.47 2158.9,1352.46 2160.87,1352.44 2162.85,1352.43 2164.83,1352.42 2166.81,1352.41 2168.79,1352.4 2170.76,1352.38 2172.74,1352.37 \n",
       "  2174.72,1352.36 2176.7,1352.35 2178.68,1352.34 2180.66,1352.32 2182.63,1352.31 2184.61,1355.44 2186.59,1363.92 2188.57,1363.91 2190.55,1363.9 2192.52,1363.89 \n",
       "  2194.5,1363.88 2196.48,1363.86 2198.46,1363.85 2200.44,1363.84 2202.42,1363.83 2204.39,1363.82 2206.37,1363.8 2208.35,1363.79 2210.33,1363.78 2212.31,1363.77 \n",
       "  2214.28,1363.76 2216.26,1363.74 2218.24,1363.73 2220.22,1363.72 2222.2,1363.71 2224.17,1363.7 2226.15,1363.68 2228.13,1363.67 2230.11,1363.66 2232.09,1363.65 \n",
       "  2234.07,1363.64 2236.04,1366.16 2238.02,1375.25 2240,1375.24 2241.98,1375.22 2243.96,1375.21 2245.93,1375.2 2247.91,1375.19 2249.89,1375.18 2251.87,1375.16 \n",
       "  2253.85,1375.15 2255.83,1375.14 2257.8,1375.13 2259.78,1375.12 2261.76,1375.1 2263.74,1375.09 2265.72,1375.08 2267.69,1375.07 2269.67,1375.06 2271.65,1375.04 \n",
       "  2273.63,1375.03 2275.61,1375.02 2277.59,1375.01 2279.56,1375 2281.54,1380.99 2283.52,1386.61 2285.5,1386.6 2287.48,1386.58 2289.45,1386.57 2291.43,1386.57 \n",
       "  2293.41,1386.57 \n",
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       "  1165.85,647.76 1167.83,651.304 1169.81,654.829 1171.79,658.335 1173.77,661.823 1175.75,665.292 1177.72,668.743 1179.7,672.175 1181.68,675.59 1183.66,678.986 \n",
       "  1185.64,682.364 1187.61,685.724 1189.59,689.066 1191.57,692.391 1193.55,695.698 1195.53,698.987 1197.51,702.258 1199.48,705.512 1201.46,708.749 1203.44,711.969 \n",
       "  1205.42,715.171 1207.4,718.357 1209.37,721.525 1211.35,724.676 1213.33,727.811 1215.31,730.929 1217.29,734.03 1219.27,737.115 1221.24,740.183 1223.22,743.234 \n",
       "  1225.2,746.27 1227.18,749.289 1229.16,752.292 1231.13,755.279 1233.11,758.25 1235.09,761.205 1237.07,764.145 1239.05,767.069 1241.03,769.977 1243,772.869 \n",
       "  1244.98,775.746 1246.96,778.608 1248.94,781.454 1250.92,784.285 1252.89,787.101 1254.87,789.902 1256.85,792.688 1258.83,795.459 1260.81,798.215 1262.79,800.956 \n",
       "  1264.76,803.683 1266.74,806.395 1268.72,809.093 1270.7,811.776 1272.68,814.445 1274.65,817.1 1276.63,819.74 1278.61,822.367 1280.59,824.979 1282.57,827.577 \n",
       "  1284.55,830.162 1286.52,832.733 1288.5,835.29 1290.48,837.833 1292.46,840.363 1294.44,842.879 1296.41,845.382 1298.39,847.872 1300.37,850.348 1302.35,852.812 \n",
       "  1304.33,855.262 1306.3,857.699 1308.28,860.123 1310.26,862.534 1312.24,864.933 1314.22,867.318 1316.2,869.691 1318.17,872.052 1320.15,874.4 1322.13,876.735 \n",
       "  1324.11,879.059 1326.09,881.369 1328.06,883.668 1330.04,885.955 1332.02,888.229 1334,890.492 1335.98,892.742 1337.96,894.981 1339.93,897.208 1341.91,899.423 \n",
       "  1343.89,901.626 1345.87,903.818 1347.85,905.999 1349.82,908.168 1351.8,910.325 1353.78,912.471 1355.76,914.607 1357.74,916.731 1359.72,918.843 1361.69,920.945 \n",
       "  1363.67,923.036 1365.65,925.116 1367.63,927.185 1369.61,929.244 1371.58,931.291 1373.56,933.328 1375.54,935.355 1377.52,937.371 1379.5,939.377 1381.48,941.372 \n",
       "  1383.45,943.357 1385.43,945.332 1387.41,947.296 1389.39,949.251 1391.37,951.196 1393.34,953.13 1395.32,955.055 1397.3,956.97 1399.28,958.875 1401.26,960.77 \n",
       "  1403.24,962.656 1405.21,964.532 1407.19,966.398 1409.17,968.256 1411.15,970.103 1413.13,971.942 1415.1,973.771 1417.08,975.591 1419.06,977.402 1421.04,979.204 \n",
       "  1423.02,980.996 1425,982.78 1426.97,984.555 1428.95,986.321 1430.93,988.078 1432.91,989.826 1434.89,991.566 1436.86,993.298 1438.84,995.02 1440.82,996.734 \n",
       "  1442.8,998.44 1444.78,1000.14 1446.75,1001.83 1448.73,1003.51 1450.71,1005.18 1452.69,1006.84 1454.67,1008.5 1456.65,1010.15 1458.62,1011.79 1460.6,1013.42 \n",
       "  1462.58,1015.05 1464.56,1016.66 1466.54,1018.27 1468.51,1019.87 1470.49,1021.47 1472.47,1023.05 1474.45,1024.63 1476.43,1026.2 1478.41,1027.77 1480.38,1029.32 \n",
       "  1482.36,1030.87 1484.34,1032.41 1486.32,1033.95 1488.3,1035.48 1490.27,1037 1492.25,1038.51 1494.23,1040.02 1496.21,1041.52 1498.19,1043.01 1500.17,1044.49 \n",
       "  1502.14,1045.97 1504.12,1047.44 1506.1,1048.91 1508.08,1050.37 1510.06,1051.82 1512.03,1053.27 1514.01,1054.71 1515.99,1056.14 1517.97,1057.56 1519.95,1058.98 \n",
       "  1521.93,1060.4 1523.9,1061.81 1525.88,1063.21 1527.86,1064.6 1529.84,1065.99 1531.82,1067.37 1533.79,1068.75 1535.77,1070.12 1537.75,1071.49 1539.73,1072.85 \n",
       "  1541.71,1074.2 1543.69,1075.55 1545.66,1076.89 1547.64,1078.22 1549.62,1079.56 1551.6,1080.88 1553.58,1082.2 1555.55,1083.51 1557.53,1084.82 1559.51,1086.12 \n",
       "  1561.49,1087.42 1563.47,1088.71 1565.44,1090 1567.42,1091.28 1569.4,1092.56 1571.38,1093.83 1573.36,1095.1 1575.34,1096.36 1577.31,1097.62 1579.29,1098.87 \n",
       "  1581.27,1100.11 1583.25,1101.35 1585.23,1102.59 1587.2,1103.82 1589.18,1105.05 1591.16,1106.27 1593.14,1107.49 1595.12,1108.7 1597.1,1109.91 1599.07,1111.11 \n",
       "  1601.05,1112.31 1603.03,1113.51 1605.01,1114.7 1606.99,1115.88 1608.96,1117.06 1610.94,1118.24 1612.92,1119.41 1614.9,1120.58 1616.88,1121.74 1618.86,1122.9 \n",
       "  1620.83,1124.06 1622.81,1125.21 1624.79,1126.36 1626.77,1127.5 1628.75,1128.64 1630.72,1129.78 1632.7,1130.91 1634.68,1132.04 1636.66,1133.16 1638.64,1134.28 \n",
       "  1640.62,1135.39 1642.59,1136.51 1644.57,1137.61 1646.55,1138.72 1648.53,1139.82 1650.51,1140.92 1652.48,1142.01 1654.46,1143.1 1656.44,1144.19 1658.42,1145.27 \n",
       "  1660.4,1146.35 1662.38,1147.43 1664.35,1148.5 1666.33,1149.57 1668.31,1150.63 1670.29,1151.7 1672.27,1152.75 1674.24,1153.81 1676.22,1154.86 1678.2,1155.91 \n",
       "  1680.18,1156.96 1682.16,1158 1684.14,1159.04 1686.11,1160.08 1688.09,1161.11 1690.07,1162.14 1692.05,1163.17 1694.03,1164.2 1696,1165.22 1697.98,1166.24 \n",
       "  1699.96,1167.25 1701.94,1168.26 1703.92,1169.27 1705.89,1170.28 1707.87,1171.29 1709.85,1172.29 1711.83,1173.29 1713.81,1174.28 1715.79,1175.28 1717.76,1176.27 \n",
       "  1719.74,1177.26 1721.72,1178.24 1723.7,1179.22 1725.68,1180.2 1727.65,1181.18 1729.63,1182.16 1731.61,1183.13 1733.59,1184.1 1735.57,1185.07 1737.55,1186.03 \n",
       "  1739.52,1187 1741.5,1187.96 1743.48,1188.91 1745.46,1189.87 1747.44,1190.82 1749.41,1191.77 1751.39,1192.72 1753.37,1193.67 1755.35,1194.61 1757.33,1195.56 \n",
       "  1759.31,1196.5 1761.28,1197.43 1763.26,1198.37 1765.24,1199.3 1767.22,1200.23 1769.2,1201.16 1771.17,1202.09 1773.15,1203.01 1775.13,1203.94 1777.11,1204.86 \n",
       "  1779.09,1205.77 1781.07,1206.69 1783.04,1207.61 1785.02,1208.52 1787,1209.43 1788.98,1210.34 1790.96,1211.24 1792.93,1212.15 1794.91,1213.05 1796.89,1213.95 \n",
       "  1798.87,1214.85 1800.85,1215.75 1802.83,1216.64 1804.8,1217.54 1806.78,1218.43 1808.76,1219.32 1810.74,1220.21 1812.72,1221.09 1814.69,1221.98 1816.67,1222.86 \n",
       "  1818.65,1223.74 1820.63,1224.62 1822.61,1225.5 1824.58,1226.37 1826.56,1227.25 1828.54,1228.12 1830.52,1228.99 1832.5,1229.86 1834.48,1230.73 1836.45,1231.59 \n",
       "  1838.43,1232.45 1840.41,1233.32 1842.39,1234.18 1844.37,1235.04 1846.34,1235.89 1848.32,1236.75 1850.3,1237.6 1852.28,1238.46 1854.26,1239.31 1856.24,1240.16 \n",
       "  1858.21,1241.01 1860.19,1241.85 1862.17,1242.7 1864.15,1243.54 1866.13,1244.38 1868.1,1245.22 1870.08,1246.06 1872.06,1246.9 1874.04,1247.73 1876.02,1248.57 \n",
       "  1878,1249.4 1879.97,1250.23 1881.95,1251.06 1883.93,1251.89 1885.91,1252.72 1887.89,1253.54 1889.86,1254.37 1891.84,1255.19 1893.82,1256.01 1895.8,1256.83 \n",
       "  1897.78,1257.65 1899.76,1258.46 1901.73,1259.28 1903.71,1260.09 1905.69,1260.9 1907.67,1261.71 1909.65,1262.52 1911.62,1263.33 1913.6,1264.14 1915.58,1264.94 \n",
       "  1917.56,1265.75 1919.54,1266.55 1921.52,1267.35 1923.49,1268.15 1925.47,1268.94 1927.45,1269.74 1929.43,1270.54 1931.41,1271.33 1933.38,1272.12 1935.36,1272.91 \n",
       "  1937.34,1273.7 1939.32,1274.49 1941.3,1275.27 1943.28,1276.06 1945.25,1276.84 1947.23,1277.62 1949.21,1278.4 1951.19,1279.18 1953.17,1279.96 1955.14,1280.73 \n",
       "  1957.12,1281.51 1959.1,1282.28 1961.08,1283.05 1963.06,1283.82 1965.03,1284.59 1967.01,1285.35 1968.99,1286.12 1970.97,1286.88 1972.95,1287.64 1974.93,1288.4 \n",
       "  1976.9,1289.16 1978.88,1289.92 1980.86,1290.67 1982.84,1291.43 1984.82,1292.18 1986.79,1292.93 1988.77,1293.68 1990.75,1294.43 1992.73,1295.17 1994.71,1295.91 \n",
       "  1996.69,1296.66 1998.66,1297.4 2000.64,1298.14 2002.62,1298.87 2004.6,1299.61 2006.58,1300.34 2008.55,1301.08 2010.53,1301.81 2012.51,1302.54 2014.49,1303.26 \n",
       "  2016.47,1303.99 2018.45,1304.71 2020.42,1305.43 2022.4,1306.15 2024.38,1306.87 2026.36,1307.59 2028.34,1308.3 2030.31,1309.01 2032.29,1309.72 2034.27,1310.43 \n",
       "  2036.25,1311.14 2038.23,1311.84 2040.21,1312.55 2042.18,1313.25 2044.16,1313.95 2046.14,1314.64 2048.12,1315.34 2050.1,1316.03 2052.07,1316.72 2054.05,1317.41 \n",
       "  2056.03,1318.1 2058.01,1318.79 2059.99,1319.47 2061.97,1320.15 2063.94,1320.83 2065.92,1321.5 2067.9,1322.18 2069.88,1322.85 2071.86,1323.52 2073.83,1324.19 \n",
       "  2075.81,1324.85 2077.79,1325.52 2079.77,1326.18 2081.75,1326.84 2083.73,1327.49 2085.7,1328.15 2087.68,1328.8 2089.66,1329.45 2091.64,1330.09 2093.62,1330.74 \n",
       "  2095.59,1331.38 2097.57,1332.02 2099.55,1332.65 2101.53,1333.29 2103.51,1333.92 2105.48,1334.55 2107.46,1335.18 2109.44,1335.8 2111.42,1336.42 2113.4,1337.04 \n",
       "  2115.38,1337.66 2117.35,1338.27 2119.33,1338.88 2121.31,1339.49 2123.29,1340.09 2125.27,1340.7 2127.24,1341.3 2129.22,1341.89 2131.2,1342.49 2133.18,1343.08 \n",
       "  2135.16,1343.66 2137.14,1344.25 2139.11,1344.83 2141.09,1345.41 2143.07,1345.99 2145.05,1346.56 2147.03,1347.13 2149,1347.69 2150.98,1348.26 2152.96,1348.82 \n",
       "  2154.94,1349.37 2156.92,1349.93 2158.9,1350.48 2160.87,1351.03 2162.85,1351.57 2164.83,1352.11 2166.81,1352.65 2168.79,1353.18 2170.76,1353.71 2172.74,1354.24 \n",
       "  2174.72,1354.76 2176.7,1355.28 2178.68,1355.79 2180.66,1356.31 2182.63,1356.82 2184.61,1357.32 2186.59,1357.82 2188.57,1358.32 2190.55,1358.81 2192.52,1359.3 \n",
       "  2194.5,1359.79 2196.48,1360.27 2198.46,1360.75 2200.44,1361.22 2202.42,1361.69 2204.39,1362.16 2206.37,1362.62 2208.35,1363.08 2210.33,1363.53 2212.31,1363.98 \n",
       "  2214.28,1364.43 2216.26,1364.87 2218.24,1365.3 2220.22,1365.74 2222.2,1366.17 2224.17,1366.59 2226.15,1367.01 2228.13,1367.42 2230.11,1367.83 2232.09,1368.24 \n",
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       "</g>\n",
       "</svg>\n"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plot(\n",
    "    spd_range,\n",
    "    fa_max_itp.(spd_range),\n",
    "    label = \"Base front axle torque\",\n",
    "    legend = :topright,\n",
    "    xlabel = \"Speed (kph)\",\n",
    "    ylabel = \"Wheel torque (Nm)\"\n",
    ")\n",
    "plot!(\n",
    "    spd_range,\n",
    "    boosted_fa_max_itp.(spd_range),\n",
    "    label=\"Boosted front axle torque\"\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can define an equation for how much force the Turbo S can exert to accelerate itself. Ideally this would be a more generalized equation with values for the Turbo S passed, but that can be done later. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "F (generic function with 1 method)"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "F(v,t) = (\n",
    "    min(\n",
    "        if t < boost_time\n",
    "            boosted_fa_max_itp(3.6*v*slip_ratio)/tire_r_front + boosted_ra_max_itp(3.6*v*slip_ratio)/tire_r_rear\n",
    "        else\n",
    "            max_tq_itp(3.6*v*slip_ratio)/((tire_r_front+tire_r_rear)/2)\n",
    "        end,\n",
    "        f_traction_max\n",
    "    )\n",
    "    - 0.5*Cd*ρ*A_frontal*v^2\n",
    "    - f_rr\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This translates into acceleration by dividing by the vehicle mass."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "a (generic function with 1 method)"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a(v,t) = F(v,t)/mass_veh"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Using the `DifferentialEquations` package, we can easily define a simple differential equation that will model full throttle performance for the Turbo S. Simple is relative, but this will give us distance traveled, speed, and acceleration over time."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "perf_calc (generic function with 1 method)"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function perf_calc(du,u,p,t)\n",
    "    du[1] = u[2]\n",
    "    du[2] = u[3]\n",
    "    u[3] = a(u[2],t)\n",
    "end"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We also want to set some initial conditions `u0` that just say we're starting at zero distance traveled, zero speed, and zero acceleration. Also, we want to run this \"simulation\" from zero to 30 seconds as most of what we're interested in can easily be done in that time."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "u0 = [0.0, 0.0, 0.0];\n",
    "tspan=(0.0,30.0);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Mercifully, the `DifferentialEquations` package allows us to set termination conditions for the simulation, so we can stop calculating when the vehicle hits 60 mph and see what the time is at that point."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.9162624121560072"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "condition(u,t,integrator) = u[2] - 26.8224; #60 mph in m/s\n",
    "affect!(integrator) = terminate!(integrator);\n",
    "cb = ContinuousCallback(condition,affect!);\n",
    "zeroTo60_ode = ODEProblem(perf_calc, u0, tspan);\n",
    "zeroTo60 = solve(zeroTo60_ode, callback=cb);\n",
    "zeroTo60.t[end]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "26.822400000000002"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "zeroTo60.u[end][2]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So we can see that the final speed was reached pretty exactly, but the time is slightly longer than the Porsche quoted 2.6 seconds. So what's happening here? It's possible that my calculations are off, but it's also possible that Porsche is allowing for a 1 foot \"rollout\" in their measurements. Basically, 0-60 times are half physics and half manufacturer \"discretion\" in measurement.\n",
    "\n",
    "However, we can see how long it takes the Turbo S to cover a foot from zero speed and subtract that off our previous answer."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.659095605691652"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "condition(u,t,integrator) = u[1] - 0.3048; #1 ft in m\n",
    "affect!(integrator) = terminate!(integrator);\n",
    "cb = ContinuousCallback(condition, affect!);\n",
    "rollout_ode = ODEProblem(perf_calc, u0, tspan);\n",
    "rollout = solve(rollout_ode, callback=cb);\n",
    "zeroTo60.t[end]-rollout.t[end]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This certainly seems close enough for a simple model using simple physics. What about the quarter mile? Porsche has said the Turbo S can do this in about 10.8 seconds."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "10.788661474027707"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "condition(u,t,integrator) = u[1] - 402.336; #quarter mile in m\n",
    "affect!(integrator) = terminate!(integrator);\n",
    "cb = ContinuousCallback(condition, affect!);\n",
    "quarter_mile_ode = ODEProblem(perf_calc, u0, tspan);\n",
    "quarter_mile = solve(quarter_mile_ode, callback=cb);\n",
    "quarter_mile.t[end]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Again, I'm calling this close enough. Granted, these numbers are also possible because I calibrated the tire `ϕ_p` parameter to match these results, so there is a risk of overfit here. But what about numbers Porsche hasn't released, like 0 to top speed?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "16.991290338125506"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "condition(u,t,integrator) = u[2] - max_spd/3.6; #top speed in m/s\n",
    "affect!(integrator) = terminate!(integrator);\n",
    "cb = ContinuousCallback(condition, affect!);\n",
    "top_speed_ode = ODEProblem(perf_calc, u0, tspan);\n",
    "top_speed = solve(top_speed_ode, callback=cb);\n",
    "top_speed.t[end]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Using highly scientific measurement from a [YouTube video of someone flooring a Turbo S](https://www.youtube.com/watch?v=SUeyRnqq49o), I'd estimate the real value for this is somewhere around 16.6 seconds. Again, not super accurate, but enough to give me confidence that I haven't just overfit the data, since this is less than 5% off. This is also within the realm of another calibratable parameter, which is the slip ratio, but I'll leave it at 15% for the time being."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "But here's something I've been super curious about: did Porsche really need to give the Taycan a transmission on the rear axle? The plot below shows part of the reason I ask, keeping in mind that the upshift is somewhere between 75 and 100 kph."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
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       "<g clip-path=\"url(#clip7300)\">\n",
       "<text style=\"fill:#000000; fill-opacity:1; font-family:Arial,Helvetica Neue,Helvetica,sans-serif; font-size:48px; text-anchor:middle;\" transform=\"rotate(0, 1478.87, 1479.62)\" x=\"1478.87\" y=\"1479.62\">150</text>\n",
       "</g>\n",
       "<g clip-path=\"url(#clip7300)\">\n",
       "<text style=\"fill:#000000; fill-opacity:1; font-family:Arial,Helvetica Neue,Helvetica,sans-serif; font-size:48px; text-anchor:middle;\" transform=\"rotate(0, 1858.08, 1479.62)\" x=\"1858.08\" y=\"1479.62\">200</text>\n",
       "</g>\n",
       "<g clip-path=\"url(#clip7300)\">\n",
       "<text style=\"fill:#000000; fill-opacity:1; font-family:Arial,Helvetica Neue,Helvetica,sans-serif; font-size:48px; text-anchor:middle;\" transform=\"rotate(0, 2237.29, 1479.62)\" x=\"2237.29\" y=\"1479.62\">250</text>\n",
       "</g>\n",
       "<g clip-path=\"url(#clip7300)\">\n",
       "<text style=\"fill:#000000; fill-opacity:1; font-family:Arial,Helvetica Neue,Helvetica,sans-serif; font-size:48px; text-anchor:end;\" transform=\"rotate(0, 258.66, 1375.89)\" x=\"258.66\" y=\"1375.89\">2500</text>\n",
       "</g>\n",
       "<g clip-path=\"url(#clip7300)\">\n",
       "<text style=\"fill:#000000; fill-opacity:1; font-family:Arial,Helvetica Neue,Helvetica,sans-serif; font-size:48px; text-anchor:end;\" transform=\"rotate(0, 258.66, 1069.89)\" x=\"258.66\" y=\"1069.89\">5000</text>\n",
       "</g>\n",
       "<g clip-path=\"url(#clip7300)\">\n",
       "<text style=\"fill:#000000; fill-opacity:1; font-family:Arial,Helvetica Neue,Helvetica,sans-serif; font-size:48px; text-anchor:end;\" transform=\"rotate(0, 258.66, 763.891)\" x=\"258.66\" y=\"763.891\">7500</text>\n",
       "</g>\n",
       "<g clip-path=\"url(#clip7300)\">\n",
       "<text style=\"fill:#000000; fill-opacity:1; font-family:Arial,Helvetica Neue,Helvetica,sans-serif; font-size:48px; text-anchor:end;\" transform=\"rotate(0, 258.66, 457.893)\" x=\"258.66\" y=\"457.893\">10000</text>\n",
       "</g>\n",
       "<g clip-path=\"url(#clip7300)\">\n",
       "<text style=\"fill:#000000; fill-opacity:1; font-family:Arial,Helvetica Neue,Helvetica,sans-serif; font-size:48px; text-anchor:end;\" transform=\"rotate(0, 258.66, 151.894)\" x=\"258.66\" y=\"151.894\">12500</text>\n",
       "</g>\n",
       "<g clip-path=\"url(#clip7300)\">\n",
       "<text style=\"fill:#000000; fill-opacity:1; font-family:Arial,Helvetica Neue,Helvetica,sans-serif; font-size:66px; text-anchor:middle;\" transform=\"rotate(0, 1317.71, 1559.48)\" x=\"1317.71\" y=\"1559.48\">Speed (kph)</text>\n",
       "</g>\n",
       "<g clip-path=\"url(#clip7300)\">\n",
       "<text style=\"fill:#000000; fill-opacity:1; font-family:Arial,Helvetica Neue,Helvetica,sans-serif; font-size:66px; text-anchor:middle;\" transform=\"rotate(-90, 89.2861, 736.431)\" x=\"89.2861\" y=\"736.431\">Wheel torque (Nm)</text>\n",
       "</g>\n",
       "<polyline clip-path=\"url(#clip7302)\" style=\"stroke:#009af9; stroke-width:4; stroke-opacity:1; fill:none\" points=\"\n",
       "  341.248,218.742 343.2,218.742 345.153,218.742 347.106,218.742 349.059,218.742 351.012,218.742 352.965,218.742 354.918,218.742 356.871,218.742 358.824,218.742 \n",
       "  360.777,218.742 362.73,218.742 364.683,218.742 366.636,218.742 368.588,218.742 370.541,218.742 372.494,218.742 374.447,218.742 376.4,218.742 378.353,218.742 \n",
       "  380.306,218.742 382.259,218.742 384.212,218.742 386.165,218.742 388.118,218.742 390.071,218.742 392.023,218.742 393.976,218.742 395.929,218.742 397.882,218.742 \n",
       "  399.835,218.742 401.788,218.742 403.741,218.742 405.694,218.742 407.647,218.742 409.6,218.742 411.553,218.742 413.506,218.742 415.459,218.742 417.411,218.742 \n",
       "  419.364,218.742 421.317,218.742 423.27,218.742 425.223,218.742 427.176,218.742 429.129,218.742 431.082,218.742 433.035,218.742 434.988,218.742 436.941,218.742 \n",
       "  438.894,218.742 440.847,218.742 442.799,218.742 444.752,218.742 446.705,218.742 448.658,218.742 450.611,218.742 452.564,218.742 454.517,218.742 456.47,218.742 \n",
       "  458.423,218.742 460.376,218.742 462.329,218.742 464.282,218.742 466.234,218.742 468.187,218.742 470.14,218.742 472.093,218.742 474.046,218.742 475.999,218.742 \n",
       "  477.952,218.742 479.905,218.742 481.858,218.742 483.811,218.742 485.764,218.742 487.717,218.742 489.67,218.742 491.622,218.742 493.575,218.742 495.528,218.742 \n",
       "  497.481,218.742 499.434,218.742 501.387,218.742 503.34,218.742 505.293,218.742 507.246,218.742 509.199,218.742 511.152,218.742 513.105,218.742 515.058,218.742 \n",
       "  517.01,218.742 518.963,218.742 520.916,218.742 522.869,218.742 524.822,218.742 526.775,218.742 528.728,218.742 530.681,218.742 532.634,218.742 534.587,218.742 \n",
       "  536.54,218.742 538.493,218.742 540.445,218.742 542.398,218.742 544.351,218.742 546.304,218.742 548.257,218.742 550.21,218.742 552.163,218.742 554.116,218.742 \n",
       "  556.069,218.742 558.022,218.742 559.975,218.742 561.928,218.742 563.881,218.742 565.833,218.742 567.786,218.742 569.739,218.742 571.692,218.742 573.645,218.742 \n",
       "  575.598,218.742 577.551,218.742 579.504,218.742 581.457,218.742 583.41,218.742 585.363,218.742 587.316,218.742 589.268,218.742 591.221,218.742 593.174,218.742 \n",
       "  595.127,218.742 597.08,218.742 599.033,218.742 600.986,218.742 602.939,218.742 604.892,218.742 606.845,218.742 608.798,218.742 610.751,218.742 612.704,218.742 \n",
       "  614.656,218.742 616.609,218.742 618.562,218.742 620.515,218.742 622.468,218.742 624.421,218.742 626.374,218.742 628.327,218.742 630.28,218.742 632.233,218.742 \n",
       "  634.186,218.742 636.139,218.742 638.092,218.742 640.044,218.742 641.997,218.742 643.95,218.742 645.903,218.742 647.856,218.742 649.809,218.742 651.762,218.742 \n",
       "  653.715,218.742 655.668,218.742 657.621,218.742 659.574,218.742 661.527,218.742 663.479,218.742 665.432,221.007 667.385,221.729 669.338,221.729 671.291,221.729 \n",
       "  673.244,221.729 675.197,221.729 677.15,221.89 679.103,224.52 681.056,224.716 683.009,224.716 684.962,224.716 686.915,224.716 688.867,225.751 690.82,227.703 \n",
       "  692.773,227.703 694.726,227.703 696.679,227.703 698.632,229.963 700.585,230.69 702.538,230.69 704.491,230.69 706.444,230.69 708.397,231.195 710.35,233.677 \n",
       "  712.302,233.677 714.255,233.677 716.208,233.677 718.161,238.386 720.114,246.974 722.067,252.583 724.02,258.192 725.973,272.74 727.926,275.369 729.879,280.978 \n",
       "  731.832,286.588 733.785,295.176 735.738,300.785 737.69,306.394 739.643,312.003 741.596,320.592 743.549,323.221 745.502,328.831 747.455,334.441 749.408,340.05 \n",
       "  751.361,348.638 753.314,354.247 755.267,359.856 757.22,365.466 759.173,371.819 761.126,376.684 763.078,382.293 765.031,387.902 766.984,393.511 768.937,402.099 \n",
       "  770.89,407.708 772.843,413.318 774.796,418.927 776.749,421.556 778.702,430.146 780.655,435.754 782.608,438.384 784.561,443.993 786.513,449.603 788.466,455.212 \n",
       "  790.419,457.842 792.372,460.471 794.325,466.081 796.278,474.669 798.231,477.299 800.184,482.908 802.137,488.518 804.09,494.127 806.043,499.736 807.996,502.365 \n",
       "  809.949,504.995 811.901,510.605 813.854,516.214 815.807,521.823 817.76,527.432 819.713,533.041 821.666,538.65 823.619,541.28 825.572,543.91 827.525,549.519 \n",
       "  829.478,555.128 831.431,560.737 833.384,566.347 835.337,568.976 837.289,574.585 839.242,580.194 841.195,582.826 843.148,585.454 845.101,591.063 847.054,593.693 \n",
       "  849.007,599.302 850.96,601.933 852.913,607.542 854.866,610.171 856.819,612.801 858.772,618.41 860.724,621.041 862.677,623.671 864.63,629.279 866.583,631.909 \n",
       "  868.536,637.518 870.489,640.149 872.442,642.778 874.395,648.387 876.348,651.017 878.301,653.647 880.254,659.256 882.207,661.886 884.16,667.495 886.112,670.125 \n",
       "  888.065,675.734 890.018,678.364 891.971,680.994 893.924,683.624 895.877,689.232 897.83,691.862 899.783,697.473 901.736,700.102 903.689,702.731 905.642,705.361 \n",
       "  907.595,707.991 909.547,713.6 911.5,716.23 913.453,718.86 915.406,721.489 917.359,724.119 919.312,726.749 921.265,729.38 923.218,732.01 925.171,737.618 \n",
       "  927.124,740.248 929.077,742.878 931.03,745.508 932.983,748.138 934.935,750.767 936.888,753.397 938.841,756.027 940.794,761.636 942.747,764.266 944.7,766.896 \n",
       "  946.653,769.526 948.606,772.156 950.559,774.786 952.512,777.415 954.465,780.045 956.418,785.654 958.371,788.284 960.323,790.914 962.276,793.544 964.229,796.174 \n",
       "  966.182,798.804 968.135,801.434 970.088,804.063 972.041,806.693 973.994,809.323 975.947,810.142 977.9,810.142 979.853,813.129 981.806,816.116 983.758,819.103 \n",
       "  985.711,819.144 987.664,821.773 989.617,824.404 991.57,825.077 993.523,826.684 995.476,829.314 997.429,831.944 999.382,834.573 1001.33,837.203 1003.29,839.833 \n",
       "  1005.24,842.463 1007.19,845.093 1009.15,847.723 1011.1,851.958 1013.05,854.945 1015.01,857.932 1016.96,860.919 1018.91,860.919 1020.86,863.502 1022.82,872.09 \n",
       "  1024.77,874.72 1026.72,877.35 1028.68,878.84 1030.63,879.631 1032.58,882.26 1034.53,884.89 1036.49,887.52 1038.44,887.801 1040.39,887.801 1042.35,887.801 \n",
       "  1044.3,889.101 1046.25,891.731 1048.2,893.775 1050.16,894.012 1052.11,896.641 1054.06,899.271 1056.02,901.901 1057.97,904.531 1059.92,905.722 1061.88,906.812 \n",
       "  1063.83,909.441 1065.78,912.072 1067.73,914.683 1069.69,914.683 1071.64,916.981 1073.59,919.611 1075.55,922.241 1077.5,924.871 1079.45,926.63 1081.4,927.151 \n",
       "  1083.36,929.782 1085.31,932.411 1087.26,932.604 1089.22,934.691 1091.17,937.321 1093.12,939.951 1095.07,941.565 1097.03,942.232 1098.98,944.862 1100.93,947.491 \n",
       "  1102.89,947.538 1104.84,949.772 1106.79,952.402 1108.75,953.512 1110.7,954.682 1112.65,957.312 1114.6,959.486 1116.56,959.592 1118.51,962.222 1120.46,964.852 \n",
       "  1122.42,965.46 1124.37,967.132 1126.32,969.763 1128.27,971.433 1130.23,972.043 1132.18,974.672 1134.13,977.303 1136.09,977.407 1138.04,979.583 1139.99,980.394 \n",
       "  1141.95,981.863 1143.9,984.493 1145.85,986.368 1147.8,986.773 1149.76,989.403 1151.71,992.033 1153.66,994.663 1155.62,995.328 1157.57,996.944 1159.52,998.315 \n",
       "  1161.47,999.224 1163.43,1001.3 1165.38,1001.5 1167.33,1004.13 1169.29,1006.76 1171.24,1007.28 1173.19,1009.04 1175.14,1010.26 1177.1,1011.32 1179.05,1013.25 \n",
       "  1181,1013.6 1182.96,1016.24 1184.91,1018.86 1186.86,1019.22 1188.82,1021.15 1190.77,1022.21 1192.72,1023.43 1194.67,1025.2 1196.63,1025.71 1198.58,1028.18 \n",
       "  1200.53,1028.18 1202.49,1030.62 1204.44,1033.25 1206.39,1034.16 1208.34,1035.53 1210.3,1037.14 1212.25,1037.81 1214.2,1040.13 1216.16,1040.13 1218.11,1042.72 \n",
       "  1220.06,1043.12 1222.01,1045 1223.97,1046.1 1225.92,1047.28 1227.87,1049.09 1229.83,1049.56 1231.78,1052.08 1233.73,1052.08 1235.69,1054.47 1237.64,1055.07 \n",
       "  1239.59,1056.75 1241.54,1058.05 1243.5,1058.05 1245.45,1058.68 1247.4,1061.04 1249.36,1061.04 1251.31,1063.59 1253.26,1064.03 1255.21,1065.87 1257.17,1067.01 \n",
       "  1259.12,1068.15 1261.07,1070 1263.03,1070.43 1264.98,1072.99 1266.93,1072.99 1268.88,1072.99 1270.84,1074.99 1272.79,1075.97 1274.74,1077.27 1276.7,1078.96 \n",
       "  1278.65,1079.55 1280.6,1081.95 1282.56,1081.95 1284.51,1084.46 1286.46,1084.93 1288.41,1086.74 1290.37,1087.92 1292.32,1089.02 1294.27,1090.91 1296.23,1091.31 \n",
       "  1298.18,1093.89 1300.13,1093.89 1302.08,1093.89 1304.04,1095.87 1305.99,1096.88 1307.94,1098.15 1309.9,1099.87 1311.85,1100.43 1313.8,1102.86 1315.75,1102.86 \n",
       "  1317.71,1105.34 1319.66,1105.84 1321.61,1107.62 1323.57,1108.83 1325.52,1108.83 1327.47,1109.55 1329.43,1111.82 1331.38,1111.83 1333.33,1114.46 1335.28,1114.8 \n",
       "  1337.24,1116.74 1339.19,1117.79 1341.14,1119.02 1343.1,1120.78 1345.05,1120.78 1347,1120.95 1348.95,1123.58 1350.91,1123.76 1352.86,1125.86 1354.81,1126.75 \n",
       "  1356.77,1126.75 1358.72,1127.79 1360.67,1129.74 1362.63,1129.74 1364.58,1129.74 1366.53,1132.35 1368.48,1132.72 1370.44,1132.72 1372.39,1134.28 1374.34,1135.71 \n",
       "  1376.3,1136.56 1378.25,1138.7 1380.2,1138.7 1382.15,1138.7 1384.11,1141.12 1386.06,1141.68 1388.01,1141.68 1389.97,1143.06 1391.92,1144.67 1393.87,1144.67 \n",
       "  1395.82,1144.99 1397.78,1147.62 1399.73,1147.66 1401.68,1147.66 1403.64,1149.55 1405.59,1150.65 1407.54,1151.83 1409.5,1153.63 1411.45,1153.63 1413.4,1153.63 \n",
       "  1415.35,1153.63 1417.31,1156.04 1419.26,1156.62 1421.21,1158.32 1423.17,1159.61 1425.12,1162.59 1427.07,1162.59 1429.02,1162.59 1430.98,1162.59 1432.93,1165.16 \n",
       "  1434.88,1165.58 1436.84,1165.58 1438.79,1167.09 1440.74,1168.57 1442.69,1168.57 1444.65,1168.57 1446.6,1168.67 1448.55,1171.3 1450.51,1171.55 1452.46,1171.55 \n",
       "  1454.41,1173.23 1456.37,1174.54 1458.32,1175.52 1460.27,1177.53 1462.22,1177.53 1464.18,1177.53 1466.13,1180.07 1468.08,1180.51 1470.04,1180.51 1471.99,1182.01 \n",
       "  1473.94,1183.5 1475.89,1183.5 1477.85,1183.94 1479.8,1186.49 1481.75,1186.49 1483.71,1186.49 1485.66,1188.5 1487.61,1189.47 1489.56,1189.47 1491.52,1189.47 \n",
       "  1493.47,1190.08 1495.42,1192.46 1497.38,1192.46 1499.33,1192.46 1501.28,1192.46 1503.24,1192.46 1505.19,1193.94 1507.14,1195.45 1509.09,1196.22 1511.05,1198.44 \n",
       "  1513,1198.44 1514.95,1198.44 1516.91,1200.78 1518.86,1201.42 1520.81,1201.42 1522.76,1201.42 1524.72,1202.36 1526.67,1204.41 1528.62,1204.41 1530.58,1204.41 \n",
       "  1532.53,1204.41 1534.48,1204.41 1536.44,1206.23 1538.39,1207.4 1540.34,1208.51 1542.29,1210.38 1544.25,1210.38 1546.2,1210.44 1548.15,1213.07 1550.11,1213.37 \n",
       "  1552.06,1213.37 1554.01,1213.37 1555.96,1213.37 1557.92,1214.3 1559.87,1216.36 1561.82,1216.36 1563.78,1216.36 1565.73,1216.36 1567.68,1218.51 1569.63,1219.34 \n",
       "  1571.59,1220.79 1573.54,1222.33 1575.49,1222.33 1577.45,1222.33 1579.4,1222.37 1581.35,1225 1583.31,1225.32 1585.26,1225.32 1587.21,1225.32 1589.16,1225.32 \n",
       "  1591.12,1226.24 1593.07,1228.3 1595.02,1228.52 1596.98,1231.14 1598.93,1231.29 1600.88,1231.29 1602.83,1231.29 1604.79,1232.73 1606.74,1234.28 1608.69,1234.28 \n",
       "  1610.65,1234.28 1612.6,1234.31 1614.55,1236.94 1616.5,1237.26 1618.46,1237.26 1620.41,1237.26 1622.36,1237.26 1624.32,1238.17 1626.27,1240.25 1628.22,1240.25 \n",
       "  1630.18,1240.25 1632.13,1240.25 1634.08,1242.38 1636.03,1243.24 1637.99,1243.24 1639.94,1243.24 1641.89,1243.96 1643.85,1246.23 1645.8,1246.23 1647.75,1246.23 \n",
       "  1649.7,1246.23 1651.66,1248.17 1653.61,1249.21 1655.56,1249.21 1657.52,1249.21 1659.47,1249.21 1661.42,1249.41 1663.37,1252.04 1665.33,1252.2 1667.28,1252.2 \n",
       "  1669.23,1252.2 1671.19,1253.62 1673.14,1255.19 1675.09,1255.19 1677.05,1255.19 1679,1255.2 1680.95,1257.83 1682.9,1258.17 1684.86,1258.17 1686.81,1258.17 \n",
       "  1688.76,1258.17 1690.72,1259.06 1692.67,1261.16 1694.62,1261.16 1696.57,1261.16 1698.53,1261.16 1700.48,1263.27 1702.43,1264.15 1704.39,1264.15 1706.34,1264.15 \n",
       "  1708.29,1264.85 1710.24,1267.13 1712.2,1267.13 1714.15,1267.13 1716.1,1267.13 1718.06,1269.07 1720.01,1270.12 1721.96,1270.12 1723.92,1270.12 1725.87,1270.12 \n",
       "  1727.82,1270.12 1729.77,1270.12 1731.73,1272.58 1733.68,1273.11 1735.63,1273.11 1737.59,1273.11 1739.54,1273.11 1741.49,1273.81 1743.44,1276.09 1745.4,1276.09 \n",
       "  1747.35,1276.09 1749.3,1276.09 1751.26,1276.09 1753.21,1277.67 1755.16,1279.08 1757.12,1279.08 1759.07,1279.08 1761.02,1279.08 1762.97,1279.08 1764.93,1281.53 \n",
       "  1766.88,1282.07 1768.83,1282.07 1770.79,1282.07 1772.74,1282.07 1774.69,1282.07 1776.64,1282.42 1778.6,1285.05 1780.55,1285.05 1782.5,1285.05 1784.46,1285.05 \n",
       "  1786.41,1285.05 1788.36,1286.28 1790.31,1288.04 1792.27,1288.04 1794.22,1288.04 1796.17,1288.04 1798.13,1290.49 1800.08,1291.03 1802.03,1291.03 1803.99,1291.03 \n",
       "  1805.94,1291.03 1807.89,1291.72 1809.84,1294.02 1811.8,1294.02 1813.75,1294.02 1815.7,1294.02 1817.66,1294.02 1819.61,1294.02 1821.56,1295.23 1823.51,1297 \n",
       "  1825.47,1297 1827.42,1297 1829.37,1297 1831.33,1297 1833.28,1299.1 1835.23,1299.99 1837.18,1299.99 1839.14,1299.99 1841.09,1299.99 1843.04,1300.33 \n",
       "  1845,1302.96 1846.95,1302.98 1848.9,1302.98 1850.86,1302.98 1852.81,1302.98 1854.76,1302.98 1856.71,1303.84 1858.67,1305.96 1860.62,1305.96 1862.57,1305.96 \n",
       "  1864.53,1305.96 1866.48,1305.96 1868.43,1305.96 1870.38,1305.96 1872.34,1307 1874.29,1308.95 1876.24,1308.95 1878.2,1308.95 1880.15,1308.95 1882.1,1308.95 \n",
       "  1884.05,1308.95 1886.01,1310.52 1887.96,1311.94 1889.91,1311.94 1891.87,1311.94 1893.82,1311.94 1895.77,1311.94 1897.73,1314.38 1899.68,1314.92 1901.63,1314.92 \n",
       "  1903.58,1314.92 1905.54,1314.92 1907.49,1314.92 1909.44,1314.92 1911.4,1314.92 1913.35,1317.54 1915.3,1317.91 1917.25,1317.91 1919.21,1317.91 1921.16,1317.91 \n",
       "  1923.11,1317.91 1925.07,1317.91 1927.02,1318.08 1928.97,1320.7 1930.93,1320.9 1932.88,1320.9 1934.83,1320.9 1936.78,1320.9 1938.74,1320.9 1940.69,1321.59 \n",
       "  1942.64,1323.88 1944.6,1323.88 1946.55,1323.88 1948.5,1323.88 1950.45,1323.88 1952.41,1325.45 1954.36,1326.87 1956.31,1326.87 1958.27,1326.87 1960.22,1326.87 \n",
       "  1962.17,1326.87 1964.12,1326.87 1966.08,1328.96 1968.03,1329.86 1969.98,1329.86 1971.94,1329.86 1973.89,1329.86 1975.84,1329.86 1977.8,1329.86 1979.75,1329.86 \n",
       "  1981.7,1329.86 1983.65,1331.78 1985.61,1332.84 1987.56,1332.84 1989.51,1332.84 1991.47,1332.84 1993.42,1332.84 1995.37,1332.84 1997.32,1332.84 1999.28,1334.94 \n",
       "  2001.23,1335.83 2003.18,1335.83 2005.14,1335.83 2007.09,1335.83 2009.04,1335.83 2010.99,1335.83 2012.95,1338.45 2014.9,1338.82 2016.85,1338.82 2018.81,1338.82 \n",
       "  2020.76,1338.82 2022.71,1338.82 2024.67,1338.82 2026.62,1338.98 2028.57,1341.61 2030.52,1341.8 2032.48,1341.8 2034.43,1341.8 2036.38,1341.8 2038.34,1341.8 \n",
       "  2040.29,1341.8 2042.24,1341.8 2044.19,1341.8 2046.15,1344.43 2048.1,1344.79 2050.05,1344.79 2052.01,1344.79 2053.96,1344.79 2055.91,1344.79 2057.86,1344.79 \n",
       "  2059.82,1344.96 2061.77,1347.59 2063.72,1347.78 2065.68,1347.78 2067.63,1347.78 2069.58,1347.78 2071.54,1347.78 2073.49,1348.47 2075.44,1350.77 2077.39,1350.77 \n",
       "  2079.35,1350.77 2081.3,1350.77 2083.25,1350.77 2085.21,1350.77 2087.16,1350.77 2089.11,1351.64 2091.06,1353.75 2093.02,1353.75 2094.97,1353.75 2096.92,1353.75 \n",
       "  2098.88,1353.75 2100.83,1353.75 2102.78,1353.75 2104.73,1353.75 2106.69,1353.75 2108.64,1353.75 2110.59,1353.75 2112.55,1356.38 2114.5,1356.74 2116.45,1356.74 \n",
       "  2118.41,1356.74 2120.36,1356.74 2122.31,1356.74 2124.26,1356.74 2126.22,1356.91 2128.17,1359.54 2130.12,1359.73 2132.08,1359.73 2134.03,1359.73 2135.98,1359.73 \n",
       "  2137.93,1359.73 2139.89,1359.73 2141.84,1360.08 2143.79,1362.71 2145.75,1362.71 2147.7,1362.71 2149.65,1362.71 2151.61,1362.71 2153.56,1362.71 2155.51,1362.71 \n",
       "  2157.46,1362.71 2159.42,1362.71 2161.37,1362.71 2163.32,1365.17 2165.28,1365.7 2167.23,1365.7 2169.18,1365.7 2171.13,1365.7 2173.09,1365.7 2175.04,1365.7 \n",
       "  2176.99,1365.7 2178.95,1365.7 2180.9,1365.7 2182.85,1367.64 2184.8,1368.69 2186.76,1368.69 2188.71,1368.69 2190.66,1368.69 2192.62,1368.69 2194.57,1368.69 \n",
       "  2196.52,1368.69 2198.48,1370.8 2200.43,1371.67 2202.38,1371.67 2204.33,1371.67 2206.29,1371.67 2208.24,1371.67 2210.19,1371.67 2212.15,1371.67 2214.1,1371.67 \n",
       "  2216.05,1373.61 2218,1374.66 2219.96,1374.66 2221.91,1374.66 2223.86,1374.66 2225.82,1374.66 2227.77,1374.66 2229.72,1374.66 2231.67,1374.66 2233.63,1374.66 \n",
       "  2235.58,1376.08 2237.53,1377.65 2239.49,1377.65 2241.44,1377.65 2243.39,1377.65 2245.35,1377.65 2247.3,1377.65 2249.25,1377.65 2251.2,1377.65 2253.16,1377.65 \n",
       "  2255.11,1377.65 2257.06,1378.19 2259.02,1380.63 2260.97,1380.63 2262.92,1380.63 2264.87,1380.63 2266.83,1380.63 2268.78,1380.63 2270.73,1380.63 2272.69,1381.35 \n",
       "  2274.64,1383.62 2276.59,1383.62 2278.54,1383.62 2280.5,1383.62 2282.45,1385.57 2284.4,1386.61 2286.36,1386.61 2288.31,1386.61 2290.26,1386.61 2292.22,1386.61 \n",
       "  2294.17,1386.61 \n",
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       "  1395.82,1036.17 1397.78,1036.67 1399.73,1037.17 1401.68,1037.67 1403.64,1040.08 1405.59,1041.97 1407.54,1042.46 1409.5,1043.69 1411.45,1046.75 1413.4,1047.23 \n",
       "  1415.35,1047.71 1417.31,1048.19 1419.26,1050.76 1421.21,1052.45 1423.17,1052.92 1425.12,1054.31 1427.07,1057.17 1429.02,1057.63 1430.98,1058.1 1432.93,1058.56 \n",
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       "  1591.12,1145.62 1593.07,1145.94 1595.02,1146.32 1596.98,1149.54 1598.93,1150.19 1600.88,1150.5 1602.83,1150.81 1604.79,1151.12 1606.74,1152.45 1608.69,1155.04 \n",
       "  1610.65,1155.34 1612.6,1155.65 1614.55,1155.95 1616.5,1156.25 1618.46,1158.55 1620.41,1160.16 1622.36,1160.46 1624.32,1160.75 1626.27,1161.05 1628.22,1161.34 \n",
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       "  1649.7,1171.14 1651.66,1171.42 1653.61,1173.3 1655.56,1175.29 1657.52,1175.57 1659.47,1175.85 1661.42,1176.13 1663.37,1176.4 1665.33,1176.68 1667.28,1179.14 \n",
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       "  1688.76,1186.54 1690.72,1187.62 1692.67,1190.38 1694.62,1190.64 1696.57,1190.9 1698.53,1191.16 1700.48,1191.42 1702.43,1193.47 1704.39,1195.25 1706.34,1195.51 \n",
       "  1708.29,1195.77 1710.24,1196.03 1712.2,1196.28 1714.15,1196.54 1716.1,1199.16 1718.06,1200.36 1720.01,1200.61 1721.96,1200.86 1723.92,1201.11 1725.87,1201.37 \n",
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       "  1747.35,1210.7 1749.3,1210.95 1751.26,1211.19 1753.21,1211.43 1755.16,1212.87 1757.12,1215.22 1759.07,1215.46 1761.02,1215.7 1762.97,1215.94 1764.93,1216.18 \n",
       "  1766.88,1216.42 1768.83,1216.66 1770.79,1218.29 1772.74,1220.44 1774.69,1220.68 1776.64,1220.91 1778.6,1221.15 1780.55,1221.38 1782.5,1221.62 1784.46,1223.82 \n",
       "  1786.41,1225.39 1788.36,1225.62 1790.31,1225.85 1792.27,1226.09 1794.22,1226.32 1796.17,1226.55 1798.13,1226.78 1800.08,1229.17 1802.03,1230.54 1803.99,1230.77 \n",
       "  1805.94,1231 1807.89,1231.23 1809.84,1231.45 1811.8,1231.68 1813.75,1234.65 1815.7,1235.44 1817.66,1235.66 1819.61,1235.89 1821.56,1236.11 1823.51,1236.34 \n",
       "  1825.47,1236.97 1827.42,1240.09 1829.37,1240.31 1831.33,1240.53 1833.28,1240.76 1835.23,1240.98 1837.18,1241.2 1839.14,1242.41 1841.09,1244.95 1843.04,1245.16 \n",
       "  1845,1245.38 1846.95,1245.6 1848.9,1245.82 1850.86,1246.04 1852.81,1246.26 1854.76,1246.47 1856.71,1247.49 1858.67,1250.21 1860.62,1250.43 1862.57,1250.64 \n",
       "  1864.53,1250.86 1866.48,1251.07 1868.43,1251.29 1870.38,1251.5 1872.34,1252.71 1874.29,1255.23 1876.24,1255.45 1878.2,1255.66 1880.15,1255.87 1882.1,1256.08 \n",
       "  1884.05,1256.29 1886.01,1256.5 1887.96,1256.71 1889.91,1257.72 1891.87,1260.44 1893.82,1260.65 1895.77,1260.86 1897.73,1261.06 1899.68,1261.27 1901.63,1261.48 \n",
       "  1903.58,1261.69 1905.54,1261.89 1907.49,1262.71 1909.44,1265.61 1911.4,1265.82 1913.35,1266.02 1915.3,1266.23 1917.25,1266.43 1919.21,1266.64 1921.16,1266.84 \n",
       "  1923.11,1267.04 1925.07,1267.66 1927.02,1270.76 1928.97,1270.96 1930.93,1271.16 1932.88,1271.36 1934.83,1271.56 1936.78,1271.76 1938.74,1271.96 1940.69,1272.77 \n",
       "  1942.64,1275.67 1944.6,1275.87 1946.55,1276.07 1948.5,1276.27 1950.45,1276.47 1952.41,1276.66 1954.36,1276.86 1956.31,1277.06 1958.27,1277.67 1960.22,1280.76 \n",
       "  1962.17,1280.95 1964.12,1281.15 1966.08,1281.34 1968.03,1281.54 1969.98,1281.73 1971.94,1281.93 1973.89,1282.73 1975.84,1285.62 1977.8,1285.81 1979.75,1286.01 \n",
       "  1981.7,1286.2 1983.65,1286.39 1985.61,1286.58 1987.56,1286.77 1989.51,1286.96 1991.47,1287.56 1993.42,1290.65 1995.37,1290.84 1997.32,1291.02 1999.28,1291.21 \n",
       "  2001.23,1291.4 2003.18,1291.59 2005.14,1291.77 2007.09,1291.96 2009.04,1292.15 2010.99,1292.33 2012.95,1295.26 2014.9,1296.01 2016.85,1296.19 2018.81,1296.38 \n",
       "  2020.76,1296.56 2022.71,1296.74 2024.67,1296.92 2026.62,1297.11 2028.57,1297.29 2030.52,1300.02 2032.48,1300.96 2034.43,1301.14 2036.38,1301.32 2038.34,1301.49 \n",
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       "  2176.99,1335.81 2178.95,1335.94 2180.9,1336.07 2182.85,1336.2 2184.8,1336.33 2186.76,1337.66 2188.71,1339.89 2190.66,1340.01 2192.62,1340.13 2194.57,1340.26 \n",
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      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plot(\n",
    "    spd_range, \n",
    "    max_tq_itp(spd_range),\n",
    "    label=\"Turbo S Base\",\n",
    "    xlabel = \"Speed (kph)\",\n",
    "    ylabel = \"Wheel torque (Nm)\",\n",
    "    yaxis=[0 13000]\n",
    ")\n",
    "plot!(\n",
    "    spd_range,\n",
    "    boosted_fa_max_itp.(spd_range)+boosted_ra_max_itp.(spd_range),\n",
    "    label = \"Turbo S Overboost\"\n",
    ")\n",
    "plot!(spd_range, traction_limit_tq*ones(size(spd_range)), label=\"Optimal traction limit\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see that below about 100 kph the limiting factor in delivering acceleration to the vehicle is the tires. In fact, it looks like the boosted performance of the Turbo S is in ridiculous excess of what can actually be used. Perhaps this is just for bragging rights; it is a Porsche after all. But we can model what the rear axle would look like with just the single gear, and calculate performance for that variant."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
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       "<g clip-path=\"url(#clip7700)\">\n",
       "<text style=\"fill:#000000; fill-opacity:1; font-family:Arial,Helvetica Neue,Helvetica,sans-serif; font-size:48px; text-anchor:middle;\" transform=\"rotate(0, 699.353, 1479.62)\" x=\"699.353\" y=\"1479.62\">50</text>\n",
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       "<g clip-path=\"url(#clip7700)\">\n",
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       "<g clip-path=\"url(#clip7700)\">\n",
       "<text style=\"fill:#000000; fill-opacity:1; font-family:Arial,Helvetica Neue,Helvetica,sans-serif; font-size:48px; text-anchor:middle;\" transform=\"rotate(0, 1467.57, 1479.62)\" x=\"1467.57\" y=\"1479.62\">150</text>\n",
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       "<g clip-path=\"url(#clip7700)\">\n",
       "<text style=\"fill:#000000; fill-opacity:1; font-family:Arial,Helvetica Neue,Helvetica,sans-serif; font-size:48px; text-anchor:middle;\" transform=\"rotate(0, 1851.68, 1479.62)\" x=\"1851.68\" y=\"1479.62\">200</text>\n",
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       "<g clip-path=\"url(#clip7700)\">\n",
       "<text style=\"fill:#000000; fill-opacity:1; font-family:Arial,Helvetica Neue,Helvetica,sans-serif; font-size:48px; text-anchor:middle;\" transform=\"rotate(0, 2235.79, 1479.62)\" x=\"2235.79\" y=\"1479.62\">250</text>\n",
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       "<g clip-path=\"url(#clip7700)\">\n",
       "<text style=\"fill:#000000; fill-opacity:1; font-family:Arial,Helvetica Neue,Helvetica,sans-serif; font-size:48px; text-anchor:end;\" transform=\"rotate(0, 231.898, 1242.37)\" x=\"231.898\" y=\"1242.37\">1000</text>\n",
       "</g>\n",
       "<g clip-path=\"url(#clip7700)\">\n",
       "<text style=\"fill:#000000; fill-opacity:1; font-family:Arial,Helvetica Neue,Helvetica,sans-serif; font-size:48px; text-anchor:end;\" transform=\"rotate(0, 231.898, 919.108)\" x=\"231.898\" y=\"919.108\">2000</text>\n",
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       "<g clip-path=\"url(#clip7700)\">\n",
       "<text style=\"fill:#000000; fill-opacity:1; font-family:Arial,Helvetica Neue,Helvetica,sans-serif; font-size:48px; text-anchor:end;\" transform=\"rotate(0, 231.898, 595.843)\" x=\"231.898\" y=\"595.843\">3000</text>\n",
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       "<g clip-path=\"url(#clip7700)\">\n",
       "<text style=\"fill:#000000; fill-opacity:1; font-family:Arial,Helvetica Neue,Helvetica,sans-serif; font-size:48px; text-anchor:end;\" transform=\"rotate(0, 231.898, 272.579)\" x=\"231.898\" y=\"272.579\">4000</text>\n",
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       "<g clip-path=\"url(#clip7700)\">\n",
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       "<g clip-path=\"url(#clip7700)\">\n",
       "<text style=\"fill:#000000; fill-opacity:1; font-family:Arial,Helvetica Neue,Helvetica,sans-serif; font-size:66px; text-anchor:middle;\" transform=\"rotate(-90, 89.2861, 736.431)\" x=\"89.2861\" y=\"736.431\">Wheel torque (Nm)</text>\n",
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       "  335.024,87.8668 337.002,88.028 338.981,88.1892 340.959,88.3504 342.937,88.5117 344.915,88.6729 346.893,88.8341 348.872,88.9953 350.85,89.1565 352.828,89.3177 \n",
       "  354.806,89.4789 356.784,89.6401 358.762,89.8013 360.741,89.9626 362.719,90.1238 364.697,90.285 366.675,90.4021 368.653,90.3999 370.631,90.3976 372.61,90.3954 \n",
       "  374.588,90.3932 376.566,90.3909 378.544,90.3886 380.522,90.3864 382.5,90.3842 384.479,90.3819 386.457,90.3797 388.435,90.3774 390.413,90.3752 392.391,90.3729 \n",
       "  394.369,90.3707 396.348,90.3684 398.326,90.3662 400.304,90.3639 402.282,90.3617 404.26,90.3594 406.238,90.3572 408.217,90.355 410.195,90.3527 412.173,90.3505 \n",
       "  414.151,90.3482 416.129,90.346 418.107,90.3437 420.086,90.3415 422.064,90.3392 424.042,90.337 426.02,90.3347 427.998,90.3325 429.976,90.3303 431.955,90.328 \n",
       "  433.933,90.3258 435.911,90.3235 437.889,90.3213 439.867,90.319 441.845,90.3168 443.824,90.3145 445.802,90.3123 447.78,90.31 449.758,90.3078 451.736,90.3055 \n",
       "  453.714,90.3033 455.693,90.3011 457.671,90.2988 459.649,90.2966 461.627,90.2943 463.605,90.2921 465.583,90.2898 467.562,90.2876 469.54,90.2853 471.518,90.2831 \n",
       "  473.496,90.2808 475.474,90.2786 477.452,90.2763 479.431,90.2741 481.409,90.2719 483.387,90.2696 485.365,90.2674 487.343,90.2651 489.321,90.2629 491.3,90.2606 \n",
       "  493.278,90.2584 495.256,90.2561 497.234,90.2539 499.212,90.2516 501.19,90.2494 503.169,90.2471 505.147,90.2449 507.125,90.2426 509.103,90.2404 511.081,90.2382 \n",
       "  513.059,90.2359 515.038,90.2337 517.016,90.2314 518.994,90.2292 520.972,90.2269 522.95,90.2247 524.928,90.2224 526.907,90.2202 528.885,90.2179 530.863,90.2157 \n",
       "  532.841,90.2134 534.819,90.2112 536.797,90.209 538.776,90.2067 540.754,90.2045 542.732,90.2022 544.71,90.2 546.688,90.1977 548.666,90.1955 550.645,90.1932 \n",
       "  552.623,90.191 554.601,90.1887 556.579,90.1865 558.557,90.1843 560.536,90.182 562.514,90.1798 564.492,90.1775 566.47,90.1753 568.448,90.173 570.426,90.1708 \n",
       "  572.405,90.1685 574.383,90.1663 576.361,90.164 578.339,90.1618 580.317,90.1595 582.295,90.1573 584.274,90.1551 586.252,90.1528 588.23,90.1506 590.208,90.1483 \n",
       "  592.186,90.1461 594.164,90.1438 596.143,90.1416 598.121,90.1393 600.099,90.1371 602.077,90.1348 604.055,90.1326 606.033,90.1303 608.012,90.1281 609.99,90.1259 \n",
       "  611.968,90.1236 613.946,90.1214 615.924,90.1191 617.902,90.1169 619.881,90.1146 621.859,90.1124 623.837,90.1101 625.815,90.1079 627.793,90.1056 629.771,90.1034 \n",
       "  631.75,90.1011 633.728,90.0989 635.706,90.0967 637.684,90.0944 639.662,90.0922 641.64,90.0899 643.619,90.0877 645.597,90.0854 647.575,90.0832 649.553,90.0809 \n",
       "  651.531,90.0787 653.509,90.0764 655.488,90.0742 657.466,90.0719 659.444,90.0697 661.422,90.0674 663.4,90.0652 665.378,90.063 667.357,90.0607 669.335,90.0585 \n",
       "  671.313,90.0562 673.291,90.054 675.269,90.0517 677.247,90.0495 679.226,90.0472 681.204,90.045 683.182,90.0427 685.16,90.0405 687.138,90.0382 689.116,90.036 \n",
       "  691.095,90.0338 693.073,90.0315 695.051,90.0293 697.029,90.027 699.007,90.0248 700.985,90.0225 702.964,90.0203 704.942,90.018 706.92,90.0158 708.898,90.0135 \n",
       "  710.876,90.0113 712.854,90.0091 714.833,90.0068 716.811,90.0046 718.789,90.0023 720.767,90.0001 722.745,89.9978 724.723,89.9956 726.702,89.9933 728.68,89.9911 \n",
       "  730.658,89.9888 732.636,89.9866 734.614,89.9843 736.592,89.9821 738.571,89.9798 740.549,89.9776 742.527,89.9754 744.505,89.9731 746.483,89.9709 748.461,89.9686 \n",
       "  750.44,89.9664 752.418,89.9641 754.396,89.9619 756.374,89.9596 758.352,89.9574 760.33,89.9551 762.309,89.9529 764.287,89.9507 766.265,89.9484 768.243,89.9462 \n",
       "  770.221,89.9439 772.199,89.9417 774.178,89.9394 776.156,89.9372 778.134,89.9349 780.112,89.9327 782.09,89.9304 784.069,89.9282 786.047,89.9259 788.025,89.9237 \n",
       "  790.003,89.9214 791.981,89.9192 793.959,89.917 795.938,89.9147 797.916,89.9125 799.894,89.9102 801.872,89.908 803.85,89.9057 805.828,89.9035 807.807,89.9012 \n",
       "  809.785,89.899 811.763,89.8967 813.741,89.8945 815.719,89.8922 817.697,89.89 819.676,89.8878 821.654,89.8855 823.632,89.8833 825.61,89.881 827.588,89.8788 \n",
       "  829.566,89.8765 831.545,89.8743 833.523,89.872 835.501,89.8698 837.479,89.8675 839.457,89.8653 841.435,89.8631 843.414,89.8608 845.392,89.8586 847.37,89.8563 \n",
       "  849.348,89.8541 851.326,89.8518 853.304,89.8496 855.283,89.8473 857.261,89.8451 859.239,89.8428 861.217,89.8406 863.195,89.8383 865.173,89.8361 867.152,89.8338 \n",
       "  869.13,89.8316 871.108,89.8294 873.086,89.8271 875.064,89.8249 877.042,89.8226 879.021,89.8204 880.999,89.8181 882.977,89.8159 884.955,89.8136 886.933,89.8114 \n",
       "  888.911,89.8091 890.89,89.8069 892.868,89.8046 894.846,89.8024 896.824,89.8001 898.802,89.7979 900.78,89.7957 902.759,89.7934 904.737,89.7912 906.715,89.7889 \n",
       "  908.693,89.7867 910.671,89.7844 912.649,89.7822 914.628,89.7799 916.606,89.7777 918.584,89.7754 920.562,89.7732 922.54,89.771 924.518,89.7687 926.497,89.7665 \n",
       "  928.475,89.7642 930.453,89.762 932.431,89.7597 934.409,89.7575 936.387,89.7552 938.366,89.753 940.344,89.7507 942.322,89.7933 944.3,91.7102 946.278,93.6271 \n",
       "  948.256,93.8947 950.235,93.8924 952.213,93.8902 954.191,93.8879 956.169,93.8857 958.147,93.8834 960.125,94.625 962.104,96.5419 964.082,98.0296 966.06,98.0274 \n",
       "  968.038,98.0252 970.016,98.0229 971.994,98.0206 973.973,98.0184 975.951,98.0162 977.929,98.0139 979.907,98.0117 981.885,98.0094 983.863,98.0072 985.842,98.8427 \n",
       "  987.82,100.76 989.798,102.153 991.776,102.151 993.754,102.149 995.733,102.147 997.711,102.144 999.689,102.142 1001.67,102.14 1003.65,103.673 1005.62,105.59 \n",
       "  1007.6,106.286 1009.58,106.284 1011.56,106.282 1013.54,106.279 1015.51,106.277 1017.49,106.275 1019.47,106.273 1021.45,106.27 1023.43,106.282 1025.41,108.198 \n",
       "  1027.38,110.115 1029.36,110.414 1031.34,110.412 1033.32,110.41 1035.3,110.408 1037.27,111.418 1039.25,113.335 1041.23,115.252 1043.21,117.17 1045.19,119.087 \n",
       "  1047.16,121.003 1049.14,127.06 1051.12,128.977 1053.1,130.894 1055.08,136.951 1057.06,138.868 1059.03,140.785 1061.01,142.701 1062.99,148.759 1064.97,150.676 \n",
       "  1066.95,152.594 1068.92,154.51 1070.9,156.426 1072.88,158.343 1074.86,164.4 1076.84,166.317 1078.82,168.234 1080.79,170.151 1082.77,172.068 1084.75,186.405 \n",
       "  1086.73,188.322 1088.71,190.239 1090.68,192.156 1092.66,194.073 1094.64,195.99 1096.62,202.047 1098.6,203.964 1100.58,205.881 1102.55,207.798 1104.53,209.714 \n",
       "  1106.51,215.771 1108.49,217.688 1110.47,219.605 1112.44,221.522 1114.42,227.579 1116.4,229.496 1118.38,231.413 1120.36,233.33 1122.34,239.387 1124.31,241.304 \n",
       "  1126.29,243.221 1128.27,245.138 1130.25,247.055 1132.23,248.972 1134.2,250.889 1136.18,256.946 1138.16,258.863 1140.14,264.92 1142.12,266.837 1144.1,268.753 \n",
       "  1146.07,270.67 1148.05,276.727 1150.03,278.644 1152.01,280.561 1153.99,282.478 1155.96,284.395 1157.94,290.453 1159.92,292.37 1161.9,294.287 1163.88,296.203 \n",
       "  1165.85,298.12 1167.83,300.037 1169.81,306.094 1171.79,308.011 1173.77,313.744 1175.75,313.741 1177.72,313.763 1179.7,315.679 1181.68,317.595 1183.66,323.652 \n",
       "  1185.64,325.569 1187.61,331.626 1189.59,333.543 1191.57,335.46 1193.55,337.377 1195.53,339.294 1197.51,341.21 1199.48,343.126 1201.46,345.043 1203.44,351.1 \n",
       "  1205.42,353.017 1207.4,354.934 1209.37,360.992 1211.35,362.909 1213.33,364.826 1215.31,366.742 1217.29,368.659 1219.27,370.576 1221.24,376.633 1223.22,378.55 \n",
       "  1225.2,380.467 1227.18,382.384 1229.16,384.302 1231.13,386.218 1233.11,388.134 1235.09,394.191 1237.07,396.108 1239.05,398.025 1241.03,399.942 1243,405.999 \n",
       "  1244.98,407.916 1246.96,409.833 1248.94,411.75 1250.92,413.667 1252.89,415.584 1254.87,421.641 1256.85,423.558 1258.83,425.475 1260.81,427.391 1262.79,429.308 \n",
       "  1264.76,431.225 1266.74,433.142 1268.72,439.199 1270.7,441.116 1272.68,447.173 1274.65,449.09 1276.63,451.007 1278.61,452.924 1280.59,454.841 1282.57,456.758 \n",
       "  1284.55,458.675 1286.52,460.592 1288.5,462.509 1290.48,464.426 1292.46,466.343 1294.44,468.26 1296.41,470.177 1298.39,472.093 1300.37,474.01 1302.35,475.927 \n",
       "  1304.33,477.843 1306.3,483.901 1308.28,485.818 1310.26,487.735 1312.24,489.651 1314.22,491.567 1316.2,493.484 1318.17,495.401 1320.15,497.318 1322.13,499.235 \n",
       "  1324.11,501.152 1326.09,503.069 1328.06,504.986 1330.04,506.902 1332.02,508.819 1334,510.736 1335.98,512.653 1337.96,514.57 1339.93,516.487 1341.91,522.544 \n",
       "  1343.89,524.461 1345.87,525.347 1347.85,525.345 1349.82,526.072 1351.8,527.988 1353.78,534.046 1355.76,535.962 1357.74,537.879 1359.72,539.797 1361.69,541.714 \n",
       "  1363.67,543.631 1365.65,545.547 1367.63,547.464 1369.61,549.381 1371.58,551.298 1373.56,553.215 1375.54,555.132 1377.52,557.048 1379.5,558.965 1381.48,560.882 \n",
       "  1383.45,562.799 1385.43,564.716 1387.41,566.633 1389.39,572.689 1391.37,574.606 1393.34,576.522 1395.32,578.439 1397.3,580.356 1399.28,582.273 1401.26,584.19 \n",
       "  1403.24,586.108 1405.21,588.025 1407.19,589.941 1409.17,591.722 1411.15,591.72 1413.13,591.718 1415.1,591.716 1417.08,591.713 1419.06,595.864 1421.04,595.862 \n",
       "  1423.02,600.012 1425,600.01 1426.97,600.008 1428.95,600.006 1430.93,600.523 1432.91,602.44 1434.89,604.357 1436.86,606.274 1438.84,608.191 1440.82,610.107 \n",
       "  1442.8,612.024 1444.78,613.941 1446.75,615.858 1448.73,617.775 1450.71,619.691 1452.69,621.608 1454.67,623.525 1456.65,625.442 1458.62,627.359 1460.6,629.04 \n",
       "  1462.58,629.038 1464.56,629.036 1466.54,635.026 1468.51,636.943 1470.49,637.335 1472.47,637.333 1474.45,638.554 1476.43,640.471 1478.41,642.388 1480.38,644.305 \n",
       "  1482.36,646.221 1484.34,648.138 1486.32,650.055 1488.3,651.972 1490.27,653.889 1492.25,655.806 1494.23,657.723 1496.21,658.07 1498.19,658.068 1500.17,659.332 \n",
       "  1502.14,661.249 1504.12,667.306 1506.1,669.223 1508.08,670.516 1510.06,670.513 1512.03,670.834 1514.01,672.75 1515.99,674.667 1517.97,676.584 1519.95,678.501 \n",
       "  1521.93,680.418 1523.9,682.335 1525.88,682.954 1527.86,682.952 1529.84,683.947 1531.82,685.863 1533.79,687.779 1535.77,689.696 1537.75,691.613 1539.73,693.53 \n",
       "  1541.71,695.395 1543.69,695.393 1545.66,695.39 1547.64,697.058 1549.62,698.975 1551.6,700.891 1553.58,702.807 1555.55,704.724 1557.53,706.641 1559.51,707.834 \n",
       "  1561.49,707.831 1563.47,708.251 1565.44,710.168 1567.42,712.085 1569.4,714.002 1571.38,715.919 1573.36,716.124 1575.34,716.121 1577.31,717.53 1579.29,719.447 \n",
       "  1581.27,721.363 1583.25,723.28 1585.23,725.197 1587.2,727.114 1589.18,728.564 1591.16,728.562 1593.14,728.725 1595.12,730.642 1597.1,732.559 1599.07,734.476 \n",
       "  1601.05,736.392 1603.03,738.309 1605.01,740.225 1606.99,741.003 1608.96,741.001 1610.94,741.835 1612.92,743.752 1614.9,745.669 1616.88,747.586 1618.86,749.295 \n",
       "  1620.83,749.293 1622.81,749.291 1624.79,755.254 1626.77,757.171 1628.75,757.59 1630.72,757.588 1632.7,758.781 1634.68,760.698 1636.66,765.887 1638.64,765.885 \n",
       "  1640.62,766.449 1642.59,768.367 1644.57,770.284 1646.55,772.2 1648.53,774.117 1650.51,776.034 1652.48,777.95 1654.46,779.867 1656.44,781.784 1658.42,782.474 \n",
       "  1660.4,782.472 1662.38,783.393 1664.35,785.31 1666.33,786.618 1668.31,786.616 1670.29,786.921 1672.27,788.839 1674.24,790.756 1676.22,790.759 1678.2,790.757 \n",
       "  1680.18,796.505 1682.16,798.422 1684.14,799.056 1686.11,799.054 1688.09,800.034 1690.07,801.95 1692.05,803.867 1694.03,805.784 1696,807.701 1697.98,809.618 \n",
       "  1699.96,811.534 1701.94,813.451 1703.92,815.368 1705.89,817.285 1707.87,819.202 1709.85,821.119 1711.83,823.036 1713.81,824.953 1715.79,826.87 1717.76,828.787 \n",
       "  1719.74,830.704 1721.72,832.62 1723.7,834.537 1725.68,836.454 1727.65,838.371 1729.63,840.288 1731.61,842.205 1733.59,844.122 1735.57,846.039 1737.55,847.956 \n",
       "  1739.52,849.873 1741.5,851.79 1743.48,853.706 1745.46,855.623 1747.44,857.54 1749.41,859.457 1751.39,861.374 1753.37,863.291 1755.35,865.208 1757.33,867.125 \n",
       "  1759.31,869.042 1761.28,870.959 1763.26,872.876 1765.24,874.793 1767.22,876.709 1769.2,878.626 1771.17,880.543 1773.15,882.46 1775.13,884.377 1777.11,886.294 \n",
       "  1779.09,888.211 1781.07,890.128 1783.04,892.045 1785.02,893.962 1787,895.879 1788.98,897.795 1790.96,899.712 1792.93,901.629 1794.91,903.546 1796.89,905.463 \n",
       "  1798.87,907.38 1800.85,909.297 1802.83,911.214 1804.8,913.131 1806.78,915.048 1808.76,916.965 1810.74,918.882 1812.72,920.798 1814.69,922.715 1816.67,924.632 \n",
       "  1818.65,926.549 1820.63,928.466 1822.61,930.383 1824.58,932.3 1826.56,934.217 1828.54,936.134 1830.52,938.051 1832.5,939.968 1834.48,941.884 1836.45,943.801 \n",
       "  1838.43,945.718 1840.41,947.635 1842.39,949.552 1844.37,951.469 1846.34,953.386 1848.32,955.303 1850.3,957.22 1852.28,959.137 1854.26,961.054 1856.24,962.97 \n",
       "  1858.21,964.887 1860.19,966.804 1862.17,968.721 1864.15,970.638 1866.13,972.555 1868.1,974.472 1870.08,976.389 1872.06,978.306 1874.04,980.223 1876.02,982.14 \n",
       "  1878,984.057 1879.97,985.973 1881.95,987.89 1883.93,989.807 1885.91,991.724 1887.89,993.641 1889.86,995.558 1891.84,997.475 1893.82,999.392 1895.8,1001.31 \n",
       "  1897.78,1003.23 1899.76,1005.14 1901.73,1007.06 1903.71,1008.98 1905.69,1010.89 1907.67,1012.81 1909.65,1014.73 1911.62,1016.64 1913.6,1018.56 1915.58,1020.48 \n",
       "  1917.56,1022.39 1919.54,1024.31 1921.52,1026.23 1923.49,1028.15 1925.47,1030.06 1927.45,1031.98 1929.43,1033.9 1931.41,1035.81 1933.38,1037.73 1935.36,1039.65 \n",
       "  1937.34,1041.56 1939.32,1043.48 1941.3,1045.4 1943.28,1047.31 1945.25,1049.23 1947.23,1051.15 1949.21,1053.07 1951.19,1054.98 1953.17,1056.9 1955.14,1058.82 \n",
       "  1957.12,1060.73 1959.1,1062.65 1961.08,1064.57 1963.06,1066.48 1965.03,1068.4 1967.01,1070.32 1968.99,1072.23 1970.97,1074.15 1972.95,1076.07 1974.93,1077.99 \n",
       "  1976.9,1079.9 1978.88,1081.82 1980.86,1083.74 1982.84,1085.65 1984.82,1087.57 1986.79,1089.49 1988.77,1091.4 1990.75,1093.32 1992.73,1095.24 1994.71,1097.15 \n",
       "  1996.69,1099.07 1998.66,1100.99 2000.64,1102.91 2002.62,1104.82 2004.6,1106.74 2006.58,1108.66 2008.55,1110.57 2010.53,1112.49 2012.51,1114.41 2014.49,1116.32 \n",
       "  2016.47,1118.24 2018.45,1120.16 2020.42,1122.07 2022.4,1123.99 2024.38,1125.91 2026.36,1127.82 2028.34,1129.74 2030.31,1131.66 2032.29,1133.58 2034.27,1135.49 \n",
       "  2036.25,1137.41 2038.23,1139.33 2040.21,1141.24 2042.18,1143.16 2044.16,1145.08 2046.14,1146.99 2048.12,1148.91 2050.1,1150.83 2052.07,1152.74 2054.05,1154.66 \n",
       "  2056.03,1156.58 2058.01,1158.5 2059.99,1160.41 2061.97,1162.33 2063.94,1164.25 2065.92,1166.16 2067.9,1168.08 2069.88,1170 2071.86,1171.91 2073.83,1173.83 \n",
       "  2075.81,1175.75 2077.79,1177.66 2079.77,1179.58 2081.75,1181.5 2083.73,1183.42 2085.7,1185.33 2087.68,1187.25 2089.66,1189.17 2091.64,1191.08 2093.62,1193 \n",
       "  2095.59,1194.92 2097.57,1196.83 2099.55,1198.75 2101.53,1200.67 2103.51,1202.58 2105.48,1204.5 2107.46,1206.42 2109.44,1208.34 2111.42,1210.25 2113.4,1212.17 \n",
       "  2115.38,1214.09 2117.35,1216 2119.33,1217.92 2121.31,1219.84 2123.29,1221.75 2125.27,1223.67 2127.24,1225.59 2129.22,1227.5 2131.2,1229.42 2133.18,1231.34 \n",
       "  2135.16,1233.26 2137.14,1235.17 2139.11,1237.09 2141.09,1239.01 2143.07,1240.92 2145.05,1242.84 2147.03,1244.76 2149,1246.67 2150.98,1248.59 2152.96,1250.51 \n",
       "  2154.94,1252.42 2156.92,1254.34 2158.9,1256.26 2160.87,1258.17 2162.85,1260.09 2164.83,1262.01 2166.81,1263.93 2168.79,1265.84 2170.76,1267.76 2172.74,1269.68 \n",
       "  2174.72,1271.59 2176.7,1273.51 2178.68,1275.43 2180.66,1277.34 2182.63,1279.26 2184.61,1281.18 2186.59,1283.09 2188.57,1285.01 2190.55,1286.93 2192.52,1288.85 \n",
       "  2194.5,1290.76 2196.48,1292.68 2198.46,1294.6 2200.44,1296.51 2202.42,1298.43 2204.39,1300.35 2206.37,1302.26 2208.35,1304.18 2210.33,1306.1 2212.31,1308.01 \n",
       "  2214.28,1309.93 2216.26,1311.85 2218.24,1313.77 2220.22,1315.68 2222.2,1317.6 2224.17,1319.52 2226.15,1321.43 2228.13,1323.35 2230.11,1325.27 2232.09,1327.18 \n",
       "  2234.07,1329.1 2236.04,1331.02 2238.02,1332.93 2240,1334.85 2241.98,1336.77 2243.96,1338.69 2245.93,1340.6 2247.91,1342.52 2249.89,1344.44 2251.87,1346.35 \n",
       "  2253.85,1348.27 2255.83,1350.19 2257.8,1352.1 2259.78,1354.02 2261.76,1355.94 2263.74,1357.85 2265.72,1359.77 2267.69,1361.69 2269.67,1363.61 2271.65,1365.52 \n",
       "  2273.63,1367.44 2275.61,1369.36 2277.59,1371.27 2279.56,1373.19 2281.54,1375.11 2283.52,1377.02 2285.5,1378.94 2287.48,1380.86 2289.45,1382.77 2291.43,1384.69 \n",
       "  2293.41,1386.61 \n",
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     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "adj_factor = (8.05/15.33)\n",
    "\n",
    "plot(\n",
    "    spd_range, \n",
    "    ra1_max_itp(spd_range*adj_factor)*adj_factor,\n",
    "    label = \"Adjusted first gear data\",\n",
    "    xlabel = \"Speed (kph)\",\n",
    "    ylabel = \"Wheel torque (Nm)\"\n",
    ")\n",
    "plot!(\n",
    "    spd_range, \n",
    "    ra2_max_itp(spd_range),\n",
    "    label=\"Second gear\"\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This data is quite messy, however, we can employ some of the tricks we used for the front motor here. We know what the max torque should be, and the second gear data shows the power limited performance pretty well. We can make another polynomial fit to the second gear data between about 105 and 250 kph, and min that with the max torque."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
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       "<g clip-path=\"url(#clip8100)\">\n",
       "<text style=\"fill:#000000; fill-opacity:1; font-family:Arial,Helvetica Neue,Helvetica,sans-serif; font-size:48px; text-anchor:end;\" transform=\"rotate(0, 231.898, 595.843)\" x=\"231.898\" y=\"595.843\">3000</text>\n",
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       "<g clip-path=\"url(#clip8100)\">\n",
       "<text style=\"fill:#000000; fill-opacity:1; font-family:Arial,Helvetica Neue,Helvetica,sans-serif; font-size:48px; text-anchor:end;\" transform=\"rotate(0, 231.898, 272.579)\" x=\"231.898\" y=\"272.579\">4000</text>\n",
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       "<g clip-path=\"url(#clip8100)\">\n",
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       "</g>\n",
       "<g clip-path=\"url(#clip8100)\">\n",
       "<text style=\"fill:#000000; fill-opacity:1; font-family:Arial,Helvetica Neue,Helvetica,sans-serif; font-size:66px; text-anchor:middle;\" transform=\"rotate(-90, 89.2861, 736.431)\" x=\"89.2861\" y=\"736.431\">Wheel torque (Nm)</text>\n",
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       "  335.024,87.8668 337.002,88.028 338.981,88.1892 340.959,88.3504 342.937,88.5117 344.915,88.6729 346.893,88.8341 348.872,88.9953 350.85,89.1565 352.828,89.3177 \n",
       "  354.806,89.4789 356.784,89.6401 358.762,89.8013 360.741,89.9626 362.719,90.1238 364.697,90.285 366.675,90.4021 368.653,90.3999 370.631,90.3976 372.61,90.3954 \n",
       "  374.588,90.3932 376.566,90.3909 378.544,90.3886 380.522,90.3864 382.5,90.3842 384.479,90.3819 386.457,90.3797 388.435,90.3774 390.413,90.3752 392.391,90.3729 \n",
       "  394.369,90.3707 396.348,90.3684 398.326,90.3662 400.304,90.3639 402.282,90.3617 404.26,90.3594 406.238,90.3572 408.217,90.355 410.195,90.3527 412.173,90.3505 \n",
       "  414.151,90.3482 416.129,90.346 418.107,90.3437 420.086,90.3415 422.064,90.3392 424.042,90.337 426.02,90.3347 427.998,90.3325 429.976,90.3303 431.955,90.328 \n",
       "  433.933,90.3258 435.911,90.3235 437.889,90.3213 439.867,90.319 441.845,90.3168 443.824,90.3145 445.802,90.3123 447.78,90.31 449.758,90.3078 451.736,90.3055 \n",
       "  453.714,90.3033 455.693,90.3011 457.671,90.2988 459.649,90.2966 461.627,90.2943 463.605,90.2921 465.583,90.2898 467.562,90.2876 469.54,90.2853 471.518,90.2831 \n",
       "  473.496,90.2808 475.474,90.2786 477.452,90.2763 479.431,90.2741 481.409,90.2719 483.387,90.2696 485.365,90.2674 487.343,90.2651 489.321,90.2629 491.3,90.2606 \n",
       "  493.278,90.2584 495.256,90.2561 497.234,90.2539 499.212,90.2516 501.19,90.2494 503.169,90.2471 505.147,90.2449 507.125,90.2426 509.103,90.2404 511.081,90.2382 \n",
       "  513.059,90.2359 515.038,90.2337 517.016,90.2314 518.994,90.2292 520.972,90.2269 522.95,90.2247 524.928,90.2224 526.907,90.2202 528.885,90.2179 530.863,90.2157 \n",
       "  532.841,90.2134 534.819,90.2112 536.797,90.209 538.776,90.2067 540.754,90.2045 542.732,90.2022 544.71,90.2 546.688,90.1977 548.666,90.1955 550.645,90.1932 \n",
       "  552.623,90.191 554.601,90.1887 556.579,90.1865 558.557,90.1843 560.536,90.182 562.514,90.1798 564.492,90.1775 566.47,90.1753 568.448,90.173 570.426,90.1708 \n",
       "  572.405,90.1685 574.383,90.1663 576.361,90.164 578.339,90.1618 580.317,90.1595 582.295,90.1573 584.274,90.1551 586.252,90.1528 588.23,90.1506 590.208,90.1483 \n",
       "  592.186,90.1461 594.164,90.1438 596.143,90.1416 598.121,90.1393 600.099,90.1371 602.077,90.1348 604.055,90.1326 606.033,90.1303 608.012,90.1281 609.99,90.1259 \n",
       "  611.968,90.1236 613.946,90.1214 615.924,90.1191 617.902,90.1169 619.881,90.1146 621.859,90.1124 623.837,90.1101 625.815,90.1079 627.793,90.1056 629.771,90.1034 \n",
       "  631.75,90.1011 633.728,90.0989 635.706,90.0967 637.684,90.0944 639.662,90.0922 641.64,90.0899 643.619,90.0877 645.597,90.0854 647.575,90.0832 649.553,90.0809 \n",
       "  651.531,90.0787 653.509,90.0764 655.488,90.0742 657.466,90.0719 659.444,90.0697 661.422,90.0674 663.4,90.0652 665.378,90.063 667.357,90.0607 669.335,90.0585 \n",
       "  671.313,90.0562 673.291,90.054 675.269,90.0517 677.247,90.0495 679.226,90.0472 681.204,90.045 683.182,90.0427 685.16,90.0405 687.138,90.0382 689.116,90.036 \n",
       "  691.095,90.0338 693.073,90.0315 695.051,90.0293 697.029,90.027 699.007,90.0248 700.985,90.0225 702.964,90.0203 704.942,90.018 706.92,90.0158 708.898,90.0135 \n",
       "  710.876,90.0113 712.854,90.0091 714.833,90.0068 716.811,90.0046 718.789,90.0023 720.767,90.0001 722.745,89.9978 724.723,89.9956 726.702,89.9933 728.68,89.9911 \n",
       "  730.658,89.9888 732.636,89.9866 734.614,89.9843 736.592,89.9821 738.571,89.9798 740.549,89.9776 742.527,89.9754 744.505,89.9731 746.483,89.9709 748.461,89.9686 \n",
       "  750.44,89.9664 752.418,89.9641 754.396,89.9619 756.374,89.9596 758.352,89.9574 760.33,89.9551 762.309,89.9529 764.287,89.9507 766.265,89.9484 768.243,89.9462 \n",
       "  770.221,89.9439 772.199,89.9417 774.178,89.9394 776.156,89.9372 778.134,89.9349 780.112,89.9327 782.09,89.9304 784.069,89.9282 786.047,89.9259 788.025,89.9237 \n",
       "  790.003,89.9214 791.981,89.9192 793.959,89.917 795.938,89.9147 797.916,89.9125 799.894,89.9102 801.872,89.908 803.85,89.9057 805.828,89.9035 807.807,89.9012 \n",
       "  809.785,89.899 811.763,89.8967 813.741,89.8945 815.719,89.8922 817.697,89.89 819.676,89.8878 821.654,89.8855 823.632,89.8833 825.61,89.881 827.588,89.8788 \n",
       "  829.566,89.8765 831.545,89.8743 833.523,89.872 835.501,89.8698 837.479,89.8675 839.457,89.8653 841.435,89.8631 843.414,89.8608 845.392,89.8586 847.37,89.8563 \n",
       "  849.348,89.8541 851.326,89.8518 853.304,89.8496 855.283,89.8473 857.261,89.8451 859.239,89.8428 861.217,89.8406 863.195,89.8383 865.173,89.8361 867.152,89.8338 \n",
       "  869.13,89.8316 871.108,89.8294 873.086,89.8271 875.064,89.8249 877.042,89.8226 879.021,89.8204 880.999,89.8181 882.977,89.8159 884.955,89.8136 886.933,89.8114 \n",
       "  888.911,89.8091 890.89,89.8069 892.868,89.8046 894.846,89.8024 896.824,89.8001 898.802,89.7979 900.78,89.7957 902.759,89.7934 904.737,89.7912 906.715,89.7889 \n",
       "  908.693,89.7867 910.671,89.7844 912.649,89.7822 914.628,89.7799 916.606,89.7777 918.584,89.7754 920.562,89.7732 922.54,89.771 924.518,89.7687 926.497,89.7665 \n",
       "  928.475,89.7642 930.453,89.762 932.431,89.7597 934.409,89.7575 936.387,89.7552 938.366,89.753 940.344,89.7507 942.322,89.7933 944.3,91.7102 946.278,93.6271 \n",
       "  948.256,93.8947 950.235,93.8924 952.213,93.8902 954.191,93.8879 956.169,93.8857 958.147,93.8834 960.125,94.625 962.104,96.5419 964.082,98.0296 966.06,98.0274 \n",
       "  968.038,98.0252 970.016,98.0229 971.994,98.0206 973.973,98.0184 975.951,98.0162 977.929,98.0139 979.907,98.0117 981.885,98.0094 983.863,98.0072 985.842,98.8427 \n",
       "  987.82,100.76 989.798,102.153 991.776,102.151 993.754,102.149 995.733,102.147 997.711,102.144 999.689,102.142 1001.67,102.14 1003.65,103.673 1005.62,105.59 \n",
       "  1007.6,106.286 1009.58,106.284 1011.56,106.282 1013.54,106.279 1015.51,106.277 1017.49,106.275 1019.47,106.273 1021.45,106.27 1023.43,106.282 1025.41,108.198 \n",
       "  1027.38,110.115 1029.36,110.414 1031.34,110.412 1033.32,110.41 1035.3,110.408 1037.27,111.418 1039.25,113.335 1041.23,115.252 1043.21,117.17 1045.19,119.087 \n",
       "  1047.16,121.003 1049.14,127.06 1051.12,128.977 1053.1,130.894 1055.08,136.951 1057.06,138.868 1059.03,140.785 1061.01,142.701 1062.99,148.759 1064.97,150.676 \n",
       "  1066.95,152.594 1068.92,154.51 1070.9,156.426 1072.88,158.343 1074.86,164.4 1076.84,166.317 1078.82,168.234 1080.79,170.151 1082.77,172.068 1084.75,186.405 \n",
       "  1086.73,188.322 1088.71,190.239 1090.68,192.156 1092.66,194.073 1094.64,195.99 1096.62,202.047 1098.6,203.964 1100.58,205.881 1102.55,207.798 1104.53,209.714 \n",
       "  1106.51,215.771 1108.49,217.688 1110.47,219.605 1112.44,221.522 1114.42,227.579 1116.4,229.496 1118.38,231.413 1120.36,233.33 1122.34,239.387 1124.31,241.304 \n",
       "  1126.29,243.221 1128.27,245.138 1130.25,247.055 1132.23,248.972 1134.2,250.889 1136.18,256.946 1138.16,258.863 1140.14,264.92 1142.12,266.837 1144.1,268.753 \n",
       "  1146.07,270.67 1148.05,276.727 1150.03,278.644 1152.01,280.561 1153.99,282.478 1155.96,284.395 1157.94,290.453 1159.92,292.37 1161.9,294.287 1163.88,296.203 \n",
       "  1165.85,298.12 1167.83,300.037 1169.81,306.094 1171.79,308.011 1173.77,313.744 1175.75,313.741 1177.72,313.763 1179.7,315.679 1181.68,317.595 1183.66,323.652 \n",
       "  1185.64,325.569 1187.61,331.626 1189.59,333.543 1191.57,335.46 1193.55,337.377 1195.53,339.294 1197.51,341.21 1199.48,343.126 1201.46,345.043 1203.44,351.1 \n",
       "  1205.42,353.017 1207.4,354.934 1209.37,360.992 1211.35,362.909 1213.33,364.826 1215.31,366.742 1217.29,368.659 1219.27,370.576 1221.24,376.633 1223.22,378.55 \n",
       "  1225.2,380.467 1227.18,382.384 1229.16,384.302 1231.13,386.218 1233.11,388.134 1235.09,394.191 1237.07,396.108 1239.05,398.025 1241.03,399.942 1243,405.999 \n",
       "  1244.98,407.916 1246.96,409.833 1248.94,411.75 1250.92,413.667 1252.89,415.584 1254.87,421.641 1256.85,423.558 1258.83,425.475 1260.81,427.391 1262.79,429.308 \n",
       "  1264.76,431.225 1266.74,433.142 1268.72,439.199 1270.7,441.116 1272.68,447.173 1274.65,449.09 1276.63,451.007 1278.61,452.924 1280.59,454.841 1282.57,456.758 \n",
       "  1284.55,458.675 1286.52,460.592 1288.5,462.509 1290.48,464.426 1292.46,466.343 1294.44,468.26 1296.41,470.177 1298.39,472.093 1300.37,474.01 1302.35,475.927 \n",
       "  1304.33,477.843 1306.3,483.901 1308.28,485.818 1310.26,487.735 1312.24,489.651 1314.22,491.567 1316.2,493.484 1318.17,495.401 1320.15,497.318 1322.13,499.235 \n",
       "  1324.11,501.152 1326.09,503.069 1328.06,504.986 1330.04,506.902 1332.02,508.819 1334,510.736 1335.98,512.653 1337.96,514.57 1339.93,516.487 1341.91,522.544 \n",
       "  1343.89,524.461 1345.87,525.347 1347.85,525.345 1349.82,526.072 1351.8,527.988 1353.78,534.046 1355.76,535.962 1357.74,537.879 1359.72,539.797 1361.69,541.714 \n",
       "  1363.67,543.631 1365.65,545.547 1367.63,547.464 1369.61,549.381 1371.58,551.298 1373.56,553.215 1375.54,555.132 1377.52,557.048 1379.5,558.965 1381.48,560.882 \n",
       "  1383.45,562.799 1385.43,564.716 1387.41,566.633 1389.39,572.689 1391.37,574.606 1393.34,576.522 1395.32,578.439 1397.3,580.356 1399.28,582.273 1401.26,584.19 \n",
       "  1403.24,586.108 1405.21,588.025 1407.19,589.941 1409.17,591.722 1411.15,591.72 1413.13,591.718 1415.1,591.716 1417.08,591.713 1419.06,595.864 1421.04,595.862 \n",
       "  1423.02,600.012 1425,600.01 1426.97,600.008 1428.95,600.006 1430.93,600.523 1432.91,602.44 1434.89,604.357 1436.86,606.274 1438.84,608.191 1440.82,610.107 \n",
       "  1442.8,612.024 1444.78,613.941 1446.75,615.858 1448.73,617.775 1450.71,619.691 1452.69,621.608 1454.67,623.525 1456.65,625.442 1458.62,627.359 1460.6,629.04 \n",
       "  1462.58,629.038 1464.56,629.036 1466.54,635.026 1468.51,636.943 1470.49,637.335 1472.47,637.333 1474.45,638.554 1476.43,640.471 1478.41,642.388 1480.38,644.305 \n",
       "  1482.36,646.221 1484.34,648.138 1486.32,650.055 1488.3,651.972 1490.27,653.889 1492.25,655.806 1494.23,657.723 1496.21,658.07 1498.19,658.068 1500.17,659.332 \n",
       "  1502.14,661.249 1504.12,667.306 1506.1,669.223 1508.08,670.516 1510.06,670.513 1512.03,670.834 1514.01,672.75 1515.99,674.667 1517.97,676.584 1519.95,678.501 \n",
       "  1521.93,680.418 1523.9,682.335 1525.88,682.954 1527.86,682.952 1529.84,683.947 1531.82,685.863 1533.79,687.779 1535.77,689.696 1537.75,691.613 1539.73,693.53 \n",
       "  1541.71,695.395 1543.69,695.393 1545.66,695.39 1547.64,697.058 1549.62,698.975 1551.6,700.891 1553.58,702.807 1555.55,704.724 1557.53,706.641 1559.51,707.834 \n",
       "  1561.49,707.831 1563.47,708.251 1565.44,710.168 1567.42,712.085 1569.4,714.002 1571.38,715.919 1573.36,716.124 1575.34,716.121 1577.31,717.53 1579.29,719.447 \n",
       "  1581.27,721.363 1583.25,723.28 1585.23,725.197 1587.2,727.114 1589.18,728.564 1591.16,728.562 1593.14,728.725 1595.12,730.642 1597.1,732.559 1599.07,734.476 \n",
       "  1601.05,736.392 1603.03,738.309 1605.01,740.225 1606.99,741.003 1608.96,741.001 1610.94,741.835 1612.92,743.752 1614.9,745.669 1616.88,747.586 1618.86,749.295 \n",
       "  1620.83,749.293 1622.81,749.291 1624.79,755.254 1626.77,757.171 1628.75,757.59 1630.72,757.588 1632.7,758.781 1634.68,760.698 1636.66,765.887 1638.64,765.885 \n",
       "  1640.62,766.449 1642.59,768.367 1644.57,770.284 1646.55,772.2 1648.53,774.117 1650.51,776.034 1652.48,777.95 1654.46,779.867 1656.44,781.784 1658.42,782.474 \n",
       "  1660.4,782.472 1662.38,783.393 1664.35,785.31 1666.33,786.618 1668.31,786.616 1670.29,786.921 1672.27,788.839 1674.24,790.756 1676.22,790.759 1678.2,790.757 \n",
       "  1680.18,796.505 1682.16,798.422 1684.14,799.056 1686.11,799.054 1688.09,800.034 1690.07,801.95 1692.05,803.867 1694.03,805.784 1696,807.701 1697.98,809.618 \n",
       "  1699.96,811.534 1701.94,813.451 1703.92,815.368 1705.89,817.285 1707.87,819.202 1709.85,821.119 1711.83,823.036 1713.81,824.953 1715.79,826.87 1717.76,828.787 \n",
       "  1719.74,830.704 1721.72,832.62 1723.7,834.537 1725.68,836.454 1727.65,838.371 1729.63,840.288 1731.61,842.205 1733.59,844.122 1735.57,846.039 1737.55,847.956 \n",
       "  1739.52,849.873 1741.5,851.79 1743.48,853.706 1745.46,855.623 1747.44,857.54 1749.41,859.457 1751.39,861.374 1753.37,863.291 1755.35,865.208 1757.33,867.125 \n",
       "  1759.31,869.042 1761.28,870.959 1763.26,872.876 1765.24,874.793 1767.22,876.709 1769.2,878.626 1771.17,880.543 1773.15,882.46 1775.13,884.377 1777.11,886.294 \n",
       "  1779.09,888.211 1781.07,890.128 1783.04,892.045 1785.02,893.962 1787,895.879 1788.98,897.795 1790.96,899.712 1792.93,901.629 1794.91,903.546 1796.89,905.463 \n",
       "  1798.87,907.38 1800.85,909.297 1802.83,911.214 1804.8,913.131 1806.78,915.048 1808.76,916.965 1810.74,918.882 1812.72,920.798 1814.69,922.715 1816.67,924.632 \n",
       "  1818.65,926.549 1820.63,928.466 1822.61,930.383 1824.58,932.3 1826.56,934.217 1828.54,936.134 1830.52,938.051 1832.5,939.968 1834.48,941.884 1836.45,943.801 \n",
       "  1838.43,945.718 1840.41,947.635 1842.39,949.552 1844.37,951.469 1846.34,953.386 1848.32,955.303 1850.3,957.22 1852.28,959.137 1854.26,961.054 1856.24,962.97 \n",
       "  1858.21,964.887 1860.19,966.804 1862.17,968.721 1864.15,970.638 1866.13,972.555 1868.1,974.472 1870.08,976.389 1872.06,978.306 1874.04,980.223 1876.02,982.14 \n",
       "  1878,984.057 1879.97,985.973 1881.95,987.89 1883.93,989.807 1885.91,991.724 1887.89,993.641 1889.86,995.558 1891.84,997.475 1893.82,999.392 1895.8,1001.31 \n",
       "  1897.78,1003.23 1899.76,1005.14 1901.73,1007.06 1903.71,1008.98 1905.69,1010.89 1907.67,1012.81 1909.65,1014.73 1911.62,1016.64 1913.6,1018.56 1915.58,1020.48 \n",
       "  1917.56,1022.39 1919.54,1024.31 1921.52,1026.23 1923.49,1028.15 1925.47,1030.06 1927.45,1031.98 1929.43,1033.9 1931.41,1035.81 1933.38,1037.73 1935.36,1039.65 \n",
       "  1937.34,1041.56 1939.32,1043.48 1941.3,1045.4 1943.28,1047.31 1945.25,1049.23 1947.23,1051.15 1949.21,1053.07 1951.19,1054.98 1953.17,1056.9 1955.14,1058.82 \n",
       "  1957.12,1060.73 1959.1,1062.65 1961.08,1064.57 1963.06,1066.48 1965.03,1068.4 1967.01,1070.32 1968.99,1072.23 1970.97,1074.15 1972.95,1076.07 1974.93,1077.99 \n",
       "  1976.9,1079.9 1978.88,1081.82 1980.86,1083.74 1982.84,1085.65 1984.82,1087.57 1986.79,1089.49 1988.77,1091.4 1990.75,1093.32 1992.73,1095.24 1994.71,1097.15 \n",
       "  1996.69,1099.07 1998.66,1100.99 2000.64,1102.91 2002.62,1104.82 2004.6,1106.74 2006.58,1108.66 2008.55,1110.57 2010.53,1112.49 2012.51,1114.41 2014.49,1116.32 \n",
       "  2016.47,1118.24 2018.45,1120.16 2020.42,1122.07 2022.4,1123.99 2024.38,1125.91 2026.36,1127.82 2028.34,1129.74 2030.31,1131.66 2032.29,1133.58 2034.27,1135.49 \n",
       "  2036.25,1137.41 2038.23,1139.33 2040.21,1141.24 2042.18,1143.16 2044.16,1145.08 2046.14,1146.99 2048.12,1148.91 2050.1,1150.83 2052.07,1152.74 2054.05,1154.66 \n",
       "  2056.03,1156.58 2058.01,1158.5 2059.99,1160.41 2061.97,1162.33 2063.94,1164.25 2065.92,1166.16 2067.9,1168.08 2069.88,1170 2071.86,1171.91 2073.83,1173.83 \n",
       "  2075.81,1175.75 2077.79,1177.66 2079.77,1179.58 2081.75,1181.5 2083.73,1183.42 2085.7,1185.33 2087.68,1187.25 2089.66,1189.17 2091.64,1191.08 2093.62,1193 \n",
       "  2095.59,1194.92 2097.57,1196.83 2099.55,1198.75 2101.53,1200.67 2103.51,1202.58 2105.48,1204.5 2107.46,1206.42 2109.44,1208.34 2111.42,1210.25 2113.4,1212.17 \n",
       "  2115.38,1214.09 2117.35,1216 2119.33,1217.92 2121.31,1219.84 2123.29,1221.75 2125.27,1223.67 2127.24,1225.59 2129.22,1227.5 2131.2,1229.42 2133.18,1231.34 \n",
       "  2135.16,1233.26 2137.14,1235.17 2139.11,1237.09 2141.09,1239.01 2143.07,1240.92 2145.05,1242.84 2147.03,1244.76 2149,1246.67 2150.98,1248.59 2152.96,1250.51 \n",
       "  2154.94,1252.42 2156.92,1254.34 2158.9,1256.26 2160.87,1258.17 2162.85,1260.09 2164.83,1262.01 2166.81,1263.93 2168.79,1265.84 2170.76,1267.76 2172.74,1269.68 \n",
       "  2174.72,1271.59 2176.7,1273.51 2178.68,1275.43 2180.66,1277.34 2182.63,1279.26 2184.61,1281.18 2186.59,1283.09 2188.57,1285.01 2190.55,1286.93 2192.52,1288.85 \n",
       "  2194.5,1290.76 2196.48,1292.68 2198.46,1294.6 2200.44,1296.51 2202.42,1298.43 2204.39,1300.35 2206.37,1302.26 2208.35,1304.18 2210.33,1306.1 2212.31,1308.01 \n",
       "  2214.28,1309.93 2216.26,1311.85 2218.24,1313.77 2220.22,1315.68 2222.2,1317.6 2224.17,1319.52 2226.15,1321.43 2228.13,1323.35 2230.11,1325.27 2232.09,1327.18 \n",
       "  2234.07,1329.1 2236.04,1331.02 2238.02,1332.93 2240,1334.85 2241.98,1336.77 2243.96,1338.69 2245.93,1340.6 2247.91,1342.52 2249.89,1344.44 2251.87,1346.35 \n",
       "  2253.85,1348.27 2255.83,1350.19 2257.8,1352.1 2259.78,1354.02 2261.76,1355.94 2263.74,1357.85 2265.72,1359.77 2267.69,1361.69 2269.67,1363.61 2271.65,1365.52 \n",
       "  2273.63,1367.44 2275.61,1369.36 2277.59,1371.27 2279.56,1373.19 2281.54,1375.11 2283.52,1377.02 2285.5,1378.94 2287.48,1380.86 2289.45,1382.77 2291.43,1384.69 \n",
       "  2293.41,1386.61 \n",
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       "  1442.8,610.278 1444.78,610.269 1446.75,612.413 1448.73,618.162 1450.71,618.154 1452.69,618.146 1454.67,618.137 1456.65,623.518 1458.62,626.03 1460.6,626.022 \n",
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       "  1680.18,783.29 1682.16,785.242 1684.14,791.182 1686.11,791.174 1688.09,791.166 1690.07,791.158 1692.05,791.149 1694.03,795.413 1696,799.042 1697.98,799.034 \n",
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       "  1719.74,806.939 1721.72,813.888 1723.7,814.745 1725.68,814.737 1727.65,814.729 1729.63,814.72 1731.61,814.712 1733.59,816.177 1735.57,822.605 1737.55,822.596 \n",
       "  1739.52,822.588 1741.5,822.58 1743.48,822.572 1745.46,822.564 1747.44,825.415 1749.41,830.456 1751.39,830.448 1753.37,830.44 1755.35,830.432 1757.33,830.424 \n",
       "  1759.31,830.415 1761.28,830.407 1763.26,833.721 1765.24,838.3 1767.22,838.292 1769.2,838.283 1771.17,838.275 1773.15,838.267 1775.13,838.259 1777.11,842.959 \n",
       "  1779.09,846.151 1781.07,846.143 1783.04,846.135 1785.02,846.127 1787,846.119 1788.98,846.111 1790.96,846.102 1792.93,851.265 1794.91,853.995 1796.89,853.987 \n",
       "  1798.87,853.978 1800.85,853.97 1802.83,853.962 1804.8,853.954 1806.78,860.503 1808.76,861.846 1810.74,861.838 1812.72,861.83 1814.69,861.822 1816.67,861.814 \n",
       "  1818.65,862.792 1820.63,869.706 1822.61,869.698 1824.58,869.69 1826.56,869.682 1828.54,869.673 1830.52,869.665 1832.5,872.03 1834.48,877.558 1836.45,877.549 \n",
       "  1838.43,877.541 1840.41,877.533 1842.39,877.525 1844.37,877.517 1846.34,877.509 1848.32,877.501 1850.3,879.405 1852.28,885.393 1854.26,885.385 1856.24,885.377 \n",
       "  1858.21,885.369 1860.19,885.36 1862.17,885.352 1864.15,885.344 1866.13,887.709 1868.1,893.236 1870.08,893.228 1872.06,893.22 1874.04,893.212 1876.02,893.204 \n",
       "  1878,893.196 1879.97,893.187 1881.95,893.179 1883.93,895.082 1885.91,901.072 1887.89,901.064 1889.86,901.055 1891.84,901.047 1893.82,901.039 1895.8,901.031 \n",
       "  1897.78,901.023 1899.76,901.015 1901.73,902.455 1903.71,908.907 1905.69,908.899 1907.67,908.891 1909.65,908.883 1911.62,908.874 1913.6,908.866 1915.58,908.858 \n",
       "  1917.56,908.85 1919.54,909.828 1921.52,916.742 1923.49,916.734 1925.47,916.726 1927.45,916.718 1929.43,916.71 1931.41,916.702 1933.38,916.693 1935.36,918.134 \n",
       "  1937.34,924.586 1939.32,924.578 1941.3,924.569 1943.28,924.561 1945.25,924.553 1947.23,924.545 1949.21,924.537 1951.19,924.529 1953.17,925.507 1955.14,932.421 \n",
       "  1957.12,932.413 1959.1,932.405 1961.08,932.397 1963.06,932.388 1965.03,932.38 1967.01,932.372 1968.99,933.813 1970.97,940.264 1972.95,940.256 1974.93,940.248 \n",
       "  1976.9,940.24 1978.88,940.232 1980.86,940.224 1982.84,940.216 1984.82,940.207 1986.79,941.186 1988.77,948.1 1990.75,948.092 1992.73,948.083 1994.71,948.075 \n",
       "  1996.69,948.067 1998.66,948.059 2000.64,948.051 2002.62,948.043 2004.6,948.035 2006.58,948.026 2008.55,954.576 2010.53,955.919 2012.51,955.911 2014.49,955.902 \n",
       "  2016.47,955.894 2018.45,955.886 2020.42,955.878 2022.4,955.87 2024.38,955.862 2026.36,961.949 2028.34,963.754 2030.31,963.746 2032.29,963.738 2034.27,963.73 \n",
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       "  2154.94,1010.68 2156.92,1010.68 2158.9,1010.67 2160.87,1010.66 2162.85,1010.65 2164.83,1014.91 2166.81,1018.54 2168.79,1018.54 2170.76,1018.53 2172.74,1018.52 \n",
       "  2174.72,1018.51 2176.7,1018.5 2178.68,1018.5 2180.66,1018.49 2182.63,1018.48 2184.61,1021.35 2186.59,1026.37 2188.57,1026.36 2190.55,1026.36 2192.52,1026.35 \n",
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       "<text style=\"fill:#000000; fill-opacity:1; font-family:Arial,Helvetica Neue,Helvetica,sans-serif; font-size:48px; text-anchor:start;\" transform=\"rotate(0, 1684.32, 269.224)\" x=\"1684.32\" y=\"269.224\">Second gear</text>\n",
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       "<g clip-path=\"url(#clip8100)\">\n",
       "<text style=\"fill:#000000; fill-opacity:1; font-family:Arial,Helvetica Neue,Helvetica,sans-serif; font-size:48px; text-anchor:start;\" transform=\"rotate(0, 1684.32, 329.704)\" x=\"1684.32\" y=\"329.704\">Hypothetical single speed</text>\n",
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      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "start_pwr_idx = findfirst(x->x>105, ra2_max_tq[:,1]);\n",
    "end_pwr_idx = findfirst(x->x>250, ra2_max_tq[:,1]);\n",
    "ss_pwr_poly = polyfit(\n",
    "    ra2_max_tq[start_pwr_idx:end_pwr_idx,1], \n",
    "    ra2_max_tq[start_pwr_idx:end_pwr_idx,2],\n",
    "    4);\n",
    "single_speed_ra_max_itp(spd) = min(560*8.05, ss_pwr_poly(spd));\n",
    "plot!(\n",
    "    spd_range,\n",
    "    single_speed_ra_max_itp.(spd_range),\n",
    "    label = \"Hypothetical single speed\"\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, we can simulate the performance for a single speed Turbo S, muhahahhahahaha!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
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       "<text style=\"fill:#000000; fill-opacity:1; font-family:Arial,Helvetica Neue,Helvetica,sans-serif; font-size:48px; text-anchor:middle;\" transform=\"rotate(0, 1467.57, 1479.62)\" x=\"1467.57\" y=\"1479.62\">150</text>\n",
       "</g>\n",
       "<g clip-path=\"url(#clip8500)\">\n",
       "<text style=\"fill:#000000; fill-opacity:1; font-family:Arial,Helvetica Neue,Helvetica,sans-serif; font-size:48px; text-anchor:middle;\" transform=\"rotate(0, 1851.68, 1479.62)\" x=\"1851.68\" y=\"1479.62\">200</text>\n",
       "</g>\n",
       "<g clip-path=\"url(#clip8500)\">\n",
       "<text style=\"fill:#000000; fill-opacity:1; font-family:Arial,Helvetica Neue,Helvetica,sans-serif; font-size:48px; text-anchor:middle;\" transform=\"rotate(0, 2235.79, 1479.62)\" x=\"2235.79\" y=\"1479.62\">250</text>\n",
       "</g>\n",
       "<g clip-path=\"url(#clip8500)\">\n",
       "<text style=\"fill:#000000; fill-opacity:1; font-family:Arial,Helvetica Neue,Helvetica,sans-serif; font-size:48px; text-anchor:end;\" transform=\"rotate(0, 231.898, 1256.61)\" x=\"231.898\" y=\"1256.61\">1000</text>\n",
       "</g>\n",
       "<g clip-path=\"url(#clip8500)\">\n",
       "<text style=\"fill:#000000; fill-opacity:1; font-family:Arial,Helvetica Neue,Helvetica,sans-serif; font-size:48px; text-anchor:end;\" transform=\"rotate(0, 231.898, 961.799)\" x=\"231.898\" y=\"961.799\">2000</text>\n",
       "</g>\n",
       "<g clip-path=\"url(#clip8500)\">\n",
       "<text style=\"fill:#000000; fill-opacity:1; font-family:Arial,Helvetica Neue,Helvetica,sans-serif; font-size:48px; text-anchor:end;\" transform=\"rotate(0, 231.898, 666.989)\" x=\"231.898\" y=\"666.989\">3000</text>\n",
       "</g>\n",
       "<g clip-path=\"url(#clip8500)\">\n",
       "<text style=\"fill:#000000; fill-opacity:1; font-family:Arial,Helvetica Neue,Helvetica,sans-serif; font-size:48px; text-anchor:end;\" transform=\"rotate(0, 231.898, 372.179)\" x=\"231.898\" y=\"372.179\">4000</text>\n",
       "</g>\n",
       "<g clip-path=\"url(#clip8500)\">\n",
       "<text style=\"fill:#000000; fill-opacity:1; font-family:Arial,Helvetica Neue,Helvetica,sans-serif; font-size:48px; text-anchor:end;\" transform=\"rotate(0, 231.898, 77.3692)\" x=\"231.898\" y=\"77.3692\">5000</text>\n",
       "</g>\n",
       "<g clip-path=\"url(#clip8500)\">\n",
       "<text style=\"fill:#000000; fill-opacity:1; font-family:Arial,Helvetica Neue,Helvetica,sans-serif; font-size:66px; text-anchor:middle;\" transform=\"rotate(0, 1304.33, 1559.48)\" x=\"1304.33\" y=\"1559.48\">Speed (kph)</text>\n",
       "</g>\n",
       "<g clip-path=\"url(#clip8500)\">\n",
       "<text style=\"fill:#000000; fill-opacity:1; font-family:Arial,Helvetica Neue,Helvetica,sans-serif; font-size:66px; text-anchor:middle;\" transform=\"rotate(-90, 89.2861, 736.431)\" x=\"89.2861\" y=\"736.431\">Wheel torque (Nm)</text>\n",
       "</g>\n",
       "<polyline clip-path=\"url(#clip8502)\" style=\"stroke:#009af9; stroke-width:4; stroke-opacity:1; fill:none\" points=\"\n",
       "  315.243,200.715 317.221,200.862 319.199,201.009 321.177,201.156 323.155,201.303 325.133,201.45 327.112,201.597 329.09,201.744 331.068,201.892 333.046,202.039 \n",
       "  335.024,202.186 337.002,202.333 338.981,202.48 340.959,202.627 342.937,202.774 344.915,202.921 346.893,203.068 348.872,203.215 350.85,203.362 352.828,203.509 \n",
       "  354.806,203.656 356.784,203.803 358.762,203.95 360.741,204.097 362.719,204.244 364.697,204.391 366.675,204.498 368.653,204.496 370.631,204.494 372.61,204.492 \n",
       "  374.588,204.49 376.566,204.487 378.544,204.485 380.522,204.483 382.5,204.481 384.479,204.479 386.457,204.477 388.435,204.475 390.413,204.473 392.391,204.471 \n",
       "  394.369,204.469 396.348,204.467 398.326,204.465 400.304,204.463 402.282,204.461 404.26,204.459 406.238,204.457 408.217,204.455 410.195,204.453 412.173,204.451 \n",
       "  414.151,204.449 416.129,204.447 418.107,204.444 420.086,204.442 422.064,204.44 424.042,204.438 426.02,204.436 427.998,204.434 429.976,204.432 431.955,204.43 \n",
       "  433.933,204.428 435.911,204.426 437.889,204.424 439.867,204.422 441.845,204.42 443.824,204.418 445.802,204.416 447.78,204.414 449.758,204.412 451.736,204.41 \n",
       "  453.714,204.408 455.693,204.406 457.671,204.403 459.649,204.401 461.627,204.399 463.605,204.397 465.583,204.395 467.562,204.393 469.54,204.391 471.518,204.389 \n",
       "  473.496,204.387 475.474,204.385 477.452,204.383 479.431,204.381 481.409,204.379 483.387,204.377 485.365,204.375 487.343,204.373 489.321,204.371 491.3,204.369 \n",
       "  493.278,204.367 495.256,204.365 497.234,204.363 499.212,204.36 501.19,204.358 503.169,204.356 505.147,204.354 507.125,204.352 509.103,204.35 511.081,204.348 \n",
       "  513.059,204.346 515.038,204.344 517.016,204.342 518.994,204.34 520.972,204.338 522.95,204.336 524.928,204.334 526.907,204.332 528.885,204.33 530.863,204.328 \n",
       "  532.841,204.326 534.819,204.324 536.797,204.322 538.776,204.319 540.754,204.317 542.732,204.315 544.71,204.313 546.688,204.311 548.666,204.309 550.645,204.307 \n",
       "  552.623,204.305 554.601,204.303 556.579,204.301 558.557,204.299 560.536,204.297 562.514,204.295 564.492,204.293 566.47,204.291 568.448,204.289 570.426,204.287 \n",
       "  572.405,204.285 574.383,204.283 576.361,204.281 578.339,204.279 580.317,204.276 582.295,204.274 584.274,204.272 586.252,204.27 588.23,204.268 590.208,204.266 \n",
       "  592.186,204.264 594.164,204.262 596.143,204.26 598.121,204.258 600.099,204.256 602.077,204.254 604.055,204.252 606.033,204.25 608.012,204.248 609.99,204.246 \n",
       "  611.968,204.244 613.946,204.242 615.924,204.24 617.902,204.238 619.881,204.236 621.859,204.233 623.837,204.231 625.815,204.229 627.793,204.227 629.771,204.225 \n",
       "  631.75,204.223 633.728,204.221 635.706,204.219 637.684,204.217 639.662,204.215 641.64,204.213 643.619,204.211 645.597,204.209 647.575,204.207 649.553,204.205 \n",
       "  651.531,204.203 653.509,204.201 655.488,204.199 657.466,204.197 659.444,204.195 661.422,204.192 663.4,204.19 665.378,204.188 667.357,204.186 669.335,204.184 \n",
       "  671.313,204.182 673.291,204.18 675.269,204.178 677.247,204.176 679.226,204.174 681.204,204.172 683.182,204.17 685.16,204.168 687.138,204.166 689.116,204.164 \n",
       "  691.095,204.162 693.073,204.16 695.051,204.158 697.029,204.156 699.007,204.154 700.985,204.152 702.964,204.149 704.942,204.147 706.92,204.145 708.898,204.143 \n",
       "  710.876,204.141 712.854,204.139 714.833,204.137 716.811,204.135 718.789,204.133 720.767,204.131 722.745,204.129 724.723,204.127 726.702,204.125 728.68,204.123 \n",
       "  730.658,204.121 732.636,204.119 734.614,204.117 736.592,204.115 738.571,204.113 740.549,204.111 742.527,204.109 744.505,204.106 746.483,204.104 748.461,204.102 \n",
       "  750.44,204.1 752.418,204.098 754.396,204.096 756.374,204.094 758.352,204.092 760.33,204.09 762.309,204.088 764.287,204.086 766.265,204.084 768.243,204.082 \n",
       "  770.221,204.08 772.199,204.078 774.178,204.076 776.156,204.074 778.134,204.072 780.112,204.07 782.09,204.068 784.069,204.065 786.047,204.063 788.025,204.061 \n",
       "  790.003,204.059 791.981,204.057 793.959,204.055 795.938,204.053 797.916,204.051 799.894,204.049 801.872,204.047 803.85,204.045 805.828,204.043 807.807,204.041 \n",
       "  809.785,204.039 811.763,204.037 813.741,204.035 815.719,204.033 817.697,204.031 819.676,204.029 821.654,204.027 823.632,204.025 825.61,204.022 827.588,204.02 \n",
       "  829.566,204.018 831.545,204.016 833.523,204.014 835.501,204.012 837.479,204.01 839.457,204.008 841.435,204.006 843.414,204.004 845.392,204.002 847.37,204 \n",
       "  849.348,203.998 851.326,203.996 853.304,203.994 855.283,203.992 857.261,203.99 859.239,203.988 861.217,203.986 863.195,203.984 865.173,203.982 867.152,203.979 \n",
       "  869.13,203.977 871.108,203.975 873.086,203.973 875.064,203.971 877.042,203.969 879.021,203.967 880.999,203.965 882.977,203.963 884.955,203.961 886.933,203.959 \n",
       "  888.911,203.957 890.89,203.955 892.868,203.953 894.846,203.951 896.824,203.949 898.802,203.947 900.78,203.945 902.759,203.943 904.737,203.941 906.715,203.938 \n",
       "  908.693,203.936 910.671,203.934 912.649,203.932 914.628,203.93 916.606,203.928 918.584,203.926 920.562,203.924 922.54,203.922 924.518,203.92 926.497,203.918 \n",
       "  928.475,203.916 930.453,203.914 932.431,203.912 934.409,203.91 936.387,203.908 938.366,203.906 940.344,203.904 942.322,203.942 944.3,205.691 946.278,207.439 \n",
       "  948.256,207.683 950.235,207.681 952.213,207.679 954.191,207.677 956.169,207.675 958.147,207.673 960.125,208.349 962.104,210.097 964.082,211.454 966.06,211.452 \n",
       "  968.038,211.45 970.016,211.448 971.994,211.446 973.973,211.444 975.951,211.442 977.929,211.439 979.907,211.437 981.885,211.435 983.863,211.433 985.842,212.195 \n",
       "  987.82,213.944 989.798,215.215 991.776,215.213 993.754,215.21 995.733,215.208 997.711,215.206 999.689,215.204 1001.67,215.202 1003.65,216.6 1005.62,218.349 \n",
       "  1007.6,218.984 1009.58,218.981 1011.56,218.979 1013.54,218.977 1015.51,218.975 1017.49,218.973 1019.47,218.971 1021.45,218.969 1023.43,218.979 1025.41,220.728 \n",
       "  1027.38,222.476 1029.36,222.748 1031.34,222.746 1033.32,222.744 1035.3,222.742 1037.27,223.664 1039.25,225.412 1041.23,227.16 1043.21,228.909 1045.19,230.658 \n",
       "  1047.16,232.405 1049.14,237.929 1051.12,239.677 1053.1,241.425 1055.08,246.949 1057.06,248.697 1059.03,250.445 1061.01,252.194 1062.99,257.718 1064.97,259.467 \n",
       "  1066.95,261.215 1068.92,262.962 1070.9,264.71 1072.88,266.458 1074.86,271.982 1076.84,273.73 1078.82,275.479 1080.79,277.227 1082.77,278.975 1084.75,292.05 \n",
       "  1086.73,293.798 1088.71,295.547 1090.68,297.295 1092.66,299.043 1094.64,300.791 1096.62,306.315 1098.6,308.063 1100.58,309.811 1102.55,311.56 1104.53,313.308 \n",
       "  1106.51,318.832 1108.49,320.58 1110.47,322.328 1112.44,324.076 1114.42,329.6 1116.4,331.348 1118.38,333.097 1120.36,334.845 1122.34,340.369 1124.31,342.117 \n",
       "  1126.29,343.865 1128.27,345.613 1130.25,347.361 1132.23,349.11 1134.2,350.858 1136.18,356.382 1138.16,358.13 1140.14,363.654 1142.12,365.402 1144.1,367.15 \n",
       "  1146.07,368.898 1148.05,374.422 1150.03,376.17 1152.01,377.918 1153.99,379.667 1155.96,381.415 1157.94,386.939 1159.92,388.688 1161.9,390.436 1163.88,392.184 \n",
       "  1165.85,393.931 1167.83,395.68 1169.81,401.204 1171.79,402.952 1173.77,408.18 1175.75,408.178 1177.72,408.198 1179.7,409.945 1181.68,411.693 1183.66,417.217 \n",
       "  1185.64,418.965 1187.61,424.489 1189.59,426.237 1191.57,427.985 1193.55,429.733 1195.53,431.481 1197.51,433.229 1199.48,434.976 1201.46,436.725 1203.44,442.248 \n",
       "  1205.42,443.997 1207.4,445.745 1209.37,451.269 1211.35,453.018 1213.33,454.766 1215.31,456.514 1217.29,458.261 1219.27,460.01 1221.24,465.534 1223.22,467.282 \n",
       "  1225.2,469.03 1227.18,470.779 1229.16,472.528 1231.13,474.275 1233.11,476.023 1235.09,481.547 1237.07,483.295 1239.05,485.043 1241.03,486.791 1243,492.315 \n",
       "  1244.98,494.063 1246.96,495.811 1248.94,497.56 1250.92,499.308 1252.89,501.056 1254.87,506.58 1256.85,508.328 1258.83,510.076 1260.81,511.824 1262.79,513.573 \n",
       "  1264.76,515.321 1266.74,517.069 1268.72,522.593 1270.7,524.341 1272.68,529.865 1274.65,531.613 1276.63,533.361 1278.61,535.109 1280.59,536.858 1282.57,538.606 \n",
       "  1284.55,540.354 1286.52,542.102 1288.5,543.85 1290.48,545.599 1292.46,547.348 1294.44,549.096 1296.41,550.843 1298.39,552.591 1300.37,554.339 1302.35,556.087 \n",
       "  1304.33,557.835 1306.3,563.36 1308.28,565.108 1310.26,566.856 1312.24,568.604 1314.22,570.351 1316.2,572.099 1318.17,573.847 1320.15,575.596 1322.13,577.344 \n",
       "  1324.11,579.092 1326.09,580.84 1328.06,582.588 1330.04,584.337 1332.02,586.085 1334,587.833 1335.98,589.581 1337.96,591.329 1339.93,593.077 1341.91,598.601 \n",
       "  1343.89,600.349 1345.87,601.158 1347.85,601.156 1349.82,601.818 1351.8,603.566 1353.78,609.09 1355.76,610.839 1357.74,612.587 1359.72,614.336 1361.69,616.084 \n",
       "  1363.67,617.832 1365.65,619.58 1367.63,621.328 1369.61,623.076 1371.58,624.824 1373.56,626.572 1375.54,628.32 1377.52,630.069 1379.5,631.817 1381.48,633.565 \n",
       "  1383.45,635.313 1385.43,637.061 1387.41,638.809 1389.39,644.333 1391.37,646.08 1393.34,647.828 1395.32,649.577 1397.3,651.325 1399.28,653.073 1401.26,654.821 \n",
       "  1403.24,656.57 1405.21,658.319 1407.19,660.066 1409.17,661.69 1411.15,661.688 1413.13,661.686 1415.1,661.684 1417.08,661.682 1419.06,665.467 1421.04,665.465 \n",
       "  1423.02,669.251 1425,669.249 1426.97,669.247 1428.95,669.245 1430.93,669.717 1432.91,671.465 1434.89,673.213 1436.86,674.961 1438.84,676.709 1440.82,678.457 \n",
       "  1442.8,680.205 1444.78,681.953 1446.75,683.702 1448.73,685.45 1450.71,687.197 1452.69,688.945 1454.67,690.694 1456.65,692.442 1458.62,694.19 1460.6,695.723 \n",
       "  1462.58,695.721 1464.56,695.719 1466.54,701.183 1468.51,702.931 1470.49,703.288 1472.47,703.286 1474.45,704.4 1476.43,706.148 1478.41,707.896 1480.38,709.644 \n",
       "  1482.36,711.392 1484.34,713.141 1486.32,714.889 1488.3,716.637 1490.27,718.385 1492.25,720.133 1494.23,721.881 1496.21,722.198 1498.19,722.196 1500.17,723.349 \n",
       "  1502.14,725.097 1504.12,730.621 1506.1,732.369 1508.08,733.548 1510.06,733.546 1512.03,733.838 1514.01,735.586 1515.99,737.334 1517.97,739.083 1519.95,740.831 \n",
       "  1521.93,742.579 1523.9,744.327 1525.88,744.892 1527.86,744.89 1529.84,745.797 1531.82,747.544 1533.79,749.292 1535.77,751.04 1537.75,752.789 1539.73,754.537 \n",
       "  1541.71,756.237 1543.69,756.235 1545.66,756.233 1547.64,757.754 1549.62,759.502 1551.6,761.25 1553.58,762.997 1555.55,764.745 1557.53,766.493 1559.51,767.581 \n",
       "  1561.49,767.579 1563.47,767.962 1565.44,769.71 1567.42,771.459 1569.4,773.207 1571.38,774.955 1573.36,775.141 1575.34,775.139 1577.31,776.424 1579.29,778.172 \n",
       "  1581.27,779.92 1583.25,781.668 1585.23,783.416 1587.2,785.165 1589.18,786.487 1591.16,786.485 1593.14,786.633 1595.12,788.382 1597.1,790.13 1599.07,791.878 \n",
       "  1601.05,793.626 1603.03,795.374 1605.01,797.121 1606.99,797.831 1608.96,797.829 1610.94,798.59 1612.92,800.338 1614.9,802.086 1616.88,803.835 1618.86,805.393 \n",
       "  1620.83,805.391 1622.81,805.389 1624.79,810.827 1626.77,812.576 1628.75,812.958 1630.72,812.956 1632.7,814.044 1634.68,815.793 1636.66,820.524 1638.64,820.522 \n",
       "  1640.62,821.037 1642.59,822.786 1644.57,824.535 1646.55,826.282 1648.53,828.03 1650.51,829.778 1652.48,831.526 1654.46,833.274 1656.44,835.022 1658.42,835.651 \n",
       "  1660.4,835.649 1662.38,836.49 1664.35,838.238 1666.33,839.431 1668.31,839.429 1670.29,839.707 1672.27,841.456 1674.24,843.205 1676.22,843.208 1678.2,843.206 \n",
       "  1680.18,848.448 1682.16,850.196 1684.14,850.774 1686.11,850.772 1688.09,851.666 1690.07,853.413 1692.05,855.161 1694.03,856.909 1696,858.658 1697.98,860.406 \n",
       "  1699.96,862.154 1701.94,863.902 1703.92,865.65 1705.89,867.399 1707.87,869.147 1709.85,870.895 1711.83,872.643 1713.81,874.391 1715.79,876.139 1717.76,877.888 \n",
       "  1719.74,879.636 1721.72,881.384 1723.7,883.132 1725.68,884.88 1727.65,886.629 1729.63,888.377 1731.61,890.125 1733.59,891.873 1735.57,893.621 1737.55,895.369 \n",
       "  1739.52,897.118 1741.5,898.866 1743.48,900.614 1745.46,902.362 1747.44,904.11 1749.41,905.858 1751.39,907.607 1753.37,909.355 1755.35,911.103 1757.33,912.851 \n",
       "  1759.31,914.599 1761.28,916.348 1763.26,918.096 1765.24,919.844 1767.22,921.592 1769.2,923.34 1771.17,925.088 1773.15,926.837 1775.13,928.585 1777.11,930.333 \n",
       "  1779.09,932.081 1781.07,933.829 1783.04,935.578 1785.02,937.326 1787,939.074 1788.98,940.822 1790.96,942.57 1792.93,944.318 1794.91,946.067 1796.89,947.815 \n",
       "  1798.87,949.563 1800.85,951.311 1802.83,953.059 1804.8,954.808 1806.78,956.556 1808.76,958.304 1810.74,960.052 1812.72,961.8 1814.69,963.548 1816.67,965.297 \n",
       "  1818.65,967.045 1820.63,968.793 1822.61,970.541 1824.58,972.289 1826.56,974.038 1828.54,975.786 1830.52,977.534 1832.5,979.282 1834.48,981.03 1836.45,982.778 \n",
       "  1838.43,984.527 1840.41,986.275 1842.39,988.023 1844.37,989.771 1846.34,991.519 1848.32,993.267 1850.3,995.016 1852.28,996.764 1854.26,998.512 1856.24,1000.26 \n",
       "  1858.21,1002.01 1860.19,1003.76 1862.17,1005.5 1864.15,1007.25 1866.13,1009 1868.1,1010.75 1870.08,1012.5 1872.06,1014.25 1874.04,1015.99 1876.02,1017.74 \n",
       "  1878,1019.49 1879.97,1021.24 1881.95,1022.99 1883.93,1024.73 1885.91,1026.48 1887.89,1028.23 1889.86,1029.98 1891.84,1031.73 1893.82,1033.48 1895.8,1035.22 \n",
       "  1897.78,1036.97 1899.76,1038.72 1901.73,1040.47 1903.71,1042.22 1905.69,1043.96 1907.67,1045.71 1909.65,1047.46 1911.62,1049.21 1913.6,1050.96 1915.58,1052.71 \n",
       "  1917.56,1054.45 1919.54,1056.2 1921.52,1057.95 1923.49,1059.7 1925.47,1061.45 1927.45,1063.19 1929.43,1064.94 1931.41,1066.69 1933.38,1068.44 1935.36,1070.19 \n",
       "  1937.34,1071.94 1939.32,1073.68 1941.3,1075.43 1943.28,1077.18 1945.25,1078.93 1947.23,1080.68 1949.21,1082.42 1951.19,1084.17 1953.17,1085.92 1955.14,1087.67 \n",
       "  1957.12,1089.42 1959.1,1091.17 1961.08,1092.91 1963.06,1094.66 1965.03,1096.41 1967.01,1098.16 1968.99,1099.91 1970.97,1101.65 1972.95,1103.4 1974.93,1105.15 \n",
       "  1976.9,1106.9 1978.88,1108.65 1980.86,1110.4 1982.84,1112.14 1984.82,1113.89 1986.79,1115.64 1988.77,1117.39 1990.75,1119.14 1992.73,1120.88 1994.71,1122.63 \n",
       "  1996.69,1124.38 1998.66,1126.13 2000.64,1127.88 2002.62,1129.63 2004.6,1131.37 2006.58,1133.12 2008.55,1134.87 2010.53,1136.62 2012.51,1138.37 2014.49,1140.11 \n",
       "  2016.47,1141.86 2018.45,1143.61 2020.42,1145.36 2022.4,1147.11 2024.38,1148.86 2026.36,1150.6 2028.34,1152.35 2030.31,1154.1 2032.29,1155.85 2034.27,1157.6 \n",
       "  2036.25,1159.34 2038.23,1161.09 2040.21,1162.84 2042.18,1164.59 2044.16,1166.34 2046.14,1168.09 2048.12,1169.83 2050.1,1171.58 2052.07,1173.33 2054.05,1175.08 \n",
       "  2056.03,1176.83 2058.01,1178.57 2059.99,1180.32 2061.97,1182.07 2063.94,1183.82 2065.92,1185.57 2067.9,1187.32 2069.88,1189.06 2071.86,1190.81 2073.83,1192.56 \n",
       "  2075.81,1194.31 2077.79,1196.06 2079.77,1197.8 2081.75,1199.55 2083.73,1201.3 2085.7,1203.05 2087.68,1204.8 2089.66,1206.55 2091.64,1208.29 2093.62,1210.04 \n",
       "  2095.59,1211.79 2097.57,1213.54 2099.55,1215.29 2101.53,1217.03 2103.51,1218.78 2105.48,1220.53 2107.46,1222.28 2109.44,1224.03 2111.42,1225.78 2113.4,1227.52 \n",
       "  2115.38,1229.27 2117.35,1231.02 2119.33,1232.77 2121.31,1234.52 2123.29,1236.26 2125.27,1238.01 2127.24,1239.76 2129.22,1241.51 2131.2,1243.26 2133.18,1245.01 \n",
       "  2135.16,1246.75 2137.14,1248.5 2139.11,1250.25 2141.09,1252 2143.07,1253.75 2145.05,1255.49 2147.03,1257.24 2149,1258.99 2150.98,1260.74 2152.96,1262.49 \n",
       "  2154.94,1264.24 2156.92,1265.98 2158.9,1267.73 2160.87,1269.48 2162.85,1271.23 2164.83,1272.98 2166.81,1274.72 2168.79,1276.47 2170.76,1278.22 2172.74,1279.97 \n",
       "  2174.72,1281.72 2176.7,1283.47 2178.68,1285.21 2180.66,1286.96 2182.63,1288.71 2184.61,1290.46 2186.59,1292.21 2188.57,1293.95 2190.55,1295.7 2192.52,1297.45 \n",
       "  2194.5,1299.2 2196.48,1300.95 2198.46,1302.7 2200.44,1304.44 2202.42,1306.19 2204.39,1307.94 2206.37,1309.69 2208.35,1311.44 2210.33,1313.18 2212.31,1314.93 \n",
       "  2214.28,1316.68 2216.26,1318.43 2218.24,1320.18 2220.22,1321.93 2222.2,1323.67 2224.17,1325.42 2226.15,1327.17 2228.13,1328.92 2230.11,1330.67 2232.09,1332.41 \n",
       "  2234.07,1334.16 2236.04,1335.91 2238.02,1337.66 2240,1339.41 2241.98,1341.16 2243.96,1342.9 2245.93,1344.65 2247.91,1346.4 2249.89,1348.15 2251.87,1349.9 \n",
       "  2253.85,1351.64 2255.83,1353.39 2257.8,1355.14 2259.78,1356.89 2261.76,1358.64 2263.74,1360.39 2265.72,1362.13 2267.69,1363.88 2269.67,1365.63 2271.65,1367.38 \n",
       "  2273.63,1369.13 2275.61,1370.87 2277.59,1372.62 2279.56,1374.37 2281.54,1376.12 2283.52,1377.87 2285.5,1379.62 2287.48,1381.36 2289.45,1383.11 2291.43,1384.86 \n",
       "  2293.41,1386.61 \n",
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       "  1601.05,793.418 1603.03,793.41 1605.01,793.403 1606.99,793.395 1608.96,797.748 1610.94,800.593 1612.92,800.586 1614.9,800.578 1616.88,800.571 1618.86,800.563 \n",
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       "  1640.62,814.907 1642.59,814.899 1644.57,818.387 1646.55,822.097 1648.53,822.089 1650.51,822.082 1652.48,822.074 1654.46,822.067 1656.44,822.06 1658.42,826.812 \n",
       "  1660.4,829.257 1662.38,829.25 1664.35,829.242 1666.33,829.235 1668.31,829.227 1670.29,829.22 1672.27,835.237 1674.24,836.418 1676.22,836.41 1678.2,836.403 \n",
       "  1680.18,836.395 1682.16,838.176 1684.14,843.593 1686.11,843.586 1688.09,843.578 1690.07,843.571 1692.05,843.563 1694.03,847.452 1696,850.761 1697.98,850.753 \n",
       "  1699.96,850.746 1701.94,850.739 1703.92,850.731 1705.89,850.724 1707.87,855.875 1709.85,857.921 1711.83,857.914 1713.81,857.907 1715.79,857.899 1717.76,857.892 \n",
       "  1719.74,857.963 1721.72,864.301 1723.7,865.082 1725.68,865.074 1727.65,865.067 1729.63,865.06 1731.61,865.052 1733.59,866.388 1735.57,872.25 1737.55,872.242 \n",
       "  1739.52,872.235 1741.5,872.227 1743.48,872.22 1745.46,872.213 1747.44,874.813 1749.41,879.41 1751.39,879.403 1753.37,879.395 1755.35,879.388 1757.33,879.381 \n",
       "  1759.31,879.373 1761.28,879.366 1763.26,882.388 1765.24,886.563 1767.22,886.556 1769.2,886.548 1771.17,886.541 1773.15,886.534 1775.13,886.526 1777.11,890.813 \n",
       "  1779.09,893.724 1781.07,893.716 1783.04,893.709 1785.02,893.701 1787,893.694 1788.98,893.687 1790.96,893.679 1792.93,898.387 1794.91,900.877 1796.89,900.869 \n",
       "  1798.87,900.862 1800.85,900.854 1802.83,900.847 1804.8,900.84 1806.78,906.813 1808.76,908.037 1810.74,908.03 1812.72,908.022 1814.69,908.015 1816.67,908.008 \n",
       "  1818.65,908.9 1820.63,915.205 1822.61,915.198 1824.58,915.19 1826.56,915.183 1828.54,915.175 1830.52,915.168 1832.5,917.325 1834.48,922.366 1836.45,922.358 \n",
       "  1838.43,922.351 1840.41,922.343 1842.39,922.336 1844.37,922.328 1846.34,922.321 1848.32,922.314 1850.3,924.051 1852.28,929.511 1854.26,929.504 1856.24,929.496 \n",
       "  1858.21,929.489 1860.19,929.482 1862.17,929.474 1864.15,929.467 1866.13,931.623 1868.1,936.664 1870.08,936.657 1872.06,936.649 1874.04,936.642 1876.02,936.635 \n",
       "  1878,936.627 1879.97,936.62 1881.95,936.612 1883.93,938.348 1885.91,943.81 1887.89,943.802 1889.86,943.795 1891.84,943.788 1893.82,943.78 1895.8,943.773 \n",
       "  1897.78,943.765 1899.76,943.758 1901.73,945.072 1903.71,950.956 1905.69,950.948 1907.67,950.941 1909.65,950.933 1911.62,950.926 1913.6,950.918 1915.58,950.911 \n",
       "  1917.56,950.904 1919.54,951.796 1921.52,958.101 1923.49,958.094 1925.47,958.086 1927.45,958.079 1929.43,958.071 1931.41,958.064 1933.38,958.057 1935.36,959.37 \n",
       "  1937.34,965.254 1939.32,965.247 1941.3,965.239 1943.28,965.232 1945.25,965.224 1947.23,965.217 1949.21,965.21 1951.19,965.202 1953.17,966.094 1955.14,972.4 \n",
       "  1957.12,972.392 1959.1,972.385 1961.08,972.378 1963.06,972.37 1965.03,972.363 1967.01,972.355 1968.99,973.669 1970.97,979.553 1972.95,979.545 1974.93,979.538 \n",
       "  1976.9,979.531 1978.88,979.523 1980.86,979.516 1982.84,979.508 1984.82,979.501 1986.79,980.393 1988.77,986.698 1990.75,986.691 1992.73,986.684 1994.71,986.676 \n",
       "  1996.69,986.669 1998.66,986.661 2000.64,986.654 2002.62,986.646 2004.6,986.639 2006.58,986.632 2008.55,992.605 2010.53,993.829 2012.51,993.822 2014.49,993.814 \n",
       "  2016.47,993.807 2018.45,993.8 2020.42,993.792 2022.4,993.785 2024.38,993.777 2026.36,999.328 2028.34,1000.97 2030.31,1000.97 2032.29,1000.96 2034.27,1000.95 \n",
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       "  2056.03,1008.08 2058.01,1008.08 2059.99,1008.07 2061.97,1008.06 2063.94,1011.93 2065.92,1015.26 2067.9,1015.25 2069.88,1015.24 2071.86,1015.24 2073.83,1015.23 \n",
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       "  2154.94,1043.77 2156.92,1043.77 2158.9,1043.76 2160.87,1043.75 2162.85,1043.74 2164.83,1047.63 2166.81,1050.94 2168.79,1050.93 2170.76,1050.93 2172.74,1050.92 \n",
       "  2174.72,1050.91 2176.7,1050.9 2178.68,1050.9 2180.66,1050.89 2182.63,1050.88 2184.61,1053.51 2186.59,1058.08 2188.57,1058.07 2190.55,1058.07 2192.52,1058.06 \n",
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       "  1541.71,752.491 1543.69,753.86 1545.66,755.224 1547.64,756.585 1549.62,757.941 1551.6,759.292 1553.58,760.64 1555.55,761.983 1557.53,763.322 1559.51,764.657 \n",
       "  1561.49,765.987 1563.47,767.313 1565.44,768.636 1567.42,769.954 1569.4,771.267 1571.38,772.577 1573.36,773.883 1575.34,775.185 1577.31,776.482 1579.29,777.776 \n",
       "  1581.27,779.065 1583.25,780.351 1585.23,781.632 1587.2,782.91 1589.18,784.184 1591.16,785.454 1593.14,786.72 1595.12,787.982 1597.1,789.24 1599.07,790.494 \n",
       "  1601.05,791.745 1603.03,792.992 1605.01,794.235 1606.99,795.474 1608.96,796.709 1610.94,797.941 1612.92,799.169 1614.9,800.394 1616.88,801.615 1618.86,802.832 \n",
       "  1620.83,804.045 1622.81,805.255 1624.79,806.462 1626.77,807.664 1628.75,808.864 1630.72,810.059 1632.7,811.252 1634.68,812.44 1636.66,813.625 1638.64,814.807 \n",
       "  1640.62,815.985 1642.59,817.16 1644.57,818.332 1646.55,819.5 1648.53,820.665 1650.51,821.826 1652.48,822.984 1654.46,824.139 1656.44,825.29 1658.42,826.438 \n",
       "  1660.4,827.583 1662.38,828.725 1664.35,829.863 1666.33,830.998 1668.31,832.13 1670.29,833.259 1672.27,834.384 1674.24,835.507 1676.22,836.626 1678.2,837.742 \n",
       "  1680.18,838.855 1682.16,839.965 1684.14,841.072 1686.11,842.176 1688.09,843.277 1690.07,844.375 1692.05,845.47 1694.03,846.561 1696,847.65 1697.98,848.736 \n",
       "  1699.96,849.819 1701.94,850.899 1703.92,851.976 1705.89,853.05 1707.87,854.122 1709.85,855.19 1711.83,856.256 1713.81,857.319 1715.79,858.378 1717.76,859.436 \n",
       "  1719.74,860.49 1721.72,861.542 1723.7,862.59 1725.68,863.636 1727.65,864.68 1729.63,865.72 1731.61,866.758 1733.59,867.793 1735.57,868.826 1737.55,869.856 \n",
       "  1739.52,870.883 1741.5,871.908 1743.48,872.93 1745.46,873.949 1747.44,874.966 1749.41,875.98 1751.39,876.992 1753.37,878.001 1755.35,879.008 1757.33,880.012 \n",
       "  1759.31,881.013 1761.28,882.012 1763.26,883.009 1765.24,884.003 1767.22,884.995 1769.2,885.984 1771.17,886.971 1773.15,887.955 1775.13,888.937 1777.11,889.917 \n",
       "  1779.09,890.894 1781.07,891.869 1783.04,892.841 1785.02,893.811 1787,894.779 1788.98,895.745 1790.96,896.708 1792.93,897.669 1794.91,898.628 1796.89,899.584 \n",
       "  1798.87,900.538 1800.85,901.49 1802.83,902.44 1804.8,903.387 1806.78,904.333 1808.76,905.276 1810.74,906.217 1812.72,907.155 1814.69,908.092 1816.67,909.026 \n",
       "  1818.65,909.959 1820.63,910.889 1822.61,911.817 1824.58,912.743 1826.56,913.667 1828.54,914.589 1830.52,915.509 1832.5,916.426 1834.48,917.342 1836.45,918.256 \n",
       "  1838.43,919.167 1840.41,920.077 1842.39,920.984 1844.37,921.89 1846.34,922.794 1848.32,923.695 1850.3,924.595 1852.28,925.493 1854.26,926.388 1856.24,927.282 \n",
       "  1858.21,928.174 1860.19,929.064 1862.17,929.953 1864.15,930.839 1866.13,931.723 1868.1,932.606 1870.08,933.486 1872.06,934.365 1874.04,935.242 1876.02,936.117 \n",
       "  1878,936.991 1879.97,937.862 1881.95,938.732 1883.93,939.6 1885.91,940.466 1887.89,941.33 1889.86,942.193 1891.84,943.054 1893.82,943.913 1895.8,944.77 \n",
       "  1897.78,945.626 1899.76,946.48 1901.73,947.332 1903.71,948.182 1905.69,949.031 1907.67,949.878 1909.65,950.724 1911.62,951.567 1913.6,952.41 1915.58,953.25 \n",
       "  1917.56,954.089 1919.54,954.926 1921.52,955.761 1923.49,956.595 1925.47,957.427 1927.45,958.258 1929.43,959.087 1931.41,959.915 1933.38,960.741 1935.36,961.565 \n",
       "  1937.34,962.388 1939.32,963.209 1941.3,964.028 1943.28,964.846 1945.25,965.663 1947.23,966.478 1949.21,967.291 1951.19,968.103 1953.17,968.914 1955.14,969.722 \n",
       "  1957.12,970.53 1959.1,971.336 1961.08,972.14 1963.06,972.943 1965.03,973.745 1967.01,974.545 1968.99,975.343 1970.97,976.14 1972.95,976.936 1974.93,977.73 \n",
       "  1976.9,978.523 1978.88,979.314 1980.86,980.104 1982.84,980.892 1984.82,981.679 1986.79,982.465 1988.77,983.249 1990.75,984.032 1992.73,984.813 1994.71,985.593 \n",
       "  1996.69,986.372 1998.66,987.149 2000.64,987.925 2002.62,988.699 2004.6,989.473 2006.58,990.244 2008.55,991.015 2010.53,991.784 2012.51,992.552 2014.49,993.318 \n",
       "  2016.47,994.083 2018.45,994.847 2020.42,995.609 2022.4,996.37 2024.38,997.13 2026.36,997.888 2028.34,998.645 2030.31,999.401 2032.29,1000.16 2034.27,1000.91 \n",
       "  2036.25,1001.66 2038.23,1002.41 2040.21,1003.16 2042.18,1003.91 2044.16,1004.66 2046.14,1005.4 2048.12,1006.15 2050.1,1006.89 2052.07,1007.63 2054.05,1008.37 \n",
       "  2056.03,1009.11 2058.01,1009.85 2059.99,1010.58 2061.97,1011.32 2063.94,1012.05 2065.92,1012.79 2067.9,1013.52 2069.88,1014.25 2071.86,1014.98 2073.83,1015.71 \n",
       "  2075.81,1016.43 2077.79,1017.16 2079.77,1017.88 2081.75,1018.61 2083.73,1019.33 2085.7,1020.05 2087.68,1020.77 2089.66,1021.49 2091.64,1022.2 2093.62,1022.92 \n",
       "  2095.59,1023.63 2097.57,1024.35 2099.55,1025.06 2101.53,1025.77 2103.51,1026.48 2105.48,1027.19 2107.46,1027.89 2109.44,1028.6 2111.42,1029.31 2113.4,1030.01 \n",
       "  2115.38,1030.71 2117.35,1031.41 2119.33,1032.11 2121.31,1032.81 2123.29,1033.51 2125.27,1034.21 2127.24,1034.9 2129.22,1035.6 2131.2,1036.29 2133.18,1036.98 \n",
       "  2135.16,1037.67 2137.14,1038.36 2139.11,1039.05 2141.09,1039.73 2143.07,1040.42 2145.05,1041.11 2147.03,1041.79 2149,1042.47 2150.98,1043.15 2152.96,1043.83 \n",
       "  2154.94,1044.51 2156.92,1045.19 2158.9,1045.86 2160.87,1046.54 2162.85,1047.21 2164.83,1047.89 2166.81,1048.56 2168.79,1049.23 2170.76,1049.9 2172.74,1050.56 \n",
       "  2174.72,1051.23 2176.7,1051.9 2178.68,1052.56 2180.66,1053.22 2182.63,1053.89 2184.61,1054.55 2186.59,1055.21 2188.57,1055.86 2190.55,1056.52 2192.52,1057.18 \n",
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       "  2214.28,1064.31 2216.26,1064.95 2218.24,1065.59 2220.22,1066.23 2222.2,1066.87 2224.17,1067.5 2226.15,1068.14 2228.13,1068.77 2230.11,1069.4 2232.09,1070.04 \n",
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       "  1007.6,86.2547 1009.58,86.2547 1011.56,86.2547 1013.54,86.2547 1015.51,86.2547 1017.49,86.2547 1019.47,86.2547 1021.45,86.2547 1023.43,86.2547 1025.41,86.2547 \n",
       "  1027.38,86.2547 1029.36,86.2547 1031.34,86.2547 1033.32,86.2547 1035.3,86.2547 1037.27,86.2547 1039.25,86.2547 1041.23,86.2547 1043.21,86.2547 1045.19,86.2547 \n",
       "  1047.16,86.2547 1049.14,86.2547 1051.12,86.2547 1053.1,86.2547 1055.08,86.2547 1057.06,86.2547 1059.03,89.2742 1061.01,92.844 1062.99,96.4009 1064.97,99.9451 \n",
       "  1066.95,103.477 1068.92,106.996 1070.9,110.502 1072.88,113.996 1074.86,117.477 1076.84,120.946 1078.82,124.402 1080.79,127.846 1082.77,131.277 1084.75,134.697 \n",
       "  1086.73,138.104 1088.71,141.499 1090.68,144.881 1092.66,148.252 1094.64,151.61 1096.62,154.956 1098.6,158.29 1100.58,161.613 1102.55,164.923 1104.53,168.221 \n",
       "  1106.51,171.508 1108.49,174.783 1110.47,178.046 1112.44,181.297 1114.42,184.536 1116.4,187.764 1118.38,190.98 1120.36,194.185 1122.34,197.378 1124.31,200.56 \n",
       "  1126.29,203.73 1128.27,206.888 1130.25,210.036 1132.23,213.172 1134.2,216.296 1136.18,219.41 1138.16,222.512 1140.14,225.603 1142.12,228.682 1144.1,231.751 \n",
       "  1146.07,234.809 1148.05,237.855 1150.03,240.891 1152.01,243.916 1153.99,246.929 1155.96,249.932 1157.94,252.924 1159.92,255.905 1161.9,258.876 1163.88,261.835 \n",
       "  1165.85,264.784 1167.83,267.722 1169.81,270.65 1171.79,273.567 1173.77,276.474 1175.75,279.37 1177.72,282.256 1179.7,285.131 1181.68,287.996 1183.66,290.85 \n",
       "  1185.64,293.694 1187.61,296.528 1189.59,299.352 1191.57,302.165 1193.55,304.968 1195.53,307.761 1197.51,310.544 1199.48,313.317 1201.46,316.08 1203.44,318.833 \n",
       "  1205.42,321.576 1207.4,324.309 1209.37,327.032 1211.35,329.746 1213.33,332.449 1215.31,335.143 1217.29,337.827 1219.27,340.501 1221.24,343.166 1223.22,345.821 \n",
       "  1225.2,348.467 1227.18,351.102 1229.16,353.729 1231.13,356.346 1233.11,358.953 1235.09,361.551 1237.07,364.14 1239.05,366.719 1241.03,369.289 1243,371.85 \n",
       "  1244.98,374.402 1246.96,376.944 1248.94,379.477 1250.92,382.001 1252.89,384.516 1254.87,387.022 1256.85,389.519 1258.83,392.007 1260.81,394.485 1262.79,396.955 \n",
       "  1264.76,399.416 1266.74,401.869 1268.72,404.312 1270.7,406.747 1272.68,409.172 1274.65,411.589 1276.63,413.998 1278.61,416.398 1280.59,418.789 1282.57,421.171 \n",
       "  1284.55,423.545 1286.52,425.911 1288.5,428.268 1290.48,430.616 1292.46,432.956 1294.44,435.288 1296.41,437.611 1298.39,439.926 1300.37,442.233 1302.35,444.532 \n",
       "  1304.33,446.822 1306.3,449.104 1308.28,451.378 1310.26,453.643 1312.24,455.901 1314.22,458.151 1316.2,460.392 1318.17,462.626 1320.15,464.851 1322.13,467.069 \n",
       "  1324.11,469.279 1326.09,471.481 1328.06,473.675 1330.04,475.861 1332.02,478.039 1334,480.21 1335.98,482.373 1337.96,484.528 1339.93,486.676 1341.91,488.816 \n",
       "  1343.89,490.949 1345.87,493.073 1347.85,495.191 1349.82,497.301 1351.8,499.403 1353.78,501.498 1355.76,503.585 1357.74,505.666 1359.72,507.738 1361.69,509.804 \n",
       "  1363.67,511.862 1365.65,513.913 1367.63,515.957 1369.61,517.993 1371.58,520.023 1373.56,522.045 1375.54,524.06 1377.52,526.068 1379.5,528.069 1381.48,530.063 \n",
       "  1383.45,532.05 1385.43,534.03 1387.41,536.003 1389.39,537.97 1391.37,539.929 1393.34,541.882 1395.32,543.827 1397.3,545.766 1399.28,547.698 1401.26,549.624 \n",
       "  1403.24,551.543 1405.21,553.455 1407.19,555.36 1409.17,557.259 1411.15,559.151 1413.13,561.037 1415.1,562.916 1417.08,564.789 1419.06,566.655 1421.04,568.515 \n",
       "  1423.02,570.368 1425,572.215 1426.97,574.056 1428.95,575.89 1430.93,577.718 1432.91,579.54 1434.89,581.355 1436.86,583.165 1438.84,584.968 1440.82,586.765 \n",
       "  1442.8,588.555 1444.78,590.34 1446.75,592.119 1448.73,593.891 1450.71,595.658 1452.69,597.418 1454.67,599.173 1456.65,600.921 1458.62,602.664 1460.6,604.401 \n",
       "  1462.58,606.131 1464.56,607.856 1466.54,609.576 1468.51,611.289 1470.49,612.997 1472.47,614.699 1474.45,616.395 1476.43,618.085 1478.41,619.77 1480.38,621.45 \n",
       "  1482.36,623.123 1484.34,624.791 1486.32,626.454 1488.3,628.111 1490.27,629.762 1492.25,631.408 1494.23,633.049 1496.21,634.684 1498.19,636.314 1500.17,637.938 \n",
       "  1502.14,639.557 1504.12,641.17 1506.1,642.779 1508.08,644.382 1510.06,645.98 1512.03,647.572 1514.01,649.159 1515.99,650.742 1517.97,652.319 1519.95,653.89 \n",
       "  1521.93,655.457 1523.9,657.019 1525.88,658.575 1527.86,660.127 1529.84,661.674 1531.82,663.215 1533.79,664.752 1535.77,666.283 1537.75,667.81 1539.73,669.332 \n",
       "  1541.71,670.849 1543.69,672.361 1545.66,673.868 1547.64,675.371 1549.62,676.868 1551.6,678.361 1553.58,679.85 1555.55,681.333 1557.53,682.812 1559.51,684.286 \n",
       "  1561.49,685.755 1563.47,687.22 1565.44,688.681 1567.42,690.136 1569.4,691.587 1571.38,693.034 1573.36,694.476 1575.34,695.914 1577.31,697.347 1579.29,698.776 \n",
       "  1581.27,700.2 1583.25,701.62 1585.23,703.035 1587.2,704.446 1589.18,705.853 1591.16,707.256 1593.14,708.654 1595.12,710.048 1597.1,711.438 1599.07,712.823 \n",
       "  1601.05,714.204 1603.03,715.581 1605.01,716.954 1606.99,718.323 1608.96,719.688 1610.94,721.048 1612.92,722.405 1614.9,723.757 1616.88,725.105 1618.86,726.45 \n",
       "  1620.83,727.79 1622.81,729.126 1624.79,730.459 1626.77,731.787 1628.75,733.112 1630.72,734.432 1632.7,735.749 1634.68,737.062 1636.66,738.371 1638.64,739.676 \n",
       "  1640.62,740.977 1642.59,742.275 1644.57,743.569 1646.55,744.859 1648.53,746.146 1650.51,747.428 1652.48,748.707 1654.46,749.983 1656.44,751.254 1658.42,752.522 \n",
       "  1660.4,753.787 1662.38,755.048 1664.35,756.305 1666.33,757.559 1668.31,758.809 1670.29,760.056 1672.27,761.299 1674.24,762.538 1676.22,763.775 1678.2,765.007 \n",
       "  1680.18,766.237 1682.16,767.463 1684.14,768.685 1686.11,769.905 1688.09,771.12 1690.07,772.333 1692.05,773.542 1694.03,774.748 1696,775.951 1697.98,777.15 \n",
       "  1699.96,778.346 1701.94,779.539 1703.92,780.728 1705.89,781.915 1707.87,783.098 1709.85,784.278 1711.83,785.455 1713.81,786.629 1715.79,787.8 1717.76,788.967 \n",
       "  1719.74,790.132 1721.72,791.293 1723.7,792.452 1725.68,793.607 1727.65,794.759 1729.63,795.909 1731.61,797.055 1733.59,798.198 1735.57,799.339 1737.55,800.476 \n",
       "  1739.52,801.611 1741.5,802.742 1743.48,803.871 1745.46,804.997 1747.44,806.12 1749.41,807.24 1751.39,808.358 1753.37,809.472 1755.35,810.584 1757.33,811.693 \n",
       "  1759.31,812.799 1761.28,813.903 1763.26,815.003 1765.24,816.101 1767.22,817.197 1769.2,818.289 1771.17,819.379 1773.15,820.466 1775.13,821.551 1777.11,822.633 \n",
       "  1779.09,823.712 1781.07,824.789 1783.04,825.863 1785.02,826.935 1787,828.003 1788.98,829.07 1790.96,830.134 1792.93,831.195 1794.91,832.254 1796.89,833.31 \n",
       "  1798.87,834.364 1800.85,835.416 1802.83,836.464 1804.8,837.511 1806.78,838.555 1808.76,839.597 1810.74,840.636 1812.72,841.673 1814.69,842.707 1816.67,843.739 \n",
       "  1818.65,844.769 1820.63,845.796 1822.61,846.821 1824.58,847.844 1826.56,848.865 1828.54,849.883 1830.52,850.899 1832.5,851.912 1834.48,852.923 1836.45,853.932 \n",
       "  1838.43,854.939 1840.41,855.944 1842.39,856.946 1844.37,857.947 1846.34,858.945 1848.32,859.941 1850.3,860.934 1852.28,861.926 1854.26,862.915 1856.24,863.902 \n",
       "  1858.21,864.888 1860.19,865.871 1862.17,866.852 1864.15,867.83 1866.13,868.807 1868.1,869.782 1870.08,870.755 1872.06,871.725 1874.04,872.694 1876.02,873.66 \n",
       "  1878,874.625 1879.97,875.588 1881.95,876.548 1883.93,877.507 1885.91,878.463 1887.89,879.418 1889.86,880.371 1891.84,881.322 1893.82,882.27 1895.8,883.217 \n",
       "  1897.78,884.162 1899.76,885.105 1901.73,886.047 1903.71,886.986 1905.69,887.924 1907.67,888.859 1909.65,889.793 1911.62,890.725 1913.6,891.655 1915.58,892.583 \n",
       "  1917.56,893.509 1919.54,894.434 1921.52,895.357 1923.49,896.278 1925.47,897.197 1927.45,898.114 1929.43,899.03 1931.41,899.944 1933.38,900.856 1935.36,901.767 \n",
       "  1937.34,902.675 1939.32,903.582 1941.3,904.487 1943.28,905.391 1945.25,906.293 1947.23,907.193 1949.21,908.091 1951.19,908.988 1953.17,909.883 1955.14,910.777 \n",
       "  1957.12,911.668 1959.1,912.558 1961.08,913.447 1963.06,914.334 1965.03,915.219 1967.01,916.102 1968.99,916.984 1970.97,917.865 1972.95,918.743 1974.93,919.621 \n",
       "  1976.9,920.496 1978.88,921.37 1980.86,922.242 1982.84,923.113 1984.82,923.982 1986.79,924.85 1988.77,925.716 1990.75,926.581 1992.73,927.444 1994.71,928.305 \n",
       "  1996.69,929.165 1998.66,930.024 2000.64,930.881 2002.62,931.736 2004.6,932.59 2006.58,933.442 2008.55,934.293 2010.53,935.143 2012.51,935.991 2014.49,936.837 \n",
       "  2016.47,937.682 2018.45,938.526 2020.42,939.368 2022.4,940.208 2024.38,941.047 2026.36,941.885 2028.34,942.721 2030.31,943.556 2032.29,944.389 2034.27,945.221 \n",
       "  2036.25,946.052 2038.23,946.881 2040.21,947.709 2042.18,948.535 2044.16,949.36 2046.14,950.183 2048.12,951.005 2050.1,951.826 2052.07,952.645 2054.05,953.462 \n",
       "  2056.03,954.279 2058.01,955.094 2059.99,955.907 2061.97,956.72 2063.94,957.531 2065.92,958.34 2067.9,959.148 2069.88,959.955 2071.86,960.76 2073.83,961.564 \n",
       "  2075.81,962.367 2077.79,963.168 2079.77,963.968 2081.75,964.767 2083.73,965.564 2085.7,966.36 2087.68,967.154 2089.66,967.948 2091.64,968.739 2093.62,969.53 \n",
       "  2095.59,970.319 2097.57,971.107 2099.55,971.893 2101.53,972.679 2103.51,973.462 2105.48,974.245 2107.46,975.026 2109.44,975.806 2111.42,976.584 2113.4,977.362 \n",
       "  2115.38,978.137 2117.35,978.912 2119.33,979.685 2121.31,980.457 2123.29,981.228 2125.27,981.997 2127.24,982.765 2129.22,983.532 2131.2,984.297 2133.18,985.061 \n",
       "  2135.16,985.824 2137.14,986.585 2139.11,987.345 2141.09,988.104 2143.07,988.861 2145.05,989.617 2147.03,990.372 2149,991.125 2150.98,991.878 2152.96,992.628 \n",
       "  2154.94,993.378 2156.92,994.126 2158.9,994.873 2160.87,995.619 2162.85,996.363 2164.83,997.106 2166.81,997.847 2168.79,998.588 2170.76,999.327 2172.74,1000.06 \n",
       "  2174.72,1000.8 2176.7,1001.54 2178.68,1002.27 2180.66,1003 2182.63,1003.73 2184.61,1004.46 2186.59,1005.19 2188.57,1005.92 2190.55,1006.64 2192.52,1007.37 \n",
       "  2194.5,1008.09 2196.48,1008.81 2198.46,1009.53 2200.44,1010.25 2202.42,1010.97 2204.39,1011.69 2206.37,1012.4 2208.35,1013.11 2210.33,1013.83 2212.31,1014.54 \n",
       "  2214.28,1015.25 2216.26,1015.95 2218.24,1016.66 2220.22,1017.37 2222.2,1018.07 2224.17,1018.77 2226.15,1019.47 2228.13,1020.17 2230.11,1020.87 2232.09,1021.57 \n",
       "  2234.07,1022.27 2236.04,1022.96 2238.02,1023.65 2240,1024.34 2241.98,1025.03 2243.96,1025.72 2245.93,1026.41 2247.91,1027.1 2249.89,1027.78 2251.87,1028.46 \n",
       "  2253.85,1029.15 2255.83,1029.83 2257.8,1030.5 2259.78,1031.18 2261.76,1031.86 2263.74,1032.53 2265.72,1033.2 2267.69,1033.88 2269.67,1034.55 2271.65,1035.21 \n",
       "  2273.63,1035.88 2275.61,1036.55 2277.59,1037.21 2279.56,1037.87 2281.54,1038.53 2283.52,1039.19 2285.5,1039.85 2287.48,1040.51 2289.45,1041.16 2291.43,1041.82 \n",
       "  2293.41,1042.47 \n",
       "  \"/>\n",
       "<polygon clip-path=\"url(#clip8500)\" points=\"\n",
       "1379.93,433.164 2280.76,433.164 2280.76,130.764 1379.93,130.764 \n",
       "  \" fill=\"#ffffff\" fill-rule=\"evenodd\" fill-opacity=\"1\"/>\n",
       "<polyline clip-path=\"url(#clip8500)\" style=\"stroke:#000000; stroke-width:4; stroke-opacity:1; fill:none\" points=\"\n",
       "  1379.93,433.164 2280.76,433.164 2280.76,130.764 1379.93,130.764 1379.93,433.164 \n",
       "  \"/>\n",
       "<polyline clip-path=\"url(#clip8500)\" style=\"stroke:#009af9; stroke-width:4; stroke-opacity:1; fill:none\" points=\"\n",
       "  1403.93,191.244 1547.93,191.244 \n",
       "  \"/>\n",
       "<g clip-path=\"url(#clip8500)\">\n",
       "<text style=\"fill:#000000; fill-opacity:1; font-family:Arial,Helvetica Neue,Helvetica,sans-serif; font-size:48px; text-anchor:start;\" transform=\"rotate(0, 1571.93, 208.744)\" x=\"1571.93\" y=\"208.744\">Adjusted first gear data</text>\n",
       "</g>\n",
       "<polyline clip-path=\"url(#clip8500)\" style=\"stroke:#e26f46; stroke-width:4; stroke-opacity:1; fill:none\" points=\"\n",
       "  1403.93,251.724 1547.93,251.724 \n",
       "  \"/>\n",
       "<g clip-path=\"url(#clip8500)\">\n",
       "<text style=\"fill:#000000; fill-opacity:1; font-family:Arial,Helvetica Neue,Helvetica,sans-serif; font-size:48px; text-anchor:start;\" transform=\"rotate(0, 1571.93, 269.224)\" x=\"1571.93\" y=\"269.224\">Second gear</text>\n",
       "</g>\n",
       "<polyline clip-path=\"url(#clip8500)\" style=\"stroke:#3da44d; stroke-width:4; stroke-opacity:1; fill:none\" points=\"\n",
       "  1403.93,312.204 1547.93,312.204 \n",
       "  \"/>\n",
       "<g clip-path=\"url(#clip8500)\">\n",
       "<text style=\"fill:#000000; fill-opacity:1; font-family:Arial,Helvetica Neue,Helvetica,sans-serif; font-size:48px; text-anchor:start;\" transform=\"rotate(0, 1571.93, 329.704)\" x=\"1571.93\" y=\"329.704\">Hypothetical single speed</text>\n",
       "</g>\n",
       "<polyline clip-path=\"url(#clip8500)\" style=\"stroke:#c271d2; stroke-width:4; stroke-opacity:1; fill:none\" points=\"\n",
       "  1403.93,372.684 1547.93,372.684 \n",
       "  \"/>\n",
       "<g clip-path=\"url(#clip8500)\">\n",
       "<text style=\"fill:#000000; fill-opacity:1; font-family:Arial,Helvetica Neue,Helvetica,sans-serif; font-size:48px; text-anchor:start;\" transform=\"rotate(0, 1571.93, 390.184)\" x=\"1571.93\" y=\"390.184\">Boosted single speed rear axle</text>\n",
       "</g>\n",
       "</svg>\n"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "boosted_single_speed_ra_max_itp(spd) = min(single_speed_ra_max_itp(spd)*370/335, 610*8.05)\n",
    "plot!(\n",
    "    spd_range,\n",
    "    boosted_single_speed_ra_max_itp.(spd_range),\n",
    "    label=\"Boosted single speed rear axle\"\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [],
   "source": [
    "F_single_speed(v,t) = (\n",
    "    min(\n",
    "        if t < boost_time\n",
    "            boosted_fa_max_itp(3.6*v*slip_ratio)/tire_r_front + boosted_single_speed_ra_max_itp(3.6*v*slip_ratio)/tire_r_rear\n",
    "        else\n",
    "            max_tq_itp(3.6*v*slip_ratio)/((tire_r_front+tire_r_rear)/2)\n",
    "        end,\n",
    "        f_traction_max\n",
    "    )\n",
    "    - 0.5*Cd*ρ*A_frontal*v^2\n",
    "    - f_rr\n",
    ")\n",
    "\n",
    "a_single_speed(v,t) = F_single_speed(v,t)/mass_veh\n",
    "\n",
    "function single_speed_perf_calc(du,u,p,t)\n",
    "    du[1] = u[2]\n",
    "    du[2] = u[3]\n",
    "    u[3] = a_single_speed(u[2],t)\n",
    "end\n",
    "\n",
    "nothing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.9162624121560072"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "condition(u,t,integrator) = u[2] - 26.8224; #60 mph in m/s\n",
    "affect!(integrator) = terminate!(integrator);\n",
    "cb = ContinuousCallback(condition,affect!);\n",
    "ss_zeroTo60_ode = ODEProblem(single_speed_perf_calc, u0, tspan);\n",
    "ss_zeroTo60 = solve(ss_zeroTo60_ode, callback=cb);\n",
    "ss_zeroTo60.t[end]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.659095605691652"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "condition(u,t,integrator) = u[1] - 0.3048; #1 ft in m\n",
    "affect!(integrator) = terminate!(integrator);\n",
    "cb = ContinuousCallback(condition, affect!);\n",
    "ss_rollout_ode = ODEProblem(single_speed_perf_calc, u0, tspan);\n",
    "ss_rollout = solve(ss_rollout_ode, callback=cb);\n",
    "ss_zeroTo60.t[end]-ss_rollout.t[end]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As a sanity check, let's look at that max torque plot again..."
   ]
  },
  {
   "cell_type": "code",
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       "  1220.06,900.44 1222.01,902.326 1223.97,904.644 1225.92,907.313 1227.87,908.125 1229.83,909.245 1231.78,912.995 1233.73,913.886 1235.69,914.681 1237.64,917.545 \n",
       "  1239.59,919.607 1241.54,920.39 1243.5,922.057 1245.45,925.291 1247.4,926.061 1249.36,926.828 1251.31,930.24 1253.26,931.695 1255.21,932.449 1257.17,934.663 \n",
       "  1259.12,937.292 1261.07,938.034 1263.03,939.053 1264.98,942.732 1266.93,943.583 1268.88,944.309 1270.84,947.074 1272.79,949.097 1274.74,951.061 1276.7,953.87 \n",
       "  1278.65,954.576 1280.6,955.343 1282.56,958.988 1284.51,960.021 1286.46,960.713 1288.41,963.227 1290.37,965.433 1292.32,966.113 1294.27,967.433 1296.23,970.811 \n",
       "  1298.18,971.481 1300.13,972.147 1302.08,975.212 1304.04,976.816 1305.99,977.471 1307.94,979.342 1309.9,982.119 1311.85,982.764 1313.8,983.439 1315.75,987.023 \n",
       "  1317.71,988.026 1319.66,988.657 1321.61,991.08 1323.57,993.257 1325.52,994.881 1327.47,997.843 1329.43,998.458 1331.38,999.069 1333.33,1002.44 1335.28,1003.63 \n",
       "  1337.24,1004.23 1339.19,1006.41 1341.14,1008.77 1343.1,1009.36 1345.05,1010.35 1347,1013.88 1348.95,1014.47 1350.91,1015.05 1352.86,1015.63 1354.81,1017.96 \n",
       "  1356.77,1020.12 1358.72,1020.68 1360.67,1021.83 1362.63,1025.16 1364.58,1025.72 1366.53,1026.27 1368.48,1026.82 1370.44,1029.32 1372.39,1031.27 1374.34,1031.81 \n",
       "  1376.3,1032.35 1378.25,1033.27 1380.2,1036.75 1382.15,1037.31 1384.11,1037.84 1386.06,1040.5 1388.01,1042.24 1389.97,1042.76 1391.92,1043.28 1393.87,1044.35 \n",
       "  1395.82,1047.65 1397.78,1048.16 1399.73,1048.67 1401.68,1049.18 1403.64,1051.61 1405.59,1053.53 1407.54,1054.03 1409.5,1055.27 1411.45,1058.36 1413.4,1058.85 \n",
       "  1415.35,1059.34 1417.31,1059.83 1419.26,1062.42 1421.21,1064.14 1423.17,1064.61 1425.12,1066.02 1427.07,1068.91 1429.02,1069.38 1430.98,1069.85 1432.93,1070.31 \n",
       "  1434.88,1073.08 1436.84,1074.59 1438.79,1075.05 1440.74,1075.5 1442.69,1076.68 1444.65,1079.76 1446.6,1080.2 1448.55,1080.65 1450.51,1083.58 1452.46,1084.89 \n",
       "  1454.41,1085.33 1456.37,1085.77 1458.32,1087.11 1460.27,1089.99 1462.22,1090.42 1464.18,1090.85 1466.13,1091.28 1468.08,1093.98 1470.04,1095.47 1471.99,1095.89 \n",
       "  1473.94,1096.31 1475.89,1097.44 1477.85,1100.5 1479.8,1100.91 1481.75,1101.32 1483.71,1101.73 1485.66,1104.21 1487.61,1105.89 1489.56,1106.29 1491.52,1106.7 \n",
       "  1493.47,1107.1 1495.42,1107.6 1497.38,1110.94 1499.33,1111.63 1501.28,1112.03 1503.24,1112.42 1505.19,1112.8 1507.14,1114.28 1509.09,1116.92 1511.05,1117.31 \n",
       "  1513,1117.69 1514.95,1118.07 1516.91,1120.9 1518.86,1122.17 1520.81,1122.55 1522.76,1122.92 1524.72,1124.17 1526.67,1127.01 1528.62,1127.38 1530.58,1127.74 \n",
       "  1532.53,1128.11 1534.48,1128.47 1536.44,1130.69 1538.39,1132.54 1540.34,1132.9 1542.29,1133.25 1544.25,1133.89 1546.2,1137.19 1548.15,1137.66 1550.11,1138.01 \n",
       "  1552.06,1138.36 1554.01,1138.71 1555.96,1140.32 1557.92,1142.75 1559.87,1143.09 1561.82,1143.43 1563.78,1143.77 1565.73,1146.74 1567.68,1147.8 1569.63,1148.13 \n",
       "  1571.59,1148.47 1573.54,1148.8 1575.49,1149.79 1577.45,1152.81 1579.4,1153.14 1581.35,1153.47 1583.31,1153.79 1585.26,1156.15 1587.21,1157.79 1589.16,1158.11 \n",
       "  1591.12,1158.43 1593.07,1158.75 1595.02,1159.14 1596.98,1162.4 1598.93,1163.05 1600.88,1163.37 1602.83,1163.68 1604.79,1163.99 1606.74,1165.35 1608.69,1167.96 \n",
       "  1610.65,1168.27 1612.6,1168.58 1614.55,1168.88 1616.5,1169.19 1618.46,1171.52 1620.41,1173.14 1622.36,1173.45 1624.32,1173.75 1626.27,1174.05 1628.22,1174.34 \n",
       "  1630.18,1174.64 1632.13,1177.55 1634.08,1178.58 1636.03,1178.88 1637.99,1179.17 1639.94,1179.46 1641.89,1180.4 1643.85,1183.39 1645.8,1183.68 1647.75,1183.97 \n",
       "  1649.7,1184.25 1651.66,1184.54 1653.61,1186.45 1655.56,1188.46 1657.52,1188.74 1659.47,1189.02 1661.42,1189.3 1663.37,1189.59 1665.33,1189.86 1667.28,1192.35 \n",
       "  1669.23,1193.77 1671.19,1194.05 1673.14,1194.32 1675.09,1194.6 1677.05,1194.87 1679,1195.14 1680.95,1198.21 1682.9,1199.03 1684.86,1199.31 1686.81,1199.58 \n",
       "  1688.76,1199.84 1690.72,1200.94 1692.67,1203.73 1694.62,1203.99 1696.57,1204.26 1698.53,1204.52 1700.48,1204.79 1702.43,1206.86 1704.39,1208.66 1706.34,1208.92 \n",
       "  1708.29,1209.19 1710.24,1209.45 1712.2,1209.71 1714.15,1209.96 1716.1,1212.62 1718.06,1213.83 1720.01,1214.08 1721.96,1214.34 1723.92,1214.6 1725.87,1214.85 \n",
       "  1727.82,1215.14 1729.77,1218.34 1731.73,1218.96 1733.68,1219.21 1735.63,1219.46 1737.59,1219.71 1739.54,1219.96 1741.49,1220.83 1743.44,1223.81 1745.4,1224.05 \n",
       "  1747.35,1224.3 1749.3,1224.55 1751.26,1224.79 1753.21,1225.04 1755.16,1226.49 1757.12,1228.88 1759.07,1229.12 1761.02,1229.36 1762.97,1229.61 1764.93,1229.85 \n",
       "  1766.88,1230.09 1768.83,1230.33 1770.79,1231.98 1772.74,1234.16 1774.69,1234.4 1776.64,1234.63 1778.6,1234.87 1780.55,1235.11 1782.5,1235.35 1784.46,1237.58 \n",
       "  1786.41,1239.17 1788.36,1239.4 1790.31,1239.64 1792.27,1239.87 1794.22,1240.1 1796.17,1240.34 1798.13,1240.57 1800.08,1242.99 1802.03,1244.38 1803.99,1244.61 \n",
       "  1805.94,1244.84 1807.89,1245.07 1809.84,1245.3 1811.8,1245.53 1813.75,1248.54 1815.7,1249.34 1817.66,1249.56 1819.61,1249.79 1821.56,1250.02 1823.51,1250.24 \n",
       "  1825.47,1250.89 1827.42,1254.04 1829.37,1254.27 1831.33,1254.49 1833.28,1254.72 1835.23,1254.94 1837.18,1255.16 1839.14,1256.39 1841.09,1258.96 1843.04,1259.18 \n",
       "  1845,1259.4 1846.95,1259.62 1848.9,1259.84 1850.86,1260.06 1852.81,1260.28 1854.76,1260.5 1856.71,1261.53 1858.67,1264.29 1860.62,1264.51 1862.57,1264.72 \n",
       "  1864.53,1264.94 1866.48,1265.16 1868.43,1265.37 1870.38,1265.59 1872.34,1266.81 1874.29,1269.37 1876.24,1269.58 1878.2,1269.8 1880.15,1270.01 1882.1,1270.23 \n",
       "  1884.05,1270.44 1886.01,1270.65 1887.96,1270.87 1889.91,1271.89 1891.87,1274.64 1893.82,1274.85 1895.77,1275.06 1897.73,1275.27 1899.68,1275.48 1901.63,1275.69 \n",
       "  1903.58,1275.9 1905.54,1276.11 1907.49,1276.93 1909.44,1279.87 1911.4,1280.08 1913.35,1280.29 1915.3,1280.5 1917.25,1280.7 1919.21,1280.91 1921.16,1281.12 \n",
       "  1923.11,1281.32 1925.07,1281.95 1927.02,1285.08 1928.97,1285.29 1930.93,1285.49 1932.88,1285.69 1934.83,1285.9 1936.78,1286.1 1938.74,1286.3 1940.69,1287.12 \n",
       "  1942.64,1290.05 1944.6,1290.26 1946.55,1290.46 1948.5,1290.66 1950.45,1290.86 1952.41,1291.06 1954.36,1291.26 1956.31,1291.46 1958.27,1292.07 1960.22,1295.2 \n",
       "  1962.17,1295.4 1964.12,1295.6 1966.08,1295.8 1968.03,1295.99 1969.98,1296.19 1971.94,1296.39 1973.89,1297.19 1975.84,1300.12 1977.8,1300.32 1979.75,1300.51 \n",
       "  1981.7,1300.71 1983.65,1300.9 1985.61,1301.09 1987.56,1301.29 1989.51,1301.48 1991.47,1302.09 1993.42,1305.21 1995.37,1305.4 1997.32,1305.59 1999.28,1305.78 \n",
       "  2001.23,1305.97 2003.18,1306.16 2005.14,1306.35 2007.09,1306.54 2009.04,1306.73 2010.99,1306.92 2012.95,1309.88 2014.9,1310.64 2016.85,1310.82 2018.81,1311.01 \n",
       "  2020.76,1311.2 2022.71,1311.38 2024.67,1311.56 2026.62,1311.75 2028.57,1311.93 2030.52,1314.7 2032.48,1315.65 2034.43,1315.83 2036.38,1316.01 2038.34,1316.19 \n",
       "  2040.29,1316.37 2042.24,1316.55 2044.19,1316.73 2046.15,1316.91 2048.1,1317.09 2050.05,1319.26 2052.01,1320.79 2053.96,1320.97 2055.91,1321.15 2057.86,1321.32 \n",
       "  2059.82,1321.5 2061.77,1321.67 2063.72,1321.85 2065.68,1322.02 2067.63,1323.99 2069.58,1325.71 2071.54,1325.89 2073.49,1326.06 2075.44,1326.23 2077.39,1326.4 \n",
       "  2079.35,1326.57 2081.3,1326.74 2083.25,1326.91 2085.21,1328.68 2087.16,1330.59 2089.11,1330.76 2091.06,1330.92 2093.02,1331.09 2094.97,1331.25 2096.92,1331.42 \n",
       "  2098.88,1331.58 2100.83,1331.74 2102.78,1331.91 2104.73,1332.07 2106.69,1332.85 2108.64,1335.74 2110.59,1335.9 2112.55,1336.06 2114.5,1336.21 2116.45,1336.37 \n",
       "  2118.41,1336.53 2120.36,1336.69 2122.31,1336.84 2124.26,1337 2126.22,1337.19 2128.17,1340.29 2130.12,1340.8 2132.08,1340.96 2134.03,1341.11 2135.98,1341.26 \n",
       "  2137.93,1341.41 2139.89,1341.56 2141.84,1341.7 2143.79,1341.85 2145.75,1344.78 2147.7,1345.49 2149.65,1345.64 2151.61,1345.78 2153.56,1345.92 2155.51,1346.07 \n",
       "  2157.46,1346.21 2159.42,1346.35 2161.37,1346.49 2163.32,1346.63 2165.28,1346.76 2167.23,1348.71 2169.18,1350.39 2171.13,1350.52 2173.09,1350.66 2175.04,1350.79 \n",
       "  2176.99,1350.92 2178.95,1351.05 2180.9,1351.18 2182.85,1351.31 2184.8,1351.44 2186.76,1352.79 2188.71,1355.05 2190.66,1355.17 2192.62,1355.3 2194.57,1355.42 \n",
       "  2196.52,1355.54 2198.48,1355.67 2200.43,1355.79 2202.38,1355.91 2204.33,1356.03 2206.29,1356.78 2208.24,1359.61 2210.19,1359.72 2212.15,1359.84 2214.1,1359.95 \n",
       "  2216.05,1360.07 2218,1360.18 2219.96,1360.29 2221.91,1360.4 2223.86,1360.5 2225.82,1360.66 2227.77,1363.71 2229.72,1364.17 2231.67,1364.27 2233.63,1364.38 \n",
       "  2235.58,1364.48 2237.53,1364.58 2239.49,1364.67 2241.44,1364.77 2243.39,1364.87 2245.35,1364.96 2247.3,1365.06 2249.25,1365.15 2251.2,1366.86 2253.16,1368.68 \n",
       "  2255.11,1368.77 2257.06,1368.85 2259.02,1368.94 2260.97,1369.02 2262.92,1369.11 2264.87,1369.19 2266.83,1369.27 2268.78,1369.35 2270.73,1369.43 2272.69,1370.15 \n",
       "  2274.64,1372.92 2276.59,1373 2278.54,1373.07 2280.5,1373.14 2282.45,1373.21 2284.4,1374.9 2286.36,1376.69 2288.31,1377.59 2290.26,1380.59 2292.22,1383.6 \n",
       "  2294.17,1386.61 \n",
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       "  946.653,636.379 948.606,636.379 950.559,636.379 952.512,636.379 954.465,636.379 956.418,637.146 958.371,638.807 960.323,640.461 962.276,642.106 964.229,643.743 \n",
       "  966.182,645.373 968.135,646.994 970.088,648.608 972.041,650.214 973.994,651.812 975.947,653.402 977.9,654.984 979.853,656.558 981.806,658.125 983.758,659.684 \n",
       "  985.711,661.236 987.664,662.78 989.617,664.316 991.57,665.845 993.523,667.366 995.476,668.879 997.429,670.385 999.382,671.884 1001.33,673.375 1003.29,674.859 \n",
       "  1005.24,676.336 1007.19,677.805 1009.15,679.267 1011.1,680.721 1013.05,682.169 1015.01,683.609 1016.96,685.042 1018.91,686.467 1020.86,687.886 1022.82,689.298 \n",
       "  1024.77,690.702 1026.72,692.1 1028.68,693.49 1030.63,694.873 1032.58,696.25 1034.53,697.62 1036.49,698.982 1038.44,700.338 1040.39,701.687 1042.35,703.029 \n",
       "  1044.3,704.365 1046.25,705.693 1048.2,707.015 1050.16,708.331 1052.11,709.639 1054.06,710.941 1056.02,712.237 1057.97,713.525 1059.92,714.807 1061.88,716.083 \n",
       "  1063.83,717.352 1065.78,718.615 1067.73,719.871 1069.69,721.121 1071.64,722.365 1073.59,723.602 1075.55,726.101 1077.5,728.826 1079.45,731.539 1081.4,734.24 \n",
       "  1083.36,736.93 1085.31,739.608 1087.26,742.275 1089.22,744.93 1091.17,747.574 1093.12,750.206 1095.07,752.828 1097.03,755.438 1098.98,758.037 1100.93,760.624 \n",
       "  1102.89,763.201 1104.84,765.767 1106.79,768.321 1108.75,770.865 1110.7,773.397 1112.65,775.919 1114.6,778.43 1116.56,780.93 1118.51,783.419 1120.46,785.898 \n",
       "  1122.42,788.366 1124.37,790.823 1126.32,793.27 1128.27,795.706 1130.23,798.132 1132.18,800.547 1134.13,802.951 1136.09,805.346 1138.04,807.73 1139.99,810.104 \n",
       "  1141.95,812.467 1143.9,814.82 1145.85,817.164 1147.8,819.497 1149.76,821.82 1151.71,824.132 1153.66,826.435 1155.62,828.728 1157.57,831.011 1159.52,833.284 \n",
       "  1161.47,835.548 1163.43,837.801 1165.38,840.045 1167.33,842.279 1169.29,844.503 1171.24,846.718 1173.19,848.923 1175.14,851.118 1177.1,853.304 1179.05,855.481 \n",
       "  1181,857.648 1182.96,859.806 1184.91,861.954 1186.86,864.093 1188.82,866.223 1190.77,868.344 1192.72,870.455 1194.67,872.557 1196.63,874.65 1198.58,876.734 \n",
       "  1200.53,878.809 1202.49,880.875 1204.44,882.932 1206.39,884.98 1208.34,887.019 1210.3,889.05 1212.25,891.071 1214.2,893.084 1216.16,895.088 1218.11,897.084 \n",
       "  1220.06,899.07 1222.01,901.048 1223.97,903.018 1225.92,904.979 1227.87,906.931 1229.83,908.875 1231.78,910.811 1233.73,912.738 1235.69,914.657 1237.64,916.567 \n",
       "  1239.59,918.47 1241.54,920.364 1243.5,922.25 1245.45,924.127 1247.4,925.997 1249.36,927.858 1251.31,929.711 1253.26,931.557 1255.21,933.394 1257.17,935.224 \n",
       "  1259.12,937.045 1261.07,938.859 1263.03,940.664 1264.98,942.462 1266.93,944.253 1268.88,946.035 1270.84,947.81 1272.79,949.577 1274.74,951.337 1276.7,953.088 \n",
       "  1278.65,954.833 1280.6,956.57 1282.56,958.299 1284.51,960.021 1286.46,961.735 1288.41,963.443 1290.37,965.142 1292.32,966.835 1294.27,968.52 1296.23,970.198 \n",
       "  1298.18,971.869 1300.13,973.532 1302.08,975.189 1304.04,976.838 1305.99,978.48 1307.94,980.115 1309.9,981.744 1311.85,983.365 1313.8,984.979 1315.75,986.586 \n",
       "  1317.71,988.187 1319.66,989.781 1321.61,991.368 1323.57,992.948 1325.52,994.521 1327.47,996.088 1329.43,997.648 1331.38,999.201 1333.33,1000.75 1335.28,1002.29 \n",
       "  1337.24,1003.82 1339.19,1005.35 1341.14,1006.87 1343.1,1008.38 1345.05,1009.89 1347,1011.39 1348.95,1012.89 1350.91,1014.38 1352.86,1015.86 1354.81,1017.34 \n",
       "  1356.77,1018.81 1358.72,1020.27 1360.67,1021.73 1362.63,1023.18 1364.58,1024.62 1366.53,1026.06 1368.48,1027.5 1370.44,1028.92 1372.39,1030.34 1374.34,1031.76 \n",
       "  1376.3,1033.17 1378.25,1034.57 1380.2,1035.97 1382.15,1037.36 1384.11,1038.75 1386.06,1040.13 1388.01,1041.5 1389.97,1042.87 1391.92,1044.24 1393.87,1045.59 \n",
       "  1395.82,1046.95 1397.78,1048.29 1399.73,1049.63 1401.68,1050.97 1403.64,1052.3 1405.59,1053.62 1407.54,1054.94 1409.5,1056.25 1411.45,1057.56 1413.4,1058.87 \n",
       "  1415.35,1060.16 1417.31,1061.45 1419.26,1062.74 1421.21,1064.02 1423.17,1065.3 1425.12,1066.57 1427.07,1067.84 1429.02,1069.1 1430.98,1070.35 1432.93,1071.6 \n",
       "  1434.88,1072.85 1436.84,1074.09 1438.79,1075.33 1440.74,1076.56 1442.69,1077.78 1444.65,1079 1446.6,1080.22 1448.55,1081.43 1450.51,1082.64 1452.46,1083.84 \n",
       "  1454.41,1085.04 1456.37,1086.23 1458.32,1087.42 1460.27,1088.6 1462.22,1089.78 1464.18,1090.95 1466.13,1092.12 1468.08,1093.28 1470.04,1094.44 1471.99,1095.6 \n",
       "  1473.94,1096.75 1475.89,1097.89 1477.85,1099.03 1479.8,1100.17 1481.75,1101.3 1483.71,1102.43 1485.66,1103.56 1487.61,1104.68 1489.56,1105.79 1491.52,1106.9 \n",
       "  1493.47,1108.01 1495.42,1109.11 1497.38,1110.21 1499.33,1111.3 1501.28,1112.39 1503.24,1113.48 1505.19,1114.56 1507.14,1115.64 1509.09,1116.71 1511.05,1117.78 \n",
       "  1513,1118.85 1514.95,1119.91 1516.91,1120.97 1518.86,1122.02 1520.81,1123.07 1522.76,1124.12 1524.72,1125.16 1526.67,1126.2 1528.62,1127.23 1530.58,1128.26 \n",
       "  1532.53,1129.29 1534.48,1130.31 1536.44,1131.33 1538.39,1132.34 1540.34,1133.35 1542.29,1134.36 1544.25,1135.37 1546.2,1136.37 1548.15,1137.36 1550.11,1138.36 \n",
       "  1552.06,1139.35 1554.01,1140.33 1555.96,1141.32 1557.92,1142.3 1559.87,1143.27 1561.82,1144.25 1563.78,1145.21 1565.73,1146.18 1567.68,1147.14 1569.63,1148.1 \n",
       "  1571.59,1149.06 1573.54,1150.01 1575.49,1150.96 1577.45,1151.9 1579.4,1152.85 1581.35,1153.78 1583.31,1154.72 1585.26,1155.65 1587.21,1156.58 1589.16,1157.51 \n",
       "  1591.12,1158.43 1593.07,1159.35 1595.02,1160.27 1596.98,1161.18 1598.93,1162.09 1600.88,1163 1602.83,1163.9 1604.79,1164.81 1606.74,1165.7 1608.69,1166.6 \n",
       "  1610.65,1167.49 1612.6,1168.38 1614.55,1169.27 1616.5,1170.15 1618.46,1171.03 1620.41,1171.91 1622.36,1172.79 1624.32,1173.66 1626.27,1174.53 1628.22,1175.4 \n",
       "  1630.18,1176.26 1632.13,1177.12 1634.08,1177.98 1636.03,1178.84 1637.99,1179.69 1639.94,1180.54 1641.89,1181.39 1643.85,1182.24 1645.8,1183.08 1647.75,1183.92 \n",
       "  1649.7,1184.76 1651.66,1185.59 1653.61,1186.42 1655.56,1187.25 1657.52,1188.08 1659.47,1188.9 1661.42,1189.73 1663.37,1190.55 1665.33,1191.36 1667.28,1192.18 \n",
       "  1669.23,1192.99 1671.19,1193.8 1673.14,1194.61 1675.09,1195.41 1677.05,1196.22 1679,1197.02 1680.95,1197.82 1682.9,1198.61 1684.86,1199.41 1686.81,1200.2 \n",
       "  1688.76,1200.99 1690.72,1201.77 1692.67,1202.56 1694.62,1203.34 1696.57,1204.12 1698.53,1204.9 1700.48,1205.67 1702.43,1206.45 1704.39,1207.22 1706.34,1207.99 \n",
       "  1708.29,1208.76 1710.24,1209.52 1712.2,1210.28 1714.15,1211.04 1716.1,1211.8 1718.06,1212.56 1720.01,1213.31 1721.96,1214.07 1723.92,1214.82 1725.87,1215.57 \n",
       "  1727.82,1216.31 1729.77,1217.06 1731.73,1217.8 1733.68,1218.54 1735.63,1219.28 1737.59,1220.02 1739.54,1220.75 1741.49,1221.49 1743.44,1222.22 1745.4,1222.95 \n",
       "  1747.35,1223.67 1749.3,1224.4 1751.26,1225.12 1753.21,1225.85 1755.16,1226.57 1757.12,1227.28 1759.07,1228 1761.02,1228.72 1762.97,1229.43 1764.93,1230.14 \n",
       "  1766.88,1230.85 1768.83,1231.56 1770.79,1232.26 1772.74,1232.97 1774.69,1233.67 1776.64,1234.37 1778.6,1235.07 1780.55,1235.77 1782.5,1236.46 1784.46,1237.16 \n",
       "  1786.41,1237.85 1788.36,1238.54 1790.31,1239.23 1792.27,1239.92 1794.22,1240.61 1796.17,1241.29 1798.13,1241.98 1800.08,1242.66 1802.03,1243.34 1803.99,1244.02 \n",
       "  1805.94,1244.69 1807.89,1245.37 1809.84,1246.04 1811.8,1246.71 1813.75,1247.38 1815.7,1248.05 1817.66,1248.72 1819.61,1249.39 1821.56,1250.05 1823.51,1250.72 \n",
       "  1825.47,1251.38 1827.42,1252.04 1829.37,1252.7 1831.33,1253.36 1833.28,1254.01 1835.23,1254.67 1837.18,1255.32 1839.14,1255.97 1841.09,1256.63 1843.04,1257.27 \n",
       "  1845,1257.92 1846.95,1258.57 1848.9,1259.22 1850.86,1259.86 1852.81,1260.5 1854.76,1261.14 1856.71,1261.78 1858.67,1262.42 1860.62,1263.06 1862.57,1263.7 \n",
       "  1864.53,1264.33 1866.48,1264.96 1868.43,1265.6 1870.38,1266.23 1872.34,1266.86 1874.29,1267.49 1876.24,1268.11 1878.2,1268.74 1880.15,1269.36 1882.1,1269.99 \n",
       "  1884.05,1270.61 1886.01,1271.23 1887.96,1271.85 1889.91,1272.47 1891.87,1273.09 1893.82,1273.7 1895.77,1274.32 1897.73,1274.93 1899.68,1275.54 1901.63,1276.15 \n",
       "  1903.58,1276.76 1905.54,1277.37 1907.49,1277.98 1909.44,1278.59 1911.4,1279.19 1913.35,1279.8 1915.3,1280.4 1917.25,1281 1919.21,1281.6 1921.16,1282.2 \n",
       "  1923.11,1282.8 1925.07,1283.4 1927.02,1283.99 1928.97,1284.59 1930.93,1285.18 1932.88,1285.78 1934.83,1286.37 1936.78,1286.96 1938.74,1287.55 1940.69,1288.14 \n",
       "  1942.64,1288.72 1944.6,1289.31 1946.55,1289.9 1948.5,1290.48 1950.45,1291.06 1952.41,1291.64 1954.36,1292.22 1956.31,1292.8 1958.27,1293.38 1960.22,1293.96 \n",
       "  1962.17,1294.54 1964.12,1295.11 1966.08,1295.69 1968.03,1296.26 1969.98,1296.83 1971.94,1297.4 1973.89,1297.97 1975.84,1298.54 1977.8,1299.11 1979.75,1299.67 \n",
       "  1981.7,1300.24 1983.65,1300.8 1985.61,1301.37 1987.56,1301.93 1989.51,1302.49 1991.47,1303.05 1993.42,1303.61 1995.37,1304.17 1997.32,1304.72 1999.28,1305.28 \n",
       "  2001.23,1305.84 2003.18,1306.39 2005.14,1306.94 2007.09,1307.49 2009.04,1308.04 2010.99,1308.59 2012.95,1309.14 2014.9,1309.69 2016.85,1310.23 2018.81,1310.78 \n",
       "  2020.76,1311.32 2022.71,1311.87 2024.67,1312.41 2026.62,1312.95 2028.57,1313.49 2030.52,1314.03 2032.48,1314.56 2034.43,1315.1 2036.38,1315.64 2038.34,1316.17 \n",
       "  2040.29,1316.7 2042.24,1317.24 2044.19,1317.77 2046.15,1318.3 2048.1,1318.82 2050.05,1319.35 2052.01,1319.88 2053.96,1320.4 2055.91,1320.93 2057.86,1321.45 \n",
       "  2059.82,1321.97 2061.77,1322.49 2063.72,1323.01 2065.68,1323.53 2067.63,1324.05 2069.58,1324.57 2071.54,1325.08 2073.49,1325.6 2075.44,1326.11 2077.39,1326.62 \n",
       "  2079.35,1327.13 2081.3,1327.64 2083.25,1328.15 2085.21,1328.66 2087.16,1329.16 2089.11,1329.67 2091.06,1330.17 2093.02,1330.67 2094.97,1331.17 2096.92,1331.67 \n",
       "  2098.88,1332.17 2100.83,1332.67 2102.78,1333.17 2104.73,1333.66 2106.69,1334.15 2108.64,1334.65 2110.59,1335.14 2112.55,1335.63 2114.5,1336.12 2116.45,1336.61 \n",
       "  2118.41,1337.09 2120.36,1337.58 2122.31,1338.06 2124.26,1338.54 2126.22,1339.03 2128.17,1339.51 2130.12,1339.98 2132.08,1340.46 2134.03,1340.94 2135.98,1341.41 \n",
       "  2137.93,1341.89 2139.89,1342.36 2141.84,1342.83 2143.79,1343.3 2145.75,1343.77 2147.7,1344.23 2149.65,1344.7 2151.61,1345.16 2153.56,1345.63 2155.51,1346.09 \n",
       "  2157.46,1346.55 2159.42,1347.01 2161.37,1347.46 2163.32,1347.92 2165.28,1348.37 2167.23,1348.83 2169.18,1349.28 2171.13,1349.73 2173.09,1350.18 2175.04,1350.62 \n",
       "  2176.99,1351.07 2178.95,1351.51 2180.9,1351.96 2182.85,1352.4 2184.8,1352.84 2186.76,1353.28 2188.71,1353.71 2190.66,1354.15 2192.62,1354.58 2194.57,1355.01 \n",
       "  2196.52,1355.44 2198.48,1355.87 2200.43,1356.3 2202.38,1356.72 2204.33,1357.15 2206.29,1357.57 2208.24,1357.99 2210.19,1358.41 2212.15,1358.83 2214.1,1359.24 \n",
       "  2216.05,1359.66 2218,1360.07 2219.96,1360.48 2221.91,1360.89 2223.86,1361.3 2225.82,1361.7 2227.77,1362.11 2229.72,1362.51 2231.67,1362.91 2233.63,1363.31 \n",
       "  2235.58,1363.71 2237.53,1364.1 2239.49,1364.49 2241.44,1364.89 2243.39,1365.27 2245.35,1365.66 2247.3,1366.05 2249.25,1366.43 2251.2,1366.81 2253.16,1367.19 \n",
       "  2255.11,1367.57 2257.06,1367.95 2259.02,1368.32 2260.97,1368.7 2262.92,1369.07 2264.87,1369.44 2266.83,1369.8 2268.78,1370.17 2270.73,1370.53 2272.69,1370.89 \n",
       "  2274.64,1371.25 2276.59,1371.61 2278.54,1371.96 2280.5,1372.31 2282.45,1372.66 2284.4,1373.01 2286.36,1373.36 2288.31,1373.7 2290.26,1374.04 2292.22,1374.38 \n",
       "  2294.17,1374.72 \n",
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       "<text style=\"fill:#000000; fill-opacity:1; font-family:Arial,Helvetica Neue,Helvetica,sans-serif; font-size:48px; text-anchor:start;\" transform=\"rotate(0, 1443.65, 329.704)\" x=\"1443.65\" y=\"329.704\">Optimal traction limit</text>\n",
       "</g>\n",
       "</svg>\n"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plot(\n",
    "    spd_range, \n",
    "    boosted_fa_max_itp.(spd_range)+boosted_ra_max_itp.(spd_range),\n",
    "    label=\"Turbo S Overboost with transmission\",\n",
    "    xlabel = \"Speed (kph)\",\n",
    "    ylabel = \"Wheel torque (Nm)\",\n",
    "    ylimit = [0 13000]\n",
    ")\n",
    "plot!(\n",
    "    spd_range,\n",
    "    boosted_fa_max_itp.(spd_range)+boosted_single_speed_ra_max_itp.(spd_range),\n",
    "    label = \"Single Speed Turbo S Overboost\"\n",
    ")\n",
    "plot!(spd_range, traction_limit_tq*ones(size(spd_range)), label=\"Optimal traction limit\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So yes, the torque to the wheels is dramatically lowered, but it's still more than the tires can handle, so the performance is identical. It's possible this way of running the rear motor allows Porsche to have better sustained performance, as it may be more efficient at another operating point and therefore reject less heat. It may also be a matter of durability, weight transfer during acceleration, or a million of the messy concerns that pop up during actually building a vehicle. Still, the reason of \"performance\" for the selection of a transmission seems... suspect. Transmissions add considerably more complexity than a simple gearbox, so I'm sure Porsche has a good reason... right?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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