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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"<div align=\"right\"><i>Peter Norvig, 23 Oct, 2017</i></div>\n",
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"\n",
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"# Bike Speed versus Grade\n",
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"\n",
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"Like most people, I bike slower when I'm going up a steep hill than on a flat road. But how much slower?\n",
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"To answer that, I downloaded data on my past rides \n",
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"from [Strava](https://www.strava.com/athletes/575579) and manipulated the `data` to create two lists: \n",
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"\n",
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"- `X`: the *grade* of each ride, in feet of ascent per mile. \n",
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"- `Y`: the *speed* of each (corresponding) ride, in miles per hour.\n",
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"\n",
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"I omit rides shorter than 30 miles, because on some short rides I was sprinting at an unsustainable speed, and on others I was slowed by city traffic. Here is the code to collect and plot the X:Y data:"
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"To answer that, I downloaded all my recorded past rides \n",
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"on [Strava](https://www.strava.com/athletes/575579) that are longer than 20 miles, out them into a text file `\"bikerides20.txt\"`, and wrote code to parse the file:"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 1,
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"metadata": {},
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"metadata": {
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"collapsed": false
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},
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"outputs": [],
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"source": [
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"%matplotlib inline\n",
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"import matplotlib.pyplot as plt\n",
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"import numpy as np\n",
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"import csv\n",
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"from collections import namedtuple\n",
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"\n",
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"def hours(sec): return float(sec) / 60 / 60\n",
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"def feet(meters): return float(meters) * 100 / 2.54 / 12\n",
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"def miles(meters): return feet(meters) / 5280\n",
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"line = 'Ride\tThu, 8/9/2018\tBRNW\t4:58:07\t68.41 mi\t3,862 ft\t' # Sample line\n",
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"\n",
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"# Read data file with three fields: distance (m), climb (m), elapsed time (sec)\n",
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"X, Y = [], []\n",
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"for (dist, climb, time) in csv.reader(open('dist-climb-time.csv')):\n",
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" if miles(dist) > 30:\n",
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" X.append(feet(climb) / miles(dist))\n",
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" Y.append(miles(dist) / hours(time))"
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"Ride = namedtuple('Ride', 'date, title, hours, miles, feet')\n",
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"\n",
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"def parse_ride(line) -> Ride:\n",
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" \"Turn a line (such as `sample`) in a Strava datafile into a `Ride`.\"\n",
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" _, date, title, time, mi, ft = line.strip().split('\\t')\n",
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" times = map(int, time.split(':')[::-1])\n",
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" miles = float(mi.split()[0])\n",
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" feet = int(ft.split()[0].replace(',', ''))\n",
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" return Ride(date, title, hours(*times), miles, feet)\n",
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"\n",
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"def hours(sec, min, hour=0): return hour + min / 60 + sec / 3600\n",
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"\n",
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"all_rides = {parse_ride(line) for line in open('bikerides20.txt')}"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"For some of the rides, the GPS was not recording elevation, so the feet field is 0. Let's eliminate those, and let's collect two vectors of numbers: one for miles per hour, and one for feet climbed per hour, and plot them:"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 2,
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"metadata": {},
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"metadata": {
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"collapsed": false
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},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"Kept 583 out of 609 rides\n"
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]
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},
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{
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"data": {
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truncated
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"image/png": 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truncated
|
||||
"text/plain": [
|
||||
"<matplotlib.figure.Figure at 0x105166cc0>"
|
||||
"<matplotlib.figure.Figure at 0x110651668>"
|
||||
]
|
||||
},
|
||||
"metadata": {},
|
||||
@@ -56,28 +76,33 @@
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"plt.plot(X, Y, 'o');"
|
||||
"rides = [r for r in all_rides if r.feet > 0]\n",
|
||||
"mph = [r.miles / r.hours for r in rides]\n",
|
||||
"fpm = [r.feet / r.miles for r in rides]\n",
|
||||
"\n",
|
||||
"plt.plot(fpm, mph, '.')\n",
|
||||
"print('Kept', len(rides), 'out of', len(all_rides), 'rides')"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"As expected, the speeds get slower as the grade gets steeper. The data has a lot of variance, and I can say that it \n",
|
||||
"looks more like a curve than a straight line, so I'll fit a cubic (degree two) polynomial to the data,\n",
|
||||
"and make the plot prettier:"
|
||||
"As expected, there is a lot of variance, but overall speeds get slower as the grade gets steeper. Just eyeballing it, it looks like a curve would be a better fit than a straight line, so I'll fit a cubic (degree two) polynomial to the data, and make the plot prettier:"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 3,
|
||||
"metadata": {},
|
||||
"metadata": {
|
||||
"collapsed": false
|
||||
},
|
||||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"image/png": 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truncated
|
||||
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAykAAAIICAYAAABq7aFNAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
|
||||
"text/plain": [
|
||||
"<matplotlib.figure.Figure at 0x10b1d1390>"
|
||||
"<matplotlib.figure.Figure at 0x119e6f860>"
|
||||
]
|
||||
},
|
||||
"metadata": {},
|
||||
@@ -90,40 +115,39 @@
|
||||
" C = np.polyfit(X, Y, n)[::-1] # Array of coefficients, reversed\n",
|
||||
" return lambda x: sum(C[i] * x ** i for i in range(n + 1)) \n",
|
||||
"\n",
|
||||
"F = poly(X, Y, 2) # defines y = F(x); x in ft/mile, y in mph\n",
|
||||
"\n",
|
||||
"def show(X, Y, F=F): \n",
|
||||
"def show(X, Y, xlabel='Grade (feet/mile)', ylabel='Speed (mph)', fit=True): \n",
|
||||
" F = poly(X, Y, 2)\n",
|
||||
" plt.rcParams[\"figure.figsize\"] = (12, 8)\n",
|
||||
" plt.style.use('fivethirtyeight')\n",
|
||||
" plt.plot(X, Y, 'o')\n",
|
||||
" X1 = list(range(int(max(X))))\n",
|
||||
" plt.plot(X1, [F(x) for x in X1], '-')\n",
|
||||
" plt.ylabel('Speed (mph)')\n",
|
||||
" plt.xlabel('Grade (feet/mile)')\n",
|
||||
" plt.plot(X, Y, '.')\n",
|
||||
" X1 = list(range(int(min(X)), int(max(X)) + 5))\n",
|
||||
" if fit: plt.plot(X1, [F(x) for x in X1], '-')\n",
|
||||
" plt.ylabel(ylabel); plt.xlabel(xlabel)\n",
|
||||
" plt.minorticks_on()\n",
|
||||
" plt.grid(True, which='major')\n",
|
||||
" plt.grid(True, which='minor', alpha=0.4)\n",
|
||||
" plt.title('Average speed vs Grade on {} rides'.format(len(X)))\n",
|
||||
" \n",
|
||||
"show(X, Y) "
|
||||
" \n",
|
||||
"show(fpm, mph) "
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"So, I average about 14 mph when the road is fairly flat, with a lot of variability from 12 to 16 mph, depending more on my level of effort than on the grade of the road. But from 60 ft/mile and up, speed falls off quickly at 1 mph for every 20 ft/mile, and by 120 ft/mile, I'm down around 10 mph, and 8.5mph at 140 ft/mile. Note that 140 ft/mile is only 2.7% grade, but if you figure a typical route is 1/3 up, 1/3 down, and 1/3 flat-ish, then that's 8% grade on the up part.\n",
|
||||
"So, I average a little under 14 mph when the overall route is fairly flat, with a lot of variability from 12 to 16 mph, depending more on my level of effort than on the grade of the road. But from 40 ft/mile and up, speed falls off quickly, and by 140 ft/mile, I'm down under 8 mph. Note that 140 ft/mile is only 2.7% grade, but if you figure a typical route is 1/3 up, 1/3 down, and 1/3 flatish, then that's 8% grade on the up part (which is at least 7 miles).\n",
|
||||
"\n",
|
||||
"I can use the polynomial `F` to estimate the duration of a route:"
|
||||
"I can use the `poly` function to estimate the duration of a route:"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 4,
|
||||
"metadata": {},
|
||||
"metadata": {
|
||||
"collapsed": true
|
||||
},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"def duration(dist, climb, F=F):\n",
|
||||
"def duration(dist, climb, F=poly(fpm, mph, 2)):\n",
|
||||
" \"Given a distance in miles and total climb in feet, return estimated time in minutes.\"\n",
|
||||
" return dist / F(climb / dist) * 60"
|
||||
]
|
||||
@@ -132,18 +156,20 @@
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"For example, to get to Pescadero from La Honda, I could take the flatter [coast route](https://www.google.com/maps/dir/La+Honda,+California/Pescadero,+California/@37.2905834,-122.3896683,12z/data=!4m19!4m18!1m10!1m1!1s0x808faed4dc6265bd:0x51a109d3306a7219!2m2!1d-122.274227!2d37.3190255!3m4!1m2!1d-122.4039496!2d37.3116594!3s0x808f062b7d7585e7:0x942480c22f110b74!1m5!1m1!1s0x808f00b4b613c4c1:0x43c609077878b77!2m2!1d-122.3830152!2d37.2551636!3e1), or the shorter [creek route](https://www.google.com/maps/dir/La+Honda,+California/Pescadero,+California/@37.2905834,-122.3896683,12z/data=!4m19!4m18!1m10!1m1!1s0x808faed4dc6265bd:0x51a109d3306a7219!2m2!1d-122.274227!2d37.3190255!3m4!1m2!1d-122.3658887!2d37.2538867!3s0x808f00acf265bd43:0xb7e2a0c9ee355c3a!1m5!1m1!1s0x808f00b4b613c4c1:0x43c609077878b77!2m2!1d-122.3830152!2d37.2551636!3e1):"
|
||||
"For example, to get to Pescadero from La Honda, I could take the flatter [coast route](https://www.google.com/maps/dir/La+Honda,+California/Pescadero,+California/@37.2905834,-122.3896683,12z/data=!4m19!4m18!1m10!1m1!1s0x808faed4dc6265bd:0x51a109d3306a7219!2m2!1d-122.274227!2d37.3190255!3m4!1m2!1d-122.4039496!2d37.3116594!3s0x808f062b7d7585e7:0x942480c22f110b74!1m5!1m1!1s0x808f00b4b613c4c1:0x43c609077878b77!2m2!1d-122.3830152!2d37.2551636!3e1), or the shorter [creek route](https://www.google.com/maps/dir/La+Honda,+California/Pescadero,+California/@37.2905834,-122.3896683,12z/data=!4m19!4m18!1m10!1m1!1s0x808faed4dc6265bd:0x51a109d3306a7219!2m2!1d-122.274227!2d37.3190255!3m4!1m2!1d-122.3658887!2d37.2538867!3s0x808f00acf265bd43:0xb7e2a0c9ee355c3a!1m5!1m1!1s0x808f00b4b613c4c1:0x43c609077878b77!2m2!1d-122.3830152!2d37.2551636!3e1); which is faster?"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 5,
|
||||
"metadata": {},
|
||||
"metadata": {
|
||||
"collapsed": false
|
||||
},
|
||||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"text/plain": [
|
||||
"6.2641828504384378"
|
||||
"(69.426193865785734, 61.816569346397067)"
|
||||
]
|
||||
},
|
||||
"execution_count": 5,
|
||||
@@ -152,17 +178,167 @@
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"coast = duration(15.7, 344)\n",
|
||||
"creek = duration(13.5, 735)\n",
|
||||
"\n",
|
||||
"coast - creek"
|
||||
"duration(15.7, 344), duration(13.5, 735)"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"This says the coast route takes 6.7 minutes longer. Good to know, but other factors are probably more important in making the choice."
|
||||
"This suggests the coast route takes 7 or 8 minutes longer. Good to know, but other factors (like the scenery) are probably more important in making the choice.\n",
|
||||
"\n",
|
||||
"# Eddington Number\n",
|
||||
"\n",
|
||||
"> *Your [Eddington Number](https://www.triathlete.com/2011/04/training/measuring-bike-miles-eddington-number_301789) is the largest integer **m** for which you have bicycled **m** or more miles on **m** different days.*\n",
|
||||
"\n",
|
||||
"Let's calculate mine, and see how many rides I need to take to improve it. I'm pretty sure I've done at least 50 rides of 50 miles, so:"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 6,
|
||||
"metadata": {
|
||||
"collapsed": false
|
||||
},
|
||||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"text/plain": [
|
||||
"{50: -17,\n",
|
||||
" 51: -5,\n",
|
||||
" 52: 0,\n",
|
||||
" 53: 3,\n",
|
||||
" 54: 7,\n",
|
||||
" 55: 10,\n",
|
||||
" 56: 12,\n",
|
||||
" 57: 16,\n",
|
||||
" 58: 20,\n",
|
||||
" 59: 26,\n",
|
||||
" 60: 28,\n",
|
||||
" 61: 34,\n",
|
||||
" 62: 37,\n",
|
||||
" 63: 40,\n",
|
||||
" 64: 43,\n",
|
||||
" 65: 45,\n",
|
||||
" 66: 47,\n",
|
||||
" 67: 51,\n",
|
||||
" 68: 52,\n",
|
||||
" 69: 56,\n",
|
||||
" 70: 57}"
|
||||
]
|
||||
},
|
||||
"execution_count": 6,
|
||||
"metadata": {},
|
||||
"output_type": "execute_result"
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"{m: m - sum(r.miles > m for r in rides)\n",
|
||||
" for m in range(50, 71)}"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"The entry `{52: 0}` means **my Eddington Number is 52**: I've done 52 rides of 52 miles or more (at least of the ones that were recorded by Strava). I'd need only 3 rides of 53 miles to add one to my number, but I'd need a whopping 57 rides of 70 miles or more to get my number up to 70. Let's look at my distribution of ride distances, for my 40+ mile rides:"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 7,
|
||||
"metadata": {
|
||||
"collapsed": false
|
||||
},
|
||||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"image/png": 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truncated
|
||||
"text/plain": [
|
||||
"<matplotlib.figure.Figure at 0x119e0d9b0>"
|
||||
]
|
||||
},
|
||||
"metadata": {},
|
||||
"output_type": "display_data"
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"X = range(40, 101)\n",
|
||||
"M = [min(X), max(X)]\n",
|
||||
"plt.plot(M, M, '-')\n",
|
||||
"show(X, [sum(r.miles > x for r in rides) for x in X], fit=False,\n",
|
||||
" xlabel='Ride Distance (miles)', ylabel='Number of Rides longer than x miles')"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"Here the gap between the straight line and the dotted line is my Eddington gap: the lines cross at 52 so that's my Eddington Number; at 60 miles the gap is 28.\n",
|
||||
"\n",
|
||||
"## Metric Eddington Number\n",
|
||||
"\n",
|
||||
"[Arthur Eddington](https://en.wikipedia.org/wiki/Arthur_Eddington) was born in 19th century England, so he used miles. You can get a more impressive number with your **metric** Eddington Number:"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 8,
|
||||
"metadata": {
|
||||
"collapsed": false
|
||||
},
|
||||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"text/plain": [
|
||||
"{70: -22,\n",
|
||||
" 71: -17,\n",
|
||||
" 72: -12,\n",
|
||||
" 73: -5,\n",
|
||||
" 74: -1,\n",
|
||||
" 75: 2,\n",
|
||||
" 76: 4,\n",
|
||||
" 77: 6,\n",
|
||||
" 78: 9,\n",
|
||||
" 79: 11,\n",
|
||||
" 80: 13,\n",
|
||||
" 81: 17,\n",
|
||||
" 82: 26,\n",
|
||||
" 83: 28,\n",
|
||||
" 84: 33,\n",
|
||||
" 85: 35,\n",
|
||||
" 86: 37,\n",
|
||||
" 87: 40,\n",
|
||||
" 88: 42,\n",
|
||||
" 89: 44,\n",
|
||||
" 90: 46}"
|
||||
]
|
||||
},
|
||||
"execution_count": 8,
|
||||
"metadata": {},
|
||||
"output_type": "execute_result"
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"def kms(ride): return ride.miles * 1.60934\n",
|
||||
"\n",
|
||||
"{m: m - sum(kms(r) > m for r in rides)\n",
|
||||
" for m in range(70, 91)}"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"My metric Eddington Number is 74, and I only need 13 rides of 80 km (50 miles) to get to 80.\n",
|
||||
"\n",
|
||||
"# H-Index\n",
|
||||
"\n",
|
||||
"Inspired by the [h-index](https://en.wikipedia.org/wiki/H-index) for scientific publications (and indirectly by Eddington), I invented a new h-index, or hill-index:\n",
|
||||
"\n",
|
||||
"> *Your **h-index** is the largest integer **h** for which you can persistently and repeatedly climb an **h** percent grade at **h** miles per hour.*\n",
|
||||
"\n",
|
||||
"My h-index is 6, because I regularly climb a 6% grade at 6 miles per hour or more, but I only occasionally climb a 7% grade at 7 mph. What's yours?"
|
||||
]
|
||||
}
|
||||
],
|
||||
@@ -182,7 +358,7 @@
|
||||
"name": "python",
|
||||
"nbconvert_exporter": "python",
|
||||
"pygments_lexer": "ipython3",
|
||||
"version": "3.5.3"
|
||||
"version": "3.6.0"
|
||||
}
|
||||
},
|
||||
"nbformat": 4,
|
||||
|
||||
Reference in new issue
Block a user