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Peter Norvig authored and 
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@@ -9,8 +9,8 @@
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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 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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"To answer that, I downloaded all my recorded past rides longer than 20 miles as ([bikerides20.txt](bikerides20.txt)). (I started recording using \n",
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"[Strava](https://www.strava.com/athletes/575579) in mid-2013, but didn't use it across all rides until 2015). Here I parse the file:"
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]
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},
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{
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@@ -28,17 +28,17 @@
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"\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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"Ride = namedtuple('Ride', 'date, title, hours, miles, feet')\n",
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"Ride = namedtuple('Ride', 'miles, feet, kind, date, title, hours')\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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" \"Parse a line from a Strava datafile into a `Ride`.\"\n",
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" kind, date, title, time, mi, ft = line.strip().split('\\t')\n",
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" times = [int(t) for t in reversed(time.split(':'))]\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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" return Ride(miles, feet, kind, date, title, hours(*times))\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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"def hours(sec, min, hour=0): return sec / 3600 + min / 60 + hour\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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@@ -47,7 +47,7 @@
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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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"I'm interested in my \"serious\" rides, so I'll focus on `rides` that are at least a marathon (26 miles) in length, and for those rides collect three vectors of numbers: miles per hour, feet climbed per mile, and total miles:"
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]
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},
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{
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@@ -57,18 +57,11 @@
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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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"image/png": 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truncated
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"image/png": "iVBORw0KGgoAAAANSUhEUgAAAXUAAAD8CAYAAACINTRsAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
|
||||
"text/plain": [
|
||||
"<matplotlib.figure.Figure at 0x110651668>"
|
||||
"<matplotlib.figure.Figure at 0x1037d2c88>"
|
||||
]
|
||||
},
|
||||
"metadata": {},
|
||||
@@ -76,19 +69,19 @@
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"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",
|
||||
"rides = [r for r in all_rides if r.miles > 26]\n",
|
||||
"mph = [r.miles / r.hours for r in rides]\n",
|
||||
"fpm = [r.feet / r.miles for r in rides]\n",
|
||||
"mls = [r.miles for r in rides]\n",
|
||||
"\n",
|
||||
"plt.plot(fpm, mph, '.')\n",
|
||||
"print('Kept', len(rides), 'out of', len(all_rides), 'rides')"
|
||||
"plt.scatter(fpm, mph);"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"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:"
|
||||
"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 quadratic (degree two) polynomial to the data, and make the plot prettier:"
|
||||
]
|
||||
},
|
||||
{
|
||||
@@ -100,9 +93,9 @@
|
||||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"image/png": 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truncated
|
||||
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAykAAAJ9CAYAAAAxAj0/AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
|
||||
"text/plain": [
|
||||
"<matplotlib.figure.Figure at 0x119e6f860>"
|
||||
"<matplotlib.figure.Figure at 0x10cfa0780>"
|
||||
]
|
||||
},
|
||||
"metadata": {},
|
||||
@@ -116,16 +109,17 @@
|
||||
" return lambda x: sum(C[i] * x ** i for i in range(n + 1)) \n",
|
||||
"\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.rcParams[\"figure.figsize\"] = (12, 10)\n",
|
||||
" plt.style.use('fivethirtyeight')\n",
|
||||
" plt.plot(X, Y, '.')\n",
|
||||
" plt.scatter(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",
|
||||
" if fit: \n",
|
||||
" F = poly(X, Y, 2)\n",
|
||||
" plt.plot(X1, [F(x) for x in X1], 'k-')\n",
|
||||
" \n",
|
||||
"show(fpm, mph) "
|
||||
]
|
||||
@@ -134,9 +128,11 @@
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"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",
|
||||
"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 around 40 or 50 ft/mile, speed falls off quickly, and by 140 ft/mile, I'm down near 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.\n",
|
||||
"\n",
|
||||
"I can use the `poly` function to estimate the duration of a route:"
|
||||
"# Estimating Duration\n",
|
||||
"\n",
|
||||
"For a route with a given distance and elevation, how long will it take to ride it?"
|
||||
]
|
||||
},
|
||||
{
|
||||
@@ -149,7 +145,7 @@
|
||||
"source": [
|
||||
"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"
|
||||
" return 60 * dist / F(climb / dist)"
|
||||
]
|
||||
},
|
||||
{
|
||||
@@ -169,7 +165,7 @@
|
||||
{
|
||||
"data": {
|
||||
"text/plain": [
|
||||
"(69.426193865785734, 61.816569346397067)"
|
||||
"(68.914878773787706, 62.368854685107713)"
|
||||
]
|
||||
},
|
||||
"execution_count": 5,
|
||||
@@ -189,7 +185,7 @@
|
||||
"\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",
|
||||
"> *Your [Eddington Number](https://www.triathlete.com/2011/04/training/measuring-bike-miles-eddington-number_301789) is the largest integer **e** for which you have bicycled **e** or more miles on **e** 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:"
|
||||
]
|
||||
@@ -204,27 +200,7 @@
|
||||
{
|
||||
"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}"
|
||||
"52"
|
||||
]
|
||||
},
|
||||
"execution_count": 6,
|
||||
@@ -233,15 +209,17 @@
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"{m: m - sum(r.miles > m for r in rides)\n",
|
||||
" for m in range(50, 71)}"
|
||||
"def eddington(distances):\n",
|
||||
" return max(e for e, d in enumerate(sorted(distances, reverse=True), 1) if d >= e)\n",
|
||||
"\n",
|
||||
"eddington(mls)"
|
||||
]
|
||||
},
|
||||
{
|
||||
"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:"
|
||||
"So **my Eddington Number is 52**: I've done 52 rides of 52 miles or more. Let's see a plot of how far I have to go to improve this number:"
|
||||
]
|
||||
},
|
||||
{
|
||||
@@ -253,9 +231,9 @@
|
||||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"image/png": 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truncated
|
||||
"image/png": 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truncated
|
||||
"text/plain": [
|
||||
"<matplotlib.figure.Figure at 0x119e0d9b0>"
|
||||
"<matplotlib.figure.Figure at 0x10cf8b940>"
|
||||
]
|
||||
},
|
||||
"metadata": {},
|
||||
@@ -263,22 +241,25 @@
|
||||
}
|
||||
],
|
||||
"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')"
|
||||
"def edplot(distances, X):\n",
|
||||
" M = [min(X), max(X)]\n",
|
||||
" plt.plot(M, M, 'r-')\n",
|
||||
" plt.title('Eddington Number = {}'.format(eddington(distances)))\n",
|
||||
" show(X, [sum(d > x for d in distances) for x in X], fit=False,\n",
|
||||
" xlabel='Ride Distance', ylabel='Number of Rides longer than distance')\n",
|
||||
" \n",
|
||||
"edplot(mls, range(46, 81))"
|
||||
]
|
||||
},
|
||||
{
|
||||
"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",
|
||||
"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, so I nneed 28 60+ mile rides to get an Eddington number of 60.\n",
|
||||
"\n",
|
||||
"## Metric Eddington Number\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:"
|
||||
"[Arthur Eddington](https://en.wikipedia.org/wiki/Arthur_Eddington) was born in 19th century England, so he used miles. You can get a bigger number using kilometers:"
|
||||
]
|
||||
},
|
||||
{
|
||||
@@ -290,40 +271,17 @@
|
||||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"image/png": 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truncated
|
||||
"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}"
|
||||
"<matplotlib.figure.Figure at 0x1038734a8>"
|
||||
]
|
||||
},
|
||||
"execution_count": 8,
|
||||
"metadata": {},
|
||||
"output_type": "execute_result"
|
||||
"output_type": "display_data"
|
||||
}
|
||||
],
|
||||
"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)}"
|
||||
"edplot([m * 1.60934 for m in mls], range(70, 101))"
|
||||
]
|
||||
},
|
||||
{
|
||||
|
||||
Reference in new issue
Block a user