This article is from the Misc Bicycles FAQs, by various authors.

Symbols:

av = average speed of a ride measured while the wheels are turning. (mph or kph) C = 1.37E-3. Calories (kcals) burned by the human body to raise one pound mass one vertical foot. This assumes a body efficiency of 24.9% and a transmission efficiency of 95%. OR C = 9.91E-3. Calories (kcals) burned to raise one kilogram one vertical meter. This assumes a body efficiency of 24.9% and a transmission efficiency of 95%. d = distance traveled. (miles or kilometers) D = the Calorie-equivalent amount of vertical climbing in feet or meters to one mile or kilometer of flat-land riding for a particular cyclist at a particular speed (mph or kph). D is called the cyclist's divisor. F = 1 assuming no energy is expended while coasting down a 6% grade. However, since the body expends some energy, F is set less than one. ([unitless]) g = gross climbing. (feet or meters) index = Calorie-equivalent flat-land riding miles or kilometers at speed v. irp = Index Rate of Progress, the average index speed of a ride including all stops and rests. (mph or kph) K = Calories burned for one mile or kilometer of flat-land riding at speed v. mirp = while-Moving Index Rate of Progress, the average index speed of a ride measured while the wheels are turning. (mph or kph) n = net climbing (feet or meters), current elevation minus starting elevation. t = total time including stops for an entire ride, ending time minus starting time. (hours) TC = total Calories burned for whole ride. v = normal instantaneous cruising speed on flat ground without ambient wind and in the chosen riding position on the bicycle. This should be a speed that can be comfortable maintained for an extended period. (mph or kph) W = total weight of the cyclist. (pounds mass or kilograms)

C is given.

av, d, g, and v may be read directly from an Avocet 50 cyclcomputer. av is

the value stored in the "average speed" buffer, and v is the instantaneous

velocity when riding under the conditions described above.

D is calculated.

F is guessed.

index is calculated.

irp is calculated.

K is calculated.

mirp is calculated

n and t may be calculated from data provided by an Avocet 50 cyclecomputer at

the beginning and at the end of a ride.

TC is calculated.

W is measured.

Note: A dietary calorie is equivalent to a kcal or Calorie.

K can be calculated with the assistance of Ken Robert's bike_power program.

Enter arguments for the following options: -wm, -wc, -a, and -v. For -wm,

enter the weight of the bicycle and accessories (water bottles, clothing,

kickstand, etc.) For -wc, enter your unclothed body weight. For argument -v,

use v, your normal instantaneous cruising speed on flat ground, a speed that

can be comfortably maintained for an extended period. Do not include stops.

Finally, enter a quadratic coefficient of air resistance (-a) that reflects you

r

typical riding position:

position a ---------- ----- standing 0.36 hoods or top 0.27 on the drops 0.172 tuck 0.145 drafting 0.12

If SI units are used, the +M option must be applied first and the -M option

must be applied last. See examples.

Take the Cal/hr figure returned by bike_power in the right-hand column and

divide by the argument you supplied for -v. This is K, your calories burned

per mile or kilometer of flat, windless riding at the chosen speed, v.

D is calculated by the following formula:

[English]:

D ft/mi = (K Cal/mi) / ((C Cal/(ft*lb))*(W lb))

[SI]:

D m/km = (K Cal/km) / ((C Cal/(m*kg))*(W kg))

or

D = K / (C*W)

F is determined by educated guess. The purpose of F is to allow some credit fo

r

expending energy on the downhills. The more you pedal on the downhills, the

lower F should be. If you only coast down hills, then F = 1. If you pedal

lightly or sometimes, then a reasonable value might be 0.9. If you hammer

down the hills, you might use F = 0.7 or so. F is always less than one.

Total Calories burned accounting for climbing and net climbing on an entire

ride is determined by:

[English]:

TC Cal = (K Cal/mi) * [(d mi) + (n ft) / (D ft/mi) + (g ft - n ft) / (2*F*(D ft/mi))]

[SI]:

TC Cal = (K Cal/km) * [(d km) + (n m) / (D m/km) + (g m - n m) / (2*F*(D m/km))]

or

TC = K * [d + n/D + (g - n)/(2*F*D)]

The first term, d, gives credit for distance covered. The second term, n/D,

gives credit for hills climbed but not descended, the net climbing credit. The

third term, (g-n)/(2*F*D), gives credit for gross climbing and descending

according to descending style, F, and deducts net climbing credit awarded by th

e

second term.

Divide through by K to obtain the index or equivalent flat-land miles.

index = d + n/D + (g - n)/(2*F*D)

For loop rides, rides that start and end in the same place, n equals zero, and

the formula simplifies:

TC = K * [d + g/(2*F*D)]

index = d + g/(2*F*D)

In addition to index, other useful quantities are "Index Rate of Progress", irp

,

and "while-Moving Index Rate of Progress", mirp. These can be calculated with

the following formulas:

[English]:

irp mph = (index miles) / (t hours)

[SI]:

irp kph = (index km) / (t hours)

[English]:

mirp mph = (index miles) / [(d miles) / (av miles/hour)]

[SI]:

mirp kph = (index km) / [(d km) / (av km/hour)]

or

irp = index / t

mirp = index / (d / av)

irp and mirp can be used to check the accuracy of index. Here's how:

Ride two rides whose indices are equal but where one has much climbing and the

other has little or no climbing. Ride both rides at normal pace. If the

indices are accurate, irp from the first ride should be close to irp from the

second ride. Also mirp from the first ride should be close to mirp from the

second ride. If a higher irp or mirp has been observed for the ride with

climbing, v may be too low. Conversely, if the ride with climbing has yielded

a lower irp or mirp, v may be too high. By adjusting v up or down and then

recalculating D, a more accurate index formula can be found.

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