 CYCLING PERFORMANCE TIPS
Last updated: 4/23/2010

Formula for the Energy Requirements of Cycling

From Bicycling Science by Frank Whitt and David Wilson, p.157

W = Cv [K1 + {K2(Cv+Cw)(Cv+Cw)} + {10.32Em(s/100 + 1.01a/g)}]

Where:

• W = power in watts
• 1 W = 1 joule/sec
• 69.78W = 1000 calories/min = 1 kilocal/min = 1 Calorie/min
• 1 Calorie = 4186 joules
• Cv = speed of cyclist in meters/sec
• 1 mph = .447 meters/sec
• 1 mph = 1.609 kilometeres/hr
• K1 and K2 are constants (see table below)
• Cw = headwind in meters/sec
• Em = mass of cyclist and bicycle in kg
• 1 pound = .4536 kg
• s = slope or grade in %
• a = acceleration of the bicycle in meters/(sec)(sec)
• g = gravitational accel = 9.806 m/sec-sec at sea level
CONSTANTS K1 &K2:
ASSUMPTIONS

K1

K2

MTN BIKE

7.845

0.3872

##### 75 kg

3.509

0.2581

Assuming:
• constant speed i.e no acceleration or deceleration
• ideal road or mtn. bike and rider
the formula can be simplified to:

W = Cv* [(K1**) + (K2**)(Cv*)(Cv*)]

*Cv is your AIR speed (ie the resistance you are pedalling against is the resistance of the air to your body and bike as you ride) and is not the GROUND speed off your computer. So if there is a head wind, add that speed to your ground speed to determine the velocity for this formula. And if it is a tail wind, subtract it from your ground speed. If you think about it, this makes sense - it is always easier to ride with a tail wind. This formula quantitates how much easier.

**The constants K1 and K2 are for a road rider/bicycle/gear of 85 kg (187 lbs) or mountaion bike/rider/gear of 95 kg (210 pounds) . If you need to be more specific, the original derivation is referenced at the top of this page. But biking is NOT an exact science, and this formula will at least get you into the right ballpark.

If you want the energy expended at the pedal in Calories/min:

Cal/min (expended at the pedal) = [(K1)(Cv) + (K2)(Cv)(Cv)(Cv)]/69.78

As the body is only 25% efficient at best in converting Calories eaten into Calories delivered as power output, the number of Calories that would need to be eaten per minute to sustain a speed of Cv mph would be:

Ingested Cal/min = {[(K1)(Cv x .497) + (K2)(Cv x .497)(Cv x .497)(Cv x .497)]/69.78}/.25

So if you know the average speed (velocity) of your ride, and the total time you were out, you can calculate the number of Calories "burned". Here are a few examples (average speed for the ride, on the flats):

• 5 mph - 7 Cal/mile - 37 Cal/hr
• 10 mph - 13 Cal/mile - 133 Cal/hr
• 15 mph - 23 Cal/mile - 349 Cal/hr
• 20 mph - 37 Cal/mile - 742 Cal/hr
• 25 mph - 55 Cal/mile - 1374 Cal/hr
• 30 mph - 77 Cal/mile - 2303 Cal/hr
For those of you that regularly ride hills, here is the formula to estimate the Calories expended for vertical gain.