CYCLING PERFORMANCE TIPS
TOTAL ENERGY REQUIREMENTS OF CYCLING
horizontal PLUS vertical work
(expressed as Calorie replacement requirements)
*****PLEASE NOTE that the variables may be labeled differently on this page*****
I. Level road (Eh=energy replacement requiredhorizontal component)
This is the formula to calculate the number of Calories needed (to be eaten) to replace those expended riding on level terrain.
 Pw = v x [3.509 + {0.2581 x (v)(v)}]
 Pc = Pw/4186.8
 Ce = Pc x T
 Ci = Ce/Eef = Eh
Where:
 Pw = power (watts)
 v = velocity or speed (m/sec)*
 Pc = power (Cal/sec)
 T = time (sec)
 Ce = Calories expended at the pedals
 Ci = Calories ingested = Eh
 Eef = efficiency of the human machine in converting food Calories (~25%)
 Eh = energy replacement requirements (Calories to be eaten)  horizontal component
Assumptions:
 75 kg rider**
 10 kg bike
 level surface
 no head wind*
*Speed 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 your 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.
**(Unfortunately, this formula is for an "ideal" rider of 75 kg. I could not find the original derivation and so cannot give you the exact changes if your weight is more or less than 75 kg. But biking is NOT an exact science, and this formula will at least get you into the right ballpark  ed)
Definitions and conversion factors:
 1 watt = 1 joule/second
 1 Cal = 1000 calories = 4186.8 joules = 4186.8 watts
II. Vertical Distance (Ev = energy replacement requiredvertical component)
When the terrain is not level, and there is vertical gain, this formula calculates the number of Calories that would need to be eaten to replace those expended for the vertical gain only.
 W = F x D
 Ce = W/CF
 Ci = Ce/Eef = Ev
Where:
 W = work (ftlbs or kgm)
 F = Force from gravity (lbs or kg)
 D = distance vertically (ft or m)
 Ce = Calories expended at the pedals
 CF = conversion factor of 3907 or 418 (for American and International Units respectively)
 Ci = Calories ingested = Ev
 Eef = efficiency of the human machine in converting food Calories (~25%)
 Ev = energy replacement requirements (Calories to be eaten)  vertical
Definitions and conversion factors:
 1 Cal = 1000 calories = 4184.8 joules
 1 joule = 74 ftlb = 0.10 kgm
 1 Cal = 3097 ftlb = 418 kgm
III. TOTAL ENERGY REQUIREMENTS  UNEVEN TERRAIN
By combining the calculations for the horizontal component of energy expenditure and the component from vertical gain, the TOTAL Caloric replacement needs for your ride can be determined.
Etotal = Eh + Ev
And finally, don't forget the approximately 50 Cal/hour for basal metabolism.
AN EXAMPLE
A 165 pound cyclist (75 kg) rides a 10 mile hilly route at an average speed of 15 mph (6.7 meter/sec). During the ride, he climbs 1500 feet (457 meters). His bicycle weighs 22 pounds (10 kg). How many Calories will he need to eat to replace the energy expended??
 Pw = 6.7 m/sec [3.509 + {0.2581 (6.7)(6.7)}]
 = 6.7 [3.509 + 11.586]
 = 101 watts
 Pc = 101/4186.8 = 0.024 Cal/sec
 T = 10/15 = 0.66 hr
 = 0.66 x 3600 sec/hr
 = 2376 sec
 Ce = 0.024 x 2376 sec = 57 Cal
 Ci = 57 Cal/.25 = 228 Cal = Eh
 W = 85 kg x 457 meters
 = 38845 kgm
 Ce = 38845/418 = 92 Cal
 Ci = 92/0.25 = 371 Cal = Ev
 Et = Eh + Ev
 = 228 Cal + 371 Cal
 = 599 Cal to replace those expended
 (plus approx 50 Cal/hr x 2/3 hrs to replace BMR Calories)
 = 599 + (2/3 x 50) = 632 total Cal to be eaten
REFERENCES
BICYCLING FUEL by Richard Rafoth Bicycle Books  San Francisco Calif 1993
BICYCLING SCIENCE by Frank Rowland Whitt et al The MIT Press Cambridge, 1985
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Cycling Performance Tips
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