Bicycle Speed & Power Calculator: Recumbents, recumbent bicycles, racing bicycles, normal bicycles, aerodynamics, air drag, rolling friction, uphill power. BMI calculator.

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Anglo-american units

metric units

Miles-to-km (or vice versa) calculator

	Racing Bicycles	Recumbents
Roadster	hands on the tops (top of handlebar)	LongWheelBase under seat steering, commuting equipped
MTB unsuspended	hands on the drops (bottom of handlebar)	ShortWheelBase under seat steering, commuting equipped
Tandem with racing bars read...	Triathlon Bicycle	ShortWheelBase above seat steering, racing equipped
	Superman Position (Racing Bicycle- 1h Record)	Lowracer above seat steering Kreuzotter race
		Lowracer with streamlining tailbox Kreuzotter race
		Streamlined Lowracer White Hawk (1h World Record)
		Streamlined Trike Quest

The comma as well as the point may be used as decimal point.
Rider's Height
Rider's Weight
Bicycle Weight
Air Temperature
Height above SeaLevel
Slope of Road		%
uphill positive, downhill negative values
Wind Speed
headwind positive, tailwind negative values
Pedaling Cadence		/min

"Change" the sort of tires? (Recumbents: calculation is based on 20inch front wheels.)	Front Wheel Tire	Rear Wheel Tire

The input field of the variable to be calculated must be empty. The result will appear in that field. With both fields filled, the variable evaluated previously will be calculated again (facilitates quick comparisons).
Power Watts	Notes:	Speed

Further results: Effective Drag Area Cw*A

Rolling Resistance Coeff. Cr

In case you enter (before clicking the "Calculate"-Button):

either the TripDistance

or the TripDuration

min

sek,

the amount of Calories Burned by the Rider =kcal (assumed efficiency: 25 percent) will be calculated.

Besides, the program will evaluate the variable whose fields are empty (Trip Distance or Trip Duration, respectively).

For coast-down simulations, set the Power value to zero and the Slope to the desired negative value.
FAQ

TopOfPage | Speed&Power | BodyMassIndex-Calculator | Text | Formulae

About the Speed&Power Calculator:

The rider's frontal area is evaluated approximately by use of the rider's body height and body weight values, and a parameter which depends from the selected kind of bicycle (see FAQ). Inside the fully streamlined bicycles, however, the rider's frontal area is assumed to be void of any influence.

The rolling friction values of the front- and rear wheel tires are calculated separately.

The calculation also regards the following parameters:
Load distribution front/rear wheel; at a given tire pressure, a wider tire generates less rolling friction but more air resistance (not true with the streamliners White Hawk and Quest whose fairings enclose the wheels almost entirely); a thicker tire wall (touring tire) tends to generate higher rolling friction; tire thread induces air vortices and thus speed-dependent additional resistance; the front wheel has more share in the air drag than the rear wheel; smaller front wheels of recumbents generate more rolling- but less air-friction. Even the air drag share of the bicycle itself is taken into account.

At low speeds a wider tire (less rolling friction) may be advantageous while, with accelerated velocity, a narrower one increasingly gets the upper hand (less air friction).

The calculated rolling resistances refer to asphalt road pavement. On a smooth velodrome surface rolling resistances may be essentially lower.

The data for the bicycles are essentially based on measurements, done with SRM Power Measuring cranks, and partly on coast-downhill comparisons.

TopOfPage | Speed&Power | BodyMassIndex-Calculator | Text | Formulae

The most essential of the formulae the Speed&Power Calculator is based on:

The following equations include any of the relevant drag components: rolling resistance, air drag (including wind speed), mechanical losses, and uphill or downhill power.
P	Rider's power
V	Velocity of the bicycle
W	Wind speed
T	Air temperature (reduced to deg. Kelvin) (influences air density)
HNN	Height above sea level (influences air density)
rho	Air density
rho_0	Air density on sea level at 0° Celsius (32°F)
P_0	Air pressure on sea level at 0° Celsius (32°F)
m	Mass of the bicycle (influences rolling friction, slope-dependent pull-down force, and normal force)
M	Mass of the rider (influences rolling friction, pull-down force, and the rider's frontal area via body volume)
A	Total frontal area (bicycle + rider)
Cw	Air resistance coefficient
g	Gravitational acceleration
Cr	Rolling resistance coefficient
Cm	Coefficient for transmission losses and losses caused by tire slippage (the latter can be heard during powerful pedal strokes at low speeds, for instance by their echo when you're riding along a vertical wall)
stg	Inclination (grade) of road (unit: percent)

rho = rho_0 * (273/T) * e^{-rho_0gHNN/P_0}	(air density via barometric formula)
	(pull-down force, normal-force-dependent rolling friction force on inclined plane (uphill or downhill))

Solving for V:

if a² + b³ > 0

if a² + b³ < 0
(casus irreducibilis; happens with sufficient downhill slope or tail wind speed)

with:

and

TopOfPage | Speed&Power | BodyMassIndex-Calculator | Text | Formulae

Relation between Body Weight, Body Height and BodyMassIndex (BMI)

The comma as well as the point may be used as decimal point.
The field of the variable to be calculated must be empty. The result will appear there.

Body Weight =

Body Height =

BMI =

Note: BMI = weight[kg] / (height[m] * height[m])
BMI<19 signifies underweight, BMI between 25 and 30 slight overweight...

With the values from this BMI-Calculator you can check how much any change of body weight or height (or both) would influence the bicycle speed or the required "human power". It is "fair" to compare riders with different heights at identical BMI values, meaning "adequately" changed body weights. It may become noticeable that even on a recumbent bicycle the rider's tallness has influence on air drag. A change of the rider's weight (meaning changed body surface area and thus frontal area) has more influence on aerodynamics than a different tallness alone.

TopOfPage | Speed&Power | BodyMassIndex-Calculator | Text | Formulae

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Last modified: 6. 5. 2009

Walter Zorn