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


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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 in / cm
Rider's Weight lb / kg
Bicycle Weight lb / kg
Air Temperature °F / °C
Height above SeaLevel ft / m
Slope of Road %
uphill positive, downhill negative values
Wind Speed mph / km/h
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 mph / km/h
Further results: Effective Drag Area Cd*A square feet Rolling Resistance Coeff. Cr 
In case you enter (before clicking the "Calculate"-Button):
either the TripDistance miles / km ft / m
or the TripDuration h min sek,
the amount of Calories Burnt by the Rider =kcal   (assumed efficiency: 22 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 from the rider's body height and weight, and a parameter which depends on the selected kind of bicycle (see FAQ). These assumptions yield good matches with frontal area measurements, and with measurements done with SRM Power Measuring cranks. Inside the fully streamlined bicycles, of course, the rider's frontal area is assumed to have no influence.
 
The rolling frictions of the front and rear wheel tires each are taken into account separately.
 
The calculation also regards the following influences:
Load distribution front/rear wheel. At wider tire tends to generate 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 friction but less air resistance. The air drag share of the bicycles themselves is taken into account too.
 
At low speeds a wider tire (less rolling friction) may be advantageous while, with higher velocity, a narrower one (less air resistance) increasingly gets the upper hand.
 
The applied rolling resistances refer to asphalt road pavement. On a smooth velodrome surface, rolling resistances may be essentially lower. Consider this also for the values that this calculator delivers for the Superman Position.
 
Most of the data and assumptions used for the calculator are based on (and match well with) frontal area measurements, and, first of all, measurements done with SRM Power Measuring cranks.
TopOfPage | Speed&Power | BodyMassIndex-Calculator | Text | Formulae

 

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

The following equations take into account all of the relevant resistance components: Rolling friction including the dynamic (speed-dependent) rolling friction, air drag including the influence of wind speed, mechanical losses, and uphill/downhill forces.
 
 
P Rider's power
V Velocity of the bicycle
W Wind speed
Hnn Height above sea level (influences air density)
T Air temperature, in ° Kelvin (influences air density)
grade Inclination (grade) of road, in percent
β ("beta") Inclination angle, = arctan(grade/100)
mbike Mass of the bicycle (influences rolling friction, slope pulling force, and normal force)
mrider Mass of the rider (influences rolling friction, slope pulling force, and the rider's frontal area via body volume)
Cd Air drag coefficient
A Total frontal area (bicycle + rider)
Cr Rolling resistance coefficient
CrV Coefficient for velocity-dependent dynamic rolling resistance, here approximated with 0.1
CrVn Coefficient for the dynamic rolling resistance, normalized to road inclination; CrVn = CrV*cos(β)
Cm Coefficient for power transmission losses and losses due to tire slippage (the latter can be heard while pedaling powerfully at low speeds)
ρ ("rho") Air density
ρ0 Air density on sea level at 0° Celsius (32°F)
p0 Air pressure on sea level at 0° Celsius (32°F)
g Gravitational acceleration
Frg Rolling friction (normalized on inclined plane) plus slope pulling force on inclined plane

 
 
Air density via barometric formula:
Air density via barometric formula
 
 
Rolling friction plus slope pulling force:
Equation for rolling friction force and slope pulling force
 
 

Power:
Equation for the required human power

 
 
Speed:
In order to solve this Power equation for Velocity V, we write it in the implicit form
Equation for the required human power
so we can use the cardanic formulae to obtain the solutions:
If a2 + b3 ≥ 0:
Velocity equation

If a2 + b3 < 0 (casus irreducibilis; in case of sufficient downhill slope or tailwind speed):
Velocity equation (casus irreducibilis)

with
Expression "a" of the velocity equation
and
Expression "b" of the velocity equation
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 = lb / kg  Body Height = in / cm 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 a change of body weight or height (or both) would influence the bicycle speed or the required propulsion power. For example, you might want to compare riders with different heights at identical BMI values, meaning "adequately" changed body weights. It may become noticeable that also on a recumbent bicycle the rider's tallness has influence on the 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: 11.9.2008

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