                             # Power Required to Ride a Bike

### Notes on Power calculations

Principle:  Calculate the force opposing motion – this has 3 components:
i)                    Rolling resistance – like friction but much lower
ii)                  Air resistance – the major component at higher speeds
iii)                 Component of weight due to gradient (+ve or –ve)

The power input  =  (total force x bike speed) / efficiency

i) Rolling resistance
Determine reaction of weight on road

R = mass  x  gravity  x  (1 – gradient2))1/2

Rolling resistance = mr  x  R

Sample Calculation

R = 95  x  9.81 x  (1- (1/202))1/2 = 931 N

FR = 0.005 x 931 = 4.7 N

ii) Air resistance

FA = ½ Cd r A v2

where   r = density of air = 1.25 kg/m3

v = speed (m/s) = speed (mph) / 2.237

v = 12 /2.237 = 5.36 m/s

FA = ½  x  0.80 x 1.25 x 0.25 x 5.362 = 3.6 N

iii) Weight component

i.e. mass x gravity x gradient

FW = 95 x 9.81 x 1/ 20 = 46.6 N

Total Force
Force on Road = Total Force opposing motion

FT =  4.7 + 3.6 + 46.6= 54.9 N

Power
Power = Force x speed / efficiency

Power = 54.9 x 5.36 / 0.98 = 300 W

### Important Observations:

Rolling resistance is independent of speed
Air resistance varies with speed squared
The weight component is independent of speed
All we need now are realistic values for mr, Cd and A (or Cd x A)