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 – gradient^{2}))^{1/2}
Rolling resistance = m_{r}
x R

Sample Calculation
R = 95
x 9.81 x
(1 (1/20^{2}))^{1/2}
= 931 N
F_{R} = 0.005 x 931 = 4.7 N 
ii) Air resistance 

F_{A} = ½ C_{d}
r A
v^{2}
where r
= density of air = 1.25 kg/m^{3}
v = speed (m/s) = speed
(mph) / 2.237

v = 12 /2.237 = 5.36
m/s
F_{A} = ½
x 0.80
x 1.25 x 0.25 x 5.36^{2}
= 3.6 N 
iii)
Weight component 

i.e. mass
x gravity x gradient 
F_{W }= 95 x
9.81 x 1/ 20
= 46.6 N 
Total Force
Force on Road = Total Force opposing
motion 
F_{T} = 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 m_{r}, C_{d} and A (or C_{d} x A) 
Why not download the spreadsheet for these
calculations
All
formulae courtesy of official
team statistician (retired)
