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) |
Why not download the spreadsheet for these
calculations
All
formulae courtesy of official
team statistician (retired)
|
