# Working out Top speed, taking Air and rolling resistance into consideration.

Hi, I am a bit stuck. I am trying to work out the top speed a motorbike can reach, I have a table with bhp and torque and the highest bhp of 150 is at 9,000 rpm. I have done the following calculations:

Diameter of tyre + wheel: 0.5m
Circumfrence of tyre + wheel: 1.5707963m (round up to 1.6m)
Final drive ratio: 2.0
RPM of wheel: 9,000 / 2 = 4500 rpm
-RPM to RPS = 4500 / 60 = 75 RPS (Revs per second)

theoratical speed of motorbike = 75 x 1.6 = 120 m/s
convert that to mph = 268 mph

but I need to derive an equation to calculate the velocity taking rolling and air resistance into consideration. Now I know I need to find the Air Resistance force by using the Drag formula and rolling resistance force using the rolling resistance formula. I am thinking of using P = FV where P is the max power output at 9,000 rpm and F = Drag force + Rolling Resistance Force. I would use my theoratical speed in my drag force equation. This would give me the velocity(V) the bike can reach on the road considering the drag and air resistance force. Am I right ? I am sort of confused because I can use the kinetic energy equation as I have the mass but then should I use the max power at 9,000 rpm. I am really confused. Am I thinking of this the right way ? Also can any of you tell me what the average rolling resistance coefficient is for the tyres on a sportsbike like kawasaki ninja ? Thank you.

jack action
Gold Member
For the top speed equations, see the theory at the bottom of this http://hpwizard.com/car-performance.html" [Broken].

For an estimation of the rolling resistance coefficient see this http://hpwizard.com/tire-friction-coefficient.html" [Broken].

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ok thanks for your help. Now I have got the power required to overcome rolling and air resistance at 220 mph. I used this formula P=FV where F = Total Force = Rolling Resistance + Air Resistance. V = 220 mph. Now how do I find the power required to reach 220 mph with the resistances. I am really confused, also can you tell me if using P=FV above is correct ?

jack action
Gold Member
In the http://hpwizard.com/car-performance.html" [Broken] I previously gave you, you have all the equations.

If you go in the Theory » Longitudinal Acceleration » Accelerating section, equation (5b) is the basic equation, which is essentially F=ma.

Keeping that in mind, you can also find the maximum tractive force which can be either power limited or traction limited. Once you know the maximum tractive force, you can define the top speed by setting the acceleration to zero in equation (5b).

If the power and traction available is greater than what is required to fight drag and rolling resistance, then, still with equation (5b), you will end up with an acceleration for your vehicle, which will increase its speed. As the speed increases, the drag increases, hence the acceleration decreases until it finally reaches zero. And that is when you have reached your top speed.

The greater the power and traction available, the greater the acceleration for a given speed, hence the quicker you will reach your top speed.

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Easiest way is to calculate using power and what rpm that power occurs at. If it's a powerful bike you'll be able to redline in top gear. Then work out the maximum possible speed the bike could go with the current gearing.

Just assume all power loss comes from drag, at top speed that loss will dwarf all the other losses so you can reasonably ignore them. So your top speed: power output = drag power. You can then find your theoretical top speed from the drag power equation.

eg. A typical sports bike would have a drag coefficient of about 0.3 (depending on the rider etc). Lets say it's max power is 120 bhp = 92kW. It has a frontal area of.. 1m^2 (to make the maths easy)

P=FV=0.5pv^3ACd

P=92,000 W
Cd=0.3
A=1 m^2
p=1.204 kg/m^3

P=0.1806V^3
92000/0.1806 = V^3
V= 79m/s
=177 mph.

Which seems kind of sensible for a sports bike.

I suspect (well definitely know) your calculation in the OP is wrong, as noone would gear a bike to go 250mph. Not even MotoGP bikes are geared for that.

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