Re: How do power and torque combine to provide acceleration and top speed?

Hello Frank.

Nice question. The relationship that you're asking about is the very one 
that sports car and bike designers give their everything to master. To 
hone this not to perfection, but to match the exact demands of your 
vehicle is the engineering behind the victory. Remembering that the torque 
delivered to the wheels is also dependent on the gearbox, a designer may 
want a lot of "low end grunt" or torque at low frequency to get a flying 
start, or he may want good "high end performance" to develop torque at 
high frequency to give good overtaking at speed. those are the only two 
racing slang terms I know, but what are the 'high end' and 'low end'? The 
answer to your question, that's what.
Accepting energy is the product of force and distance (E = Fs), it follows 
that power, being energy per unit time (usually joules per second), is the 
product of force and velocity (E = Fv). Now think about a rotary shaft. 
Force derives from torque, the product of force and radius (T = Fr). Speed 
at the rim of the shaft is the product of rotary frequency, pi, and the 
radius (S = 6.28 r w). If both of these quantities are the constituents of 
power, then they must be inversely proportional. For a given power, you 
may have high revs and low torque, or high torque and low revs. All pretty 
simple so far, but you were asking about motor bikes...

Before buying your Ducati 916SP or Kawasaki ZZR1100 you may like to 
examine its Power Curve - the graph of power (plotted vertically) against 
rpm (horizontally). You may look at a linear graph up to about 9000 rpm at 
which point the graph will tail off as various inefficiencies and the laws 
of physics start to impose penalties on the bike's performance. Choose 
your rpm (say 5000), read off the power curve to get the power of the bike 
at that rpm (say 50bhp). That is the power developed at that particular 
frequency for that engine. It will differ from the 'high end' of the curve 
to the 'low end' of the curve. Now you can calculate the torque at the 
drive shaft, and if you know the gear ratios, you can work out the torque 
on the back wheel. If you know the radius of the wheel you can work out 
the force developed on the road. If you know the mass of yourself and the 
bike, you can calculate how quickly you'll get away at the lights!

I hope that clears it up for you. Please ride carefully.

Best regards,
Justin Roux