Torque vs power - what accelerates my motorbike

Many times I see people ask questions about torque and power, asking what kind of engine is needed – high torque or high power – to gain best acceleration. Here I will try to explain relation between power and torque on a motorbike example…

The thing that moves your motorbike around is the force that tire exerts on pavement. I will call this force ‘the thrust force’. If the thrust force is greater than drag forces (mostly wind resistance) then your motorbike accelerates. If the thrust force is exactly equal to the drag, then your motorbike keeps running at constant speed.

There is a very simple formula that tells how much your motorbike will accelerate if we know the net force acting on it: a=(Ft-Fd)/m (where ‘a’ is the acceleration, ‘Ft’ is thrust force, ‘Fd’ is drag force and ‘m’ is the mass of the motorbike, driver and cargo). To make your motorbike accelerate faster you must either decrease its mass or increase thrust force (or you can even decrease drag force, but effect will be small on low speeds).

So, how large is the thrust force? It changes depending on how much throttle you give and what gear you use…. please, read further.

At any moment, the amount of the thrust force depends on the amount of torque exerted on the driving (rear) wheel of your motorbike. Larger the torque, larger the force. There is a simple formula: Ft=Mw/r (where ‘Ft’ is thrust force, ‘Mw’ is torque on the wheel and ‘r’ is wheel radius). You can see that the thrust force also depends on wheel radius – smaller the wheel radius, larger the force, greater the acceleration (theoretically). But you can rarely change the radius of motorbike wheels, and even if you can there are usually more convenient ways to make the same (like changing the gearbox ratio - so, read further).

One important side-note: The thrust force is also very limited by friction between tire and pavement, and cannot pass over this limit. That is why often the best way to achieve better acceleration is by installing stickier tires.

The torque is a bit foggy term for those that never liked physics. In the world of wheels and axles, the torque is a value that is analogue to the force of the linear world. The torque tells with how much ‘strength’ something is twisted (while the force tells with how much ‘strength’ something is pushed/pulled). With the already mentioned (M=F*r) formula you can convert torque to force and vice versa… force can cause torque (like when you use a wrench), and torque can cause force.

So how large is the torque on your motorbike driving wheel? Well it depends on two things: on the torque generated at engine shaft, and on the gearbox ratio. The formula is simple: Mw=Me*N (where ‘Mw’ is torque on the wheel, ‘Me’ is the torque on the engine shaft, and ‘N’ is gearbox ratio – like 1:N).

As you can see, the gearbox ratio is very important. This is not surprising because the function of the gearbox is to adjust the torque level at your driving wheel. Larger the gear ratio, more torque on the wheel, more thrust force and therefore greater the acceleration…. again, in theory only. It is important to note that there is no sense to put 1:1000 gear into your motorbike – you may achieve great acceleration with this, but only for very short time because you will hit on maximum engine revs while still driving very slowly… and you would have to have some impossibly sticky tires.

Still, for greater acceleration, one must keep gears low as long as possible (late shifting).

And how much torque is there on engine shaft? Well this depends on your engine capabilities and how much throttle you give. Engine capabilities are described with torque curve. Torque curve tells what is the maximum torque (that is, ‘on full throttle’) the engine can produce at any given engine revs.

Still, absolute value of your engine torque is not that important for your motorbike acceleration. Even if your engine can generate only a small torque, you can easily enlarge it by using higher gear ratio in your gear box. Yes yes, we said that high gear ratio reduces maximum speed of your motorbike – but what if your low-torque engine is the one that can run into very high revs? This way, even with high gear ratio you could still obtain some respectable speed, and have acceptable acceleration at the same time.

Strange, isn’t it? You can have high-torque-low-revs engine or you can have low-torque-high-revs engine, and both can achieve similar results. You only need lower gear ratio on the first one and higher gear ratio for the second one... It really is that way.

Okay, if torque doesn’t matter, what matters then? What matters is product of the torque and revs. You must multiply the torque that is your engine capable with max revs that your engine can achieve – the product will be a good estimation of acceleration capacity of your engine… Do engine manufacturers already give this number in their engine specification datasheets? Yes, of course, this is the first number you see – the power!

The power is the product of torque and rotation speed.

Because gearbox ratios are always near-optimal in real-world motrobikes, you can quickly estimate their acceleration abilities only by looking at the engine power and motorbike overall weight (mass).

For more precise acceleration estimation, you must consult either power curve or torque curve. Their shapes are important. For example some engines will not want to accelerate your bike at low revs, but will go mad at high revs, while other engines may provide more constant acceleration over full range.

Obviously, from the torque curve we can produce the power curve of an engine and vice versa. Reasonably, the power curve will have its maximum at higher revs than the torque curve. But either of these two curves is enough to predict the acceleration behavior of your bike (sure, you must also know: gear ratios, rear wheel diameter, tire/pavement friction coefficient, aerodynamic drag and rolling resistance, mass of vehicle+driver+petrol+anything). This should be enough for ‘a regular person’.

As for gearboxes, it is better if they have greater number of ratios because with large number of gear ratios you can hold your engine at narrow rev band. Of course that you will choose the band that is around peek-power*** on the power curve… Actually, if you had a continuous-variable-transmission, you could keep your engine always exactly at the peek-power gaining maximal acceleration. There are however technological reasons why normal motorbikes don’t use transmissions with 30 gear ratios nor CVTs.

…long time ago, when I was still young, people were talking about power of their cars. Fine. But then, suddenly, everybody started talking about torque. A big step back, I would say. If you need to describe acceleration capacity of your engine with a single number – the maximal output mechanical power is the best value.

Danijel Gorupec, 2011

*** In the original version of this article I erroneously reffered to the peek-toruqe (instead to the peek-power) in this paragraph. In a way, this negated the meaning of the whole article... The mistake was kindly observed and reported by Kamil Vratny. Thanks Kamil for saving my article!