Everybody’s got an opinion on when you should shift up for maximum acceleration, but they can’t all be right. Here’s how to change gear for maximum acceleration.
SOME SAY YOU SHOULD CHANGE gear at redline for maximum acceleration. Some reckon do it at the engine RPM for peak torque. Others say at peak power. Are any of these theories correct, or none?
Let’s work through some definitions first. Torque is turning force, and it is irrespective of speed. If you try to unscrew the lid on a stuck jar you’re generating torque even if the lid doesn’t move.
Then we have work, which is when force is applied to an object that moves the object. How quickly that object moves is power, or in this case how quickly torque is applied. An object has to move for work to be done. Did you know you can do the same work as your car’s engine? You can. Imagine pushing your car down the road for 200 metres. The engine could do that too, and it would do it a lot quicker, so we say the engine is more powerful. Still, the same amount of work is done, because the definition of work doesn’t involve time (you can mention this to your boss if you like).
In much the same way, your engine might produce 300Nm of torque, yet you too can produce that torque. You’ve seen “Nm” thousands of times in car specifications, but what exactly is it?
First, mass and weight. Mass is how much matter an object contains, whereas weight is the force on the mass, usually gravity. A Newton is a unit of force, named after Sir Isaac, that is equal to the force that would give a mass of one kilogram an acceleration of one metre per second per second. As the earth’s gravitational pull is about 9.8m/s2, a mass of 1 kg has force of 9.8 Newtons, say 10N. This is its weight, and although it should really be called a kilogram-force it is commonly just called a kilogram. The is the same term and quantity as its mass, but only on earth. A mass of 1000 kg and hence a weight of 1000kg on earth would only weigh 165kg on the moon Let’s also say the mass is split 50:50, front:rear (we go along with the myth and pretend that’s ideal), and at rest, so is the weight. When the car brakes hard for a corner we get a weight shift to the front. The weight might change to 550kg on the front axle, 450kg on the rear. This is due to the front accelerating downwards, i.e. adding to the acceleration due to gravity, with the opposite happening at the rear.
However, the mass of the car is unchanged, and the total for both is still 1000kg. And if we took that car to the moon it would weigh about 165kg, but its mass would remain the same.
Now we can get back to torque. A Newton-metre (Nm) is the torque (turning force) that is applied when one Newton of force is applied to a lever one metre long. In real terms, imagine a one-metre long spanner on a nut with a one kilogram weight on the end of the spanner. That’s roughly ten Newton-metres of torque.
If you weigh 100kg and stand on the end of a 0.3 metre long spanner then you too can produce 300Nm, same as your engine. However, the engine can produce that 300Nm at high speed, say 5000 revolutions per minute (RPM). Humans cannot spin spanners at 5000rpm, so while the torque may be the same, the human’s power is much less. Let’s get back to the acceleration question, where we want to accelerate as quickly as possible. Here we invoke one of the most famous equations of all time:
F = M x A or, force = mass x acceleration.
To find acceleration, we can rearrange it like so:
A = F / M
acceleration = force divided by mass.
The mass of the car is constant. The force (torque) applied to it is not. The force delivered to the wheels is a function of the engine torque multiplied by the transmission gear, differential gear and diameter of the tyre, allowing for various friction losses on the way. Nevertheless, it is still force, F, and the more force you have, the more A, acceleration, you’re going to enjoy. So it’s pretty simple. The car will accelerate the fastest in any given gear at the brief moment maximum torque is delivered, or the largest possible F (force).
Is the answer then to change gear around the point at which the engine produces its maximum torque? Not quite, because we’re concerned with the torque produced at the wheels, and that means we need to consider gearing. So here’s the answer – the point to change up a gear for maximum acceleration is the point when you’ll get better acceleration in the higher gear. In other words, the point when you’ll generate more torque at the wheels in the higher gear. Or redline, if that comes first.
Let’s break that down a bit. Car engines produce torque from idle and increase it up to a point. Taking the Mitsubishi Evo Final Edition as an example, that’s 3500rpm at which the engine produces its peak 414Nm of torque. It also produces a maximum power of 226kW at 6500rpm. Because power is simply how fast torque is produced then we can figure out how much torque is produced at 6500rpm:
torque = (kW x 9549) / rpm
332 = (226 x 9549) / 6500 or, 332Nm.
The number 9549 is a constant used to derive power from torque and RPM for metric units (kW and Nm), and the equivalent is 5252 if you do the maths with imperial numbers (lb/ft and hp). Now we have to consider gearing, and let’s take the second to third gear split. The second gear ratio is 1.95, and the third gear is 1.44. These are the ratios of engine speed (RPM) to gearbox output shaft speed. As these are reductions it means that in first gear the engine spins 1.95 revolutions but the gearbox output shaft spins 1.95 times.
So at peak torque RPM (3500) in second gear we get 414 x 1.95 = 807Nm at the gearbox output shaft. In third gear at 3500rpm it’d be 414 x 1.44 = 598Nm, quite a lot less, so remembering A = F / M, less acceleration. Now if we rev second gear all the way to 6500rpm then we get 332Nm of torque, and 332 x 1.95 = 647. This is critical – we’re producing more torque at 6500rpm in second gear (647Nm) than we are at the engine’s max torque at 3500rpm in third gear (598Nm). Because we want to generate maximum torque at the wheels then it looks like it’s best to run the engine high up into the rev range and then change gear. Which corresponds to what we know in real life, changing gear in an Evo at say 4500rpm instead of 6500rpm is not going to win any drag races. Here’s a picture of the Evo to enjoy while you take a breather. 
So how do you know exactly when to shift up? You’d need to know exactly what torque is produced for any given engine RPM, otherwise known as a torque curve. We’ve used only two data points only above, max torque and max power (for which we calculated the torque value), simply because those two are commonly provided by car manufacturers. You’d also need gear ratios for each gear, and to do it properly as well as figure out 0-100 times, also the final drive (differential ratio), tyre diameter, coefficient of traction of the driving tyres, and the coefficient of drag so you can account for aerodynamics. Plus a decent amount of maths skill. It could be for the Evo the ideal shift point is above 6500rpm, but we don’t have a torque curve for it, just knowledge of two points on that curve. Then we have to deal with the start. It would be easy to assume that when maximum torque is applied the wheels don’t spin, but they typically do, 2WDs especially. Simply, if the torque available to the wheels exceeds the traction then there’s no point sending more torque, you’ll just wheelspin and that’s slow.
Things get more complicated again because there’s a particular amount of wheelspin (technically, slip) that’s just right for maximum acceleration – no more, no less – but figuring out exactly that amount, and then the amount of revs required to generate it becomes rather complicated. If all that sounds like too much work and you just want a simple answer then I’m sorry, there isn’t one. Actually, that’s not true, I’m not in the least bit sorry.
So, finally, the answer to the original question. For maximum acceleration it’s wrong to change gear at maximum power, and at maximum torque. It’s also wrong to change gear so that the revs average out over the max torque or power figures. If any of these techniques result in the ideal acceleration that’s coincidence. Instead, you need to change gear such that maximum average torque is delivered to the wheels with consideration to gearing, which means a change up when the torque you can deliver in the higher gear exceeds that of the gear you’re in now. And to achieve that, if you want a basic rule of thumb, sports cars are generally designed so that if you change up close to redline you’ll maximise acceleration.
By the way, we have a full review of the Final Edition Evolution Lancer, plus an explanation of how it works, and a full review of the Lexus RC F.
9549 not a constant
since rpm are not SI units, convert kiloWatts to Watts, minutes to seconds, and use radians per second
60000 / 2 Pi = 9549.2965855137 (your not constant)
Thanks ‘101. I had been told this article is already too complex, but here at PM we don’t believe in the tl;dr approach as so many things require a more detailed and nuanced explanation. There’s enough wrong and lightweight material on the web without us adding to it.
That said, we do have to draw the line somewhere, and for our readers the concept of RPM is easier to grasp than radians per second, and kW are already familiar via car spec sheets. Hence the simplification.
Obviously gears provide increased revolutions at the cost of Torque. In 7th gear at peak Torque rpm ( of the engine) maximum torque is not obtained at wheels due to torque reduction because of gears. Suppose if engine was directly connected to wheels, would you still say that maximum acceleration(instantaneous, not average) is achieved at redline rather than peak torque?
Consider it this way, In second gear itself, is maximum acceleration achieved at 6100 ( redline) or is maximum acceleration achieved at 1500-4500? ( Peak torque rpm band), speed being irrelevant here.
There is a difference between the maximum acceleration in any gear which is when the engine is at max torque assuming no traction problems, and the best point to change gear which is typically redline.
‘So it’s pretty simple. The car will accelerate the fastest in any given gear at the brief moment maximum torque is delivered, or the largest possible F (force)’ agree with you on the force comment but not the torque, maximum torque in any gear is not the maximum acceleration value for that gear.
Picture a hypothetical engine, one that produces 500 torque at 1000 RPM and 495 torque @ 4000 PRM, it would be absurd to argue that the car with that engine will accelerate faster at 1000 rpm than at 4000 rpm, yes torque is less that but the work done lets say in 10s of acceleration (lets assume a CVT transmission) will be nearly 4 times greater thus the car will cover longer distance in that time thus IT WOULD HAVE accelerated quicker.
Exactly. HP matters to acceleration, not just torque. What a of people dont understand is you cannot simply rely on torque, as a force to measure acceleration, per F=MA, because an engine isn’t designed to apply a constant torque/force. The rate at which torque is being applied is also relevant.