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How to get Maximum Acceleration
by Michael R. Clements

My interest in cars goes all the way back to my earliest memories, and ever since I took my first physics course as a young teenager I would constantly debate with my friends about torque, power, gearing and speed. Our standard topics of debate were what determined acceleration vs. what determined top speed, and at what RPM to shift for maximum acceleration. We all understood the basic physics about Force, Mass and Acceleration and their rotational analogs of Torque and Rotational Inertia. We also were all familiar with the standard phrase, "Torque is acceleration but power is top speed." But somehow this never seemed quite right (it isn't) and these ideas were never enough to resolve the debates.

 

Basics

First, let's talk about torque and gearing. Given the number of people I've met in car and motorcycle racing, I'd say it is a common belief that torque is the single most important factor determining the acceleration of a car. And in fact, twisting force -- torque -- really does determine the acceleration of the car. But it is torque at the wheel of the car that matters, and this is where the confusion starts. You can get lots of torque at the wheel of the car without having much torque at the crankshaft of the engine (think motorcycle). And conversely, you can have lots of torque at the crankshaft yet still fail to get much at the wheel (think diesel).

Anyone who has ridden a 10 speed bicycle intuitively understands gearing. Suppose one gear is spinning at RPM1 with torque T1, and another gear is spinning twice as fast with half the torque. If the second gear is run through a 2:1 reduction gear the final output spins with torque T1 at speed RPM1. That is, the 2:1 reduction gear halves the speed and doubles the torque. Intuitively, gearing it down gives it more force, but sacrifices rotational speed.

In short, torque is not conserved through the drivetrain. One can always trade rotational speed for torque, and vice versa. This is precisely what gearing does.

In a car, the most fundamental gear ratio we are concerned with is the total ratio between the speed of the crankshaft and that of the wheel. If the crankshaft is spinning R times as fast as the wheel, the torque at the wheel is R times that at the crank. So if you can spin the crankshaft fast enough, you can get lots of torque at the wheel of the car, even if you don't have much at the crankshaft.

Armed with this knowledge, let's take an example. Engine A generates a maximum torque of 100 ft.-lbs. at 3,000 RPM. Engine B also generates a maximum torque of 100 ft.-lbs., but it happens at 6,000 RPM. Which engine would you put in your race car?

Many people would take engine A, reasoning that its torque is more "accessible" since it doesn't have to rev as high. However, engine B is far better. It revs twice as high as A but gets the same torque. So engine B can use gear ratios that are twice as short without sacrificing speed. Since the wheel torque is equal to crankshaft torque multiplied by the gear ratio, engine B can produce twice as much torque at the wheel of the car. Yes, that means twice the acceleration.

Now I'm sure many of you are asking, "why not put those same short gears in engine A?" You can; but it limits your speed because engine A can't rev as high. You'll only be able to go half as fast in any given gear. And every time you shift up to the next gear, you're losing acceleration because you're getting less torque at the wheel of the car. For example, if you both start out in 1st gear you will be racing head-to-head. But soon, say around 20 mph, you have to shift to 2nd. But your competitor, using engine B, can stay in 1st gear until 40 MPH (since you both have the same gear ratios but he can rev twice as high). So you begin to fall behind and your competitor blows by you. In fact, he's got twice the overall acceleration you have.

Some might argue that engine A would be quicker off the line, even though B would eventually pass it. This is based on the intuitive notion that both cars are initially standing still and engine A has more low end torque than engine B. But in this case intuition leads us astray with two mistaken assumptions. First, just because an engine achieves its peak torque at higher RPM does not mean it has less torque at lower RPMs. But more importantly, we are not concerned with torque at the engine crankshaft, we care only about torque at the wheel of the car. And since engine B has twice the gear ratio as engine A, it will get off the line just as quickly as engine A even if it has only half the low end torque at the engine crankshaft.

Regardless of the gear ratios you use with Engine A, your competitor using engine B will always blow you away because at any given speed, you've only got half the acceleration he does. Since we assumed that both cars have the same torque and the same weight, we just scrapped the common belief that torque determines acceleration.

Being able to rev the engine high is just as important as making good torque. Engine RPM multiples or leverages the torque at the crankshaft. But RPM alone doesn't make a car go fast, either. RPM and torque both are equally important, since it is the product of the two that makes the car go.

Please check back next week for part 2 of Mike's article, Gearing

To contact Michael R. Clements send an email to: mike@mclements.net

This article was published on Saturday 03 November, 2007.
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