Horsepower Versus Torque
Here's an explanation of how torque and horsepower relate to each other and at what rpm you should shift for maximum acceleration:
1. The short answer is to always shift at maximum rpm (redline) for maximum acceleration.
2. The long, boring explanation is that torque at the rear wheels is what accelerates the vehicle forward, but engine horsepower is the best indicator of acceleration capability.
The more torque that is applied to the rear wheels, the faster the vehicle will accelerate. This is due to Newton's law which states:
Force = Mass * Acceleration which can be rewritten as Acceleration = Force / Mass
Torque is force acting at a distance. The more torque, the more force assuming the distance remains the same. For a rear wheel drive vehicle, distance is the rolling radius of the rear tire which we can assume is constant.
There are two factors which determine torque at the rear wheels:
1. Engine torque
2. Torque multiplier effect of the drivetrain (transmission and differential ratios)
The drivetrain does two things; both of which are good:
1. It matches the engine rpm with the wheel rpm. An engine needs to operate at much higher rpms than the wheel so the drivetrain lowers the rpm to the wheel by the drivetrain ratio.
2. It also multiplies the engine torque by the same ratio. This effect is often overlooked and is key to why high revving engines produce better acceleration.
Torque and horsepower are related by this simple equation (in English units):
Horsepower = Torque X RPM / 5252
So higher torque at the same rpm results in more horsepower as will the same torque at higher rpm. At 5252 rpm, torque in pounds feet will be equal to horsepower. There is nothing magic about this constant and rpm; they are merely the result of the units used to describe torque and power. The constant and rpm for metric units are different.
While torque to the rear wheels is what actually accelerates the vehicle, horsepower is the best indicator of an engine's capability to produce acceleration. The reason for this is that for the same engine torque, a higher engine rpm requires a higher drivetrain ratio for the same wheel rpm. A higher drivetrain ratio multiplies the engine torque more resulting in more torque at the rear wheels thus producing more acceleration. For example, if two engines produce the same torque, but the first has twice the horsepower, the first can produce twice as much torque to the rear wheels.
The bottom line is we can take better advantage of the torque multiplier effect of the drivetrain by using an engine that revs higher and produces more horsepower.
When to shift depends on two factors:
1. Engine torque
2. Transmission gear ratios
The goal is to keep the most torque at the rear wheels for maximum acceleration. When accelerating, engine torque is continuously changing and for most engines reaches a peak well below maximum horsepower rpm or maximum rpm (redline). As we've seen, torque to the rear wheels also depends on the multiplier effect of the transmission. (The differential ratio remains constant regardless of which gear we use so we can disregard it for comparing different shift points.) What we need to do is compare the torque output from the transmission before and after the shift. If the resulting torque is lower, then we don't shift; if it is higher, we shift.
There are three rpm points that are commonly recommended for where to shift. They are:
1. Maximum torque rpm
2. Maximum horsepower rpm
3. Maximum rpm (redline)
Here's an example using the engine torque curve and transmission gear ratios of the 2010 BMW R1200RT motorcycle. Any vehicle, car or motorcycle, can be evaluated as long as you have its torque versus rpm curve and transmission gear ratios. The first example is for the shift from first to second gear, but all gear changes can and should be evaluated.
1. Maximum Torque RPM which is 6,000 rpm: Before the shift, the engine torque is 120 pounds feet. The first gear ratio is 2.28 so the transmission output torque is 120 X 2.28 = 273.6 pounds feet.
After the shift, engine rpm must decrease to keep the same wheel rpm. The second gear ratio is 1.58. The new rpm will be 1.58 / 2.28 * 6000 = 4158.
At 4,158 rpm, the new engine torque is 108 pounds feet. The resulting transmission output torque is 108 X 1.58 = 170.6 pounds feet.
We were producing 273.6 pounds feet of torque from the transmission prior to the shift and only 170.6 pounds feet of torque after the shift so it makes no sense to shift yet.
2. Maximum Horsepower RPM which is 7,750 rpm: Evaluting the transmission output torque as before, before the shift the torque is 223 pounds feet and after the shift is 170.6 pounds feet. So again, we don't want to shift yet.
3. Maximum RPM (Redline) which is 8,500 rpm: Before the shift, the transmission output torque is 200.6 pounds feet while after is 184.9 pounds feet. So we wouldn't like to shift, but must do so as we've reached the maximum permissable rpm.
So for this motorcycle, we wouldn't shift from first to second gear until reaching maximum rpm.
We can evaluate the shift point from second to third gear in exactly the same manner. Here's the summary:
1. Maximum Torque RPM: Before the shift is 189.6 pounds feet while after is 143.6 pounds feet. We won't shift yet.
2. Maximum Horsepower RPM: Before the shift is 154.8 pounds feet while after is 148.7 pounds feet. We won't shift yet.
3. Maximum RPM (Redline): Before the shift is 139 pounds feet while after is 138.6 pounds feet. In this case, the transmission output torque is the same before and after the shift so we should shift here. This shift point also corresponds with the maximum permissable rpm.
We could evaluate the other gear shift points as well, but for all of them, the maximum rpm shiftpoint is best.
The bottom line is that for normal engines, maximum rpm (redline) is the best shiftpoint for maximum acceleration. However, as most engines have maximum horsepower rpm closely below maximum rpm, it makes little difference if you shift early at that point. For diesel engines which produce their maximum torque well below maximum rpm, it might make sense to shift earlier. Only an evalution of the engine torque and transmission ratios will tell for sure.