| I recently read through a lengthy message board thread discussing horsepower and torque and it made me realize that many important principles dealing with this subject are not commonly understood. While engine performance is not a subject I typically cover, I’m going to take a short break from the Car Control Fundamentals series to tackle this subject because it is not just important for racers, but to just about anyone who has ever shopped for a car. So in this article, we’ll take an in-depth look at power and torque, and we’ll do it… by riding a bicycle. This is a good way to learn about the subject because, just like in a car, we can feel the results, but on a bicycle, we can also directly feel how that power and torque is being produced. |  |
Torque
When we push on the pedal of a bicycle, we are starting the same basic process that happens in a car engine when the expanding gasses from combustion push on the piston. This force then applies a torque through the drivetrain, which then goes to the wheels. When we ride a bike, the downward force from our foot on the pedal also applies a torque through the drivetrain, which then goes to the rear wheel. Whether we are driving a car or riding a bike, torque is very important because it is what determines our acceleration.
When we ride a bike, it’s pretty easy to feel the connection between torque and acceleration. We can directly feel how pressing the pedal harder moves the bike forward faster. This greater pedal force increases torque through the bicycle’s drivetrain, which increases the torque rotating the rear wheel. It’s actually this rear wheel torque that determines acceleration because, just as the force from our foot created the torque when it pushed down on the pedal, the torque rotating the rear wheel now produces a force where the tire meets the ground, which pushes the bike forward. The end result is that if we push the pedal twice as hard, we double the force pushing the bike forward.
There is another way to double the torque at the bike’s wheel without having to pedal any harder though, and that is by changing gears. If we halve the gear ratio so that the rear wheel now only rotates half as much for each pedal rotation, then we have just doubled our leverage on it. With this increased leverage, we can now double the torque at the rear wheel by pedaling with the same force, but twice as fast. From the rear wheel’s perspective however, everything is exactly the same in either case because we are simply doubling the power.
When we push on the pedal of a bicycle, we are starting the same basic process that happens in a car engine when the expanding gasses from combustion push on the piston. This force then applies a torque through the drivetrain, which then goes to the wheels. When we ride a bike, the downward force from our foot on the pedal also applies a torque through the drivetrain, which then goes to the rear wheel. Whether we are driving a car or riding a bike, torque is very important because it is what determines our acceleration.
When we ride a bike, it’s pretty easy to feel the connection between torque and acceleration. We can directly feel how pressing the pedal harder moves the bike forward faster. This greater pedal force increases torque through the bicycle’s drivetrain, which increases the torque rotating the rear wheel. It’s actually this rear wheel torque that determines acceleration because, just as the force from our foot created the torque when it pushed down on the pedal, the torque rotating the rear wheel now produces a force where the tire meets the ground, which pushes the bike forward. The end result is that if we push the pedal twice as hard, we double the force pushing the bike forward.
There is another way to double the torque at the bike’s wheel without having to pedal any harder though, and that is by changing gears. If we halve the gear ratio so that the rear wheel now only rotates half as much for each pedal rotation, then we have just doubled our leverage on it. With this increased leverage, we can now double the torque at the rear wheel by pedaling with the same force, but twice as fast. From the rear wheel’s perspective however, everything is exactly the same in either case because we are simply doubling the power.
Power
Power is relatively easy to understand from a mathematical perspective, as it’s simply force multiplied by speed. Whether we pedal with twice the force or twice the speed, we produce twice the power. If we start pedaling twice as hard and twice as fast, then we produce four times as much power. Power will go up or down in direct proportion with either. But while we’ve seen how torque is relatively easy to understand, it can sometimes be hard to see the effects of power. For example, if we start pedaling with a constant force, this means we will be applying a constant torque to the drivetrain and wheel so we will have a constant rate of acceleration. This steady acceleration means that we will also need to pedal progressively faster as our speed increases, however. Although we won’t be pedaling any harder and our acceleration will remain constant, our pedaling speed will be increasing and so this means our power output will also be increasing. This constant acceleration and increasing power leads us to a very important principle. Achieving the same rate of acceleration requires an increasing level of power as speed rises. Although this is easier to notice when riding a bike, we’ll see how it can cause some confusion when examining car performance. It’s also important to understand that this need for increasing power is separate from the effects of aerodynamic drag, which can also increase power requirements as speed rises.
Power is relatively easy to understand from a mathematical perspective, as it’s simply force multiplied by speed. Whether we pedal with twice the force or twice the speed, we produce twice the power. If we start pedaling twice as hard and twice as fast, then we produce four times as much power. Power will go up or down in direct proportion with either. But while we’ve seen how torque is relatively easy to understand, it can sometimes be hard to see the effects of power. For example, if we start pedaling with a constant force, this means we will be applying a constant torque to the drivetrain and wheel so we will have a constant rate of acceleration. This steady acceleration means that we will also need to pedal progressively faster as our speed increases, however. Although we won’t be pedaling any harder and our acceleration will remain constant, our pedaling speed will be increasing and so this means our power output will also be increasing. This constant acceleration and increasing power leads us to a very important principle. Achieving the same rate of acceleration requires an increasing level of power as speed rises. Although this is easier to notice when riding a bike, we’ll see how it can cause some confusion when examining car performance. It’s also important to understand that this need for increasing power is separate from the effects of aerodynamic drag, which can also increase power requirements as speed rises.
Peak Torque and Peak Power
So now that we have a basic understanding of how torque, speed, and power are related, let’s take a look at how all this applies when talking about a car. It’s typically quite easy to find torque and power numbers for most cars and with a little research, a dyno chart is often available as well, which shows how torque and power changes throughout an engine’s rev range. Below we have an example dyno chart and we can see how this engine reaches its maximum torque at 4000 rpm. We can also see that maximum power is achieved at 8000 rpm, but to test our understanding, let’s discuss all this in terms of percentages. We can see that torque has dropped to 75% of its maximum at 8000 rpm, but since the engine is spinning twice as fast, it is now putting out 150% as much power as it did at the 4000 rpm torque peak. Remember that power simply goes up or down in direct proportion with torque and speed, so 75% as much torque spinning twice as fast equals 150% as much power.
So now that we have a basic understanding of how torque, speed, and power are related, let’s take a look at how all this applies when talking about a car. It’s typically quite easy to find torque and power numbers for most cars and with a little research, a dyno chart is often available as well, which shows how torque and power changes throughout an engine’s rev range. Below we have an example dyno chart and we can see how this engine reaches its maximum torque at 4000 rpm. We can also see that maximum power is achieved at 8000 rpm, but to test our understanding, let’s discuss all this in terms of percentages. We can see that torque has dropped to 75% of its maximum at 8000 rpm, but since the engine is spinning twice as fast, it is now putting out 150% as much power as it did at the 4000 rpm torque peak. Remember that power simply goes up or down in direct proportion with torque and speed, so 75% as much torque spinning twice as fast equals 150% as much power.
Let’s now take this engine through its rev range to see how all this would feel from the driver’s standpoint. To make this easier to follow, we’ll stay in a single gear that has the car reach 85 mph at its 8500 rpm redline. Engine speed and wheel speed are linked when in gear, so this means our engine rpm will simply be 100 times our vehicle speed. 85 mph x 100 = 8500 rpm. We’ll then begin on the left side of the chart with a rolling start at 10 mph and 1000 rpm. As we go to maximum throttle, vehicle speed and engine rpm will begin to rise together as we move across the chart. We can see that this will cause torque and power to both increase, so we would be pushed into our seat harder and harder as our acceleration rate climbs until we reach the torque peak at 40 mph. At this point, we can see that power will continue to rise, but torque now starts to drop, so what effect will this have on our acceleration? As we’ve learned, acceleration is determined by wheel torque, and since our wheel torque is currently linked to our engine torque through our current gear, as engine torque starts to drop at 4000 rpm, our acceleration rate will also start to drop.
That is only until we start to approach the engine’s peak power at 8000 rpm however, at which point our high-revving engine starts to show its true potential as we feel a surge of… even less acceleration as torque continues to drop even further.
That is only until we start to approach the engine’s peak power at 8000 rpm however, at which point our high-revving engine starts to show its true potential as we feel a surge of… even less acceleration as torque continues to drop even further.
Acceleration Matches the Torque Curve
Although it might seem like we should be able to feel some increase in acceleration at an engine’s power peak, it is important to understand that a car’s acceleration rate will closely follow the shape of its engine’s torque curve, not its power curve. As we learned earlier, we need an increasing level of power to achieve the same level of acceleration as speed rises. This is a linear relationship, so double the speed requires double the power, and it is not a coincidence that this matches the equation for power, because it is the same principle at work. The results of this is that when engine rpm and wheel speed are mechanically linked when a vehicle is in gear, the engine’s power, as well as the vehicle’s need for power, both increase at the same rate. From the driver’s perspective, this causes the speed part of the power equation to seemingly cancel out and all that we feel is the effect of the rising and falling torque. This doesn’t mean that an engine’s torque curve is more important than its power curve however. So far, we have just been unable to notice the effects of power because our car has remained in a single gear. Once we start changing gears however, we’ll finally be able to start seeing the true potential of engine power.
Although it might seem like we should be able to feel some increase in acceleration at an engine’s power peak, it is important to understand that a car’s acceleration rate will closely follow the shape of its engine’s torque curve, not its power curve. As we learned earlier, we need an increasing level of power to achieve the same level of acceleration as speed rises. This is a linear relationship, so double the speed requires double the power, and it is not a coincidence that this matches the equation for power, because it is the same principle at work. The results of this is that when engine rpm and wheel speed are mechanically linked when a vehicle is in gear, the engine’s power, as well as the vehicle’s need for power, both increase at the same rate. From the driver’s perspective, this causes the speed part of the power equation to seemingly cancel out and all that we feel is the effect of the rising and falling torque. This doesn’t mean that an engine’s torque curve is more important than its power curve however. So far, we have just been unable to notice the effects of power because our car has remained in a single gear. Once we start changing gears however, we’ll finally be able to start seeing the true potential of engine power.
More Power Equals More Wheel Torque
Similarly to how we did earlier on the bike, let’s now halve the gear ratio in our car so we can compare the acceleration from our engine’s peak torque rpm and peak power rpm at the same vehicle speed. To start, let’s say that we were originally in 2nd gear and our new halved gear ratio will be 1st gear. As discussed earlier, in 2nd gear, the engine was at the 4000 rpm torque peak at 40 mph and we saw how this was the fastest acceleration we achieved in that gear. Now in 1st gear however, the engine would be at its 8000 rpm power peak at 40 mph because it is now rotating twice as fast for each wheel rotation. Remember that we would only have 75% as much torque at 8000 rpm, but since the engine is spinning twice as fast, it is putting out 150% as much power. Given that the wheels would still be rotating at the same speed however, 150% as much power going to them will result in 150% as much wheel torque and therefore greater acceleration. Except for what might be lost to drivetrain friction along the way, power at the wheels will always match power from the engine, and just as power from the engine goes up or down proportionally with either torque or speed, the resulting power at the wheels works the same way. If we have more power at the wheels, but the same wheel speed, then we have more wheel torque.
Similarly to how we did earlier on the bike, let’s now halve the gear ratio in our car so we can compare the acceleration from our engine’s peak torque rpm and peak power rpm at the same vehicle speed. To start, let’s say that we were originally in 2nd gear and our new halved gear ratio will be 1st gear. As discussed earlier, in 2nd gear, the engine was at the 4000 rpm torque peak at 40 mph and we saw how this was the fastest acceleration we achieved in that gear. Now in 1st gear however, the engine would be at its 8000 rpm power peak at 40 mph because it is now rotating twice as fast for each wheel rotation. Remember that we would only have 75% as much torque at 8000 rpm, but since the engine is spinning twice as fast, it is putting out 150% as much power. Given that the wheels would still be rotating at the same speed however, 150% as much power going to them will result in 150% as much wheel torque and therefore greater acceleration. Except for what might be lost to drivetrain friction along the way, power at the wheels will always match power from the engine, and just as power from the engine goes up or down proportionally with either torque or speed, the resulting power at the wheels works the same way. If we have more power at the wheels, but the same wheel speed, then we have more wheel torque.
The key takeaway here is that, at any given vehicle speed, the torque at the wheels will be directly proportional to an engine’s current power output. This power can also come from any combination of engine torque and engine speed. Whether we hit the NOS and gain 20% more torque at our current rpm or downshift and increase rpm by 20% with the same engine torque, the resulting 20% increase in torque at the wheels will be the same, because the increase in power going to them is the same. Remember though, as the vehicle speed changes, the same level of power will result in different levels of acceleration, so let’s jump back in our car now to see how that works.
Twice the Wheel Speed Equals Half the Wheel Torque
After accelerating past the 8000 rpm power peak at 40 mph in 1st gear, we would soon need to shift before hitting the redline. Once we shift up to 2nd gear, we would be back in our original gear ratio which has the engine reach its 8000 rpm power peak again at 80 mph and we’ve now learned this means we would achieve the maximum possible wheel torque and therefore acceleration at that speed. What’s important to understand however, is that this wheel torque would only be half of what it was at 40 mph and so acceleration would also be significantly less. Astute readers will recognize this is because of the exact same principle we have already learned, which is reflected in the formula for power. With the same level of power going to them, but having to rotate twice as fast, our wheels will only get half the torque. The end result is that as a vehicle gains speed, the same level of power will produce proportionally less and less torque at the wheels, as those wheels also must rotate faster and faster.
After accelerating past the 8000 rpm power peak at 40 mph in 1st gear, we would soon need to shift before hitting the redline. Once we shift up to 2nd gear, we would be back in our original gear ratio which has the engine reach its 8000 rpm power peak again at 80 mph and we’ve now learned this means we would achieve the maximum possible wheel torque and therefore acceleration at that speed. What’s important to understand however, is that this wheel torque would only be half of what it was at 40 mph and so acceleration would also be significantly less. Astute readers will recognize this is because of the exact same principle we have already learned, which is reflected in the formula for power. With the same level of power going to them, but having to rotate twice as fast, our wheels will only get half the torque. The end result is that as a vehicle gains speed, the same level of power will produce proportionally less and less torque at the wheels, as those wheels also must rotate faster and faster.
Peak Power vs Average Power
So taking what we’ve learned, let’s now look at what an engine’s power figures can tell us about vehicle performance. First off, we’ve seen how an engine’s peak power only occurs at one specific speed in each gear, so just looking at this figure alone will only give us a limited picture of a vehicle’s capabilities. Instead, we need to look at the power produced throughout the entire rpm range that a vehicle will use to get a more complete picture of its performance. For example, one engine could have less peak power than another engine, but still might produce better acceleration if it has a broader power band that has more overall power throughout the rev range. We can see in the illustration below how this broad power band engine would have superior acceleration during the majority of the rev range and the narrow power band engine with higher peak power would only be faster in the small part of the rev range near the top.
So taking what we’ve learned, let’s now look at what an engine’s power figures can tell us about vehicle performance. First off, we’ve seen how an engine’s peak power only occurs at one specific speed in each gear, so just looking at this figure alone will only give us a limited picture of a vehicle’s capabilities. Instead, we need to look at the power produced throughout the entire rpm range that a vehicle will use to get a more complete picture of its performance. For example, one engine could have less peak power than another engine, but still might produce better acceleration if it has a broader power band that has more overall power throughout the rev range. We can see in the illustration below how this broad power band engine would have superior acceleration during the majority of the rev range and the narrow power band engine with higher peak power would only be faster in the small part of the rev range near the top.
This also shows the importance of the transmission when it comes to vehicle performance, however. If we matched the narrow power band engine with a close ratio gearbox where engine rpm wouldn’t drop as much with each shift, the engine could more easily stay in the upper part of the power band. This could allow the narrow power band engine to produce superior acceleration if it didn’t need to go into the lower part of the rpm range where the broad power band engine would be faster.
It’s also important to understand that using a close ratio transmission would make the broad power band engine produce better acceleration as well, however. Closer gear ratios will allow any engine to stay more centered around its power peak between gear changes, which will increase its average power output. This does come at the cost of needing to change gears more often, but assuming the time lost during the additional gear changes doesn’t outweigh the time gained from the higher average power, it will be faster. This is why modern dual-clutch transmissions (DCT) provide such a significant performance advantage. There is minimal time lost with each gear change, so often 8 or more gears are used allowing very close ratios that can keep an engine much closer to the peak of its power band. Taking this same principle even further, a continuously variable transmission (CVT) can theoretically maximize an engine’s power usage. As a vehicle accelerates, the CVT would be able to progressively change the gear ratio in order to keep an engine at its peak power rpm, always producing the maximum wheel torque and therefore acceleration possible.
It’s also important to understand that using a close ratio transmission would make the broad power band engine produce better acceleration as well, however. Closer gear ratios will allow any engine to stay more centered around its power peak between gear changes, which will increase its average power output. This does come at the cost of needing to change gears more often, but assuming the time lost during the additional gear changes doesn’t outweigh the time gained from the higher average power, it will be faster. This is why modern dual-clutch transmissions (DCT) provide such a significant performance advantage. There is minimal time lost with each gear change, so often 8 or more gears are used allowing very close ratios that can keep an engine much closer to the peak of its power band. Taking this same principle even further, a continuously variable transmission (CVT) can theoretically maximize an engine’s power usage. As a vehicle accelerates, the CVT would be able to progressively change the gear ratio in order to keep an engine at its peak power rpm, always producing the maximum wheel torque and therefore acceleration possible.
Horsepower
To wrap up this article, let’s talk about horsepower. So far, we have primarily been using the more universal terms power and torque, but just as a pound-foot (lb⋅ft) is one way of measuring torque, horsepower (hp) is simply one way to measure power. The formula for horsepower is also relatively simple. It is hp = lb⋅ft torque x RPM / 5,252. The number 5,252 in the equation might seem a bit random, but this specific number is used simply because it was decided long ago that a horse should be able to rotate 1 pound-foot of torque 5,252 times per minute, equaling one “horse” power. To put this another way, if we put a horse on a bicycle with one foot long cranks, the horse should be able to rotate the pedals with 1 pound of force 5,252 times per minute, or about 87.5 times per second. I doubt a horse would be able to pedal that fast, so if we change the gearing, we can flip this so that the horse would only need to pedal once per second with 87.5 pounds of force.
Putting it in these terms seems to make achieving the power output of a horse actually attainable by a human, and it is, for a trained cyclist over a short distance. Horses have actually been measured generating up to about 15 horsepower for a short time, however. The horsepower measure was not meant to represent the maximum possible output of a horse, but rather their average work rate over an extended period. This was important when the measurement was created, because horses were one of the primary work animals of the time and the creators of early steam engines needed a way of explaining what their new invention was capable of. It’s an interesting origin story, but I still find it quite funny that while the engines of today bear little resemblance to those early machines and we’re more interested in how fast they can get us to 60 than how much grain they can mill, but we still use the original work-animal based unit to measure them.
To wrap up this article, let’s talk about horsepower. So far, we have primarily been using the more universal terms power and torque, but just as a pound-foot (lb⋅ft) is one way of measuring torque, horsepower (hp) is simply one way to measure power. The formula for horsepower is also relatively simple. It is hp = lb⋅ft torque x RPM / 5,252. The number 5,252 in the equation might seem a bit random, but this specific number is used simply because it was decided long ago that a horse should be able to rotate 1 pound-foot of torque 5,252 times per minute, equaling one “horse” power. To put this another way, if we put a horse on a bicycle with one foot long cranks, the horse should be able to rotate the pedals with 1 pound of force 5,252 times per minute, or about 87.5 times per second. I doubt a horse would be able to pedal that fast, so if we change the gearing, we can flip this so that the horse would only need to pedal once per second with 87.5 pounds of force.
Putting it in these terms seems to make achieving the power output of a horse actually attainable by a human, and it is, for a trained cyclist over a short distance. Horses have actually been measured generating up to about 15 horsepower for a short time, however. The horsepower measure was not meant to represent the maximum possible output of a horse, but rather their average work rate over an extended period. This was important when the measurement was created, because horses were one of the primary work animals of the time and the creators of early steam engines needed a way of explaining what their new invention was capable of. It’s an interesting origin story, but I still find it quite funny that while the engines of today bear little resemblance to those early machines and we’re more interested in how fast they can get us to 60 than how much grain they can mill, but we still use the original work-animal based unit to measure them.
I hope you enjoyed this article as much as I enjoyed making it. It was a great diversion before getting back to the Car Control Fundamentals Series and if you have any questions, please use the comments section below. If you are interested in learning more about the science of cars and racing, we also offer The Science of Speed book series, available through our bookstore or at popular retailers such as Amazon.
Adam Brouillard
Adam Brouillard
