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Old 11-20-2012, 02:15 PM
Bandem Bandem is offline
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Horsepower vs Torque Relevance and Explanation Attempt!

Engine horsepower and engine torque is perhaps the single most misunderstood subject amongst people and even proclaimed car enthusiasts. The importance of the two values have been argued for as long as engines have existed and that is solely due to lack of understanding in physics and how powertrains really work in cars. In order to fully form an understanding, the very basics must be thoroughly grasped.

Defining Horsepower and Torque:

There are certain basic and fundamental equations that apply to physics upon which the foundations of more complex areas of knowledge are based on. An important concept to understand is motion. Motion is described by a few characteristics. Distance, Velocity, Acceleration, and Jerk. This will be explained with empirical units commonly used when discussing cars as well as in context.

Distance: is just a length in physical space of one dimension. Distance is measured in miles.

Velocity: is how much distance is traveled in a given period of time. Velocity is measured in miles per hour. For every single hour, the distance traveled X amount of miles. Velocity is the change in distance over time. Velocity is a characteristic of motion that cannot be felt. Traveling at a constant velocity cannot be known through a physical sense, because traveling at a constant velocity has no net force. Even if a force needs to be applied to maintain a constant velocity, it will be canceled out by the force of friction required and therefore the driver feels no force and therefore does not feel anything.

Acceleration: is how much velocity is changing in a given period of time. Acceleration is measured in miles per hour per hour. For every single hour, the velocity gained is an X amount of miles per hour. Acceleration is the change in velocity over time. Acceleration requires force and is therefore felt by the driver.

Jerk: is how much acceleration is changing in a given period of time. Jerk is measured in miles per hour per hour per hour. For every single hour, the acceleration gained is an X amount of miles per hour per hour. Jerk is the change in acceleration over time. Jerk requires a change in force, because a change in force causes a change in acceleration and is also felt by the driver. In automobile terms, jerk accounts for the fact that force is not applied instantly, but rather over a period of time.

Now, the set of terms to explain are how changes of different aspects of motion can be quantified or changed.

Force: Force is anything that causes an object to change velocity which means cause it to accelerate.

Torque: Torque is a force applied on a lever in rotation. If force is a push then torque is a twist. It is simply force applied on a lever of which the length is equally important as the magnitude of the force itself. It is shown as Newton meters except it is the amount of force that is applied on a given length lever.

Work & Energy: Work is the application of force through a certain distance. If a person applies a given force on a cart through a given distance then that person has done work. Energy is the capacity to do work and in this case, is kinetic energy. Both are measured in the same units. Work as well as energy is measured as Newton Meters which is commonly referred to as Joules.

Power: Power is the amount of work done over a period of time. If a person applies a given force on a cart through a given distance in a given period of time, that person has made an X amount of power. If that person can do it in less time then they have produced more power. Power is measured in watts. Approximately 746 watts equates to one horsepower.

Now lets place all of those terms in equations with explanations.

Velocity=Distance/Time <-Self Explanatory.

Acceleration=Force/Mass <-Force and mass is directly proportional to acceleration. Less mass and more force equate to more acceleration.

Kinetic Energy=(1/2)(Mass)(Velocity^2) <-This is the energy that an object has due to motion. It accounts for the velocity of motion as well as mass, however the values are not proportional. A car requires four times more energy to just double velocity. The ability to double velocity is defined as energy. Once that energy has been used and the velocity has doubled, it means that work was done on the object. Energy and work are very similar and both important.

Work=Final Kinetic Energy-Initial Kinetic Energy <-Work is the change in kinetic energy, as mention above, changing velocity of a car changes its energy. Work is just representing the change in energy.

Power=Work/Time <-Power takes into account how fast work can be done. While work just represents a change in energy or in our case, velocity, it never accounts for how long it takes for it do so. Doubling velocity may take 5 seconds or 10 seconds. The shorter the time span means that work can be applied at a faster rate and therefore that means more power is applied. Power is how much time it takes to accelerate an object through a certain distance or more simply, how much time it takes for an object of a given mass to change velocity and thereby automatically changing its energy. Given a cars mass and power, its possible to calculate the time it takes that car to reach a certain speed. Don't rush to do this yet, because as seen later on, it is entirely inaccurate in a realistic scenario.

Now things get interesting. To better understand these equations, they can be re-arranged to better fit the uses of analyzing a car.

If Power=Work/Time then Power=(Force X Distance)/Time. Since Velocity=Distance/Time then Power=Force X Velocity.

Power=Force X Velocity


^These equations (same equation just re-arranged) mean that power dictates the force that can applied at a given velocity. Provided the power is constant at all times (such as a battery) then as velocity increases, force decreases. In order to apply more force at a higher velocity, more power must be used. The relationship is inverse.

This leads to the final combined and most critical equation of cars.

Acceleration=(Power/Velocity)/Mass <-This means that to increase acceleration at a given speed, the power must be increased and/or the mass must be reduced. To achieve more acceleration, there must be less velocity so that it takes less energy to accelerate.

It is extremely important to note that torque and work/energy not be confused due to the similar appearing units. Even though the units appear similar, they are entirely different things and is also a common area of confusion amongst many proclaimed car enthusiasts. Nm in Torque is very different from Nm in work or energy. Torque is still a force by nature so work applied due to torque would can represented as Nm-m. The force on a lever of given distance is torque while the circumference (distance) through which that force is applied is the work created by that torque applied through a certain distance in a rotational manner.

Engines are weak:

An engine, even the most powerful around are much weaker than many realize. An average grown human can take the flywheel of most street engines in use today and hold it in place even if the engine is operating at maximum throttle. A street engine commonly has ~200ft-lbs of torque at maximum, its commonly even less. 200lbs of force isn't enough to do much of anything on a car. So how is it that these tiny and weak engines are able to accelerate such heavy cars so quickly. The answer to that is speed and gearing.

Suppose a person is tasked to use a 1ft lever and turn it around a pivot. A strong person may easily provide the same torque as a street engine. Now suppose that person was tasked to turn that pivot as fast as they can. A revolution or maybe even two per second is a reasonable estimate. Now, lets multiply that by 60 seconds to find the revolutions per minute. (2*60=120rpm). So a person is turning that at 120rpm (Rounds Per Minute). Well….most street engines operate over 2000rpm and can usually go up to 7000rpm. That can be dozens of times faster.

So now the question arises of why that's significant. Why does it matter that an engine can spin fast even though it isn't strong. Well the answer to that is gearing which will be talked about later.

Torque versus RPM:

Remember the equation of Power? Its Power=Force*Velocity. In car world, Power=Torque*RPM. Torque is a type of force and RPM is a speed. RPM is rounds per minute which is a distance in a time. Torque is a rotational force and RPM is a rotational speed. So power can be increased by either increasing RPM and/or increasing Torque.


Now comes the important summation of understanding everything discussed above. To understand gearing, a basic understanding of mechanical advantage must be acquired first. So what is mechanical advantage? Mechanical advantage is using leverage to amplify force. This brings us back to the equation of power. Leverage is largely based on the principle of conservation of energy which can be shown by both equations for energy and equations for power. Since time is constant in leverage for both sides of a pivot then the energy as well as power must be equal. Since distance as well as velocity changes then force must also change in order for the energy and power to remain constant.

Imagine a seesaw, the simplest form of leverage that can be demonstrated. A seesaw is a long bar that has a pivot or fulcrum in the middle. In the case of a see saw, the pivot point is directly in the middle of the bar. Now suppose two people sat on the seesaw of different weights. Due to leverage the people of different weights can perfectly balance the seesaw by simply sitting at different distances from the center of the seesaw. If the seesaw is a total of 20 feet and the two people on it are 200 pounds and 150 pounds then how would they balance it. Its all about torque. Since the pivot is exactly in the middle at 10 feet, then the 150 pound person would be exerting a torque of 150 pounds at 10 feet. This can simply be converted to having 1500ft-lbs, because typical measurements of torque in the automotive world use the distance of the leverage as constant being 1 foot. 150 pounds on a 10 foot lever would be equivalent of 1500 pounds on a 1 foot lever. Yes, this means that the 150 pound person can balance the seesaw if a 1500 pound object was placed 1 foot from the other side of the pivot. The two forces would cancel each other out and the seesaw would be in equilibrium. Since the seesaw must be balanced then the 200 pound person must be sitting at a certain distance away from the pivot that allows that person to exert 1500ft-lbs of torque. This is just a simple equation of (150lbs*10)=(200lbs*X). Solve for X and the answer is 7.5ft. At the point of the pivot, both people will be exerting the same torque and cancel each other out simply by changing the length of their leverage.

The reason why this works is conservation of energy and here is why. If the seesaw with the two people moves back and forth, the 150lbs person would be moving a greater distance than the 200lbs person, because they are sitting further from the pivot. Since Work=Force*Distance, the only thing constant is Work due to the law of conservation of energy. If the Distance is different for the two people, then the force must also be different in order to compensate and have the same amount of work to conserve energy. This can also be shown by the power equation. Since Power=Force*Velocity, then the two people travel at different velocities when the seesaw is moving and therefore the force must change to compensate and produce the same power output. Leverage can change force, but it can never change energy and as a result it cannot change power. Torque and force can be manipulated, but power and energy of a system must always be conserved.

Gears operate on the same exact principle with no exceptions. It is just easier to visualize a simple lever device. In gears, everything is about speed and torque. When multiplying torque, the speed is reduced. When dividing torque, speed is increased. Torque and speed have an inverse relationship. This is why in a car, the highest gear has the lowest torque (and therefore acceleration), but allows for the highest achievable speed on the road.

So suppose a car is placed in the highest gear at 5mph. In many cars, this is 6th gear. The driver will notice how the acceleration is very poor, however the RPM of the engine is gaining at a slow rate also. Now if the car is placed in 1st gear, the car will accelerate faster, but the RPM of the engine will also shoot up faster. This faster acceleration can only be maintained for as long as the engine allows, which is until it reaches redline. Once the engine is at redline, the driver must shift to 2nd gear. What this means is that the driver is sacrificing torque and acceleration, for more speed. 2nd gear will bring down the rpm of the engine and allow the car to keep accelerating to a faster velocity until once again it must shift to 3rd gear and sacrifice even more torque to gain more speed. This is why in cars, the transmission and gearing system (which also includes differentials and tire diameter) are designed for tremendous torque multiplication to be able to accelerate cars at what people consider a reasonable rate.

Here are three very important equations regarding engine power, torque, and the torque at the wheels. This is all using imperial system units which is the reason for the constants.



Wheel Torque=((Engine Torque)*(Transmission Gear)*(Differential Gear))/(Rolling Radius of Tire)

The torque provided to the wheels is vastly different from the torque the engine creates, because it is multiplied many times.

Lets simplify this now. Suppose there was an engine on a stand that was mated with a special transmission. This transmission has three special factors. It has an infinite amount of gear ratios, each gear ratio is infinitely close to the ratio before as well as after it, and it can be switched between each gear infinitely fast. This means that this transmission can hold the engine at a constant rpm at any velocity that the transmission outputs. At which RPM would the transmission then proceed to hold the engine? Would it be at the peak power or the peak torque? In a street engine, the engine is always producing less torque at its peak power rpm then it does when it is at peak torque rpm. If power is merely a calculation then why would a transmission optimally hold an engine at peak power? The answer is multiplication.

The greatest acceleration at any given speed occurs only at the peak power, not the peak torque, because despite less torque at the peak power….the multiplication due to gearing is always greater and always will compensate as well as supersede the torque provided at peak torque.

Lets take a look at an example. Suppose there is an engine with the following specifications:

Peak Power=200hp @ 6,000rpm

Peak Torque=200ft-lb @ 4,000rpm

So now lets use equations to find the torque provided at peak power as well as the power provided at peak torque.

Torque @ Peak power RPM (6,000rpm)=175ft-lb

Power @ Peak torque RPM (4,000rpm)=152hp

Notice here that less power is produced at peak torque. Here is the significance to that. Suppose we have a rear wheel drive vehicle with a transmission gear of 4:1, a differential gear of 4:1, and a loaded tire radius of 1 foot.

At the peak torque rpm, the car will be traveling at 17.8mph.

The car in this case will be delivering ((200ft-lb)(4)(4))/(1) total pounds of force to the road. By dividing the tire radius, we are finding the force applied to the road itself at the very outer edge of that tire.

After doing the math, the force will be 3200lbs. Remember that weight is a force, because weight is Mass*Gravity (with varying units).

Now what kind of force would the car have at the same speed of 17.8mph if only the engine had been at peak power rpm instead of peak torque. In order to accomplish that, the gearing must be changed. It doesn't matter what we change so lets do the transmission gear ratio. For this speed, the transmission ratio would now have to be 6:1 instead of 4:1.

In this case the car will be delivering (175ft-lb)(6)(4)/(1) total pounds of force to the road. After doing the math, the force is 4200lbs.

So the force at peak power is 4200lbs at 17.8mph while the force at peak torque is 3200lbs at 17.8. That's over 31% more torque at the wheels. So as can be seen, despite less engine torque, power allows for more torque at the wheels through multiplication.

Area under the curve:

Peak power and peak torque are just instant values that occur at a point in the rpm range of an engine. As important and significant as they are, the amount of torque and power an engine produces throughout its rpm range is also important if the car is using gears. If a continuously variable transmission is issued, it could keep an engine at its peak power rpm and adjust gears for every speed so that torque multiplication is maximum for every speed. Since street cars at this point still use gears, it means that one magnitude of torque multiplication (a gear) must be kept for a range of speeds, not just one speed.

If an engine is placed on a dynamometer it will provide a chart of an engine's torque through its rpm range. Power is then calculated from that curve. So then the question is raised, which curve is more important?

When an engine is on a stand, the power is more important. Based on the power curve, the gearing system can be set. This is shown by the area under the curve….aka the integral. Once an engine already has a system of gears, it means that its potential is now limited and acceleration in a given gear will in fact mimic the torque curve since torque is the only thing that is changing if the gearing is constant. The power curve, or at least part of it, shows the true performance potential of an engine when mated with a conventional transmission or gearing system. Once an engine is already mated with gearing then the torque curve shows what happens when accelerating.

The torque will remain the same in area no matter which RPM it is presented at. The power curve however will be larger at higher rpm's, which is why torque and rpm are equally important with regards to power and therefore performance. An engine that is already mated with a transmission already has its performance potential taken advantage of only to the extent of its gearing. The longer the gears are then the less potential of power that engine is used, because it is operating further away from peak power.

An engine with the same torque at higher rpm's can use steeper gearing ratios to achieve the same speed due to gearing which

means that they can achieve much greater acceleration. So a 2.4L F1 engine with a relatively small amount of torque, but high horsepower is just as capable as an engine with the same horsepower even if it has a thousand ft-lb of torque, such as a truck engine.

Due to gearing, a theoretical top speed if accounting for air resistance is based on peak power, not peak torque.

Shifting Points:

There is a lot of debate on shifting points with cars. Simply put, shifting at any point other than redline is almost always bad. Even if torque is drastically declining at redline, the torque at the wheels from remaining in a lower gear will almost always compensate and still provide better acceleration then the next gear.

Differential modification theory (Short or long gears):

Changing out a differential can yield significant performance gains. Shorter gears keep rpm closer to peak power and therefore improve acceleration of a car. This is due to more torque multiplication. However, due to limited amounts of gears, top speed is sacrificed when this is done.

The rule of engines:

1) That peak horsepower IS the single most important and ONLY important aspect of an engine's maximum performance ability. This case scenario only happens if this engine is always running at its peak power rpm and that can only happen with a CVT designed for this. There are no *if's*, *and's* or *buts* for this.

2) In the real world when comparing normal cars, the most important aspect of an engine's performance capabilities when mated with a conventional gear based transmission is the power curve. This is because the area under the curve of a different operating range takes into account the torque and rpm which is what is needed to determine the best ratio of gear multiplication to use for that engine.

3) Peak Horsepower is the best indicator usually of a cars performance at first glance (ignoring weight). Most websites provide only provide specifications on peak torque rpm and peak horsepower rpm. Out of the two values, the Peak Horsepower alone will provide the best predicament of performance. Torque provides much less prediction accuracy, because trucks and work-horse vehicles have relatively low horsepower and very high torque levels, because they use diesel engines operating at high stroke to bore ratios and requiring immense compression. They cannot spin to high rpm's. A high peak horsepower says that most likely, the vehicle is producing more torque at high rpm's and therefore most "likely" has more performance potential. In most cases, the car with a better horsepower/weight will win.

4)Once an engine is already mated with a transmission, such as a car, the torque curve must be used, not the power curve to determine force exerted to the road. The given power has already been taken advantage of to a certain and limited extent by the gearing and cannot be used anymore, so the power curve in this case is irrelevant. Since the car remains in the same gear over a variety of speeds, the power may be increasing, but the acceleration is decreasing, because the torque is decreasing and the car is not compensating for that with steeper gearing and therefore the power curve doesn't apply when an engine is already connected to a transmission. So basically if you want to compare the performance of your car against a friend's car (not the engine, but the CAR), which already have wheels, a differential and a transmission set in, then use the torque curve of the engine.

5)Two engines making the same power, (peak power in the case of a CVT or power under the curve in the operation range given by gearing) are equals in all aspects regardless of any torque, displacement or any other factors.

So what have we learned?

Horsepower is more important than torque. Common sense, physics, mathematics and real life all prove it. More horsepower is more important, because it means more torque delivered to the road to accelerate the car, because it all has to go back to the gearing system. However, peak horsepower and torque numbers say little in terms of daily driven cars sold on markets today due to the variability in the curves and gearing purposes set in them. So next time a friend argues that his obnoxiously huge American muscle car V8 has *tons* of torque to compensate for its low horsepower, tell them they don't know what they're talking about. A small 1.8L engines like ones made in Japan and Germany are just as capable if they put out similar horsepower averages, except due to their higher rpm they are a lot more complex and advanced. Remember, when going from idle, torque at low rpm does help with daily drive-ability. However in a drag race and any performance situation, horsepower is what really counts. Thank you for reading. Always remember that the key to the entire war is *gearing*. If you don't account for gearing than the game can change a lot, but then again there would be no point since gearing is used everywhere. Torque of an engine is an absolutely meaningless value in real life performance of a car. We can sum everything into one, three word statement.


Last edited by Bandem; 12-22-2013 at 07:59 PM.
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