Hey everyone.

I've been a long time reader on the forum, but this is the first time I've actually decided to make a post.

Recently I was reading through a thread that got a little out of hand on the subject of torque and horsepower, the thread nor the names of those involved being of any relevant importance as mentioning them would just add fuel to the fire, and I thought that I would take it upon myself to explain how each is measured, calculated, used, and give some common, physical examples of each one in action and how each is important.

DISCLAIMER: THIS IS BY NO MEANS AN ATTEMPT TO START ANY SORT OF FIGHT OR TO TAKE SIDES WITH ANYBODY!!!

With that said, any questions are more than welcome and are encouraged, as I am happy to clarify anything I've said or anything that anyone might be feeling a little vague on.

Oh, the reason I know a thing or two about this is because I'm a Mechanical Engineering student soon to graduate with a strong background in Physics, Statics, and Dynamics.

To begin, I'll start by defining the base quantities of any and all Newtonian equations:

Time (t)

Mass (m)

Length (l)

The most basic equation is VELOCITY. Velocity is the distance traveled in a given amount of time. There are two kinds of velocity. LINEAR VELOCITY is the velocity when traveling in a straight line, and is written as

V = ( l / t )

ANGULAR VELOCITY (sometimes called rotational velocity) is the angle traveled in a given amount of time and is written as

V = (change in angle / t ).

An example of linear velocity, think of a truck that travels 60 miles in two hours. 60 miles divided by 2 hours comes to a velocity of 30 mph.

An example of angular velocity, think of a tire spinning on a car. If the tire is spinning at 100 rpm, that's 360 degrees one hundred times in one minute, or 36000 degrees per minute. This comes to 600 degrees of rotation per second.

After velocity comes one that we all know and love, ACCELERATION. Acceleration is the change in velocity per amount of time, otherwise known as the rate at which velocity changes.

A = (change in velocity/time) = ( l/t/t ) = ( l/t^2)

For instance, if you're traveling at 50 feet per second and then accelerate to 100 feet per second in a matter of 10 seconds, the linear acceleration is

[(100ft/s - 50ft/s)/10s] = 5ft/s^2

For an angular example, if a wheel is rotating at 600 degrees per second angular velocity and then increases to 1200 degrees per second angular velocity in a matter of 10 seconds, the angular acceleration is

[(1200 deg/s - 600 deg/s)/10s] = 60 deg/s^2

Next after acceleration comes FORCE. Force is an acceleration applied to a mass.

F = m*A = (m)( l/t^2)

Weight is the most common example of force. A human being has a certain mass, and the acceleration acting on the mass is gravity. Gravity has a value of 32.2 ft/s^2 at sea level on the planet Earth. Multiply your mass by gravity and you get your weight.

An example of angular force would be a flywheel of a given mass being acted on by an angular acceleration.

Next is one of the big ones in this discussion, WORK. Work is defined as a force applied across a displaced distance.

W = F*l = m*A*l = (m)( l/t^2)(l) = (m)(l^2/t^2)

For linear applications, work is simple. It's simply the force applied across a distance. For example, if someone pushes a box with a force of 100 lbs and it moves 10 ft, the work done is (100 lbs)(10 ft) = 1000 ft-lb

For angular applications, work is more commonly known as TORQUE. Torque is the force applied perpendicular to the distance from the center of rotation to the point where force is applied. For example, if you have a ratchet (acts as a lever arm), and the ratchet is 2 ft long, and you pull on the ratchet so that your arm makes a perfect L with the ratchet (ratchet is 90 degrees to your arm) with a force of 50 lbs, the work, or TORQUE, is (2 ft)(50 lb) = 100 ft-lb of torque.

And finally is the second big one in this discussion, POWER. Power is simply work (or torque) divided by time. More specifically, power is the change in work per a given period of time

P = W/t = (F*l)/t = (m*A*l)/t = (m)(l^2/t^2)/t = (m)(l^2/t^3)

A good example of power would be a person attempting to turn a very heavy wheel with your hands. You must apply a torque to the wheel to turn it, but you can't turn it very fast because, oh, let's say you're tired. You can however keep it turning at a steady, slow pace. Even if applying a large torque to the wheel, it's spinning very slowly (time to rotate is very great), so now your torque is being divided by a large number, so the power applied to the wheel is low.

Now, let's say that you just woke up and had a few energy drinks. You apply the same torque to the same wheel, but now you're full of energy and can move your hands much faster, rotating the wheel at a faster rate (time to rotate is now very small), so now your torque is being divided by a small number, so the power applied to the wheel is high.

Here's where the big difference between power and torque comes into place.

Torque is a force applied across a distance. Let's say a 4000 lb truck with 36 inch tires and 4.56 gears with a 3:1 first gear ratio is going up a 30 degree incline. Doing a few small trigonometry calculations will yield a force along the slope of 2000 lb. So now we have 2000 lbs acting perpendicular to a tire with a distance from center to outside of 18 inches, or 1.5 ft. The torque created on the truck's axle by gravity will now be (2000 lb)(1.5 ft) = 3000 ft-lb. So, the torque created by the engine and transferred through the gears must overcome the 3000 ft-lb. If you take a Ranger 4.0 SOHC with approximately 240 ft-lb of torque through the gear ratios mentioned, you get (240 ft-lb)(4.56)(3.0) = 3283.2 ft-lb. Therefore, this setup would be able to overcome torque on the truck due to gravity and move forward.

Power is a measure of how quickly torque is applied, or in other words, the rate at which torque is applied. If we take our torque example, we have the truck making 3283.2 ft-lb uphill and gravity making 3000 ft-lb downhill. This gives us a 283.2 ft-lb favor uphill. Now, if the engine (and therefore axle) is turning relatively slowly, the time between each revolution will be relatively large, let's say, half a second. Take our 283.2 ft-lb of torque and divide by 0.5 seconds and we'll get 566.4 ft-lb/s, which is only slightly over one horsepower (1 HP = 550 ft-lb/s). Now, let's say we have the engine (and therefore axle) rotating 5 times faster than before. Now each revolution will only take 0.1 seconds. Take our 283.2 ft-lb or torque and divide by 0.1 seconds and we get 2832 ft-lb/s, which is just over five horsepower. The difference between the two situations is that, although they have the same torque and therefore can haul the same load, the one with more horsepower can haul that same load at a higher speed.

So here we can see the big difference between torque and horsepower. Torque implies how much of a load something can haul, where as horsepower implies how fast it can be hauled. For instance, a motor with 150 horsepower and 300 ft-lb of torque at a given rpm can haul a 1000 lb load at half the speed that a motor with 300 horsepower and 300 ft-lb of torque at the same rpm can haul it at.

This is why a diesel with 300 HP and 600 ft-lb of torque can haul twice the load at the same speed as a half ton gasoline with 300 HP and 300 ft-lb of torque.

Finally, I'm going to address whether or not horsepower is real. Horsepower is just a unit of power. It is very real, but to say it's just a calculation isn't very correct. For some reason, the standard English system decided that 1 HP had to equal 550 ft-lb/s, something to do with horses and buckets of water, etc. So while that is just a calculated combination of other units, it does have unique use and meaning as I've pointed out in the previous few paragraphs. Both TORQUE and POWER (horsepower simply being a unit of power) are different but critical to automotive function. If we look at their formulas in terms of the base quantities we see that:

TORQUE = (m)(l^2/t^2) and POWER = (m)(l^2/t^3)

So yes, power is torque divided by time, but if you look at them, neither are by any means their own thing. They're both just the ba$tard children of mass, length, and time. With this said, all machines that measure any of the quantities (velocity, acceleration, work, etc.) that i mentioned above, they're really only measuring a combination of mass, length, and time, sometimes with known values such as that of gravity. At any rate though, whether it's a floor scale or a dyno, it's all based off of mass, length, and time. Being a little more specific in the case of the dyno, a dyno doesn't measure horsepower or torque, it measures values of length and time and uses a known value of mass for the roller to calculate both torque and power (see equations above).

Ok, it's 2:30 in the morning and I'm done with the technical discussion. I would like to address a few things about this discussion before I go though:

1. I realize that there are indeed more complex explanations and examples that could have been used for this discussion, but simplicity more often than not yields the best results and I feel that in this case, that couldn't have been more true.

2. I focused most of the detailed explanation on linear equations. I put detail into the angular equations when needed, but didn't go too far into them because I feel that to fully understand them one needs a fairly thorough knowledge of trigonometry. Not everybody has that, so I tried my best to explain things with the most basic math possible that just about anyone can make sense of. Again, simplicity is good

3. I didn't list any equations for horsepower or torque because I wouldn't have felt right doing that without explaining exactly how they work (things like why torque and horsepower cross at 5252 rpm, etc), and again that takes a lot of trig or at the very least geometry. If anything else, I just didn't think it necessary to go into this, but if anyone wants to know, feel free to ask.

4. This was made to be a simple explanation of torque and horsepower, how they work, and their differences. I hope everyone enjoyed this

Again I'd like to state that by no means am I taking sides with anyone in any sort of argument. I would however LOVE if people came up with any sorts of questions. I'd be happy to answer them. I hope everyone enjoys my first post, and I'm looking forward to contributing to the Ranger-Forums community!