I’ve seen many people on various forums that I am a member of asking questions out of curiosity about how a sportbike with 600cc/1000cc engines can produce so much more power than much larger cruiser engines that are 1000+ cc’s, why diesel engines are notorious for insane amounts of torque, and why they have such low RPM limits, blah blah blah, or any other engine/power/torque related question really.
This is something I’m typing up to try an help provide a better understanding of how and why certain engines of various sizes and cylinder counts produce more power and/or more torque than others.

So this is why engines do what they do:

First, we have to introduce something known as “work” in the physics world.
The equation we’re dealing with is:
w = fd
Work = force x displacement. Displacement, in this case, refers to a physical unit of measureable distance or motion and force is simply force, an application of pressure measured in pounds, killograms, newtons, or whatever you wish to use. Work is a quantity of force that is being applied through a range of motion. An example of this would be applying a consistent 5lbs. of force to a box as it’s pushed 1ft. across the floor. We will later use this equation to represent torque produced by a piston pushing down on the crankshaft of an engine.

Second, we have to introduce the concept of “power.”
P = w/t
Power = work/time, or, “amount of ‘work’ done per unit of time.”

Now for the engine related crap that (I hope) you care about.
Torque is force exerted around a radius. I will be talking about torque in units of lb.-ft. Let’s say you’re trying to break a lug nut free from your car tire. We’ll say that 200lb.-ft. of torque is required to free the rusty lug nut. You have the choice between using the ****ty 1ft. long tire iron that Volkswagen gave you and the 2ft. long breaker bar that you purchased after you bought your 2000 Volkswagen GTI because you knew ahead of time that the ****ty piece of **** tire iron that Volkswagen gave you really is the ****tiest piece of **** in the history of pieces of ****. Now, the piece of **** will work just fine, but you will have to exert 200lbs. of pressure on the end of if to reach the 200lbs-ft of torque. This is hard to do if you only weigh 180 lbs and instead of loosening the bolt, you end up lifting both your feet off the ground as you press down on the turd-iron. If you choose the 2ft. long breaker bar, only 100lbs of pressure is need to produce the 200lbs-ft of torque.
We can use torque as the ‘f’ in our ‘work’ equation, but since it is exerted through a radius, the displacement is going to be an angle measure instead of actual distance. This angle measure will be measure in Radians instead of Degrees. 2π radians is equal to 360º.

So from all this, so far, we can assemble an arbitrary unit of power.
Power = Torque x 2π x RPM
The 2π represents one full revolution, then it gets multiplied by RPMs to acquire how many times per minute the angle measure of 2π occurs. But wait! You may be asking “Aren’t we supposed to be dividing something by a unit of time?” The answer to that question is Yes. But since RPM already accounts for a number of “rev’s / minute,” it has sort of been snuck into place already. If we were to rewrite this equation, to look more like the original on paper, it would look like this:
Power = (Torque x 2π x aNumberOfRevolutions) / 1 minute
You see, number on the bottom of the division problem is a 1, so it doesn’t need to actually be written. That’s what the “Per Minute” part of RPM is for anyhow.
To convert this arbitrary and generic unit of power into Horsepower, there’s just one more step.

1HP is defined as: 550lbs.-ft./second
Since we are dealing with RPM’s, converting this to minutes will make our lives a ot easier, so: 1HP = 33,000lbs.-ft./minute
To convert our generic ‘Power’ into units of horsepower we simply need to divide it by 33,000 and we arrive at: (keep in mind that ‘Torque’ is in units of lbs.-ft.)
HP = (Torque x 2π x RPM)/33,000
To clean it up a bit, the 2π and the 33,000 reduce, which leaves us with the final and easy to use equation of:
HP = (Torque x RPM)/5252
Because 2π goes into 33,000 about 5252.113…………. times.
From all of this so far, it’s easy to understand that saying an engine produces X amount of horspower, is really the same as saying that it produces Y amount of torque, Z times per minute.

Now to see why certain engines produce more torque than others of comparable size and why certain engines may produce more power than others of a comparable size. Let’s look at two hypothetical single piston engines first, in order to keep things simple. Engine A and engine B both have a displacement of 150cc’s. That means by the end of the intake stroke both have drawn in 150cc’s of a mixture of air and fuel. We’re assuming the air-to-fuel ratio is the same in each engine. Engine A has a very short stroke but a very fat and wide bore, engine B has a very long stroke but a very thin and narrow bore. Picture a tall and thin cylindrical container sitting next to a short and wide cylindrical container. Both contain the same volume of air and fuel but are different shapes. These ‘containers’ are the insides of each engines cylinder with the piston in it’s bottom-dead-center position. As the pistons in each cylinder rise during the compression stroke, they are compressing their 150cc’s of air/fuel. When each engines fire at the beginning of their power strokes, the same amount of energy is released in each, as both have the same quantity of air and fuel. Engine B has a longer stroke and because of this, the throw on the crankshaft that the piston is pushing on is of the same length. Engine A has a short stroke and thus, has an equally short throw on the crankshaft. Think of the previously painted picture of the super duper ****tastic Volkswagen tire iron vs. the much longer breaker bar. Engine B’s cylinder pressure is being exerted upon a much longer crankshaft throw, therefore it’s going to produce more twisting force(torque) on its crankshaft than the same amount of pressure pushing down on engine A’s piston which has the much shorter crankshaft throw. Engine B produces WAY much more torque than engine A, dispite being the same size, because of the additional leverage its piston has on the crankshaft.
Now just think, for each single complete revolution, each engines piston is moves up once and down once. For every revolution, each piston must move a distance equal to twice its stroke length . At 1 RPM engine A’s piston moves a distance of X per minute and engine B’s piston moves a distance of 3X per minute. The piston in engine B is moving three times as fast as the piston in engine A despite the fact that both engines are rotating at the same speed. This piston speed, along with the friction and heat that comes from rubbing against the cylinder walls, is whats going to dictate the maximum safe RPM for each engine. Suppose engine B can only safely rev to 5,000 RPM while engine A is capable of 15,000 RPM. Use your imagination along with the HP = (Torque x RPM)/5252 equation and you can begin to see how truly different these 150cc single cylinder engines are.

Begin thinking about cylinder count as well. “Most” engines today are even firing 4-stroke engines. That means that each cylinder fires an equal number of rotational crankshaft degrees from one another and that EVERY cylinder fires once within every 2 RPM interval(4 strokes: intake, compression, power, exhaust and each is 180º of crankshaft rotation). An even firing 4 cylinder will have a power stroke every 180º of crankspin, a 6 cylinder will have a power stroke every 120º of crankspin, an 8 cylinder will fire every 90º of crankspin, and so on and so on. A 4 cylinder has a power stroke every 180º, so as soon as one piston is done providing power, another start providing power. The individual power strokes provide MANY MANY times the Mean Torque that the engine produces. This is because the power stroke must provide enough torque in the power stroke to push through to the exhaust stroke in which torque is lost pushing gasses out of the engine, through the intake stroke in which torque is lost sucking in air and fuel, and then through the compression stroke in which compressed air and fuel are actually exerting torque on the crankshaft in the OPPOSITE direction of which it’s supposed to be rotating. If you look at a graph of how much torque is acting on the crankshaft of an engine you will see both POSITIVE and NEGATIVE amounts of torque. The more cylinders you have in an engine, the narrower the intervals between power strokes becomes. 6 cylinders actually have 60º of power stroke overlap, so when one cylinder fires, another will also fire 120º later and both pistons will be producing torque at the same time for another 60º. In an 8 cylinder this overlap is even greater. So the more cylinders in an engine, the shorter the gap between the POSITIVE and NEGATIVE torque extremes becomes. It’s not uncommon for 8+ cylinder engines to not produce ANY negative torque at all, instead the maximum POSITIVE torque drops off slightly and never has a chance to go negative because of the overlap.

 

Did you author this or copy it from elsewhere?

 

Typed it up myself on microsoft word haha.

 

Awesome write up. I learned a lot from it. Thanks!