Horsepower = Torque x RPM divided by 5252

[08Rhino450SE]

Horsepower is a measurement of how much work (force over distance) an engine can do while including the time it took to do the work. Horsepower is a function of a given amount of torque (force) acting over a given distance within a given amount of time (rpm). A simple example of torque (performing work over a specified distance) is applying a force of one pound over a distance of one foot. This is equivalent to one pound-foot of work (force over distance). However, the definition of horsepower also includes a time factor. So let's now assume we applied a force of one pound over a distance of one foot and did it in one minute. This would be equivalent to a small fraction of a horsepower (because James Watt's definition of one horsepower is performing 33,000 pound-feet of work in one minute).

We can relate horsepower to the internal combustion engine by associating the three factors involved (force, distance and time) in the following manner:
(1) Force is equivalent to the amount of combustion pressure applied to a given square area of the piston dome,
(2) Distance is equivalent to the engine's stroke length, and
(3) Time is defined by the rpm or speed at which the engine is turning.

At any given rpm, horsepower is directly proportional to torque. By increasing torque at a specified rpm, horsepower increases at a corresponding amount. If torque remains constant but rpm increases, then horsepower increases in direct proportion to rpm. Even when torque starts to drop off (beyond the engine's torque peak), as long as rpm increases faster than torque drops, horsepower will still increase.

Horsepower can also be described as how much and how often a cylinder fills, and how often it fires in a specified time. However, keep in mind that horsepower is a calculated number, so the only practical method for determine horsepower is by first measuring engine torque and rpm with a dynamometer.

Since horsepower is equal to torque multiplied by rpm, any torque increase results in a power increase at a given rpm level. This is why it is better to concentrate on improving torque instead of horsepower for the best performance. Top racers and engine builders concentrate on improving torque within the rpm range the engine needs to operate.

Torque is determined by the percentage a cylinder is filled at a given rpm. The greater the cylinder fill, the greater the torque will be. If power is to be increased, it's crucial to improve the engine's ability to breathe. Peak torque is reached when the engine runs out of air or loses its ability to breathe better. This is the point of maximum cylinder fill. An engine can continue to make more horsepower even when torque is falling as long as rpm is increasing faster than torque is falling. So, if maximum torque is the point of maximum cylinder fill, then maximum horsepower is the point where torque is falling off faster than rpm is increasing.

For a given engine combination, displacement, intake and exhaust tracts, cylinder head, cam specifications, stroke and rod length are among the factors that control the amount of torque and the torque peak. Additionally, mean airflow velocity can also have a significant effect on peak torque rpm. As rpm increases, the engine pumps more air until intake velocity increases to the point where port friction loss stops the increase in air intake. Mean flow velocity is dependent upon runner or pipe cross-sectional area, not volume. Consequently, peak torque rpm can be controlled by selecting parts with specific cross-sectional areas. Another reason airflow velocity is important is because cylinder filling increases as the square of velocity, but only linearly as airflow increases.

Even though all engines produce torque, an engine that produces peak torque at low rpm is often referred to as a torque engine, while one that produces peak torque at high rpm is typically referred to as a horsepower engine. Since torque and horsepower curves always cross at 5252 rpm, an engine will always produce more pound-foot of torque than horsepower below 5252 rpm, and more horsepower than pound-foot of torque above 5252 rpm. This explains how a four-cylinder import engine that revs to 13,000 rpm can produce higher horsepower than a v-twin engine, while yielding less torque at the crankshaft. Long stroke, small bore (under square) engines like the v-twin typically are lower revving with high torque below 5252 rpm. Conversely, big bore, short stroke (over square) engines normally are higher revving and produce lots of torque at high rpm for high horsepower from a relatively low crankshaft torque reading.

Most riders generally prefer a torque engine with a wide flat torque band over a peaky, high horsepower engine producing power in a narrow rpm range because the rider doesn't have to work as hard trying to keep the engine's rpm in the power band.

This writeup is abridged from Chapter 7 of the V-Twin Tuner's Handbook, Volume One, by D. William Denish, and is For Educational Purposes Only.

[08Rhino450SE]

Horsepower = Torque x RPM divided by 5252

Part 2

There are numerous ways to increase an engine's torque. The most obvious is described by the adage 'there's no substitute for cubic inches.' More cubic inches results in more torque, especially if the displacement is added through a longer stroke. In general, increasing stroke shifts the torque peak to a lower rpm. This is especially true for a long stroke engine built with a stock flowing head. On the other hand, improving an engine's ability to breathe moves the torque peak to a higher rpm.

Carburetor selection should be based on matching the carb's cfm airflow to the engine's displacement and rpm limit. Too large of a carb reduces air velocity through the venturi, reducing the signal to the jets and resulting in poor atomization and less metering accuracy. The consequence is less torque along with poor throttle response and rideability.

By installing a high flowing cylinder head, cylinder fill and torque will increase, but a modified head improves torque mostly at midrange and high rpm. To maximize horsepower and still maintain torque at the bottom end, consider the following. Basically, airflow should be matched to engine displacement and rpm. For a given cfm airflow, keep valves and ports as small as possible because mean airflow velocity has a significant effect on where torque peaks and the amount of torque at low rpm. As rpm increases, an engine pumps air until intake velocity increases to the point where port friction loss stops the increase in air intake. Mean flow velocity is dependent upon intake runner or exhaust pipe cross-sectional area, not volume. Therefore, peak torque rpm can be controlled by selecting parts with specific cross-sectional areas.

Smaller valves and ports maximize velocity for improved cylinder fill and exhaust scavenging at low rpm. The ratio of the valve seat I.D. to the valve head diameter is critical for flow and torque. Changing the ratio will change high and low lift flow numbers. The lower the ratio, the larger the seat radius becomes, but the smaller the throat diameter. A smaller throat diameter tends to reduce high lift flow. The optimum ratio usually gets smaller as the valve diameter gets smaller. Port and valve shapes, along with bore and stroke, are other factors that contribute to the ideal ratio.

Another important cylinder head consideration that affects volumetric efficiency is combustion chamber design. Increasing combustion efficiency through optimized combustion chamber design and fuel distribution will improve not only volumetric efficiency but also thermal efficiency, thus resulting in increased torque.

Increasing the compression ratio to the maximum allowed by the gasoline octane will add torque to any engine. However, when a long duration cam is also installed, the effect of a compression increase is of much greater magnitude, especially at low rpm. Cam timing (especially the intake valve closing) must be matched to the compression ratio to achieve an optimum engine. Cam manufacturers deliberately keep the intake valve open for many degrees after the piston reaches bottom dead center to improve cylinder fill and torque at high rpm. But at low rpm a late closing intake reduces cylinder fill and torque. Torque lost at low rpm can be regained by increasing the engine's mechanical compression ratio, so the corrected compression ratio maintains a predetermined level.

For example, assume an engine has a mechanical compression ratio of 10.5:1 and a corrected ratio of 9.3:1. Closing the intake valve later will reduce the engine's corrected ratio, but increasing the mechanical ratio beyond 10.5:1 can bring the corrected ratio back to 9.3:1. A street engine with a good combustion chamber setup and run on pump gas can handle about 9:1 to 9.3:1 corrected compression ratio without suffering detonation, while an engine fed race gas can handle a 11:1 and 13:1 or higher corrected compression ratio.

Of the four valve-timing events, the closing of the intake and opening of the exhaust have the greatest effect on torque output. Closing the intake valve late increases high rpm horsepower at the expense of low end torque. Nevertheless, remember that increasing the mechanical compression ratio recovers much of the lost low end torque. Closing the intake valve early does just the opposite of closing it late. Be careful of closing the intake valve too early with high compression because the engine can easily become detonation prone.

On the exhaust side, opening the exhaust valve later extracts the maximum amount of energy from the expanding gases and increases bottom end torque, but opening it too late creates pumping losses and severely hurts top end power. On the other hand, opening the exhaust valve early improves top end torque at the expense of the bottom end. An early opening exhaust is best suited to high engine speeds ad high compression. Obviously there are tradeoffs. To maximize bottom and midrange torque, select a cam that closes the intake valve early and opens the exhaust valve late.

This writeup is abridged from Chapter 7 of the V-Twin Tuner's Handbook, Volume One, by D. William Denish, and is For Educational Purposes Only.

[Yotehunter66]

Holy smokes man! You had to have cut and pasted that. That would be a lot to type.

[moobster]

Now that, is a GREAT POST. Thank you.

[08Rhino450SE]

Holy smokes man! You had to have cut and pasted that. That would be a lot to type.

i wish. typing was the most useful course i ever took in high school haha.
it's a great book, but it's hard to find now.

[SteveS]

i wish. typing was the most useful course i ever took in high school haha.
it's a great book, but it's hard to find now.

Typing was not your typical guy course in my day, that is what secretaries (what are they again?) were supposedly for. I took the course and it has proved very handy over the years. Engineering (CAD) has kind of ruined me in that I now type by touch with my left hand but I single finger poke with my right hand (mouse and number-pad hand). Ah well, ruined for life.

Did the author of this book tuck away any teachings about how to get the money to put all of this knowledge to good use? Or are you going to keep that to yourself? LOL

Thanks for the effort of transcribing it and making it available to us!

[08Rhino450SE]

i went to an all male prep school. what a waste. oh, but the typing teacher was pretty hot. (at the ripe old age of 17, in an all boys school, all the female teachers were hot!)

the book contains a lot of pro engine design and tuning secrets, race math, reference tables etc. that apply to professionals and weekend weirdos alike.

i highly recommend it to anyone that wants to understand why that internal combustion engine works the way it does.

[madmax 1]

great post Denny , thanks