Ask most people who are interested in tuning their car what the engine's power output is and they will be able to tell you. Ask about the torque or the torque per litre and chances are you get a blank look. Power and torque are just twin aspects of the same maths that determines how an engine performs and anyone wanting to tune an engine ought to benefit from a better understanding of the what the figures mean. To start we need to explain some definitions.

TORQUE

Torque is a twisting force about an axis of rotation. It is measured in units of force times distance from the axis. When you tighten a bolt you exert a torque on it. If the spanner is 1 foot long and you exert a force of 10 pounds on the end of it then you apply a torque of 10 foot pounds. If the spanner is 2 feet long then the same force would apply a torque of 20 foot pounds. Whether the torque applied creates movement or not is a separate issue. If the bolt has already been tightened to a torque of 50 foot pounds and you apply a spanner to it using a torque of 20 foot pounds then it won't move any further.

WORK

Work is also measured in units of force times distance but there is a subtle distinction between Torque and Work. For work to take place there must be movement involved. Work can be defined as the product of force times distance moved. Lets imagine we have a sack of grain on the floor weighing 100 pounds and we want to lift it onto a table 3 feet high - we would need to do 300 foot pounds of work against gravity to achieve this.

POWER

Power is the rate at which work is done. The more power a thing generates, the more work it can do in a given space of time. Lets imagine we ask a small child and an adult to both lift the sack of grain above onto the table. The adult might be able to lift the whole sack in one go but the child would probably not. However the child could take a pan and lift the grain one panful at a time until the whole 100 pounds was on the table. It would take longer but the end result would be the same. Both the child and the adult would have done 300 foot pounds of work but at different rates - we can therefore say that the adult was more "powerful" than the child.

If the adult lifted the whole bag in one go in 5 seconds then he would have done work at the rate of 300 foot pounds in 5 seconds - i.e. 300 x 60/5 = 3,600 foot pounds per minute. If the child took 1 minute with the pan then his rate of doing work would be 300 foot pounds per minute - only 1 twelfth the rate of the adult. In other words the adult generated 12 times as much power as the child.

The more power a car engine generates, the more work it can do in a given period of time. This work might be driving the car at high speed against air resistance, moving the car up a steep hill or just accelerating the car rapidly from rest.

HORSEPOWER

It was James Watt who refined Newcomen's steam engine design and turned it into a machine capable of doing work at a reasonably efficient rate. The most common applications of steam power in the early days were pumping water or lifting coal from mines. As far as coal is concerned it was horses that did most of this work before the coming of steam power.

Watt needed to be able to rate the power output of his steam engines in order to advertise them. He decided that the most sensible unit of power to compare them to was the rate at which a horse could do work. He tested the ability of a variety of horses to lift coal using a rope and pulley and eventually settled on the definition of a "Horsepower" as 33,000 foot pounds per minute - or 550 foot pounds per second. In fact the horses he tested could not keep up a steady work rate as high as this (he actually averaged them at 22,000 foot pounds per minute) but being a conservative man he added 50% to the rate he measured in case other people had more powerful horses than he had tested. Maybe modern engine builders might take note of the good sense of James Watt and not be quite so optimistic in the power claims for their own engines!!

So a horse walking at a comfortable speed of 5 feet per second would need to raise a weight of 110 pounds to do work at the rate of 1 Horsepower. Not so hard you might think - in fact a strong man can do that amount of work - but only in short bursts. A horse can easily do work at a faster rate than this but again not without rest. A steam engine, provided you keep it fueled can run continuously. Watt's measurement was designed to take account of the fact that machines can run for ever but animals or men need to stop and rest from time to time.

BHP and HP

All the B means is "brake". The old word for a dyno - because the engine torque was measured by applying a brake to the flywheel rather than a torque converter or electrical motor which is how it's done nowadays. There's no other difference between the two and they both just mean horsepower.

HOW TORQUE AND POWER RELATE

The final part of the story is to see how we calculate power from torque or vice versa. Let's imagine we have a pulley at the top of a mine that is 1 foot in radius - or 2 feet in diameter. At the bottom of the mine, at the end of a rope leading round the pulley is a bag of coal weighing 100 pounds. Instead of using a horse to pull on the rope let's connect an engine to the pulley - perhaps by bolting the pulley to the crankshaft of the engine.

In order to lift the coal we need to apply a torque of 100 foot pounds to the pulley because the coal is pulling down with a force of 100 pounds applied at 1 foot from the axis of rotation. In other words the Torque applied is the Weight times the Radius of the pulley. If the engine turns the pulley at 1 revolution per minute how much work is being done?

Well for each turn of the pulley the coal will rise the same amount as the circumference of the pulley which is 2 pi times the radius = 3.14 x 2 = 6.28 feet. So in 1 minute the engine will do 628 foot pounds of work.

We can rearrange the above in terms of torque and speed:

The rate of work being done (or Power) is Force x Distance per minute = Weight x radius x 2 pi x rpm foot pounds per minute. However we already know that Weight times Radius = Torque so we can equally say:

Power = Torque x 2 pi x rpm

To turn this into Horsepower we need to divide by 33,000. Our final equation therefore becomes:

Horsepower = Torque x 2 pi x rpm / 33000 which simplifies to:

Horsepower = Torque x rpm / 5252.

This is the universal equation that links torque and horsepower. It doesn't matter whether we are talking about petrol engines, diesel engines or steam engines. If we know the rpm and the torque we can calculate horsepower. If we know horsepower and rpm we can calculate torque by rearranging the equation above:

Torque = Horsepower x 5252 / rpm

Hopefully you can also see that when an engine is turning at 5252 rpm, its torque and horsepower figure is the same. Next time you see a graph of the torque and horsepower of an engine check to see that the lines cross at 5252 rpm. If not then the graph is wrong. This only applies of course if the power is being measured in horsepower and the torque in foot pounds and both lines are shown on the same axes. There are many other units in which torque and horsepower can be measured - for example power can be measured in Watts and torque in Newton metres. Unless we need to convert to such continental measures we can usually stick to horsepower and foot pounds.

One measure to be aware of though is the "continental horsepower" or PS. This stands for "PferdeStarke" - the German translation of "horse power". In France you sometimes see the same measure being called a "CV" for Cheval Vapeur. This measure was chosen in Europe as being the closest thing to a horsepower that could be expressed in nice round metric units - 75 kilogramme metres per second to be exact. It is commonly used by car manufacturers nowadays and tends to get used synonymously with bhp although it is actually a slightly smaller unit of power. One PS is about 98.6% of one bhp. The conversion table below covers the units most commonly used to express power and torque.

To convert from: To: Multiply by:

BHP PS 1.01387

BHP Ft Lbs/second 550

BHP Watts 745.7

PS Kg M/second 75

PS Ft Lbs/second 542.476

PS Watts 735.5

Kilowatts BHP 1.341

Kilowatts PS 1.360

Lb Ft Nm 1.356

Bloody Car Magazines

Have you noticed that magazines now tend to quote power in horsepower and torque in Newton metres? In fact they aren't even really doing that properly. What they quote as horsepower is actually PS because that's what the manufacturers use and the muppets who write for the magazines don't know the difference between PS and BHP. Ok so there's only 1.4% difference between the two measures but it's just one more thing that adds to the trend for power figures ending up being overstated. The main point is that Newton metres aren't from the same system of measurement as PS in the first place. This is how it should work.

1 bhp is 550 foot pounds per second. The correct measure of torque when power is stated in bhp is foot pounds.

1 PS is 75 kilogram metres per second. The correct measure of torque when power is stated in PS is kilogram metres.

1 kilowatt is 1000 Newton metres per second. The correct measure of torque when power is stated in kilowatts is Newton metres.

Most people have at least a vague idea what horsepower is but very little understanding of torque. Ask the average person how many bhp his engine is rated at and he'll know the answer but ask him about the torque figures and you get blank looks. Now that the magazines are using two different systems of measurement it's even more confusing. Most British (or American) engineers are familiar with foot pounds and the rules for estimating how many foot pounds per litre an engine should be able to produce. If you carry on reading these articles you'll see some of those rules in the next section and they are the best measure for deciding whether a power claim is true or false. But how many Newton metres per litre should an engine be able to produce? With so many conversion factors flying about even I can't remember it all off the top of my head and I do this sort of thing every day. So to make sense of a car test these days I have to get my crib sheet out, convert PS to BHP, Newton metres to pound feet and finally get some idea of what is really happening. Kilogram metres don't even translate nicely into Newton metres because the conversion is the value of g which is 9.81.

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TORQUE

Torque is a twisting force about an axis of rotation. It is measured in units of force times distance from the axis. When you tighten a bolt you exert a torque on it. If the spanner is 1 foot long and you exert a force of 10 pounds on the end of it then you apply a torque of 10 foot pounds. If the spanner is 2 feet long then the same force would apply a torque of 20 foot pounds. Whether the torque applied creates movement or not is a separate issue. If the bolt has already been tightened to a torque of 50 foot pounds and you apply a spanner to it using a torque of 20 foot pounds then it won't move any further.

WORK

Work is also measured in units of force times distance but there is a subtle distinction between Torque and Work. For work to take place there must be movement involved. Work can be defined as the product of force times distance moved. Lets imagine we have a sack of grain on the floor weighing 100 pounds and we want to lift it onto a table 3 feet high - we would need to do 300 foot pounds of work against gravity to achieve this.

POWER

Power is the rate at which work is done. The more power a thing generates, the more work it can do in a given space of time. Lets imagine we ask a small child and an adult to both lift the sack of grain above onto the table. The adult might be able to lift the whole sack in one go but the child would probably not. However the child could take a pan and lift the grain one panful at a time until the whole 100 pounds was on the table. It would take longer but the end result would be the same. Both the child and the adult would have done 300 foot pounds of work but at different rates - we can therefore say that the adult was more "powerful" than the child.

If the adult lifted the whole bag in one go in 5 seconds then he would have done work at the rate of 300 foot pounds in 5 seconds - i.e. 300 x 60/5 = 3,600 foot pounds per minute. If the child took 1 minute with the pan then his rate of doing work would be 300 foot pounds per minute - only 1 twelfth the rate of the adult. In other words the adult generated 12 times as much power as the child.

The more power a car engine generates, the more work it can do in a given period of time. This work might be driving the car at high speed against air resistance, moving the car up a steep hill or just accelerating the car rapidly from rest.

HORSEPOWER

It was James Watt who refined Newcomen's steam engine design and turned it into a machine capable of doing work at a reasonably efficient rate. The most common applications of steam power in the early days were pumping water or lifting coal from mines. As far as coal is concerned it was horses that did most of this work before the coming of steam power.

Watt needed to be able to rate the power output of his steam engines in order to advertise them. He decided that the most sensible unit of power to compare them to was the rate at which a horse could do work. He tested the ability of a variety of horses to lift coal using a rope and pulley and eventually settled on the definition of a "Horsepower" as 33,000 foot pounds per minute - or 550 foot pounds per second. In fact the horses he tested could not keep up a steady work rate as high as this (he actually averaged them at 22,000 foot pounds per minute) but being a conservative man he added 50% to the rate he measured in case other people had more powerful horses than he had tested. Maybe modern engine builders might take note of the good sense of James Watt and not be quite so optimistic in the power claims for their own engines!!

So a horse walking at a comfortable speed of 5 feet per second would need to raise a weight of 110 pounds to do work at the rate of 1 Horsepower. Not so hard you might think - in fact a strong man can do that amount of work - but only in short bursts. A horse can easily do work at a faster rate than this but again not without rest. A steam engine, provided you keep it fueled can run continuously. Watt's measurement was designed to take account of the fact that machines can run for ever but animals or men need to stop and rest from time to time.

BHP and HP

All the B means is "brake". The old word for a dyno - because the engine torque was measured by applying a brake to the flywheel rather than a torque converter or electrical motor which is how it's done nowadays. There's no other difference between the two and they both just mean horsepower.

HOW TORQUE AND POWER RELATE

The final part of the story is to see how we calculate power from torque or vice versa. Let's imagine we have a pulley at the top of a mine that is 1 foot in radius - or 2 feet in diameter. At the bottom of the mine, at the end of a rope leading round the pulley is a bag of coal weighing 100 pounds. Instead of using a horse to pull on the rope let's connect an engine to the pulley - perhaps by bolting the pulley to the crankshaft of the engine.

In order to lift the coal we need to apply a torque of 100 foot pounds to the pulley because the coal is pulling down with a force of 100 pounds applied at 1 foot from the axis of rotation. In other words the Torque applied is the Weight times the Radius of the pulley. If the engine turns the pulley at 1 revolution per minute how much work is being done?

Well for each turn of the pulley the coal will rise the same amount as the circumference of the pulley which is 2 pi times the radius = 3.14 x 2 = 6.28 feet. So in 1 minute the engine will do 628 foot pounds of work.

We can rearrange the above in terms of torque and speed:

The rate of work being done (or Power) is Force x Distance per minute = Weight x radius x 2 pi x rpm foot pounds per minute. However we already know that Weight times Radius = Torque so we can equally say:

Power = Torque x 2 pi x rpm

To turn this into Horsepower we need to divide by 33,000. Our final equation therefore becomes:

Horsepower = Torque x 2 pi x rpm / 33000 which simplifies to:

Horsepower = Torque x rpm / 5252.

This is the universal equation that links torque and horsepower. It doesn't matter whether we are talking about petrol engines, diesel engines or steam engines. If we know the rpm and the torque we can calculate horsepower. If we know horsepower and rpm we can calculate torque by rearranging the equation above:

Torque = Horsepower x 5252 / rpm

Hopefully you can also see that when an engine is turning at 5252 rpm, its torque and horsepower figure is the same. Next time you see a graph of the torque and horsepower of an engine check to see that the lines cross at 5252 rpm. If not then the graph is wrong. This only applies of course if the power is being measured in horsepower and the torque in foot pounds and both lines are shown on the same axes. There are many other units in which torque and horsepower can be measured - for example power can be measured in Watts and torque in Newton metres. Unless we need to convert to such continental measures we can usually stick to horsepower and foot pounds.

One measure to be aware of though is the "continental horsepower" or PS. This stands for "PferdeStarke" - the German translation of "horse power". In France you sometimes see the same measure being called a "CV" for Cheval Vapeur. This measure was chosen in Europe as being the closest thing to a horsepower that could be expressed in nice round metric units - 75 kilogramme metres per second to be exact. It is commonly used by car manufacturers nowadays and tends to get used synonymously with bhp although it is actually a slightly smaller unit of power. One PS is about 98.6% of one bhp. The conversion table below covers the units most commonly used to express power and torque.

To convert from: To: Multiply by:

BHP PS 1.01387

BHP Ft Lbs/second 550

BHP Watts 745.7

PS Kg M/second 75

PS Ft Lbs/second 542.476

PS Watts 735.5

Kilowatts BHP 1.341

Kilowatts PS 1.360

Lb Ft Nm 1.356

Bloody Car Magazines

Have you noticed that magazines now tend to quote power in horsepower and torque in Newton metres? In fact they aren't even really doing that properly. What they quote as horsepower is actually PS because that's what the manufacturers use and the muppets who write for the magazines don't know the difference between PS and BHP. Ok so there's only 1.4% difference between the two measures but it's just one more thing that adds to the trend for power figures ending up being overstated. The main point is that Newton metres aren't from the same system of measurement as PS in the first place. This is how it should work.

1 bhp is 550 foot pounds per second. The correct measure of torque when power is stated in bhp is foot pounds.

1 PS is 75 kilogram metres per second. The correct measure of torque when power is stated in PS is kilogram metres.

1 kilowatt is 1000 Newton metres per second. The correct measure of torque when power is stated in kilowatts is Newton metres.

Most people have at least a vague idea what horsepower is but very little understanding of torque. Ask the average person how many bhp his engine is rated at and he'll know the answer but ask him about the torque figures and you get blank looks. Now that the magazines are using two different systems of measurement it's even more confusing. Most British (or American) engineers are familiar with foot pounds and the rules for estimating how many foot pounds per litre an engine should be able to produce. If you carry on reading these articles you'll see some of those rules in the next section and they are the best measure for deciding whether a power claim is true or false. But how many Newton metres per litre should an engine be able to produce? With so many conversion factors flying about even I can't remember it all off the top of my head and I do this sort of thing every day. So to make sense of a car test these days I have to get my crib sheet out, convert PS to BHP, Newton metres to pound feet and finally get some idea of what is really happening. Kilogram metres don't even translate nicely into Newton metres because the conversion is the value of g which is 9.81.

_________________