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 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 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 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.
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 who
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 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.
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 |