bhp & torque.pdf

fast tech / TECH / BHP & TORQUE /

fast tech

MAX POWER

Horsepower and torque:

what are they exactly,

and how do you calculate

those all-important ﬁ gures?

Stu explains all.

enjoyed

last month’s article about rolling

roads and weren’t too upset by

some of the things you read about

why most of the ﬁ gures they

generate for ﬂ ywheel power are

wrong. But it did bring me neatly

into a topic about the ﬁ gures they

generate, or, more accurately the

units they use to clarify the graphs

they generate.

These units of measurement

are of course the horsepower

and torque. It is quite surprising

how many people don’t know the

difference between the two when

they really should do, so I am going

to dedicate this month to explaining

precisely all you will ever need to

know about power and torque, how

it’s derived and what the difference

is between the two.

Having worked as a tuner

for 17 years, Stewart ‘Stu’

Sanderson is one of the

most-respected names in

the business.

A Level 5-trained fuel-

injection technician, in the

past Stu has worked for a

Ford Rallye Sport dealer, a

well-known fuel-injection

specialist and various

tuning companies.

Then seven years ago he

joined forces with Kenny

Walker and opened up

Motorsport Developments

near Blackpool (01253

508400, www.remapping.

co.uk ), specialising in engine

management live remapping,

as well as developing a range

of Evolution chips which are

now sold all over the world.

He’s also jointly responsible

with Webmaster, Petrucci for

www.passionford.com .

Started in 2003, it’s grown

rapidly from a few friends

contributing, to one of the

biggest Ford communities on

the web.

Stu’s enviable knowledge

of the workings of modern-

day Ford performance engines

means that every month he’s

just the man to explain how

and why things work, and

most importantly how they

can be improved.

using common procedures. If

we take a spanner that is 1 ft long

and put it over a nut and then hang

a 10 lb weight from the end of it, we

would be exerting a rotational force

of 10 ft.lb on the nut. If we hung

a 30 lb weight off the end of the

spanner it would then exert 30 ft.lb

of rotational force on the nut.

Conversely, if we extended the

spanner to 2 ft long, and used the

same 30 lb weight on the end, we

would then exert a force of 60 ft.lb.

In a nutshell, the correct formula to

use for calculation of torque output

is force exerted x distance from the

axis. If that doesn’t make sense,

please read it again until it does so

that you can proceed further, as it’s

the most important part for you to

grasp before moving on to tackle

the rest.

a simple

deﬁ nition, work is the transfer of

energy from one thing to another.

It is, however, often mistakenly

believed to be the torque itself.

This is a common mistake, and is

because it uses the same units of

measurement, such as ft.lb and

Newton metres (Nm). Even so it is

not the same at all, as we can often

exert torque and actually achieve no

work at all. A good example of this is

when we apply our 30 ft.lb to a bolt

already tightened to 60 ft.lb. We will

be exerting the torque as expected,

but it will not turn the nut and thus it

will not result in any work done. The

work done must be expressed as a

movement. The correct formula to

use for calculation of work done is

force exerted x distance moved. No

movement = no work done. Simple...

and this brings us neatly to power.

WHAT IS TORQUE?

Before you can fully understand

horsepower, ﬁ rst you must

understand torque, so this is

where we will start. Torque is

simply a twisting force used to

rotate an object around an axis.

The measurement used to express

torque is most commonly ‘foot

pound’ (expressed normally as ft.lb

or lb.ft).

This measurement unit is actually

very simple to visualise and express

WHAT IS WORK DONE?

Work isn’t often talked about when

referring to cars, but it needs to be

explained as it relates to power. As

WHAT IS POWER?

Power is the amount of work

done in a period of time, so

TORQUE = FORCE X DISTANCE

2 ft

1 ft

Words: Stewart Sanderson

Both these pulling forces (a

and b) will result in the same

rotational torque at the nut

FORCE OF 20 lbs FORCE OF 10 lbs

FAST FORD NOVEMBER 2007

0125

MAX POWER

I HOPE you

fast tech

/ TECH / BHP & TORQUE /

fast tech

HORSEPOWER = TORQUE ( ft.lb)

X ENGINE SPEED/5252

to 181 ft per minute and multiplied

that by the 180 lb of force the horse

pulled (181x180) and came up with

32,580 ft.lb per minute. That ﬁ gure

was rounded off to 33,000 ft.lb per

minute, the very same ﬁ gure we still

use today.

So, what’s the relationship

between power and torque?

This is quite simple to work out by

using this equation: torque (ft.lb) x

engine speed/5252 = horsepower.

So if you have an engine that

generates 200 ft.lb of torque at 3000

rpm you multiply the two together

and then divide it by 5252 and you

ﬁ nd that you have an engine that

develops 114.24 bhp @ 3000 rpm:

(200x3000/5252 = 114.24 bhp)

Some rolling road operators provide torque ﬁ gures from dyno runs in

Nm making the 5252 rpm crossover rule redundant (see ‘5252? Why?’)

turning force across as much of

our engine’s operating range as

possible because for one, it makes

it easier to drive, and two, it does

make it accelerate better at any

given engine speed. Now nearly

all road engines I can think of are

designed to have a peak volumetric

efﬁ ciency (VE) somewhere between

2000 and 4000 rpm.

The torque ﬁ gure will pretty much

always peak at the engine’s peak VE

range, so wherever you feel that big

shove in the back as you accelerate

your engine, that’s the peak torque

and peak VE point of the engine that

you are feeling.

The engine tends to lose torque

as it moves further away from

this peak efﬁ ciency area it was

designed to operate in, be that

slower or faster.

But as the engine is going faster

and faster it will still do more work

in any given time frame due to it

processing more air/fuel, and so the

horsepower ﬁ gure should continue

to climb as the engine is revved

faster whilst the torque falls off as

we go further away from the peak

torque and VE.

So, the key to making good

horsepower is to keep the torque

ﬁ gure high for as long as possible.

That way, our horsepower graph will

be climbing steeply.

Just remember: the torque is the

actual turning force generated by

your engine, and the horsepower is

the amount of work that torque

can do for you at that particular

engine speed.

1 FOOT IN

1 SECOND

550 LB

the more power an engine

develops, the more work it

can get done in any given

time span.

Power can be best described by

comparing two different humans.

If we take a strong human and

a weak human and ask them to

move 500 lb of sandbags from the

ground, and put them on a shelf 1

ft above the ground, the big strong

man may be able to lift all of the

sandbags up onto the shelf in one

go, but the weaker man may have

to move a few at a time, and take

10 goes. Both men will have done

500 ft.lb of work, but the stronger

man did it much faster, thus he

would be deemed more powerful

as he is now proven to be able to

do the same amount of work, but

in less time than the less powerful

man When related to a car, the

more power an engine has the

more work it can get done in less

time. This work may be perceived

as powering a car up a large hill, or

maybe accelerating the car hard on

a long straight road.

when he came to market his steam

engine. In those days, the accepted

power source was horses, and Watt

needed to ﬁ nd a way to compare

the capabilities of his new steam

engine to the horse. He spent a long

time comparing and measuring

a horse’s ability to do work in a

given time span, and he eventually

decided upon a formula that gave

a good indication of an average

horse’s work ability.

Watt measured a horse’s ability to

lift coal up a mineshaft using a rope

and a pulley. After much calculation,

he settled on the deﬁ nition of one

horsepower being 33,000 lb.ft per

minute... This basically means he

decided that a horse was capable

of moving 33,000 lb of weight, 1 ft in

1 minute. How he came up with this

ﬁ gure is actually quite interesting so

I will tell you about it...

He studied an average horse

attached to a typical mill (say

grinding corn) walking around a

24 ft diameter circle. He calculated

that the horse pulled with a force of

180 lb, although to my knowledge

nobody has ever detailed how he

came up with that ﬁ gure in the ﬁ rst

place, but it is known that he did.

He noted that a horse normally

made 144 trips around the circle

in an hour which, when calculated

out to revolutions per minute

meant that the horse travelled at

a speed of 180.96 ft per minute.

Watt simply rounded off the speed

5252 ? WHY?

Your next question is I expect going

to be what’s the 5252 ﬁ gure used

for? Where did that come from?

Well, remember that 33,000 ft.lb

per minute? Well, if we break that

down into seconds (divide it by 60)

we get 550 ft.lb per second. So we

know that one unit of bhp = 550 ft.lb

per second.

The units of torque are in lb.ft

of course, so to get from torque to

horsepower we need to find out

what the ‘per second’ unit is going

to be for the torque, and we get

this by multiplying the torque by

engine speed. Of course, engine

speed is normally referred to in

revolutions per minute (rpm) and

since we want a ‘per second’ unit

we need to convert revolutions

per minute into revolutions per

second which as it happens is

quite easy. We just divide the

revs per minute number by 60,

of course because we have

60 seconds in a minute.

Now, what we need next is a

dimensionless unit for revolutions.

This unit already exists and is in fact

called a radian. A radian is a ratio

of the length of an arc divided by

the length of a radius, so the units

of length cancel out and you’re

WHAT IS HORSEPOWER?

So what is horsepower, then?

Well, James Watt came up with the

measurement of horsepower for us

IN A NUTSHELL

Hopefully after reading this

article you will now understand

the following:

1. The turning power generated by

an engine is actually the torque.

2. The horsepower ﬁ gures quoted

about engines simply relate to how

much work can be done by that

torque in a given time.

You may also have heard the

statement, usually in the pub, that

sounds something like: “Horsepower

sells cars, but torque wins races”. Is

that true? Well, yes and no. I feel that

the person who ﬁ rst quoted that

doesn’t actually understand what

he is talking about as without torque

you have no horsepower to start

with, so his horsepower would be

pretty damn useless at winning any

races without any torque wouldn’t

they? So, it’s kind of a meaningless

quote. However, it does have a ring

of truth if broadened somewhat and

related to a road car.

Looking at a road engine — as

most of us are — we want as much

HORSEPOWER CAN

BE CONVERTED INTO

OTHER UNITS AS WELL

1 HORSEPOWER = 746 WATTS

So if you took a 1 horsepower horse and put it on a treadmill, it

could operate a generator producing a continuous 746 watts.

P r

Above: a Radian is a dimen-

sionless unit for revolutions

left with a dimensionless measure.

You can think of a revolution as

a measurement of an angle. One

revolution is 360 degrees of a circle.

Since the circumference of a circle

is (2 x pi x radius), there are 2-pi

radians in a revolution. To convert

revolutions per minute to radians

per second, you multiply rpm by

(2-pi/60), which equals 0.10472

radians per second. This ﬁ nally

gives us the ‘per second’ unit we

need to calculate horsepower. So

let’s see how this works out all

together shall we? We need to get

to horsepower, which is 550 ft.lb

per second, using torque measured

in lb.ft and engine speed measured

in rpm, so if we divide the 550 ft.lb

by the 0.10472 radians per second

(engine speed), we get 550/0.10472,

which equals 5252.

So, if you multiply torque by

engine speed and divide the product

by 5252, rpm is converted to radians

per second and you can get from

torque to horsepower. Simple eh?

No, I agree it’s not, but at least

somebody else did it all for us and

we just need to remember the result

of it all which was 5252.

1 HORSEPOWER FOR AN HOUR = 2545 BTU

If you took that 746 watts and ran it through an electric heater

for an hour, it would produce 2545 BTU (where a BTU is the

amount of energy needed to raise the temperature of 1 lb of

water 1 degree F).

OTHER MEASUREMENTS USED

radians in a revolution. To convert

revolutions per minute to radians

per second, you multiply rpm by

(2-pi/60), which equals 0.10472

radians per second. This ﬁ nally

gives us the ‘per second’ unit we

need to calculate horsepower. So

let’s see how this works out all

together shall we? We need to get

to horsepower, which is 550 ft.lb

per second, using torque measured

in lb.ft and engine speed measured

in rpm, so if we divide the 550 ft.lb

by the 0.10472 radians per second

(engine speed), we get 550/0.10472,

It’s worth noting here

that all these ﬁ gures

are related to the units

we use here in the UK

and US, namely bhp

and ft.lb of torque. But

there are others in use.

On the continent

you tend to see PS

— this stands for

PferdeStarke, the

German equivalent

of horsepower. In

some other European

countries you will

often hear the term

CV, which stands

for Cheval Vapeur.

These measures

were chosen in

Europe because

they were a little

easier to express in

nice, round metric

numbers but it’s

worth knowing that

one PS or CV is actu-

ally only 0.986 bhp.

1 BTU = 1055 JOULES

Presumably, a horse producing 1 horsepower would burn 641

calories in one hour if it were 100 per cent efﬁ cient.

[OR 252 GRAM-CALORIES OR 0.252 FOOD CALORIES]

Most manufacturers now quote

PS instead of bhp. Hence the

Fiesta ST is 150 PS (148 bhp)

‘Torque wins races’, so the saying

goes. If only it was as easy as that!

So, if you multiply torque by

engine speed and divide the product

by 5252, rpm is converted to radians

per second and you can get from

torque to horsepower. Simple eh?

No, I agree it’s not, but at least

somebody else did it all for us and

we just need to remember the result

FAST FORD NOVEMBER 2007

NOVEMBER 2007

0127

are related to the units

we use here in the UK

and US, namely bhp

and ft.lb of torque. But

there are others in use.

— this stands for

PferdeStarke, the

German equivalent

of horsepower. In

some other European

CV, which stands

for Cheval Vapeur.

These measures

were chosen in

Europe because

nice, round metric

numbers but it’s

worth knowing that

one PS or CV is actu-

ally only 0.986 bhp.

FAST FORD NOVEMBER 2007

0127

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