15 Work per minute, power and horsepower

14



The Motor Vehicle



precisely the same as that for the power output in watts, except that p, D and

L are in units of 1bf/in2, in and ft, and the bottom line of the fraction is

multiplied by 550.

Following the formation of the European common market, manufacturers

tended to standardise on the DIN (Deutsche Industrie Norm 70 020) horsepower, which came to be recognised as an SI unit. In 1995, however, the ISO

(International Standards Organisation) decreed that horsepower must be

determined by the ISO 1585 standard test method. This standard calls for

correction factors differing from those of the DIN as follows: 25°C instead

of 20°C and 99 kPa instead of 1013 bar, respectively, for atmospheric

temperature and pressure, and these make it numerically 3% lower than the

DIN rating. The French CV (chevaux) and the German PS (pferdestarke),

both meaning ‘horse power’, must be replaced by the SI unit, the kilowatt,

1 kW being 1.36 PS.



1.16



Piston speed and the RAC rating



The total distance travelled per minute by the piston is 2LN. Therefore, by

multiplying by two the top and bottom of the fraction in the last equation in

Section 1.15, and substituting S – the mean piston speed – for 2LN, we can

express the power as a function of S and p: all the other terms are constant

for any given engine. Since the maximum piston speed and bmep (see Section

1.14) tend to be limited by the factors mentioned in Section 1.19, it is not

difficult, on the basis of the dimensions of an engine, to predict approximately

what its maximum power output will be.

It was on these lines that the RAC horsepower rating, used for taxation

purposes until just after the Second World War, was developed. When this

rating was first introduced, a piston speed of 508 cm/s and an mep of

620 kN/m2 and a mechanical efficiency of 75% were regarded as normal.

Since 1 hp is defined as 33000 lbf work per minute, by substituting these

figures, and therefore English for SI metric dimensions in the formula for

work done per minute, Section 1.15, and then dividing by 33 000, we get the

output in horsepower. Multiplied by the efficiency factor of 0.75, this reduces

to the simple equation—

2

bhp = D n = RAC hp rating

2.5

For many years, therefore, the rate of taxation on a car depended on the

square of the bore. However, because it restricted design, this method of

rating for taxation was ultimately dropped and replaced by a flat rate. In the

meantime, considerable advances had been made: mean effective pressures

of 965 to 1100 kN/m2 are regularly obtained; improved design and efficient

lubrication have brought the mechanical efficiency up to 85% or more; and

lastly, but most important of all, the reduction in the weight of reciprocating

parts, and the proper proportioning of valves and induction passages, and the

use of materials of high quality, have made possible piston speeds of over

1200 cm/s.



1.17



Indicated and brake power



The power obtained in Section 1.15 from the indicator diagram (that is,



General principles of heat engines



15



using the mep) is known as the indicated power output or indicated horsepower

(ipo or ihp), and is the power developed inside the engine cylinder by the

combustion of the charge.

The useful power developed at the engine shaft or clutch is less than this

by the amount of power expended in overcoming the frictional resistance of

the engine itself. This useful power is known as the brake power output or

brake horsepower (bpo or bhp) because it can be absorbed and measured on

the test bench by means of a friction or fan brake. (For further information

on engine testing the reader is referred to The Testing of Internal Combustion

Engines by Young and Pryer, EUP.)



1.18



Mechanical efficiency



The ratio of the brake horsepower to the indicated horsepower is known as

the mechanical efficiency.

Thus—



Mechanical efficiency =



bpo

bhp

or

=η

ipo

ihp



and

bpo or bhp = Mechanical efficiency × ipo (or ihp)



π

4 × 60 × 2 × 2

For BS units, divide by 550, as explained in Section 1.15.

For SI units, η × pD 2 S × n ×



=

=



1.19



η pD 2 S

η pD 2 S

or

168 067

305.58

η pDSn

η 2 Sn

or

168 067

305.58



Limiting factors



Let us see to what extent these factors may be varied to give increased

power.

It has been shown that the value of p depends chiefly on the compression

ratio and the volumetric efficiency, and has a definite limit which cannot be

exceeded without supercharging.

The diameter of the cylinder D can be increased at will, but, as is shown

in Section 1.24, as D increases so does the weight per horsepower, which is

a serious disadvantage in engines for traction purposes. There remain the

piston speed and mechanical efficiency. The most important limitations to

piston speed arise from the stresses and bearing loads due to the inertia of the

reciprocating parts, and from losses due to increased velocity of the gases

through the valve ports resulting in low volumetric efficiency.

A comparison of large numbers of engines of different types, but in similar

categories, shows that piston speeds are sensibly constant within those

categories. For example, in engines for applications where absolute reliability

over very long periods is of prime importance, weight being only a secondary



16



The Motor Vehicle



consideration, piston speeds are usually between about 400 and 600 cm/s,

and for automobile engines, where low weight is much more important,

piston speeds between about 1000 and 1400 cm/s are the general rule. In

short, where the stroke is long, the revolutions per minute are low, and vice

versa.



1.20



Characteristic speed power curves



If the mean effective pressure (mep) and the mechanical efficiency of an

engine remained constant as the speed increased, then both the indicated and

brake horsepower would increase in direct proportion to the speed, and the

characteristic curves of the engine would be of the simple form shown in

Fig. 1.5, in which the line marked ‘bmep’ is the product of indicated mean

effective pressure (imep) and mechanical efficiency, and is known as brake

mean effective pressure (bmep). Theoretically there would be no limit to the

horsepower obtainable from the engine, as any required figure could be

obtained by a proportional increase in speed. It is, of course, hardly necessary

to point out that in practice a limit is imposed by the high stresses and

bearing loads set up by the inertia of the reciprocating parts, which would

ultimately lead to fracture or bearing seizure.

Apart from this question of mechanical failure, there are reasons which

cause the characteristic curves to vary from the simple straight lines of Fig.

1.5, and which result in a point of maximum brake horsepower being reached

at a certain speed which depends on the individual characteristics of the

engine.

Characteristic curves of an early four-cylinder engine of 76.2 mm bore

and 120.65 mm stroke are given in Fig. 1.6. The straight radial lines tangential

to the actual power curves correspond to the power lines in Fig. 1.5, but the

indicated and brake mean pressures do not, as was previously assumed,

remain constant as the speed increases.

On examining these curves it will be seen first of all that the mep is not

constant. It should be noted that full throttle conditions are assumed – that is,

the state of affairs for maximum power at any given speed.

At low speeds the imep is less than its maximum value owing partly to

carburation effects, and partly to the valve timing being designed for a

moderately high speed; it reaches its maximum value at about 1800 rev/min,

and thereafter decreases more and more rapidly as the speed rises. This



Power & mep



imep

bmep

ihp



bh



p



Engine speed



Fig. 1.5



45



950



imep

40

850



bmep

750



ro



ro



we



we



po



po



te

d



Mech l



90



eff y



10

80



5

0

0



500



1000



250



1500

2000

Rev/min

500

750



2500

1000



Mechanical effy per cent



15



550



ak

e



ica

20



650



Br



In

d



Power - kW



25



ut

pu



30



t



ut

pu



t



35



17



Mean effective pressure kN/m2



General principles of heat engines



3000

1250



Piston speed cm/s stroke 120.65 mm

3

Fig. 1.6 Power curves of typical early side-valve engine, 3-in bore and 4 4 in stroke

(76.2 and 120.65 mm)



falling off at high speeds is due almost entirely to the lower volumetric

efficiency, or less complete filling of the cylinder consequent on the greater

drop of pressure absorbed in forcing the gases at high speeds through the

induction passages and valve ports.

When the mep falls at the same rate as the speed rises, the horsepower

remains constant, and when the mep falls still more rapidly the horsepower

will actually decrease as the speed rises. This falling off is even more marked

when the bmep is considered, for the mechanical efficiency decreases with

increase of speed, owing to the greater friction losses. The net result is that

the bhp curve departs from the ideal straight line more rapidly than does the

ihp curve. The bmep peaks at about 1400 rev/min, the indicated power at

3200 and the brake power at 3000 rev/min, where 33.5 kW is developed.

Calculations of bmep P from torque, and vice versa are made using the

following formula—



P=



2π Q

bar

LANn



or



Q = PLANn newton

2π

This applies to a two-stroke engine, which has one power stroke per revolution.

Because a four-stroke engine has only one power stroke every two revolutions,

we must halve result, so we have—



18



The Motor Vehicle



bmep = 125.66 × 10–5 × 106 × Q/V kilonewton

where V = LAN = the piston displacement in cm3 and 1 bar = 0.000001 N/m2.



1.21



Torque curve



If a suitable scale is applied, the bmep curve becomes a ‘torque’ curve for

the engine, that is, it represents the value, at different speeds, of the mean

torque developed at the clutch under full throttle conditions – for there is a

direct connection between the bmep and the torque, which depends only on

the number and dimensions of the cylinders, that is, on the total swept

volume of the engine. This relationship is arrived at as follows—

If there are n cylinders, the total work done in the cylinders per revolution

is—

Work per revolution = p × π D 2 × L × n × 1 joules

2

4

(see Section 1.15), if L is here the stroke in metres. Therefore the work at the

clutch is—

Brake work = η × p × π D 2 L × n × 1 joules.

2

4

But the work at the clutch is also equal to the mean torque multiplied by the

angular distance moved through in radians, or T × 2π newton-metres per

revolution if T is measured in SI units.

Therefore—

T × 2π = η × p × π D 2 × L × n ×

4



1

2



or,



 π D 2 × L × n

4



T = ηp ×

4π

Now π D2 × L × n is the total stroke volume or cubic capacity of the engine,

4

which may be denoted by V, Therefore we have—



T = ηp × V

4π

where ηp the bmep and V/4π is a numerical constant for the engine, so that

the bmep curve is also the torque curve if a suitable scale is applied.

In the case of the engine of Fig. 1.6, the bore and stroke are 76.2 mm and

120.65 mm respectively, and V is 2.185 litres.

Thus,



T = η p × 2.185

4π



and the maximum brake torque is—

T = 762 × 0.1753 = 133.6 Nm.



General principles of heat engines



19



It is more usual to calculate the bmep (which gives a readier means of

comparison between different engines) from the measured value of the torque

obtained from a bench test.

Indicated mean pressure and mechanical efficiency are difficult to measure,

and are ascertained when necessary by laboratory researches.

Mean torque, on the other hand, can be measured accurately and easily by

means of the various commercial dynamometers available. The necessary

equipment and procedure are in general use for routine commercial tests. It

is then a simple matter to calculate from the measured torque the corresponding

brake mean pressure or bmep—



ηp or bmep = T × 4π /V

The usual form in which these power or performance curves are supplied

by the makers is illustrated in Figs 1.7 and 1.8, which show torque, power,

and brake specific fuel consumption curves for two Ford engines, the former

for a petrol unit and the latter a diesel engine. In both instances, the tests

were carried out in accordance with the DIN Standard 70020, which is

obtainable in English from Beuth-Vertrieb GmbH, Berlin 30. The petrol unit

is an overhead camshaft twin carburettor four-cylinder in-line engine with a

bore and stroke of 90.8 by 86.95 mm, giving a displacement of 1.993 litres.

Its compression ratio is 9.2 to 1. The diesel unit is a six-cylinder in-line

engine with pushrod-actuated valve gear and having a bore and stroke of

104.8 mm by 115 mm respectively, giving a displacement of 5948 cm3. It

has a compression ratio of 16.5 :1.



1.22



Effect of supercharging on bmep and power



140

130



55



Power – kW



60



120



50

45

40

35

30

25

20

15

10



110

1000



Power



900



bmep



800

700

0.400

0.350



Spec fuel



0.300

0.250



1000 2000 3000 4000 5000

Speed–rev/min



6000



bmep –

kN/m2



150

Torque



Spec fuel cons –

kg/kW–hr



70

65



Torque –

Nm



Figure 1.9 illustrates two aspects of supercharging and its effect on bmep (or

torque) and power.

The full lines represent the performance curves of an unblown engine

with a somewhat steeply falling bmep characteristic. The broken lines (a)



Fig. 1.7 Typical performance curves for an overhead camshaft, spark-ignition engine.

High speeds are obtainable with the ohc layout



Torque



350

300

250

700

600

500



90



Power – kW



80

bmep



70

60



bhp



50

40



0.275

0.250

0.225

0.200

3000



30

Spec. fuel



20

1000



1500



2000

2500

Speed rev/min



bmep –

kN/m2



100



Torque –

Nm



The Motor Vehicle



Brake spec. fuel cons

kg/kWh



20



Fig. 1.8 Performance curves of a diesel engine. The fact that torque increases as speed

falls off from the maximum obviates the need for excessive gear-changing

(b)



(a)



ep



(a)



w



er



bm



Po



Power and bmep



(b)



Speed



Fig. 1.9 Supercharging



and (b) represent two different degrees of supercharge applied to the same

engine.

The curves (a) indicate a degree of progressive supercharge barely sufficient

to maintain the volumetric efficiency, bmep and therefore torque, at their

maximum value, through the speed range.

There would be no increase of maximum piston load or maximum torque,

though there would be an appreciable increase in maximum road speed if an

overspeed top gear ratio were provided – the engine speed range remaining

the same.

Curves (b) show an increase of power and bmep through the whole range,

due to a greater degree of supercharging. The maximum values of piston

loads and crankshaft torque would also be increased unless modifications to

compression ratio and possibly to ignition timing were made with a view to

reducing peak pressures. This would have an adverse effect on specific fuel

consumption, and would tend to increase waste heat disposal problems, but

the former might be offset by fuel saving arising from the use of a smaller



General principles of heat engines



21



engine operating on a higher load factor under road conditions, and careful

attention to exhaust valve design and directed cooling of local hot spots

would minimise the latter risk.



1.23



Brake specific fuel consumption



When the simple term specific fuel consumption is used it normally refers to

brake specific fuel consumption (bsfc), which is the fuel consumption per

unit of brake horsepower. In Figs 1.7 and 1.8 the specific fuel consumption

is given in terms of weight. This is more satisfactory than quoting in terms

of volume, since the calorific values of fuels per unit of volume differ more

widely than those per unit of weight. It can be seen that the specific fuel

consumption of the diesel engine is approximately 80% that of the petrol

engine, primarily due to its higher compression ratio. Costs of operation,

though, depend not only on specific fuel consumption but also on rates of

taxation of fuel. The curves show that the lowest specific fuel consumption

of the diesel engine is attained as the fuel : air ratio approaches the ideal and

at a speed at which volumetric efficiency is at the optimum. In the case of the

petrol engine, however, the fuel : air ratio does not vary much, and the

lowest specific fuel consumption is obtained at approximately the speed at

which maximum torque is developed – optimum volumetric efficiency.

The fuel injection rate in the diesel engine is regulated so that the torque

curve rises gently as the speed decreases. A point is reached at which the

efficiency of combustion declines, with rich mixtures indicated by sooty

exhaust. This torque characteristic is adopted in order to reduce the need for

gear changing in heavy vehicles as they mount steepening inclines or are

baulked by traffic. The heavy mechanical components, including the valve

gear as well as connecting rod and piston assemblies of the diesel engine,

and the slower combustion process, dictate slower speeds of rotation as

compared with the petrol engine.

In Figs 1.7 and 1.8, the curves of specific fuel consumption are those

obtained when the engine is run under maximum load over its whole speed

range. However, in work such as matching turbochargers or transmission

systems to engines, more information on fuel consumption is needed, and

this is obtained by plotting a series of curves each at a different load, or

torque, as shown in Fig. 1.10. Torque, however, bears a direct relationship to

bmep and, since this is a more useful concept by means of which to make

comparisons between different engines, points of constant bsfc are usually

plotted against engine speed and bmep, the plots vaguely resembling the

contour lines on an Ordnance Survey map.

The curves in Fig. 1.10 are those for the Perkins Phaser 180Ti, which is

the turbocharged and charge-cooled version of that diesel engine in its sixcylinder form. Such a plot is sometimes referred to as a fuel consumption

map. Its upper boundary is at the limit of operation above which the engine

would run too roughly or stall if more heavily loaded; in other words, it is the

curve of maximum torque – the left-hand boundary is the idling speed, while

that on the right is set by the governor. For a petrol engine, the right-hand

boundary is the limit beyond which the engine cannot draw in any more

mixture to enable it to run faster at that loading .

Over much of the speed range, there are two speeds at which an engine

will run at a given fuel consumption and a given torque. A skilful driver of



22



The Motor Vehicle



1300

1200

1100

1000



800

700



205 h

W

g/k



Bmep (kN/m2.)



900



21



0



215

0

22



600



23



500



0



24



0

260



400



28



300



1000 1200



1400 1600 1800



2000 2200



0



2400 2600



Engine speed (rev/min)



Fig. 1.10 Fuel consumption map for the Perkins Phaser 180Ti turbocharged and

aftercooled diesel engine, developing 134 kW at 2600 rev/min



a commercial vehicle powered by the Phaser 180Ti will operate his vehicle

so far as possible over the speed range from about 1200 to 2000 rev/min,

staying most of the time between 1400 and 1800 rev/min, to keep his fuel

consumption as low as possible. The transmission designer will provide him

with gear ratios that will enable him to do so, at least for cruising and

preferably over a wider range of conditions, including up- and downhill and

at different laden weights.

The bearing of the shape of these curves on the choice of gear ratios is

dealt with in Chapter 22, but an important difference between the petrol

engine and the steam locomotive and the electric traction motor must here be

pointed out.

An internal combustion engine cannot develop a maximum torque greatly

in excess of that corresponding to maximum power, and at low speeds the

torque fails altogether or becomes too irregular, but steam and electric prime

movers are capable of giving at low speeds, or for short periods, a torque

many times greater than the normal, thus enabling them to deal with gradients

and high acceleration without the necessity for a gearbox to multiply the

torque. This comparison is again referred to in Section 22.9.



General principles of heat engines



1.24



23



Commercial rating



The performance curves discussed so far represent gross test-bed performance

without the loss involved in driving auxiliaries such as water-pump, fan and

dynamo. For commercial contract work corrected figures are supplied by

manufacturers as, for example, the ‘continuous’ ratings given for stationary

industrial engines.

Gross test-bed figures, as used in the USA, are sometimes referred to as

the SAE performance, while Continental European makers usually quote

performance as installed in the vehicle and this figure may be 10 to 15% less.



1.25



Number and diameter of cylinders



Referring again to the RAC formula (see Section 1.19), it will be seen that

the power of an engine varies as the square of the cylinder diameter and

directly as the numbers of cylinders.

If it is assumed that all dimensions increases in proportion to the cylinder

diameter, which is approximately true, then we must say that, for a given

piston speed and mean effective pressure, the power is proportional to the

square of the linear dimensions. The weight will, however, vary as the cube

of the linear dimensions (that is, proportionally to the volume of metal), and

thus the weight increases more rapidly than the power. This is an important

objection to increase of cylinder size for automobile engines.

If, on the other hand, the number of cylinders is increased, both the power

and weight (appropriately) go up in the same proportion, and there is no

increase of weight per unit power. This is one reason for multicylinder

engines where limitation of weight is important, though other considerations

of equal importance are the subdivision of the energy of the combustion,

giving more even turning effort, with consequent saving in weight of the

flywheel, and the improved balancing of the inertia effects which is obtainable.

The relationship of these variables is shown in tabular form in Fig. 1.11,

in which geometrically similar engine units are assumed, all operating with

the same indicator diagram. Geometrical similarity implies that the same

materials are used and that all dimensions vary in exactly the same proportion

with increase or decrease of cylinder size. All areas will vary as the square

of the linear dimensions, and all volumes, and therefore weights, as the cube

of the linear dimensions. These conditions do not hold exactly in practice, as

such dimensions as crankcase, cylinder wall and water jacket thicknesses do

not go up in derect proportions to the cylinder bore, while a multi-cylinder

engine requires a smaller flywheel than a single-cylinder engine of the same

power. The simplified fundamental relationships shown are, however, of

basic importance.

It can be shown on the above assumptions that in engines of different

sizes the maximum stresses and intensity of bearing loads due to inertia

forces will be the same if the piston speeds are the same, and therfore if the

same factor of safety against the risk of mechanical failure is to be adopted

in similar engines of different size, all sizes of engine must run at the same

piston speed, torque, power and weight, and gas velocities through the valves.



1.26



Power per litre



This basis of comparison is sometimes used in connection with the inherent



24



The Motor Vehicle

Variable



A



B



C



Piston

speed

Stroke



1



1



1



1



2



1



Rev/Min



1



1

2



1



Bore



1



2



1



Total

piston area



1



4



4



Power



1



4



4



Mean

torque

Volumetric

capacity



1



8



4



1



8



4



Weight



1



8



4



1



1

2



1



Power

weight



Engine

A



B



C



Max. inertia

1

1

1

stress

Mean gas

1

1

1

velocity

Relative value of variables in similar engines

[For same indicator diagram]



Fig. 1.11



improvement in performance of engines, but such improvement arises from

increase in compression ratio giving higher brake mean pressures, the use of

materials of improved quality, or by tolerating lower factors of safety or

endurance. The comparison ceases to be a comparison of similar engines, for

with similar engines the power per litre (or other convenient volume unit)

may be increased merely by making the cylinder smaller in dimensions, and

if the same total power is required, by increasing the number of the cylinders.

Thus in Fig. 1.11 all the three engines shown develop the same power per

unit of piston area at the same piston speed and for the same indicator

diagram, but the power per litre of the small-cylinder engines is double that

of the large cylinder, not because they are intrinsically more efficient engines

but because the smaller volume is swept through more frequently.

Thus, high power per litre may not be an indication of inherently superior

performance, whereas high power per unit of piston area is, since it involves

high mean pressures or high piston speed or both, which are definite virtues

provided that the gain is not at the expense of safety or endurance.



1.27



Considerations of balance and uniformity of torque



In the next chapter consideration is given to the best disposition of cylinders

to give dynamic balance and uniformity of torque, which are factors of vital

importance in ensuring smooth running.