- Email: [email protected]
Big cars, too, can be light on fuel
Resources and Conservation, 10 (1983) 85-102
Elsevier Science Publishers B.V., Amsterdam
85
- Printed in The Netherlands
BIG CARS, TOO, CAN BE LIGHT ON FUEL
H.-J. FiiRSTER Daimler-Benz
AG, 7000 Stuttgart 60 (Federal Republic of Germany)
(Received July 25, 1982; accepted in revised form December 27, 1982)
ABSTRACT This paper challenges the widespread opinion that “big car = high fuel consumption, small car = low fuel consumption” with an analysis of fuel consumption and with the objective of contributing towards the understanding of the actual interrelation between fuel consumption and car concept. In order to make the influencing factors clear two car concepts are compared which differ regarding unladen weight and net power by factors of 2 and 4, respectively. It is shown that the power required to overcome the driving resistance increases disproportionately slowly with the size of the car and that in certain driving modes the power requirement for the accessories of a large car reaches the value required to overcome the driving resistance. The large difference in consumption between large and small cars is due to the fact that the demand for high acceleration reserves in top gear forces the engine to run in a range of poor efficiency and that the possibilities of reducing the driving resistance are not yet being fully utilized. The conflicting aims of running the engine in the range of favourable efficiency on one side, and the demand for high acceleration reserves without frequent manual change of gear on the other side, can be solved by using automatic transmissions with adequate shifting programmes. It is certain that the future large cars will have a lower fuel consumption than they do today.
INTRODUCTION
There is the old rule of thumb about fuel consumption and vehicle weight: “100 kg extra weight means 1 litre more fuel consumption per 100 km.” This is obviously a convenient relationship which seems to be backed up by the data available on cars on the market, as shown in Fig. 1. Naturally, the converse of this law is adopted as conventional wisdom too: to keep down fuel consumption, automobiles must be kept light and small. Any automotive engineer who sets out to bring down the consumption of a big car by reducing the weight in accordance with this rule is in for a bitter disappointment. Fuel consumption also depends on driving style and cycle, but anything between 200 and 400 kg weight has to be done away with to save as little as 1 litre of fuel over 100 km. There must, therefore, be other factors
86 fuel consumption Be 0
25 11100 km
28 vehicles tested sookm.lookg by Automobil-Revue from 1968 to 1970 ’ highway / interurban speedy
20
??
1I
highway smooth
,: 15
”
.
0
60
Fig. 1. Fuel consumption
ldO0
1500
kg 2600 empty weight G
in relation to unladen weight.
at work which have a greater influence on fuel consumption This paper will try to clarify these questions.
than weight.
SOME OF THE MAIN FACTORS
Fuel consumption analysis Fuel consumption depends on the following: (1) the work needed to overcome resistance to the motion of the vehicle; (2) power requirements for auxiliary drives, such as the alternator, power steering, air-conditioning, etc.; (3) the efficiency with which the engine converts the chemical energy in the fuel into mechanical energy at the wheels. In the following, the aim is to demonstrate that the driving power does not change in proportion to the size of the vehicle, that in certain driving ranges the power to drive the auxiliary unitscan have values comparable to the driving power, and that the efficiency of the engine or the specific fuel consumption at the operating point is the decisive factor which determines actual fuel consumption. Dependence
of driving performance
on vehicle size
The first step is to decide on a criterion for “vehicle size,” e.g., weight, payload, engine power or the useful space for passengers and luggage. In Fig. 2 the payload volume is indicated against the weight for a range of European cars. By every rule of engineering, the weight of a vehicle with an
87 payload
volume MB 240 D long 7
4/
/
rn’
I
500
1000
1500 kg empty weight
Fig. 2. Payload volume against unladen weight for various vehicles.
engine, transmission, two axles and four wheels should increase at a slower rate than the useful space since in every case, even with zero useful space, some weight for the structure remains. Interestingly enough, however, the contrary situation prevails in vehicles built today. If the line in Fig. 2 were extrapolated to zero weight it would intersect the ordinate at a useful space of more than 2 m3. Only when the same model is offered in different lengths does the old rule hold good. Quite obviously, there is a series of factors unrelated to that of useful space which determine the weight of a vehicle. As a rule, the lower range of “small” cars on the market is characterized by the following aspects: low price, small to cramped passenger compartment, small luggage space, low engine power output, low driving performance, minimum interior furnishing and no auxiliary features, but also low weight and low fuel consumption.
88
At the top end of the scale, “large” cars are characterized by: high price, spacious passenger compartment, large luggage space, high engine power output, high driving performance, generous interior furnishing and numerous auxiliary devices, but also high weight and high fuel consumption. It is these characteristics, increasing as they do with vehicle size, which are responsible for the considerable increase in weight and the unmistable rise in fuel consumption associated with larger cars. If large and small cars are today compared as to weight and fuel consumption, in reality characteristics are being compared which have little to do with the useful size of the vehicles. In this paper it is not accepted that vehicle weight is the indicator of “size,” with everything it implies, and we examine to what extent fuel consumption can be balanced even in the presence of widely differing car weights. As is well known, the tractive resistance of a vehicle which has to be overcome is dependent on two components: F wheel = m (gfcos a + g sin (Y+ a) + $p c,Au2 where Fwheel = tractive resistance, m = mass of the vehicle, g = acceleration of gravity, f = rolling resistance coefficient, cr = gradient angle, c = acceleration, p = density of air, cW = drag coefficient, A = frontal area, u = velocity. Some of the factors are proportional to the vehicle weight, such as rolling, gradient and acceleration resistances. The air resistance, being proportional to the frontal area of the vehicle, to the aerodynamic coefficient and to the square of the driving speed, becomes the most important factor at higher speeds. Keeping constant the size and the space of a car, the weight can be reduced by making greater use of light metal and fiber-reinforced plastics. Generally these light weight materials are more expensive than steel and, therefore, their proportion can be higher in cars where a higher selling price can be achieved. It is quite certain that large cars will not get any heavier in the future, but one would not venture to predict reductions in weight since the extra load imposed by safety measures such as anit-lock systems, air bags and belt tensioners, and possible legal requirements on exhaust emisssions and noise control must be accommodated. The rolling resistance coefficent, f, has dropped considerably due to the use of radial tires but is still surprisingly higher in passenger cars, compared with commercial vehicles. To make calculations, rolling resistance values are used according to Fig. 3, which are a little higher in the case of light vehicles, particularly at medium speeds. The inclination here is to predict at least a tendency towards smaller rolling resistance coefficients with increased weight. In climbing a hill a vehicle gains potential energy which can be used to overcome the rolling and air resistance when going downhill. Therefore, the gradient resistance, (mg sin ar) will increase fuel consumption only when the brakes have to be applied when going downhill. Otherwise, climbing and downhill driving will not add much to fuel consumption, as Fig. 4 shows. Here fuel consumption is indicated against the speed for travelling from
89 coefficient
of rolling friction f
0.03 i Subcompact car 2.0 bar 145 SR 13 (2000 N/wheel) 0.02
-
d Large car, 2.5 bar 195170 HR14 (4000 N/wheel)
0.01 -
01
0
50
100
150
200 km/h driving speed v
Fig. 3. Coefficient
of rolling friction against driving speed for subcompact
fuel consumption
and large car.
Be
tana + 0,06
0
25
50
75
100
125 km/h 150 driving speed v
Fig. 4. Fuel consumption
against driving speed for various gradients.
point A to point B on a level road and on different uphill and downhill gradients. The acceleration resistance, (ma), can be positively influenced by the driver by accelerating only when it makes sense, and by making the most of the kinetic energy. The air resistance of a vehicle is influenced by the value (c,A) where c, is the drag coefficient and A the frontal area. A increases in proportion to the useful volume but far less than in proportion to the weight of the vehicle. The reason for this resides in the given minimum space requirement for the driver and one passenger sitting side by side. The drag coefficient, cW , nowadays the object of intensive research, may be smaller for long vehicles than short ones, all other factors being equal, as shown in Fig. 5. Though this aero-
drag coefficient
short car
Fig. 5. Improvement
of drag coefficient
by extension
long cer
and tail retraction.
dynamic coefficient may vary substantially from one model of car to another today, with some small vehicles having a low value of cw, and large ones a high value, the advantages which the laws of physics bestow on longer vehicles will certainly be exploited in the future. Hence, the product (c,A) which determines drag will in future be almost independent of vehicle weight, as illustrated in Fig, 6. To make the following investigation into the fuel consumption of different cars as clear as possible, two extreme cars in weight and power will be compared. Carl subcompact
unladen weight load limit reference weight power engine type no auxiliaries
800 400 1000 40 4
kg kg kg kW in line, 1.2 litre carburettor
car2 large
unladen weight load limit reference weight power engine type all auxiliary systems
1600 kg 500 kg 1850 kg 160 kW V8, 4.0 litre fuel injection
Rolling resistance coefficient, as per Fig. 3 and aerodynamic drag (c,A), equals 0.7. Fig. 7 gives the travelling resistance, Fwbeel, against the driving
91
Maximum vehicle cross section A rn2
2.0
1.5
1 .o Cw.A
m2
---
z-
7
expected ’ in Mure
\
Drag coefficient C,
04
500
0
1000
1500
kg
empty weight G
Fig. 6. Maximum
vehicle cross-section
and drag coefficient
against unladen weight.
speed. When speed increases there is less and less difference in the traction resistance F of the two extreme vehicle types. Whereas at 50 km/h the driving force for the larger car is 55% higher than the driving force for the subcompact, it is only 12% higher at 145 km/h, the top speed of the subcompact. Fig. 8 shows the driving power over the driving speed for the two vehicles, the two curves are close together. Auxiliary
drives
Small cars have only the auxiliaries essential for the engine such as water pump, alternator and fan, which are partly electrically driven. Large vehicles, on the other hand, are generally fitted with a whole series of accessory devices serving the purpose of safety, travel quality and comfort such as an anti-lock braking system, airbag and seat-belt tensioner, air-conditioning sys-
92
Faubl Subcompact 1000 kg
Large car 1850 kg
2
1
0
V’
is
0
50
is
100
li5
Fig. 7. Traction resistance for large and subcompact
150
175
260 km/h driving speed
cars.
pow*r for traction
P
- largecBr
kW
-- subcompact car
1850 kg 1000 kg
150
125
25
0
0
25
50
Fig. 8. Power for traction
75
100
125
150
175
MO 225 km/h driving apeed
against driving speed for large and subcompact
car.
93 power of accessory
drive Pact
kW power steering air condition automatic transmission
pact
15’
10.
torque
Mace
-30 Nm .20
0
1000
2000
3000
4000
0 5000 min-’ 6000 engine speed n
Fig. 9. Power and torque of accessory drive against engine speed.
tern, automatic transmission, power steering, level control system, electric seat adjustment and window winding, etc. The only one of these systems which can be considered essential in terms of vehicle weight is the power steering. All of them immediately add weight. There are no real “heavyweights” among them, but taken together these accessories can increase the unladen weight of a car easily by more than 100 kg. This is one of the reasons for the greater unladen weight of larger cars. The auxiliary units which have to be driven to function continuously take their power from the engine, as shown in Fig. 9. Though the power level depends on the actual load on the accessories, a high load condition is a rarity; the only system that can work constantly at high load is the air-conditioner, during hot weather - but when it is cold it is not on at all. The decisive parameter determining the power consumption of auxiliary units is the rpm involved. The units and systems, power steering pump, fan, transmission oil pump, refrigerant compressor and alternator must be chosen so that their size permits them to work adequately at engine idling speed. However, since there may be a factor of more than 10 between engine idling and maximum speed, this means considerable oversizing at high engine speeds.
94
In the lower speeds up to 70 km/h the power requirements of ry drives can be quite easily equal the driving power output. This power must also be found when the car is at a standstill. Auxiliary unit power cannot simply be added to driving power they may be quite different at the same driving speed depending between the engine and the drive wheel speed.
the auxiliaadditional because on the ratio
Energy conversion efficiency If the extra fuel consumption of large cars as observed in practice, Fig. 1, is more different from that of small cars than is to be expected from the power required, even taking into account the still greater aerodynamic drag encountered today and the power requirements of auxiliary equipment, the explanation can only lie in the differing energy conversion efficiency of the engines. The engines chosen are derived from good series-produced engines and reflect the optimum available in each case at the present time. In order not to complicate comparisons, no account is taken of such possible future developments as higher compression ratios and anti-knock sensors, variable compression ratios, supercharging or cylinder cut-off, and the comparison is limited to gasoline engines because the problems there are greater. However, it will be obvious that many of the above-mentioned development possibilites can only be achieved at the expense of substantial cost penalties, so they are more likely to be applicable to big cars. Generally, large engines reach a higher maximum efficiency than small ones. This is brought out in the non-dimensional representation shown in Engine 4.0 I, 160 kW
tow le M/M 0
Engine
I .2 I, 40
kW
efficiency
to ‘rql MI/M
1 .a
0.5
C
( 0.5
1.0 engme speed n/no
0.5
1.0 engme speed n/no
Fig. 10. Performance map for various engines related to maximum power.
95 efficiency
7
35 % 30 7 opt, subcompact
car
+i opt large car
25
20
15
10
5
0
1 25
Fig. 11. Efficiency
75
100
125
kw
150 power P
of subcompact
and large CBTSagainst power.
Fig. 10, where all dimensions are standardized with those of the point of maximum power output. The areas of similar efficiency include areas of different power. When the power necessary to drive the cars is not very different, engines must be compared with regard to similar power. Also their consumption when idling is of importance. Figure 11 compares the optimal efficiency of both engine sizes against power output. Though the large engine achieves better maximum efficiency, there is nevertheless a region at low power where the small engine is definitely superior and this is the power range needed for speeds up to 100 km/h. This is nowadays the real handicap of big engines, and development will concentrate on this fact (supercharging, cylinder cut-off, variable compression, etc.) as already mentioned. As regards idling consumption, Fig. 12, the difference between the large and the small engine may become small if in future greater attention is paid to achieving low idling speeds. The idling speed of large engines can be kept below that of small engines, so that part of the different frictional losses can be compensated.
96 0 automatic transmission and accessones 31 automatic transmission ‘3: mechanical transmission
idling fuel consumption 1
kg
\ .
-4
idling speed
‘.
--
--
500
cyk+ -
6 cyl.+ -
1
2
3
8 cyl. 4
5
I
3
Engine swept volume
Fig. 12. Idling fuel consumption against engine swept volume.
The fuel consumption when idling rises when the engine has to work against the stalled turbine of a torque converter and still more if auxiliary systems have to be driven. For the following comparison of fuel consumption between the small and the large car, the performance characteristics of the engine used are shown in Figs. 13 and 14 on the same scale. In each diagram travelling resistance is indicated. The parameter cpnotes the relation of the engine speed in which the driving resistance curve intersects the hyperbola of maximum power output, referred to engine speed at top power. Therefore, cp= 1 is the driving resistance line through the engine point of maximum power. cp> 1, here 1.1, results in higher acceleration, cp< 1, here 0,7, results in an overdrive character. cpfor the power requirements of engine plus auxiliaries was chosen in such a way that both with and without auxiliary drives the engine reaches final power output at the same rpm; this means that other rear axle ratios belong to cp= 1 both with and without auxiliary drives. The diagram shows that the driving resistance line passes increasingly through areas of lower fuel consumption the smaller the value of cp,i.e. the slower the engine turns at the same speed of travel. Because this is a well known fact another criterion is obviously required in
97
torque M 200 Nm 150.
100
I
fuel consumption be g/kWh
50
0 L0
1000
2000
3000
5000
4000
6000 min-1 engine speed
rad/s m/s
_i _ engine speed r driving speed
Fig. 13. Performance map for a subcompact car (engine 1.2 litre, 40 torque M fuel consumption be [g/kWh]
“,“I
l\\\\LLGzA\\
250
luded 0
1000
2000
3000
4000
5000
6000 min
’
engine speed
Fig. 14. Performance map for a large car (engine 4.0 litre, 160 kW).
kW).
98 - large car with accessories acceleration 1.27
gradient
-- subcompact car
l-
m/s2
%
lo-
lo-
0.8.
8
0.8
6-
0.4.
4.
0.2.
2.
driving speed
Fig. 15. Acceleration and gradient reserve against driving speed.
order to understand why values of q > 1 have nevertheless so far generally also been selected for the big car. This additional criterion is the acceleration and climbing reserve in top gear without changing gear. This is shown in Fig. 15. A large vehicle with cp = 1.1 has much more acceleration in reserve than the small car and this difference increases markedly as speed rises. Of course, values of q < 1 would be possible even with a small car, but then the acceleration reserve gets too small that there is a risk drivers would either no longer use this gear or use it only rarely, which would have the opposite effect on economy. Fuel consumption The “classical” basic approach was taken by choosing cp = 1, the dotted line, for the small vehicle and cp = 1.1 for the big one, the line at the top of Fig. 16. Differences between the two vehicles as regards fuel consumption are particularly marked at low driving speeds - the price that is paid for the much greater climbing and acceleration reserves available in top gear, again referring to Figs. 15 and 16 must always be considered together. When fuel is expensive consumption can be much reduced with values of cp< 1. If, for example, the same average acceleration behavior without changing gear is acceptable for both large and small cars, a value of cp = 0.7 can be chosen for the big car in the example. This gives similar mean acceleration times of about 31 s from 60 to 120 km/h but fuel consumption drops for the large car by as much as 30% (curve 3, Fig. 16). If, in addition, the auxiliary systems were removed there would be very little difference between the consumption curves for large and small cars (curves 4 and 5, Fig. 16).
99 fuel consumption 30. 11100 km - large car wth accessones 25.
-- subcompact
car without accessories
20.
15. ‘) without accessories
01 0
25
50
Fig. 16. Fuel consumption
75
100
125
150
175
200
against driving speed for large and subcompact
225 km/h driving speed
cars.
Automatic transmissions with four speeds lend themselves particularly well to such a design concept with cp-4 1, selecting as they do, whenever possible, the most economical gear and shifting back when acceleration is needed. In addition to the comparison of fuel consumption in a steady state driving mode, the behavior of the cars in a town driving mode has to be contemplated. The comparisons are based on the Europa Test (ECE-cycle) which not only prescribes the amount of acceleration, speed and deceleration and the idling periods, but for a manually shifted gear box also the gears which have to be selected, shown in Fig. 17. It is quite interesting to note that the fuel consumption during the Europa Test (ECE-cycle) can be quite different according to the shifting specification and this is true especially of cars with manually shifted gearboxes (small car). With a shifting pattern A, the consumption would increase by 1.8 l/100 km or; with shifting pattern C, decrease by 1.0 l/100 km compared with the official gear selection. In the case of the large vehicle with automatic transmission it can be seen in Fig. 18 that the special shifting programme (B) brings about only a slight improvement of the consumption as compared to the normal version (A). In addition, the influence of a direct rear axle ratio cpsmaller than 1 which was very important at higher speeds has no great influence in the ECE city driving mode. On the other hand the handicap of large vehicles regarding fuel consumption in this test can obviously be reduced if the driver has not to follow the official acceleration pattern but applies the brakes as little as possible, using the kinetic energy to overcome the driving resistance, as shown in Fig. 19.
100 driving speed v
50’ km/h 40 fuel consumption I,65
1
11100 km
shdting pattern
Fig. 17. Influence of shifting - pattern on the fuel consumption _ mechanical transmission. driving speed v
of a subcompact
car with
fuel consumption 1/10Okm
Fig. 18. Influence of overall transmission ratio, rp, and shifting pattern A and B on fuel consumption of a large car with automatic transmission.
The result of a consumption calculation for a modified Europa Test (ECEcycle), Fig. 19, shows that with a given maximum speed of 50 km/h, and steady length and duration of the cycles, the ECE consumption can be reduced by 1.4 l/100 km due to the longer overrun conditions. Figure 20, finally, gives the summarized results of the consumption calculations, both for the large and subcompact car. Taking the values of the subcompact car as a unit, the large car naturally has a somewhat higher fuel consumption which, however, amounts to only 1.46 in the official ECE cycle, 1.27 at 90 km/h and at 1.16 at 120 km/h. In the combined Euromix cycle,
101 drlvlng speed ” 50 km/h
fuelConsumption
40
l/100 km
1455 13
30 20 10
0
loo0 -
distance covered s
ill. Sal_-_I
600.
shaftmg pattern A
400-
A
8
200-
0
1 20
0
40
SO
SO
120
100
140
160 time
180
IS5 set
t
Fig. 19. Influence of driving style on fuel consumption in ECE cycle if driven economically (average speed in cycle sections is constant).
fuel consumption
IllOOkm
5
-9.81
1
I influence driver
0.45
f E
f
B 8
f
I-
in flwncs cycle
of
subcompact
car
of
(mechanicaltransmission)
influencaof CY0le
E
E
i
constant speed
large cfar (autome~ic transmission)
Fig. 20. Influence of driver and driving mode on fuel consumption of large and subcompact car.
i ECE, $90 km/h and t 120 km/h, the fuel consumption of the subcompact is 8.2 litre/lOO km and of the large vehicle 10.7 litres/lOO km. The results of Fig. 20 have been entered in Fig. 21 and demonstrate that fuel consumption of larger (heavier) vehicles may increase less than 1 l/100
102 fuel consumption 25
Be
*
l/l 00 km 20.
28 vehicles tested by Automobil-Revue from 1968 to 1970 ’ highway
/ interurban
* highway
smooth
speedy
kg 2000 empty weight G
Fig. 21. Fuel consumption against unladen weight.
km and 100 kg weight, in fact giving only about 0.3 l/100 km and 100 kg weight difference in the given example. CONCLUSION
The sometimes considerable difference in fuel consumption between big cars and small ones is the result of, first, the power requirements of the many accessories installed in the large cars and second and above all, the desire for large reserves of acceleration in top gear without having to change down, which forces large engines to work in a region of low efficiency. But with the methods described in the paper the additional fuel consumption of a large car with twice the weight and four times the power can be reduced to about 30%, which means less than 0.3 litre/lOO km/100 kg weight difference. Because many further improvements to reduce fuel consumption which are under development and which may be more easily included in high-price cars have not been taken into consideration, it seems certain that in the future even large cars will have a low fuel consumption.
Elsevier Science Publishers B.V., Amsterdam
85
- Printed in The Netherlands
BIG CARS, TOO, CAN BE LIGHT ON FUEL
H.-J. FiiRSTER Daimler-Benz
AG, 7000 Stuttgart 60 (Federal Republic of Germany)
(Received July 25, 1982; accepted in revised form December 27, 1982)
ABSTRACT This paper challenges the widespread opinion that “big car = high fuel consumption, small car = low fuel consumption” with an analysis of fuel consumption and with the objective of contributing towards the understanding of the actual interrelation between fuel consumption and car concept. In order to make the influencing factors clear two car concepts are compared which differ regarding unladen weight and net power by factors of 2 and 4, respectively. It is shown that the power required to overcome the driving resistance increases disproportionately slowly with the size of the car and that in certain driving modes the power requirement for the accessories of a large car reaches the value required to overcome the driving resistance. The large difference in consumption between large and small cars is due to the fact that the demand for high acceleration reserves in top gear forces the engine to run in a range of poor efficiency and that the possibilities of reducing the driving resistance are not yet being fully utilized. The conflicting aims of running the engine in the range of favourable efficiency on one side, and the demand for high acceleration reserves without frequent manual change of gear on the other side, can be solved by using automatic transmissions with adequate shifting programmes. It is certain that the future large cars will have a lower fuel consumption than they do today.
INTRODUCTION
There is the old rule of thumb about fuel consumption and vehicle weight: “100 kg extra weight means 1 litre more fuel consumption per 100 km.” This is obviously a convenient relationship which seems to be backed up by the data available on cars on the market, as shown in Fig. 1. Naturally, the converse of this law is adopted as conventional wisdom too: to keep down fuel consumption, automobiles must be kept light and small. Any automotive engineer who sets out to bring down the consumption of a big car by reducing the weight in accordance with this rule is in for a bitter disappointment. Fuel consumption also depends on driving style and cycle, but anything between 200 and 400 kg weight has to be done away with to save as little as 1 litre of fuel over 100 km. There must, therefore, be other factors
86 fuel consumption Be 0
25 11100 km
28 vehicles tested sookm.lookg by Automobil-Revue from 1968 to 1970 ’ highway / interurban speedy
20
??
1I
highway smooth
,: 15
”
.
0
60
Fig. 1. Fuel consumption
ldO0
1500
kg 2600 empty weight G
in relation to unladen weight.
at work which have a greater influence on fuel consumption This paper will try to clarify these questions.
than weight.
SOME OF THE MAIN FACTORS
Fuel consumption analysis Fuel consumption depends on the following: (1) the work needed to overcome resistance to the motion of the vehicle; (2) power requirements for auxiliary drives, such as the alternator, power steering, air-conditioning, etc.; (3) the efficiency with which the engine converts the chemical energy in the fuel into mechanical energy at the wheels. In the following, the aim is to demonstrate that the driving power does not change in proportion to the size of the vehicle, that in certain driving ranges the power to drive the auxiliary unitscan have values comparable to the driving power, and that the efficiency of the engine or the specific fuel consumption at the operating point is the decisive factor which determines actual fuel consumption. Dependence
of driving performance
on vehicle size
The first step is to decide on a criterion for “vehicle size,” e.g., weight, payload, engine power or the useful space for passengers and luggage. In Fig. 2 the payload volume is indicated against the weight for a range of European cars. By every rule of engineering, the weight of a vehicle with an
87 payload
volume MB 240 D long 7
4/
/
rn’
I
500
1000
1500 kg empty weight
Fig. 2. Payload volume against unladen weight for various vehicles.
engine, transmission, two axles and four wheels should increase at a slower rate than the useful space since in every case, even with zero useful space, some weight for the structure remains. Interestingly enough, however, the contrary situation prevails in vehicles built today. If the line in Fig. 2 were extrapolated to zero weight it would intersect the ordinate at a useful space of more than 2 m3. Only when the same model is offered in different lengths does the old rule hold good. Quite obviously, there is a series of factors unrelated to that of useful space which determine the weight of a vehicle. As a rule, the lower range of “small” cars on the market is characterized by the following aspects: low price, small to cramped passenger compartment, small luggage space, low engine power output, low driving performance, minimum interior furnishing and no auxiliary features, but also low weight and low fuel consumption.
88
At the top end of the scale, “large” cars are characterized by: high price, spacious passenger compartment, large luggage space, high engine power output, high driving performance, generous interior furnishing and numerous auxiliary devices, but also high weight and high fuel consumption. It is these characteristics, increasing as they do with vehicle size, which are responsible for the considerable increase in weight and the unmistable rise in fuel consumption associated with larger cars. If large and small cars are today compared as to weight and fuel consumption, in reality characteristics are being compared which have little to do with the useful size of the vehicles. In this paper it is not accepted that vehicle weight is the indicator of “size,” with everything it implies, and we examine to what extent fuel consumption can be balanced even in the presence of widely differing car weights. As is well known, the tractive resistance of a vehicle which has to be overcome is dependent on two components: F wheel = m (gfcos a + g sin (Y+ a) + $p c,Au2 where Fwheel = tractive resistance, m = mass of the vehicle, g = acceleration of gravity, f = rolling resistance coefficient, cr = gradient angle, c = acceleration, p = density of air, cW = drag coefficient, A = frontal area, u = velocity. Some of the factors are proportional to the vehicle weight, such as rolling, gradient and acceleration resistances. The air resistance, being proportional to the frontal area of the vehicle, to the aerodynamic coefficient and to the square of the driving speed, becomes the most important factor at higher speeds. Keeping constant the size and the space of a car, the weight can be reduced by making greater use of light metal and fiber-reinforced plastics. Generally these light weight materials are more expensive than steel and, therefore, their proportion can be higher in cars where a higher selling price can be achieved. It is quite certain that large cars will not get any heavier in the future, but one would not venture to predict reductions in weight since the extra load imposed by safety measures such as anit-lock systems, air bags and belt tensioners, and possible legal requirements on exhaust emisssions and noise control must be accommodated. The rolling resistance coefficent, f, has dropped considerably due to the use of radial tires but is still surprisingly higher in passenger cars, compared with commercial vehicles. To make calculations, rolling resistance values are used according to Fig. 3, which are a little higher in the case of light vehicles, particularly at medium speeds. The inclination here is to predict at least a tendency towards smaller rolling resistance coefficients with increased weight. In climbing a hill a vehicle gains potential energy which can be used to overcome the rolling and air resistance when going downhill. Therefore, the gradient resistance, (mg sin ar) will increase fuel consumption only when the brakes have to be applied when going downhill. Otherwise, climbing and downhill driving will not add much to fuel consumption, as Fig. 4 shows. Here fuel consumption is indicated against the speed for travelling from
89 coefficient
of rolling friction f
0.03 i Subcompact car 2.0 bar 145 SR 13 (2000 N/wheel) 0.02
-
d Large car, 2.5 bar 195170 HR14 (4000 N/wheel)
0.01 -
01
0
50
100
150
200 km/h driving speed v
Fig. 3. Coefficient
of rolling friction against driving speed for subcompact
fuel consumption
and large car.
Be
tana + 0,06
0
25
50
75
100
125 km/h 150 driving speed v
Fig. 4. Fuel consumption
against driving speed for various gradients.
point A to point B on a level road and on different uphill and downhill gradients. The acceleration resistance, (ma), can be positively influenced by the driver by accelerating only when it makes sense, and by making the most of the kinetic energy. The air resistance of a vehicle is influenced by the value (c,A) where c, is the drag coefficient and A the frontal area. A increases in proportion to the useful volume but far less than in proportion to the weight of the vehicle. The reason for this resides in the given minimum space requirement for the driver and one passenger sitting side by side. The drag coefficient, cW , nowadays the object of intensive research, may be smaller for long vehicles than short ones, all other factors being equal, as shown in Fig. 5. Though this aero-
drag coefficient
short car
Fig. 5. Improvement
of drag coefficient
by extension
long cer
and tail retraction.
dynamic coefficient may vary substantially from one model of car to another today, with some small vehicles having a low value of cw, and large ones a high value, the advantages which the laws of physics bestow on longer vehicles will certainly be exploited in the future. Hence, the product (c,A) which determines drag will in future be almost independent of vehicle weight, as illustrated in Fig, 6. To make the following investigation into the fuel consumption of different cars as clear as possible, two extreme cars in weight and power will be compared. Carl subcompact
unladen weight load limit reference weight power engine type no auxiliaries
800 400 1000 40 4
kg kg kg kW in line, 1.2 litre carburettor
car2 large
unladen weight load limit reference weight power engine type all auxiliary systems
1600 kg 500 kg 1850 kg 160 kW V8, 4.0 litre fuel injection
Rolling resistance coefficient, as per Fig. 3 and aerodynamic drag (c,A), equals 0.7. Fig. 7 gives the travelling resistance, Fwbeel, against the driving
91
Maximum vehicle cross section A rn2
2.0
1.5
1 .o Cw.A
m2
---
z-
7
expected ’ in Mure
\
Drag coefficient C,
04
500
0
1000
1500
kg
empty weight G
Fig. 6. Maximum
vehicle cross-section
and drag coefficient
against unladen weight.
speed. When speed increases there is less and less difference in the traction resistance F of the two extreme vehicle types. Whereas at 50 km/h the driving force for the larger car is 55% higher than the driving force for the subcompact, it is only 12% higher at 145 km/h, the top speed of the subcompact. Fig. 8 shows the driving power over the driving speed for the two vehicles, the two curves are close together. Auxiliary
drives
Small cars have only the auxiliaries essential for the engine such as water pump, alternator and fan, which are partly electrically driven. Large vehicles, on the other hand, are generally fitted with a whole series of accessory devices serving the purpose of safety, travel quality and comfort such as an anti-lock braking system, airbag and seat-belt tensioner, air-conditioning sys-
92
Faubl Subcompact 1000 kg
Large car 1850 kg
2
1
0
V’
is
0
50
is
100
li5
Fig. 7. Traction resistance for large and subcompact
150
175
260 km/h driving speed
cars.
pow*r for traction
P
- largecBr
kW
-- subcompact car
1850 kg 1000 kg
150
125
25
0
0
25
50
Fig. 8. Power for traction
75
100
125
150
175
MO 225 km/h driving apeed
against driving speed for large and subcompact
car.
93 power of accessory
drive Pact
kW power steering air condition automatic transmission
pact
15’
10.
torque
Mace
-30 Nm .20
0
1000
2000
3000
4000
0 5000 min-’ 6000 engine speed n
Fig. 9. Power and torque of accessory drive against engine speed.
tern, automatic transmission, power steering, level control system, electric seat adjustment and window winding, etc. The only one of these systems which can be considered essential in terms of vehicle weight is the power steering. All of them immediately add weight. There are no real “heavyweights” among them, but taken together these accessories can increase the unladen weight of a car easily by more than 100 kg. This is one of the reasons for the greater unladen weight of larger cars. The auxiliary units which have to be driven to function continuously take their power from the engine, as shown in Fig. 9. Though the power level depends on the actual load on the accessories, a high load condition is a rarity; the only system that can work constantly at high load is the air-conditioner, during hot weather - but when it is cold it is not on at all. The decisive parameter determining the power consumption of auxiliary units is the rpm involved. The units and systems, power steering pump, fan, transmission oil pump, refrigerant compressor and alternator must be chosen so that their size permits them to work adequately at engine idling speed. However, since there may be a factor of more than 10 between engine idling and maximum speed, this means considerable oversizing at high engine speeds.
94
In the lower speeds up to 70 km/h the power requirements of ry drives can be quite easily equal the driving power output. This power must also be found when the car is at a standstill. Auxiliary unit power cannot simply be added to driving power they may be quite different at the same driving speed depending between the engine and the drive wheel speed.
the auxiliaadditional because on the ratio
Energy conversion efficiency If the extra fuel consumption of large cars as observed in practice, Fig. 1, is more different from that of small cars than is to be expected from the power required, even taking into account the still greater aerodynamic drag encountered today and the power requirements of auxiliary equipment, the explanation can only lie in the differing energy conversion efficiency of the engines. The engines chosen are derived from good series-produced engines and reflect the optimum available in each case at the present time. In order not to complicate comparisons, no account is taken of such possible future developments as higher compression ratios and anti-knock sensors, variable compression ratios, supercharging or cylinder cut-off, and the comparison is limited to gasoline engines because the problems there are greater. However, it will be obvious that many of the above-mentioned development possibilites can only be achieved at the expense of substantial cost penalties, so they are more likely to be applicable to big cars. Generally, large engines reach a higher maximum efficiency than small ones. This is brought out in the non-dimensional representation shown in Engine 4.0 I, 160 kW
tow le M/M 0
Engine
I .2 I, 40
kW
efficiency
to ‘rql MI/M
1 .a
0.5
C
( 0.5
1.0 engme speed n/no
0.5
1.0 engme speed n/no
Fig. 10. Performance map for various engines related to maximum power.
95 efficiency
7
35 % 30 7 opt, subcompact
car
+i opt large car
25
20
15
10
5
0
1 25
Fig. 11. Efficiency
75
100
125
kw
150 power P
of subcompact
and large CBTSagainst power.
Fig. 10, where all dimensions are standardized with those of the point of maximum power output. The areas of similar efficiency include areas of different power. When the power necessary to drive the cars is not very different, engines must be compared with regard to similar power. Also their consumption when idling is of importance. Figure 11 compares the optimal efficiency of both engine sizes against power output. Though the large engine achieves better maximum efficiency, there is nevertheless a region at low power where the small engine is definitely superior and this is the power range needed for speeds up to 100 km/h. This is nowadays the real handicap of big engines, and development will concentrate on this fact (supercharging, cylinder cut-off, variable compression, etc.) as already mentioned. As regards idling consumption, Fig. 12, the difference between the large and the small engine may become small if in future greater attention is paid to achieving low idling speeds. The idling speed of large engines can be kept below that of small engines, so that part of the different frictional losses can be compensated.
96 0 automatic transmission and accessones 31 automatic transmission ‘3: mechanical transmission
idling fuel consumption 1
kg
\ .
-4
idling speed
‘.
--
--
500
cyk+ -
6 cyl.+ -
1
2
3
8 cyl. 4
5
I
3
Engine swept volume
Fig. 12. Idling fuel consumption against engine swept volume.
The fuel consumption when idling rises when the engine has to work against the stalled turbine of a torque converter and still more if auxiliary systems have to be driven. For the following comparison of fuel consumption between the small and the large car, the performance characteristics of the engine used are shown in Figs. 13 and 14 on the same scale. In each diagram travelling resistance is indicated. The parameter cpnotes the relation of the engine speed in which the driving resistance curve intersects the hyperbola of maximum power output, referred to engine speed at top power. Therefore, cp= 1 is the driving resistance line through the engine point of maximum power. cp> 1, here 1.1, results in higher acceleration, cp< 1, here 0,7, results in an overdrive character. cpfor the power requirements of engine plus auxiliaries was chosen in such a way that both with and without auxiliary drives the engine reaches final power output at the same rpm; this means that other rear axle ratios belong to cp= 1 both with and without auxiliary drives. The diagram shows that the driving resistance line passes increasingly through areas of lower fuel consumption the smaller the value of cp,i.e. the slower the engine turns at the same speed of travel. Because this is a well known fact another criterion is obviously required in
97
torque M 200 Nm 150.
100
I
fuel consumption be g/kWh
50
0 L0
1000
2000
3000
5000
4000
6000 min-1 engine speed
rad/s m/s
_i _ engine speed r driving speed
Fig. 13. Performance map for a subcompact car (engine 1.2 litre, 40 torque M fuel consumption be [g/kWh]
“,“I
l\\\\LLGzA\\
250
luded 0
1000
2000
3000
4000
5000
6000 min
’
engine speed
Fig. 14. Performance map for a large car (engine 4.0 litre, 160 kW).
kW).
98 - large car with accessories acceleration 1.27
gradient
-- subcompact car
l-
m/s2
%
lo-
lo-
0.8.
8
0.8
6-
0.4.
4.
0.2.
2.
driving speed
Fig. 15. Acceleration and gradient reserve against driving speed.
order to understand why values of q > 1 have nevertheless so far generally also been selected for the big car. This additional criterion is the acceleration and climbing reserve in top gear without changing gear. This is shown in Fig. 15. A large vehicle with cp = 1.1 has much more acceleration in reserve than the small car and this difference increases markedly as speed rises. Of course, values of q < 1 would be possible even with a small car, but then the acceleration reserve gets too small that there is a risk drivers would either no longer use this gear or use it only rarely, which would have the opposite effect on economy. Fuel consumption The “classical” basic approach was taken by choosing cp = 1, the dotted line, for the small vehicle and cp = 1.1 for the big one, the line at the top of Fig. 16. Differences between the two vehicles as regards fuel consumption are particularly marked at low driving speeds - the price that is paid for the much greater climbing and acceleration reserves available in top gear, again referring to Figs. 15 and 16 must always be considered together. When fuel is expensive consumption can be much reduced with values of cp< 1. If, for example, the same average acceleration behavior without changing gear is acceptable for both large and small cars, a value of cp = 0.7 can be chosen for the big car in the example. This gives similar mean acceleration times of about 31 s from 60 to 120 km/h but fuel consumption drops for the large car by as much as 30% (curve 3, Fig. 16). If, in addition, the auxiliary systems were removed there would be very little difference between the consumption curves for large and small cars (curves 4 and 5, Fig. 16).
99 fuel consumption 30. 11100 km - large car wth accessones 25.
-- subcompact
car without accessories
20.
15. ‘) without accessories
01 0
25
50
Fig. 16. Fuel consumption
75
100
125
150
175
200
against driving speed for large and subcompact
225 km/h driving speed
cars.
Automatic transmissions with four speeds lend themselves particularly well to such a design concept with cp-4 1, selecting as they do, whenever possible, the most economical gear and shifting back when acceleration is needed. In addition to the comparison of fuel consumption in a steady state driving mode, the behavior of the cars in a town driving mode has to be contemplated. The comparisons are based on the Europa Test (ECE-cycle) which not only prescribes the amount of acceleration, speed and deceleration and the idling periods, but for a manually shifted gear box also the gears which have to be selected, shown in Fig. 17. It is quite interesting to note that the fuel consumption during the Europa Test (ECE-cycle) can be quite different according to the shifting specification and this is true especially of cars with manually shifted gearboxes (small car). With a shifting pattern A, the consumption would increase by 1.8 l/100 km or; with shifting pattern C, decrease by 1.0 l/100 km compared with the official gear selection. In the case of the large vehicle with automatic transmission it can be seen in Fig. 18 that the special shifting programme (B) brings about only a slight improvement of the consumption as compared to the normal version (A). In addition, the influence of a direct rear axle ratio cpsmaller than 1 which was very important at higher speeds has no great influence in the ECE city driving mode. On the other hand the handicap of large vehicles regarding fuel consumption in this test can obviously be reduced if the driver has not to follow the official acceleration pattern but applies the brakes as little as possible, using the kinetic energy to overcome the driving resistance, as shown in Fig. 19.
100 driving speed v
50’ km/h 40 fuel consumption I,65
1
11100 km
shdting pattern
Fig. 17. Influence of shifting - pattern on the fuel consumption _ mechanical transmission. driving speed v
of a subcompact
car with
fuel consumption 1/10Okm
Fig. 18. Influence of overall transmission ratio, rp, and shifting pattern A and B on fuel consumption of a large car with automatic transmission.
The result of a consumption calculation for a modified Europa Test (ECEcycle), Fig. 19, shows that with a given maximum speed of 50 km/h, and steady length and duration of the cycles, the ECE consumption can be reduced by 1.4 l/100 km due to the longer overrun conditions. Figure 20, finally, gives the summarized results of the consumption calculations, both for the large and subcompact car. Taking the values of the subcompact car as a unit, the large car naturally has a somewhat higher fuel consumption which, however, amounts to only 1.46 in the official ECE cycle, 1.27 at 90 km/h and at 1.16 at 120 km/h. In the combined Euromix cycle,
101 drlvlng speed ” 50 km/h
fuelConsumption
40
l/100 km
1455 13
30 20 10
0
loo0 -
distance covered s
ill. Sal_-_I
600.
shaftmg pattern A
400-
A
8
200-
0
1 20
0
40
SO
SO
120
100
140
160 time
180
IS5 set
t
Fig. 19. Influence of driving style on fuel consumption in ECE cycle if driven economically (average speed in cycle sections is constant).
fuel consumption
IllOOkm
5
-9.81
1
I influence driver
0.45
f E
f
B 8
f
I-
in flwncs cycle
of
subcompact
car
of
(mechanicaltransmission)
influencaof CY0le
E
E
i
constant speed
large cfar (autome~ic transmission)
Fig. 20. Influence of driver and driving mode on fuel consumption of large and subcompact car.
i ECE, $90 km/h and t 120 km/h, the fuel consumption of the subcompact is 8.2 litre/lOO km and of the large vehicle 10.7 litres/lOO km. The results of Fig. 20 have been entered in Fig. 21 and demonstrate that fuel consumption of larger (heavier) vehicles may increase less than 1 l/100
102 fuel consumption 25
Be
*
l/l 00 km 20.
28 vehicles tested by Automobil-Revue from 1968 to 1970 ’ highway
/ interurban
* highway
smooth
speedy
kg 2000 empty weight G
Fig. 21. Fuel consumption against unladen weight.
km and 100 kg weight, in fact giving only about 0.3 l/100 km and 100 kg weight difference in the given example. CONCLUSION
The sometimes considerable difference in fuel consumption between big cars and small ones is the result of, first, the power requirements of the many accessories installed in the large cars and second and above all, the desire for large reserves of acceleration in top gear without having to change down, which forces large engines to work in a region of low efficiency. But with the methods described in the paper the additional fuel consumption of a large car with twice the weight and four times the power can be reduced to about 30%, which means less than 0.3 litre/lOO km/100 kg weight difference. Because many further improvements to reduce fuel consumption which are under development and which may be more easily included in high-price cars have not been taken into consideration, it seems certain that in the future even large cars will have a low fuel consumption.