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1951 Uphill Work
  THE towing performance of a car is its overall performance when towing a particular caravan and includes such items as performance on hills, freedom from snaking at higher speeds, adequate stiffness of rear suspension, adequate engine cooling, and driving comfort.
The towing power of a car is its ability to accelerate and to climb hills when the car’s weight is increased by the weight of the caravan and is comparatively easy to assess. Provided there is adequate weight on the driving wheels it makes little difference to hill climbing ability either where the combined weight is located or how many road wheels there are; it is thus sufficient to consider simply a car of weight equal to the combined car and caravan weights without any van trailing behind.
The performance figures of cars, as given from the road tests published in The Motor , are therefore a good guide to their power to tow caravans since simple ratios enable their towing power to be calculated from the performance figures given.
The man towing a caravan is probably most interested in hill climbing ability and, if the individual weights of the car and caravan are known, the maximum gradient which can be climbed in bottom gear from a standing start on the hill (denoted below by S) is given with adequate accuracy by the formula :

where s is the max. gradient without caravan in a given gear, W1, is the weight of the car, W2 is the weight of the caravan, C is the gear used to Climb s, and R6 is the bottom gear ratio.
The gear box efficiency varies with the gear in use and is lowest for bottom gear. It is preferable in calculating bottom gear performance to use the lowest gear for which test figures are given, which is usually second gear.
Optimistic figures will be obtained by using the figures for higher gears; there is more variation in efficiency with a four-speed than with a three-speed gear box.
Thus, as an example, Th e Motor Road Test No. 9/50 gives the maximum second gear gradient of the Vauxhall Velox as 1 in 5.9. If a Berkeley Courier with all-up weight of 30 cwt. is being towed the maximum gradient with or 1 in 6.2. Thus the Velox towing the Courier could climb from a standing start a hill of which the gradient did not exceed 1 in 6.2.
Table 1, given below, shows, together with other data, the weight of caravan which a number of typical cars, selected from The Motor Road Tests can tow from a standing start up gradients of 1 in 6 and 1 in 8. As explained later an estimate can be made of the distance which can be climbed up steeper gradients with a flying start.


The table shows that little reliance can be placed on any figure of towable caravan weight per litre of engine capacity since the figures vary considerably. The main causes of such variation are the bottom gear ratio and the weight of the car itself.

  An attempt will now be made to evaluate a figure which does represent the towing power of a car. The term “tractive effort" will be familiar to those who were interested in railway locomotives in the days of their youth and represents the power available for hauling a train. The tractive effort of a car is the pull available for hauling the combined weight of car and caravan.
It may be difficult for the layman to understand the expression “engine torque", but he can accept the fact that for a fixed roadwheel size the tractive effort is directly proportional to the product of engine torque and overall gear ratio, thus being a maximum in bottom gear.
The engine torque is independent of the gear ratio and has a constant value as long as the graph of developed brake horse power against engine r.p.m. is a straight line; for most cars engine torque is constant over a fairly wide range of engine speed, falling away at bothe low and high engine r.p.m. In towing it is largely the performance at low road speeds, that is at low engine r.p.m, in any gear, which is important and for good towing performance it is desirable that the engine torque should be high at low engine r.p.m.
An idea of how good the engine torque is at low r.p.m, can be obtained from the top gear acceleration figures. The acceleration times are a measure of the tractive effort for the car alone and, for comparable type cars, the larger the ratio of the 20-to-40 m.p.h. acceleration time to the 10-to-30 m.p.h. acceleration time, termed the low r.p.m, torque merit figure in Table 1, the less the falling away of torque at low engine r.p.m.
  The larger torque merit figure for smaller cars is due to lower top gear ratio which gives higher r.p.m, for a similar road speed, and though this means good towing performance of small loads at comparable road speeds, it does not necessarily mean a high engine torque at low engine r.p.m.
There are two methods of determining the tractive effort of a car. The first is by the measured "Tapley Pull" in lbs. per ton as given in the Motor Road Tests, and the second is by calculation of the specific displacement in litres per ton mile (denoted below as D) from particulars of the car. The calculated specific displacement in top gear is given in the Motor Road Test and the relationship between the two is given by the formula:
  The specific displacement in top gear (D t) can be calculated from the formula:
  where C is the engine capacity in litres, W1 is the weight of the car in tons and V is the engine revs, per mile in top gear.
The first two figures are readily available though it should be remembered the weight is the laden weight including passengers. The engine revolutions per mile are seldom given in the maker’s particulars but can be roughly calculated from the formula below which assumes the road wheel diameter to be 26 inches.
V—783 X Top Gear Ratio.
The measured formula for tractive effort in bottom gear (T) is thus :
  where W1 is again the weight of the car in tons, R, is the bottom gear ratio, and R is the given gear ratio.
The calculated formula for tractive effort is:
The ratio of caravan weight towable to car weight, that is the number of times its own weight which a car can pull, is equal to
  Table II shows a comparison for a number of cars of the measured Tapley Pull as given by road tests, and the calculated Tapley Pull which is equal to
  e.g, for the Vauxhall Velox the calculated Tapley pull in top gear is

It will be seen that there is sufficient agreement between the two values for a rough estimate of towing power to be made without making an actual road test of the car.
Figure 1 shows the percentage of car's weight which can be towed up different gradients for different values of Tapley Pull, or specific displacement, of the car alone. The figure for higher gears are always given in the road tests, and the values for other gears can be calculated, the value in bottom gear being, of course, the greatest. For estimating bottom gear pull the figure given for the lowest gear should be used.

  To calculate the Tapley pull in another gear, multiply the Tapley pull
  in which R, is the other gear ratio and R is the given gear ratio.
  From Figure 1 the approximate gradients which a car towing a caravan can surmount in any gear can thus be read. Taking the Velox again, the Tapley pulls in the three gears are:- Top, 235 ; second, 375 ; bottom, 782. The gradients which can be climbed with a caravan weight 90% of the car weight are thus approximately: Top’, T in 18; second, 1 in 11 bottom, 1 in 6.
From the point of view : of towing comfort it is obviously undesirable to have to do too much gear changing and an estimate of .the -towing power in each gear is helpful. Some manu facturers appear to consider that the weight of caravan should not exceed the weight of the car but the author’s
experience of towing a Courier with a Velox, and other tests made with, a Vanguard towing an Ambassador , seem to make the choice of this value rather arbitrary.
  All the figures quoted previously have been based on the assumption that the hill is required to be climbed from a standing start. Whilst this is desirable in towing and makes for safe driving, it is nevertheless possible, due to stored kinetic energy, to surmount steeper gradients than those
previously calculated if the car and caravan are moving fairly quickly at the moment when the steeper gradient is met. The distance which can be climbed on a gradient steeper than the steady climb gradient is independent of the weight of the car and caravan and depends only on the initial speed at which the gradient is met and the excess gradient to be climbed.
If the car is put in neutral and the car and caravan allowed to coast to rest up any gradient, the slope distance it will coast is equal to
  Table III shows the coasting distances on a number of different gradients.
If the engine is kept going the slope distance is, of course, increased. The actual value in fact is equal to
  Thus, if the steady climb gradient is, 1 in 10 and the actual gradient is 1 in 9, the slope distance will in theory be 10 times the coasting distance. In actual practice the figure will probably be nearer 5 due to road friction and decreasing engine torque at low engine speeds.
  It will be seen that the slope distance depends mainly on the initial speed and the difference between actual gradient and steady climb gradient. If the car is underpowered the importance of maintaining a high speed and of having only short coasting periods when changing gear can thus be appreciated.
It so happens that the number of seconds required for acceleration in top from 10 to 30 m.p.h, is approximately the same as the gradient which can be climbed. Figure 1 can, therefore, be used to estimate acceleration times from 10 to 30 m.p.h, in top. The Velox with 90% its own weight will thus take 18 seconds to reach 30 m.p.h, from m.p.h, and it is well to remember this increased time when trying to pass on the road. By using 2nd gear the time could be decreased to some seconds but this figure only holds for a car which has a maximum in second of about 50 m.p.h, as otherwise the falling off of torque at high engine r.p.m, will decrease the acceleration before 30 m.p.h, is reached.
  Help From The Son

It is hoped that this article is not too technical for the ordinary man who wants to know what caravan his car can tow. All calculations can be done by simple proportion, preferably with a slide rule. If father finds the formulae too much for him his schoolboy son will probably be able to cope.
To anybody who only reads the conclusions and wants an approximate formula the following, based on average performance figures, is given:— Weight of caravan in cwts. towable up gradient of 1 in 6 is equal to (l|x bottom gear ratio x capacity in litres) less weight of car in cwts. Thus for the Humber Hawk :—
Weight of caravan towable=(l£x 16.19x2.267)—29.5 up 1 in 6 gradient =25.5 cwts. Figures calculated by the above approximate formula give maximum errors of about 5 cwt.

  The Caravan November 1951
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