SOME BRAKING PROBLEMS
HOW ROAD SURFACES AND CHASSIS DESIGN AFFECT THE BRAKES.
DRIVERS frequently have heated arguments as to the methods of obtaining maximum braking efficiency, with special regard to the amount of braking force which should be applied to each axle for the best results.
Opinions on this subject often have little or no relation to the mechanical facts which govern this problem. In fact, I have -had motorists tell me, with as much assurance as they would state the day of the week, exactly what is the ideal ratio of braking force for all cars under all conditions.
Naturally, most sports car owners know a bit more about the matter, and it is well enough known that on a surface which gives a very good grip, such as dry concrete, there is a ‘piling-up “effect, due to the weight being thrown on to the front axle. which allows a greater force to be applied to the front brakes without locking the wheels.
This gives a very good stopping distance, but cannot be used for normal work, as under conditions where the grip is less, as on a wet road, less weight is thrown on the front wheels, and they will lock before the rear brakes have reached their full useful effect.
It is this piling up effect which I wish to go into, and show how the required ratio varies continuously, and therefore the resulting ratio decided by the makers must be, as with most things in motoring, a compromise to suit the average conditions, with the further provision that the system must not tend to promote accidents when conditions vary from the average.
In my diagram we have an outline of a small racing car with a wheelbase of 9ft., in which the centre of gravity is xft. from the ground when loaded and halfway between the axles. The reactions between the road and the tyres are pi and p2, acting of course vertically and together equal to the weight of the car, which can be W. When the car is stationary, pi will be equal to p2. We are not concerned with this, but rather with the conditions when the car is being
braked to its maximum, when we wish to know the best proportion of braking force for each axle.
This will be shown to depend on three things : (1) the length of wheel base, (2) the position of the C. of G., and (3) on the co-efficient of friction p between the tyres and the road surface.
Assume for a start that the car in our diagram is being stopped, and that all wheels are just on the point of locking—this being the best possible condition for stopping. What is required is the ratio of braking force for such conditions. The forces acting on the car under these conditions are : Vertically, the weight of the car W acting downwards through G, and the reactions at the tyres pi and p2 acting upwards and together equal to W; horizontally, the braking forces at the tyres p x p2 and p x p2, equal and opposite to the forward force due to the momentum of the car acting through G. (W —
P1 + P2.).
The next process, referred to in text-books as “taking moments,” is to consider the tilting couple acting about various points of the car so as to find the relative values of pi and p2, which, of course, also give us the required relative values of the braking on each axle. The couples about the point a are as follows :— Clockwise :
(1) g. (pi 4. p2) lbs. ft.
(2) px (pi + p2) lbs. ft.
Anticlockwise : 9 p2 lbs. ft.
The total couples in each direction are equal to each other.
.•.(% +px) (pi + P2) = 9 132. The couples about the point b are as follows :— Clockwise :
(1) px (pi + p2) lbs. ft.
(2) 9 pi lbs. ft. Anticlockwise :
4, (pi + p2) lbs. ft.
(Pi + 9p2) + 9pi— (PI = P2) or (4 — px) (pi + p2) = 9 p2. From this it follows that the ratio of pressure of back and front wheels, which is pi P2 which is also the ratio of brake force required, is :— 9 — 2 px 9+ 2 px or for any length of wheelbase the ratio will be / px 1 4. 2 px
Where / is the wheelbase, x the height of the C of G from the ground and p the coefficient of friction between the tyres and the road. In applying this expression, assume that the car in the diagram, which has a 9ft. wheelbase, has its C. of G. lft. 6in. from the ground, and that it is braking hard on a surface where P = 1
We can then find the best arrangement for the brake operating leverages. The ratio will be 7.5 = 0.71 approximately. 10.5 In other words, the rear brakes
should have just under the pressure applied that the front brakes have.
Suppose the same car be taken on to a rough concrete surface where, due to the interlocking effect of the tyre tread and the surface, p may reach a value of 1. The correct ratio will then be 9 — 3
9 + 3 or 0.5, showing how extra pressure (double that on the rear) on the front brakes can be used on exceptional surfaces. If the brakes are designed with such a ratio, however, and the car taken on a slippery surface with p equal to 0.2, the correct ratio will be approximately 0.9 for best results.
Otherwise the front wheels will lock well before the rear have had a chance to exert their full grip.
This shows how impossible it is on a normal, straightforward system to cater exactly for all braking conditions, and why a compromise which has been tried out in practice must be arrived at. This formula is exactly correct only if the C. of G. is midway between the axles, but if it is slightly forward, or behind it, it will only be
slightly altered, and the variations for different conditions will he similar. It can also be used to show the effect of a higher or lower centre of gravity and a shorter or longer wheelbase.
It is obvious from the formula that a lower centre of gravity, i.e. a smaller value for x, will make the ratio of adhesion of the front and rear wheels less affected by changes in surface, as if x is small, 2 px is also small, and the expression remains nearer to unity.
A similar effect is obtained with a longer wheelbase. If the opposite extreme is considered, a very short and high vehicle braking on rough concrete at its maximum, say with a wheelbase of 6ft. and the C. of G. 3ft. from the ground, will make the formula equal to zero.
In other words, the back wheels will cease to adhere at all and the car will turn end over end ! However, such a shape of vehicle, if it ever existed, was probably not fitted with front brakes at all, so we need not worry unduly over such a possibility! In fact, if anyone asks you what is the correct ratio of braking effort on the front and rear wheels of a car, you can truthfully say, ” It all
depends ” ! —B.
Following various enquiries from readers as to the actual possible stopping distances of a car, we give the following table for a car with perfectly proportioned brakes on a dry concrete road where the coefficient of friction is 1.
The distance increases in proportion to the square of the speed. 10 m.p.h. 3.5 ft.
15 „ 7.5 ft.
20 ., 13 ft.
30 „ 30 ft.
40 ,, 54 ft.
50 83 ft.
6° 31 121 ft.
70 160 ft.
80 „ 210 ft.
90 „ 274 ft.
100 „ 330 ft.
The fact that these distances are sometimes improved on in practice is due to the interlocking effect of the tyre tread and the road surface.
A Change of Address.
NEW showrooms have been opened at Stratton House, Piccadilly, by University Motors, sole distributors in London for M.G. cars.
The company’s branch showrooms are being closed, and all business will be concentrated at Stratton House, where there is accommodation for over thirty cars.
The two service and repair shops in Carrington Street, and Cheyne Walk, Chelsea, and the garages in Lawn, Street and Clarges Street, are to be retained.
The First English “500.”
THERE is no doubt whatever that the motorcycle most wifl,ely used in Europe is the 500 c.c. solo. There are always more” 3f’s ” than other types in races and trials, and nowadays they are almost invariably of the o.h.v. pattern.
It is interesting to note that in a booklet recently published, by the British Cycle and Motorcycle Manufacturers and Traders Union— Early Days in the British Motorcycle Industry “—the credit for producing the first wholly English 500 c.c. motorcycle is given to the New Imperial company. This machine was exhibited at the Stanley Show in 1901.
It was the only motorcycle shown in an exhibition of pedal cycles and, as a matter of fact, only six were made, one of which was sold at the Show, the others being used by members of the staff.
Remote Controls for the Gear Change.
ONE unsatisfactory point which is sometimes met with in cars which have been modified from standard to sports type is the inaccessibility of the gear lever. To meet the requirements of owners who wish to overcome this, various firms are now marketing special remote gear control systems. There is, for example, the StearnsLayton device, which comprises an aluminium casing, on the end of which is cast a flange. This bolts on to the top of the gearbox, and at the other end is a gate and, lever of orthodox type. The action of the latter is conveyed to the selectors through a flat steel strip. This has a central fulcrum point, consisting of a steel roller which slides between two guides. The movement of the lever is thus reversed at the selector end of the system. Made specially for Wolseley ” Hornets ” and Morris models, the
Stearns-Layton unit costs 50s., or 55s. with a de luxe finish. It is marketed by E. C. Stearns and Co., 16, Fulham. Road, South Kensington, London, S.W.3. Another remote control made for “
Hornets’ is the Alta, which is obtainable from V. W. Derrington., of 159, London Road, Kingston-on-Thames. As can be seen from the accompanying illustration, it is of neat and clean design, and it can be attached simply by removing the standard lever, and, bolting it on with the four studs provided. The price is 59/6.