3asic principles :of braking: 1
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N THIS SERIES, over the past 'ew months, the various :omponents used on air braking ;ystems, as fitted to modern ;ommercial vehicles, have been ;xamined. Now a simple ;xplanation of the basic theory ;onceming the retardation of iehicles will be attempted. I ieliberately use the word 'attempted": to try to discuss ;uch a complex subject in ;imple terms is very difficult. Figure 1, reproduced by
;ourtesy of the Department of Transport, Crown Copyright, .ihows the forces acting on a iingle wheel of a motor vehicle with the brake being applied. The load on the tyre is the direct result of the force of gravity and this downward force results in the upward reaction Rat the point the trye makes contact with the road. The braking force F, Figure 1, will cause the wheel to slow down.
At first it is difficult to visualise force F and probably the easiest way is to consider what happens on the roller type brake testing machine used at testing stations. (See Figure 2) Here, the wheels on which the brakes are being tested, are revolved by rollers on which they are resting. The brake is applied and the force needed to turn the wheels against the resistance of the brake is measured. It is this force we are considering at F in Figure 1.
The maximum braking effect is obtained when the force F does not quite prevent the wheel from turning. If this limit is exceeded the wheel locks and the tyre "skates" along the road surface. When this condition arises no additional braking effort can be obtained.
If the ratio F/R is plotted against percentage slip (0 percent being equivalent to a freely rolling wheel and 100 per cent a wheel in the locked position) then on different surfaces a family of curves will be obtained, as shown in Figure 3. (again by permission of the DTp). The diagram shows that as the ratio F/R increases so does the percentage slip until a limiting value is reached after which any attempt to increase the brake force F will cause the slip to increase almost instantaneously to 100 per cent. The value of F/R at which this occurs is called the coefficient of adhesion between the tyre and the road surface and is usually denoted by the Greek letter (mu).
The actual value of [.t will depend on the actual conditions prevailing at the time A wet or icy road will reduce dramatically the coefficient of adhesion, especially when the vehicle is fitted with smooth tyres.
Because the contact between the tyres of a vehicle and the road depends on gravity, then the force exerted by the brake can never exceed that of gravity. Thus, in theory, the maximum deceleration which can take place can only equal the acceleration due to gravity. A
influence of gravity, increases its speed by 32.2ft per second, per second. This increase in speed is written as 32.2ft/sec2. This means that the velocity increases by 32.2ft per second every second. The modern equivalent, in metric terms is 9.8m/s2.
One hundred per cent braking efficiency is where the rate of deceleration or retardation is at this rate of 9.8m/s2 and this results in a stopping distance of about 30ft at 30mph. A brake of this efficiency can be obtained under freak conditions, but is not really desirable in ordinary service. One can imagine the passengers in the rear seat of a coach finishing up with the driver if brakes were as powerful as this. What would happen to the standing passenger on a bus does not bear thinking about.
It is unfortunate that the word "efficiency" has become so widely used for this purpose. The layman, and some magistrates and lawyers consider that unless a vehicle has brakes of 100 per cent braking efficiency there is something wrong with them, where actually brakes are in excellent condition if 80 per cent efficiency is recorded.
Some engineers refer to braking efficiency in terms of g, 100 per cent efficiency equalling 1 g; 50 per cent efficiency as 0.5 g and 60 per cent as 0.6g.
More about braking efficiency and stopping distances in my next article.