What They Indicate and How They Work.
By B. G. MANTON, B.Sc., A.M.I.C.E.
A speedometer has become a built-in component of every car’s equipment and an engine revolution counter is a standard fitment on the facia board of many sports models and not a few of the more expensive tourers, but an accelerometer, although of considerable use and interest, seems to be looked upon by many drivers as a highly complicated and mysterious instrument whose indications are incomprehensible to anyone but a fully qualified engineer, although this is by no means the case.
There are many different types of accelerometer, designed for as many different purposes—some are certainly cumbersome and elaborate, with electrically driven self-recording mechanism which draws out a chart showing exactly how the acceleration changes throughout a given period of movement, but others are remarkably simple and compact and among these there are two, in particular, which are specially intended for the use of motorists and automobile engineers—the ” Wimperis ” and the ” Tapley ” instruments.
Both are entirely self-contained, requiring no connection to any moving part of the vehicle, and a great deal of useful information may be obtained from their readings without any profound technical knowledge. They enable an accurate analysis and definite measurements to be made, under ordinary running conditions, of every feature of a car’s performance, giving the values, for instance, of engine pull and acceleration on each gear, braking efficiency, road gradients, losses due to friction in the car’s mechanism and the combined effect of wind pressure and road resistance ; moreover, if the weight and the speed of the vehicle are known, an accelerometer provides a quick and simple means of determining the brake-horse-power at that particular speed.
The ” Wimperis ” Accelerometer.
The ” Wimperis ” instrument is a very handy little appliance, the entire mechanism being enclosed in a brass case, about four inches in diameter and three inches in depth. When in use it is placed on the floor of the vehicle, or on any convenient flat platform, with the circular faces of the casing in a horizontal position. The bottom of the case has two fixed supports and an adjustable levelling screw and the upper face is glass-covered, revealing a graduated dial and an indicating pointer, rather resembling a speedometer. The instrument must be placed in such a way that an arrow on the dial points in the direction of motion of the vehicle and must be levelled up carefully so that the pointer indicates zero when the vehicle is stationary on a level stretch of road. The scale is graduated to read acceleration and retardation in “feet per second per second,” these indications being supplemented by gradient readings, marked in red numerals, since the instrument also acts as a gradient meter when the vehicle under test is either standing still or travelling at a uniform speed.
The expression “feet per second per second” has a somewhat cryptic sound and requires, perhaps, a little further elucidation. Imagine that a car is speeding up from a standing start and that its velocity is read from a speedometer at the end of every second, the readings being, 5, 10, 15, 20, 25 and 30 miles per hour respectively. The speed is obviously increasing by 5 miles per hour during every interval of one second and we may therefore state that the acceleration is 5 miles per hour per second. But 5 miles per hour is equivalent to 7.3 feet per second and, adopting the standard method of enumeration, the acceleration, in the form of “feet per second per second” is, consequently, 7.3.
The working principle of the instrument depends upon the movement of a thin metal disc, mounted on a vertical spindle so that it can spin round in a horizontal plane. The disc is made “lop-sided,” or out of balance, by the simple expedient of cutting out a hole eccentrically, so that the centre of gravity no longer coincides with the geometrical centre about which it is pivoted. The support, however, is sufficiently rigid to keep it horizontal, while permitting free motion around the vertical axis. When the arrow on the dial is pointing in the direction of motion and the pointer is reading zero, the disc is so placed that its lack of balance will have a maximum effect and a rotary movement ensues as soon as the vehicle moves forward. The spinning motion of the disc is controlled by a coil spring and damped by a simple magnetic device to keep it within reasonable bounds and is conveyed to the indicating pointer through a train of gear-wheels, the weights of the various moving parts being proportioned with extreme care so that the amplitude of the swing set up in the disc, and reproduced by the pointer, gives an accurate measure of the acceleration, or retardation, over a wide range.
When acting as a gradient meter, the whole instrument, of course, assumes a tilted position, corresponding to the slope of the hill, and the disc swings round until a position of equilibrium is reached, whereupon the pointer will indicate the appropriate gradient.
The Tapley Performance Meter.
The “Tapley Performance Meter” is made in several forms and may be attached permanently to the facia board, or the steering column, or temporarily attached to a special bracket and thus changed over easily from vehicle to vehicle. Like the ” Wimperis ” instrument, it is very compact and quite self-contained, but its working principle is different, depending, as it does, upon the action of a pendulum. The latter is pivoted so as to swing to and fro in the direction of motion of the car or cycle, and, in order to damp down the oscillations, which would, of course, be too jerky for accurate observations under running conditions if entirely uncontrolled, the heavy swinging arm and its pivot are enclosed in a sealed case, filled with a special liquid. The underside of this case is made of very thin copper and the pendulum itself is magnetised with sufficient intensity to influence a second pivoted arm which swings to and fro outside the sealed case and, by this simple method of magnetic attraction, exactly reproduces the motion of the controlling pendulum within. The motion of the outside arm is transmitted through gearing to a revolving scale which is visible in a small window in the dial of the instrument, the indications being read off against a fixed index mark. One popular pattern of the ” Tapley ” meter gives dual readings—the engine pull in
pounds per ton” and the gradient value, and although acceleration is not directly registered, the instrument is, like the ” Wimperis ” type, a combined accelerometer and gradient indicator. This latter feature, however, will only function accurately when the vehicle under test is either stationary or moving at a uniform speed.
The “Pounds per Ton” Unit.
Both the engine pull and the resistances overcome thereby are very frequently expressed as so many pounds per ton weight of car” and this mode of valuation may be visualised by imagining that the vehicle under test is coupled to a trailer which, itself, is weightless and frictionless. The forces resisting motion under ordinary running conditions are the wind pressure, the frictional resistances in the mechanism, and the friction between the tyres and the road, while we have, in addition, the gravitational resistance which occurs when the vehicle is ascending a gradient. We must next imagine that these forces are represented by weights and that they are removed from their respective spheres of action and loaded on to the frictionless and weightless trailer and we will suppose that the coupling between the trailer and the leading vehicle consists of an ordinary spring-balance. When the vehicle begins to move, a certain pull will be registered on the balance, corresponding to the initial acceleration from a standing start and, as the speed settles down to a steady figure, the reading of the spring-balance will diminish and then remain stationary until some change occurs in the gradient, the wind pressure, or the nature of the road surface. The reading of the balance in pounds divided by the weight of the car in tons will give the engine pull in pounds per ton, at any instant, needed for overcoming the sum total of the various resistances to motion. If, however, the speed is not constant, the indications of the spring-balance will show the extra pull needed for producing acceleration.
By a well-known law of mechanics, a pull of 70 pounds per ton will produce an acceleration of one foot per second per second and a resistance of 70 pounds per ton will produce a retardation of one foot per second per second, provided, in both cases, that the mass on which the force is acting is perfectly free to move. It therefore follows that if an acceleration, or retardation is recorded as so many feet per second per second, as in the case of the ” Wimperis ” instrument, this figure multiplied by 70 will give the force in pounds per ton which is causing the change in speed.
What an Accelerometer Tells.
As an example of the utility and interest of both the ” Wimperis ” and ” Tapley ” instruments let us consider two simple tests, with some typical figures which might well be obtained in actual practice : First, imagine that a car is speeded up to 35 miles per hour on a level road and the ignition then switched off, so that the various resistances to traction will come into play unhindered and thus produce a retardation. Suppose that the retardation reading on a Wimperis instrument, when the speed has dropped to 30 miles per hour, is 1.4 feet per second per second. This corresponds to a retarding force of 1.4 x 70, or 98 pounds per ton, and this figure would therefore appear on the dial of a Tapley performance meter, were we using the latter. This represents the sum total of all the “slowing-up ” influences on the level and the engine must develop an equal pull of 98 pounds per ton if they are to be counteracted and the car propelled at a uniform speed. It should be noted, however, that both instruments will read zero at constant velocity on a level road and the engine pull needed for neutralising the tractive resistances is consequently unrecorded during the actual running and can only be determined from the retardation test just described.
If, however, the engine can develop a greater pull than the 98 pounds per ton previously referred to, the surplus pull will be converted into acceleration which will be registered immediately on a Wimperis accelerometer as so many feet per second per second, whereas a Tapley instrument will tell us the actual value of that surplus in pounds per ton, and, naturally enough, the greater the surplus pull available, the greater will be the liveliness of the car.
But our surplus may also be absorbed in climbing a gradient and here we come across another simple relationship : the ratio between the vertical rise of a hill and the length of the slope is the same as the ratio between the force needed to overcome the resistance due to gravity and the weight of the car. If the hill has a grade of 1 in 12, for example, this means, strictly speaking, a rise of 1 foot for every 12 feet measured horizontally, but unless we are considering gradients of about 1 in 4 or steeper, the horizontal distance is very nearly the same as the length of the slope, and we may say, without serious error, that the ratio 1/12 representing the gradient is the same as the ratio between the pull required to overcome the effect of gravity and the total weight of the vehicle, i.e., for every ton of the latter the engine must exert a pull of 1/12 ton, or 187 pounds, in counteracting gravity alone.
We now come to our second test : this is to discover the gradient which the car will climb “all out” at a steady 30 miles per hour—the same speed as that used for the retardation test. Suppose, for convenience, that this gradient is the one previously referred to, namely 1 in 12. Both the Wimperis and the Tapley instruments will record the slope on their gradient scales” and the latter, in addition, will show the corresponding pull of 187 pounds per ton absorbed in overcoming the gravitational resistance. Hence the total pull now being developed by the engine is (i) 98 pounds per ton for overcoming the tractive resistances discovered from the retardation test, which, of course, are the same on the hill as on the level road provided that the type of surface and the wind pressure are the same, plus (ii) 187 pounds per ton for overcoming the gravitational resistance of the incline. This gives a total pull of 285 pounds per ton weight of car.
Finding the B.H.P.
If we know, in addition, the total weight of the car and its load, we are now in a position to ascertain the brake-horse-power developed at 30 miles per hour in top gear. This is done by means of a simple formula, thus : Multiply the total pull by the weight of the car in cwts., and the speed in miles per hour, and divide the product by 7500. If, for instance, the weight of the car under test is 25 cwts., the available brake-horse-power at 30 m.p.h. in top gear is : (285 x 25 x 30)/7500, which gives 28.5.
It will be appreciated from this that an accelerometer enables an owner-driver to obtain valuable information concerning his car’s performance in a far more precise form than that derived from a road test with a speedometer only, and for determining such a vital detail as the brake-horse-power, under various conditions, the quick and simple accelerometer method presents a marked contrast to the only other alternative : that of mounting the car on a special test-bed with all its elaborate instruments and mechanism—a proceeding entirely impossible for the ordinary driver, who may, nevertheless, desire to take an intelligent scientific interest in his car’s behaviour.
Several motorcar factories have excellent test tracks surrounding their works, but the track which has just been built by the Hillman company is unique in that its surface has been purposely roughened to approximate Colonial conditions.
Tests on this new track in no way replace the wual extensive road tests. They are in addition to them and are carried out mainly with a view to discovering body rattles or imperfections in the springs, shock absorbers and steering. If any minor faults are found they are rectified on the spot ; this is obviously more effective than later adjustments in the final test shop.