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The Force It Takes to Stop a Motor Car To the Editor of the Scientific American : In the issue of July 4th this year there was an inquiry with reference to the force required to stop a motor car, and you announced that you would be glad to hear from your readers on the problem. I have seen no response in the later issues and would submit the following as an approximate solution of the problem. The specific inquiry was--what will it take in weight or power to stop an automobile weighing 3,500 pounds, traveling 20 miles an hour, Within 30 feet. One and one half times the number of miles an hour is a very close approximation to the number of feet per second, and we may, therefore, take the velocity of the car as 30 feet per second. The energy of the assumed car in foot-pounds is, therefore, approximately 3,500 X 30 X 30 64.4 --V or 48,913 foot-pounds. As the car is to be stopped in 30 feet, the force in pounds required to be exerted throughout the stop is 48,913 30 1,630, which is nearly one half of the weight of the car. E ---- From the equation h 2g for a falling body, we should also find that the height through which the car would fall in acquiring the velocity of 30 feet per second, is about 14 feet, and as this is a little less than one half the distance in which the car is assumed to be stopped, it will require a force of a little less than the space of 30 feet to absorb the energy of the car one half of the weight of the car acting through (1) and bring it to rest. 1 -- 1 X 3,500 1,638, which con- firms the previous computation. The time required to bring the car to rest is equal to the distance, divided by one half of the velocity at the moment when the stopping force begins to act, in this case 30 X 30 2. The work, 48,913 foot-pounds, is, therefore, performed in two seconds, or at the rate of 24,456 foot-pounds per second, and as a horse-power performs 550 footpounds of work per second there would be an exertion 24,456 -T- 550 44 horse-power in bringing the car to rest. Conversely 44 horse-power would generate a velocity of 20 miles per hour in a space of 30 feet, if nothing but the inertia of the car were taken into account. As a practical matter there would also be the road friction, running gear friction, air resistance and the like to be overcome, so that much more than 45 horsepower would be required to accelerate the car to that speed within that distance, if it were possible to be done. For a like reason somewhat less than the force or power computed as above would be required as a braking force to stop the car, for the road friction and air resistance would assist, and the running gear friction acts in effect as a brake, in so far as it opposes the free rotation of the wheels. It is much more important to know the minimum distance in which a cur can be brought to a stop frem a given speed, than to know the force required or power consumed. There is no difficulty in making brakes to give the maximum retardation attainable by braking action. The limit to the retarding effect, and to the reduction of distance within which the stop can be made, depends upon the frictional or tractional hold of the wheels on the road surface, and this varies greatly with the condition of the road, being very small on a wet and muddy or, greasy surface. Without having any definite information, I judge that the coefficient of friction between a good gravel or macadam road and the usual pneumatic tire without chains is about 0.4, and that it is rarely more, and frequently much less than that in ordinary driving conditions. If we take the coefficient' of friction of tire on road as 0.4 we have only four tenths of one half of the weight of the car as the maximum retarding resistance derivable from the brakes, when, as is usually the case, the brakes are on the driving pair of wheels only, and the weight of the car is about equally divided between the front and rear wheels. We have computed that it takes a force of about one half the weight of the car to stop the car within 30 feet, from a speed of 20 miles per hour. We have, however, less than a quarter of the weight of the car available as a retarding force, and consequently from 60 to 65 feet is the shortest distance in which a car can be stopped from that speed by the brakes on a level road with an excellently holding road surface. The distance, it will be seen, does not depend upon the weight of the car, except for wind and road friction resistances and the like, which are not very large factors in coming down from 20 miles per hour. A three-ton car can be stopped by its brakes in about as short a distance as a motor cycle, although it would take a much larger number of telegraph poles to bring the car up short than it would to stop the motor cycle. Drivers should also remember that the distance in which a car can be stopped by the brakes increases as the square of the speed. It is four times as great from a speed of 40 miles per hour as from 20 miles per hour, and 9 times as great from a speed of 60 miles per hour. About 250 feet is the least distance in which a car can be stopped from 40 miles per hour, and over 500 feet from 60 miles per hour. The wind resistance gives quite an appreciable aid, however, at the higher speeds. In stopping from 20 miles per hour the car will travel 45 feet before its speed is reduced to 10 miles per hour, and 15 feet further in coming to a full stop from the 10-mile speed. Except with an excellent road surface the distances will be much greater, and possibly by the use of chains they might be reduced a little, but if a driver is willing to subject his car and tires to the strain I think he will find by actual test that the distances above given are the best he can make. Of course if all four wheels were equipped with brakes the distances would be about one half of those above indicated. There are various other factors that might he discussed if space were available. A general formula for the least distance in which a car can be stopped by its brakes (on rear wheels only) is: D -9 where n is the distance in feet. v is the velocity in feet per second. 0 is the acceleration of gravity in feet per second. is the coefficient of friction of tire on road. It will afford a reasonably safe margin to take as 0.3 (30 per cent), and a good working approximation is afforded by dividing the square of the velocity by 10 to give the distance in which the car can be stopped on a good road surface in good condition, i. e., n 110 V ; or, divide the square of the speed in miles per hour by 4.4, or say by 5, to give an easily computed result with a reasonable margin of safety. This would give 80 feet as the distance when the speed is 20 miles per hour. Boston, Mass. Joseph P. Livermore. The War of the Nations To the Editor of the Scientific American : Without entering Into the partisanships or race animosities of Europe, without taking sides in what is their affair, and not ours, on a basis of our natural sympathies, does it not still behoove us to consider what effect the result of this great conflict may have on our own interests and destinies as a nation? For that such an effect it will have is undeniable. Should the allies win, the status quo ante bellum will be largely resumed so far as the world outside of Europe is concerned except for the annihilation of German commerce. It is true England will no longer be menaced by Germany, therefore will be more strongly co- .firmed in her naval superiority; but, on the other hand, England will still have enough to take care of with the other nations without resuming her quondam position of bully against this nation. Should, on the other hand, the allies be defeated, Germany would become supreme on the seas and assume the Napoleonic rOle of France a century ago, Assuming this position can be maintained, the German navy and mercantile marine would dominate the world. Which, then, is most to our interest as a nation? The prime, if not only, fact to remember in deciding this question is that whereas England has always supported our Monroe Doctrine, Germany has always been hostile to it ; in fact, we may say that but for England we never could have supported it until now. Germany is, among the nations, a bounder or climber, as the English aptly term one who eagerly elbows his way to the front without regard to the rights or interests of others. With her rapidly growing power she has asserted her voice more and more loudly in Weltpoli-tik,' ' and without considering her eager competition in the South American trade as being other than an amicable one, we cannot properly neglect to note her as-sertiveness in matters closely touching our own sphere of interest, notably in the Mexican and San Domingan muddles. It is well understood that Germany covets naval stations or other territorial outposts in the West Indies, and it cannot be a bad guess that she would follow the same tactics to get . them as she did, for example, in the case of Kiao Chao, or Austria in the case of Bosnia, or both of them in the present war. The Teutonic policy of territorial forward movement has always been one of sudden seizures, taking would-be opponents by surprise and then pleading fait accompli. With Germany in the ascendant, it goes without saying that we should have to greatly strengthen our naval power and to maintain the utmost vigilance to prevent some such surprise against us somewhere in the new world, with the almost certainty of becoming ultimately embroiled ourselves in a war with Germany that would reduce us, as it previously reduced the other nations, to a secondary place. To these considerations is to be added that of similarity of national ideal as between Germany and the allies. Germany puts forward as her great slogan the repression of the slavic barbarians"; but the facts of history are not to be forgotten. Without even mentioning the century-long friendliness of Russia for the United States, unbroken by any unfriendly act, let us go back again to the sequel of the Napoleonic wars when the so-called Holy Alliance was formed by Russia, Prussia and Austria with the object of upholding absolutism in general and preventing the revolt of the Spanish colonies in America in particular. It was this very Holy Alliance, led by the three European autocrats, but opposed, be it remembered, both by Great Britain and France, that led to the establishment of our historic Monroe Doctrine. Names and circumstances have changed, but national character has not. Western Europe and the United States still remain the free countries of the world, and eastern Europe holds the absolutist countries ; the dividing line between them is clear, and so is the interest af the United States. The effort of one country or one race to dominate all the others must ultimately come to naught ; such has ever been the history of the world, and all such empires but one have been of brief duration, the single exception being due to the enormous concentration of civilization at a single point. Ultimately such an empire as that of Napoleon expands until it falls to pieces of its own weight, but in the meantime such a military predominance as that threatened by the Teutonic civilization at this time, even for a few years, would work serious and possibly irreparable injury to our interests. Milwaukee, Wis. George W. Colles. An Opinion of Our War Number To the Editor of the Scientific American : I wrote you on yesterday that the Scientific American for September 5th had not been received. I beg to inform you that it came this morning. I am sorry to have troubled you, and trust this will reach you before you have sent us another copy. Permit me to say this paper contains far the most complete and comprehensive information in regard to the war that I have seen anywhere. I am buying an extra copy for my personal pleasure. My husband, the late William Ogilvie, ex-Governor of the Yukon Territory, was for many years a constant reader of the Scientific American. and one of your very strong friends. I feel you may be pleased to know this. (Mrs.) O. P. R. Ogilvie, Ottawa, Canada. Librarian, Mines Branch. For Passing Through Mine Fields To the Editor of the Scientific American : In these days of loose floating mines would not a rope net device projected off both sides of the bow of a slow-moving ship (after the manner of the familiar cowcatcher on a locomotive) tend to lessen the danger of destruction by such mines? It seems to me the slow speed of vessel (which is presumed under such conditions) would deflect a mine in many cases and at least prevent a percentage, even though small, of losses at the present time. I have been told by friends that this is an impractical suggestion and altogether not feasible. Will you kindly give me your opinion on the subject? New York. Charles P. Fry. [The idea is not altogether impracticable. If the net were of wire and capable of being lowered on booms from the bows, it would form an effective mine-exploder, when a ship was passing, at slow speed through a mine field.--ED.] Artificial Rubber from Coke Oven Gases AT a recent meeting of the Iron and Steel Institute in London, its president made this significant statement : It is being sought to obtain from coke oven gases those hydrocarbons the derivatives of which are found in rubber. Experiments that have been made permit the foreshadowing of the manufacture of artificial rubber from this source.
