Cycling art, energy, and locomotion

by Robert P. Scott

It is evident that one of the greatest, if not the very greatest, of the requirements of a practical road wheel, or a man-motor carriage, is that the power of the rider shall be transmitted to the said wheel in the most direct manner possible; that is, by causing the strain to come upon the muscles in such a way that these muscles shall be placed in the best possible position to overcome such strain, and to take advantage of such conditions as nature has already provided for, in training our muscles to the work we have had to do under the old régime, without the wheel.

The muscles of man are best adapted to a direct pull or push. If we push upon a weight with the muscles at an angle to the direction in which we want the weight to move, the effective power is limited in the same way that the effect upon a weight is limited if we push at it in a direction at an angle to that in which we wish to move it; that is to say, not the total, but only a portion of the power will be effective in moving the weight.

The above facts apply particularly to our subject when we desire to transmit motion to a wheel by means of the weight or gravity of our bodies. Gravity acting downward in a vertical line, if we are not placed over the resistance, the resultant effect is in proportion to the cosine of the angle at which we work, as follows:

Let W = the weight of the man and a be the centre of gravity and also the location of the source of power of said weight, and let c represent the point at which it is desired to apply the power to turn the wheel.

Power angle.

Now, it is known that the weight W, acting by gravity in the direction ab, may be taken as proportional to the length of the line ab, and the portion of the pressure P in the direction ac, which will be effective to turn the wheel, may be taken as proportional to the length of the line ac; that is, ^P _W = ^ac_ab, or P = ^ac_abW, where ^ac_ab is evidently always less than unity. Now, if the angle bac is thirty degrees, and W = 150 pounds, W times ^ac_ab is 130 pounds. Or, by trigonometry, the weight W, acting in the direction ab, by gravity as in working a cycle, will have a resultant in the direction ac representing the power acting to turn the wheel equal to W cos bac. If the angle bac is thirty degrees and W = 150 pounds, then W cos bac = 130 pounds. Now, in order to still get one hundred and fifty pounds of force on the wheel, a pull on the handle-bars would have to be given sufficient to make up the lost twenty pounds, which the rider would get without any pull on the bars if placed directly over the work. This pull, while not fatiguing to the legs beyond the necessary requirement of power, is an entire loss of work in the arms, and must tell on the system. This is all an additional loss to that which ensues from the fact that nature has fitted us to stand upright and not to work in an angular position; our every-day experience in walking gives us practice in a direct vertical strain on the muscles of the body, and we should make it a point to apply our force as nature intended, in so far as it is applicable to our wheel method. These conditions apply more or less to any form of locomotion, and particularly to the cycle.

From the foregoing remarks we are amply justified in drawing the conclusion that the resultant force available in the application of the physical power of man is in proportion to the cosine of the angle at which he exercises this force. We are well aware that many apparent variations will occur when so rigid a mathematical fact comes to be applied to the exercise of man’s energy in driving a bicycle; but all we care for is to lead the reader well up to the point by means of reasoning, which we hope will give at least a partial hypothesis for a conclusion well demonstrated by practical experience. We assert that when we consider the application of the gravity of the body to work on either a bicycle, or to other work of similar requirements, our mathematical demonstration is strictly true. It is justifiable, therefore, from a purely theoretical stand-point, to say that the rider of a bicycle wants to get directly over the work; let us see how our experience demonstrates this conclusion.

Take first the differences between a modern ordinary bicycle and the old velocipede, or “bone-shaker,” so called. The former is lighter and better made; but the one great difference is that the rider is more nearly over his work. It was this one advance which encouraged the development of other minor differences which had been roughly thought out before. In fact, the Patent Office shows that many of these improvements were on record, but there would have been little use for them if the rider had not worked himself up into a place where he could do something. Just who raised him up from a midway position between the two wheels, the saddle seventy-five degrees back of the vertical through the drive-wheel axle, as in the old bone-shaker, to nearly the top of the forward wheel, working at an angle of thirty degrees, as in some ordinaries, we will not attempt to say; but when he got there he has been willing, for a long time at least, to try to stay there, even at the expense of frequently going down on the other side, much to his annoyance, particularly as the general construction of the thing compelled him to go down the other end up, which end nature did not intend for terrestrial impact. It may as well be stated just here, however, that when our rider raised and moved his saddle forward he would have gone clear up to the vertical had it not been that it was absolutely impossible for him to stay there at all without hanging a heavy counter-balance somewhere in the neighborhood of the rear wheel, a scheme which, by the way, has been really recommended in modern cycle history.

One excuse for dwelling upon the foregoing dissertation is that many casual observers and some riders, strange as it may seem, assert that in the development of the modern rear-driving Rover pattern, we have been retrograding to the old velocipede, whereas, in fact, we have made another step forward of a similar nature to that spoken of before in raising the rider up above the point of application of power. In the Rover machine we have landed the rider practically where, as before said, he could not remain at all before; but in this new machine he has gained the advantage of being able to stay there.