Ankle-power.
The diagram shows the sections 1 to 8, and also gives an idea of the extra power. To see the direct circular resultant force to turn the wheel, imagine the length of a crank from m to n without ankle-motion and then m n plus n o for the length of the crank with ankle-motion added. I have been able at each of the points a and i to get thirty pounds when the crank crosses the vertical line at the top and bottom. Thus it is discovered that by means of this ankle-motion on both cranks simultaneously, I can get a force of sixty pounds in the direction to turn the wheel, at a time when absolute dead centre would otherwise occur, amounting to two-fifths of the maximum pressure resulting from my entire weight on one crank at the best possible point, directly out in front, going down.
I have more than verified the results shown by the cyclograph by suspending a fifty-four-inch bicycle, with six-inch cranks, above the floor, placing myself in the saddle, and having an attendant attach a twenty-pound weight at a point on the rim, ninety degrees from the bottom. This weight I was able to raise at the dead-centre point of both cranks,—that is, vertically up and down,—which shows a real power at the pedals of ninety pounds, or forty-five pounds on each, and I do not suppose that I am by any means an expert in ankle-motion. The above ninety pounds is a much greater showing than I made on the cyclograph in actual running, but it is reasonably certain that, by practice, even such an amount could be obtained.
In the case of no ankle-motion,—that is, with a direct downward pressure on the crank,—a tangential force in the direction available in turning the wheel begins as the crank crosses the vertical at the top, and then increases as the sine of the angle the crank makes with the vertical, until such angle reaches ninety degrees or extends out horizontally, after which the power decreases as the sine of the angle the crank makes with the vertical below the centre until the crank crosses at the bottom, at which point the power ceases.
To represent this variation of power by actual length of lines, appended will be found a diagram, [Fig. 2], showing the tangential resultant or force to turn the wheel, imparted by a one-hundred-and-fifty-pound man with and without the use of ankle-motion.
A A is a line showing the divisions of the angles through which the crank passes in its revolution around the axle. The line a f i is a sine curve.
Using the middle section and beginning at the point a, which is that at which the crank crosses the vertical above the axle, making a zero angle therewith, we have a direct downward pressure and, without ankle-motion, zero power. Now, by means of ankle-motion on one crank at this point we get thirty pounds of power, represented by the length of the line from a to b; and by ankle-motion on both cranks we have sixty pounds, represented by the total length of the line from a to c. After the crank has advanced forward fifteen degrees, we have thirty-nine pounds of direct power (m n), and then adding the ankle-power of twenty-three pounds (n o), we have a total resultant of sixty-two pounds, represented by the length of the next line (m o), and so on up, the direct power increasing and the ankle-power diminishing till we come to the top of the curve f, when we have one hundred and fifty pounds of direct power. Passing through the angle of ninety degrees, and now counting from the vertical below the axle, we decrease in power inversely as we increased before.
[Fig. 1] will show a little more graphically to the eyes of some casual readers how the power expands. Take d a f i e as the regular swing of the crank with no power at a, then d b f h e as the increase of power on one and the dotted lines c and g as the auxiliary ankle-power on the other crank added.
Fig. 2.
