Popular Science Monthly/Volume 73/November 1908/Deductions from the Records of Running in the Last Olympiad






By Professor A. E. KENNELLY


IT is much to be regretted that after all the races held in the ancient days of Greece and Rome, when the laurel crown of victory was the height of ambition in youthful manhood, we have no means of comparing the achievements of their runners with our own. We shall never know how their track speeds compare with those of modern times, because records did not become possible until after the invention and development of the portable chronometer.

The olympiads, or quadrennial athletic meetings of ancient Greece, were held in such national renown, that they served as historical epochs for the chronological establishment of events. Owing, however, to the absence of sufficiently precise instruments for measuring and recording time, each race or speed-contest, although an event of great momentary importance, was necessarily cut off from all comparison with similar preceding or succeeding races. The victor in each race overcame the opponents who contested with him shoulder to shoulder; but there could be no means of determining whether the victor of a given event in one olympiad excelled the victor in other olympiads.

With the introduction of the stop-watch, races ceased to be merely momentary efforts for mastery in speed. To the interest of the local and passing contest was added the new interest of the perennial contest, and of the record. In the racing of the finest horses, the record has come to be regarded as the principal event, and the winning of the race as the secondary event, after the excitement of the occasion has subsided. In the racing of the swiftest men, the record is gaining in importance; but we still attach principal attention to the winning of the race, as did our predecessors in ante-chronometer days. Medals are given for races won and not for records beaten.

It is, perhaps, our attachment to the interest of the momentary race, and our ordinary indifference to the record, that accounts for the absence of enquiry into the laws of racing speeds. If we ask either an athlete, or a non-athlete who is athletically informed, what is the relation of a runner's speed over a long course to that over a short course, he will immediately reply that a racer over a short course, like 100 meters, runs at a higher speed than over a long course, like 3 kilometers. But if he is pressed for an estimate as to how much faster the racer runs as the course is shortened, he will either be likely to express indifference, or to intimate the opinion that a precise answer is impossible. Nevertheless, it is self-evident that the long list of records which have been established up to this date for runners on courses varying from 20 yards up to more than 600 miles, determine the average speed which the makers of those records severally adopted.

The records reported in the New York Times as having been made by the winners of the flat races in the London Olympiad last July are collected in the following table:

Length of
Actual Time.
Speed over
Meters per
Winners Time Esti-
mated ac-
cording to
the Logarith-
mic Straight
Line. Sees.
100 10 .8 9 .26 Walker 10 .45 -0 .35 -3 .2
200 22 .4 8 93 Kerr 22 .8 +0 .4 +1 .8
400 48 .4 8 .26 [1] 49 .7 +1 .3 +2 .7
800 112 .8 7 .09 Sheppard 108 .4 -4 .4 -3 .9
1,500 243 .4 6 .16 Sheppard 220 .0 -23 .4 -9 .6
42,190 10,518 4 .01 Hayes 9,390 -1,128 -10 .7

In the accompanying illustration, these records are plotted on a specially ruled paper known to engineers as "logarithm-paper" or "log-paper," in which equal multiples scale equal distances, both vertically and horizontally. The horizontal scale represents course-distances in meters. The vertical scale represents running times in seconds. The stars near the numerals 1, 2, 4, 8, 15 and 420, locate the Olympian records for 100, 200, 400, 800, 1,500 and 42,190 meters, respectively, according to the table already considered. The various circular dots indicate world's records for running, taking the best from professional and amateur lists published in the New York "World" Almanac. The straight line is drawn through the record for 500 yards (457. meters), and also through the record for 7 1 /2 miles (12,070 meters). This straight line offers a simple approximate quantitative relation between record times and distances in races from 100 meters to 50,000 meters.

Considering first the black dots, or world's records, independently of the Olympic records, it will lie seen that between 100 and 400 meters most of the records fall slightly below the straight line. This means that within that range the record times are shorter, or the speeds

PSM V73 D391 Olympic and world records in running races.png
Diagram showing World's Records and Olympic Records in Running Races.

somewhat higher, than those represented by the line. Then, from 500 to 5,000 meters, the dots fall above the line. That is, the times are longer, or speeds somewhat lower, than those prescribed by the line within this range. From 5,000 to 12,000 meters, the agreement between the dots and the line is close. Between 12,000 meters and 32,000 meters, the clots again fall below the line; while beyond 32,000 meters, they change sides and rise above it.

Turning now to the Olympic records, we may notice that the 200and 400-meter stars lie close to the line; but slightly above the nearest corresponding world's records. None of the Olympic record stars lie below the corresponding world's records; but the 100-and 800-meter stars lie close to the corresponding dots. The farthest away from the line is the 42,190-meter star. It is to be. remembered, however, that the Marathon race is run over country roads, up hill and down dale; whereas all the other races are run on a smooth and level track. This circumstance may account for all, and must at least account for part, of the fact that the Marathon record is 10.7 per cent., or 1,128 seconds, behind the time set by the straight line. As for the smaller discrepancies in the other Olympic records, it is to be remembered that the contestants in Olympic games are amateurs, whereas the world's records are the best that professional as well as amateur champions have been able to secure in all racing annals up to date.

So far as appears on its face, the illustration suggests that the existing world's records offer a better chance of being lowered between 500 and 5,000 meters, than those below 500 meters, or those between 5,000 and 12,000 meters. It is, in fact, generally conceded that races up to the quarter mile (400 meters), inclusive, are the most strenuous, and that races of from half a mile to three miles usually leave the runners in a less completely exhausted condition. If this concession be denied, and we take it for granted that all these records from 100 meters to 50,000 meters call for like strenuousness of sustained effort and degree of physical exhaustion from equally good athletes, it is hard to explain the oscillations of the record dots in groups from one side of the straight line to the other.

The straight line in the illustration stands, however, for much more than a mere indication of possibilities in regard to records. It also involves the conclusion that any record-making runner becomes exhausted very rapidly as his average speed is increased. For example, in the above table of Olympic records, it appears that the athlete Sheppard held an average speed of 7.09 meters-per-second over the 800meter course; but only C.16 meters-per-second over the 1,500-meter course. We may safely assume that Sheppard arrived in each case at the winning post, "run out" or practically exhausted in running power; because if he had arrived with any residual running energy, he would have thrown it into acceleration on the last lap. Consequently, when he ran at 6.16 meters-per-second he ran himself out in 243.4 seconds; but when he increased his average speed, to 7.09 meters-per-second, he ran himself out in 112.8 seconds, or in less than half the time. That is, increasing his average speed 15 per cent, exhausted him in-46.3 per cent, of the time. The law of the straight line in the illustration is, in fact, that the time of exhaustion is inversely as the ninth power of the speed within the limits of racing speeds; so that a record-maker, if he were able to double his speed, would become exhausted 512 times more quickly. Of course, the straight line can only.be regarded as an approximation to the actual conditions, and we are not justified in asserting that the law of the inverse ninth power applies strictly. The exhaustion time as the inverse ninth power of the average speed is an average law, derived from the world's records, as made by a number of different individuals at different times. It is, however, certain that whether the time of exhaustion for any particular racer is as the inverse ninth, eighth or other power of his speed, it is a relatively high inverse power. We may safely conclude from the records that a record-making runner can not increase his speed within racing limits without bringing down his time of exhaustion very rapidly. Otherwise, the record times over different lengths of course would surely follow a different series.

It further follows from this deduction that a record-making runner can not afford to run at an unduly high speed for any appreciable time during his race; because, if he were to do so, he would thereby exhaust himself at a yet more unduly great rate. It would seem that in order to make his best time he must keep to a uniform pace, at least to a first approximation. It is evident that on the last lap he will put forth all his remaining effort, and spurt if he can; because he should arrive at the goal run out if he has done his utmost. If, however, he is able to spurt to a marked extent on his last lap, he has held too much energy in reserve, which he consumes unduly rapidly at the higher speed. According to the logic here set forth, he should have been able to reach the goal more quickly by a slight uniform increase in speed over the whole course.

According, then, to the deductions that the straight line of the illustration leads up to, an athlete of record-making quality should be enabled to make his best time over his best course or courses, by being paced at a uniform rate, say with an automobile. This, however, assumes that the runner would exert himself as fully behind an automobile as when running shoulder to shoulder with an antagonist. This is, perhaps, treating an athlete like a mere automaton, instead of like a human being. It seems more reasonable to suppose that an athlete's best performance can only be elicited under the spur and incentive of individual competition. Besides, the interest of a race to the onlookers would probably be greatly diminished if instead of the struggle of a number of racers were substituted the effort of a racer to keep up with a motor.

Nevertheless, the opposite proposition will be likely to meet with general approval; namely, that the worst way to elicit a good performance from a record-making type of runner is to incite him to an unduly high speed at some part of the course before the end. The average speed of a record-making Olympic runner on a 100-meter course is given in the table as 9.26 meters per second. In the 1,500-meter race, Sheppard averaged, as we have already seen, 6.16 meters-per-second. Suppose that he commenced, say, by running at 9.26 meters-per-second. This would have been only 50 per cent, more than his average speed. It is clear that, had he done so, he would have been run out in 10 seconds. Again, if he had commenced by running at 7.09 meters-per-second, his average speed over the 800-meter course, and not quite 15 per cent, above his average speed over the 1,500-meter course, he would have been run out after 112.8 seconds, or only about half way.

It seems possible, however, to combine the incentive of shoulder-to-shoulder competition with uniform pace-making, and without loss of interest to the spectators, by running a light flag or pennant by the side of the track, on a slender wire of steel or phosphor-bronze. It would only be necessary to set short posts beside the track, each supporting a light metallic guide-pulley. Over all these pulleys would run the wire alongside the track, making a complete loop or endless chain. The wire would be propelled at some point in the course by a small electric motor, driven by a portable storage battery, as in the outfit of an electric automobile. An attendant at the motor would be charged with the duty of keeping the speed of the motor and wire uniform at that corresponding to the record for the particular event. By means of a stroboscopic fork, i. e., a tuning-fork carrying slotted wings on its prongs, through which a rotating target carried by the motor appears to stand still, it is readily possible to keep the speed of such a motor and wire constant to within a small fraction of one per cent.

When the runners were placed and ready to start, a small flag would be gripped on the running wire a few paces behind the men. As this flag reached the starting line, the starter would fire his pistol. Owing to the starting inertia of the men, the flag would gain a few feet at the first, and the runners would get under way with the flag slightly ahead. Since the flag would reach the winning post in record time, it would be the object of the men to outdistance it at that point. According to the reasoning above presented, they should best be able to do this by keeping close to the flag, which would serve as pacemaker. They should certainly be advised thereby if they started off at too high a speed. The spectators would have the advantage of seeing not only the contest of the actual runners; but also a contest with the "ghost" of the best runner that heretofore had made the record of that event his own, as impersonated in the flag running beside the track.

In raising the ghost of the record runner as above, there might be a danger of hurting the race by the runners losing heart if they failed to keep up with the flag. There might also be a danger of the spectators' losing interest if the flag removed all temptation from the runners to jockey for first place, thus tending to sustain monotony at the expense of sport. Whether these dangers are serious could only be determined by actual trial.

It would, of course, be possible to reduce the speed of the flag, by preconcerted arrangement, to a more readily attainable local record, in place of a more ambitious world's record. One per cent, reduction in speed might make a very marked difference in this respect. There can be little doubt that the flag and motor-driven wire would be a useful device in the training of runners for the track at suitably graded speeds.

The same line of reasoning applies to other races. If the world's records in walking, swimming, skating, rowing, horse-running, horse-trotting and horse-pacing be similarly analyzed, and plotted on logarithm paper, the points will be found to fall very nearly upon a straight line in each case.[2] Moreover, all of the straight lines have the same, or at least substantially the same, inclination, or represent and involve substantially the same law of fatigue. The only exception is found in bicycle-riding.

  1. This contest was reported "no race" in the New York Times of July 24. The time, however, is here taken as that of the best preceding trial heat, won by Haswelle.
  2. "An Approximate Law of Fatigue in the Speeds of Racing Animals," by A. E. Kennelly, Proceedings of the American Academy of Arts and Sciences, Vol. XLII. No. 15, December, 1906.