The Spirit of the Links

by Henry Leach

The mistake that he made, which was exposed to him by his son, set him out on a new line of thought, and showed him vaguely where his error was, though not the nature of it. And the discovery which he made at the outset was a startling one, and it may cause some astonishment to the player of to-day who will reflect upon it for a moment. The steadiest, most constant, and most persistent force with which we are generally acquainted is the force of gravity. It is always there; it acts unceasingly upon everything. To defeat gravity, therefore, is almost for a while to suspend the working of Nature. Suddenly it burst upon the mind of the Professor that the golf ball was made as it were to defeat gravity, and so in a sense it does. He found this out by observing the time of flight of the ball, and discovering that it was nearly twice as long as it ought to be, if gravity had free and unfettered play. This is to say, that if gravity were allowed to act in the usual way on the ball from start to finish, as it acts on other things, it was quite inevitable by all the laws of nature and science that a drive of 200 yards would be completed in three and a half seconds. If a man threw a ball so as to describe as nearly as possible the same trajectory as a golf ball, and to stop at the same spot, it would only take three and a half seconds. But the golf ball takes six and a half seconds! Somehow or other it was clear that gravity was being beaten all the way. If it were not so, it would be impossible for the golf ball to remain in the air so long while it was accomplishing such a short flight. That was the great mystery that the professor had to solve, and he solved it at last. It may be said here, in passing, and will be more fully explained another time, that he found out that it was due to the rotation given to the ball by the club, and the nature of the stroke when it was struck from the tee, a rotation which in many ways was responsible for some most extraordinary happenings; all of which the golfer will be a much wiser man for having knowledge of. But before he could go thoroughly into the mystery of this rotation he had to make many other preliminary investigations, and some of the results of these may be quoted.

One of the Professor’s first efforts was in the direction of finding out the speed with which the ball left the club; and it was a long time—years, in fact—before he came to any definite understanding on the point; so difficult did he find the investigation, despite all the experiments he made, the formulæ that he applied to them, and the scientific instruments that he brought to bear on the problem. He had a very capable observer, Mr. T. Hodge, making examinations of the flight of balls driven in actual play at St. Andrews, by the help of the instrument known as the Bashforth Chronograph, with which the speed of bullets is measured; and, what with the results arrived at in this way and others, he came to the conclusion that the initial speed of the ball was over 500 feet a second, which speed, of course, was lost very quickly as the resistance of the air was encountered.

With this as his starting-point, he made many deductions; but subsequently he found that he was wrong in the original assumption.

A vast number of calculations and experiments followed. In a cellar he constructed a complicated pendulum arrangement, to the bob of which there was attached a large screen with a thick clay surface, and against this he got several well-known golfers to drive their hardest, and made the most minute calculations as to the effect upon the pendulum. The clay was scattered in all directions, damage was done, and the golfers complained that under such circumstances they were not able to drive their best. The pendulum and the strangeness of the whole arrangement “put them off.” Some time afterwards he constructed an improved pendulum, the clay screen being fixed on to lengths of clock spring, and when this was placed in a doorway the golfers were again set to drive at it.

What with one thing and another the Professor at last came to the final and definite conclusion, that the ball started from the club at a speed, in the case of a good drive, of about 240 feet a second, but that in the case of exceptional balls it sometimes was as much as 300 or even 350 feet per second. This, of course, was with the gutta ball; and the resiliency and initial speed of the rubber-cored ball being certainly much greater, it is fair to believe that the average initial speed of a well-driven ball in these days is quite 300 feet a second; or, to put it in another way, over two hundred miles an hour. Great as this speed appears, it might be mentioned incidentally that the muzzle velocity of a bullet from a Maxim gun is generally about 2000 feet a second, or about seven times as fast.

III

While he was at work on these reckonings he dispelled one fallacy, which, notwithstanding, is commonly held by golfers to the present day. Most players think that when driving and following through well the ball hangs on the face of the club, as it were, for long enough for the club to do something in the way of guiding it. How brief is the time in which the actual stroke is made for good or ill was proved conclusively in a very striking manner, and that time was set down—the whole time of impact—as that in which the club, moving at 300 feet a second, passed through about four times the linear space by which the side of the ball was flattened. Putting this space down, nowadays, at about ⅛ in., and reckoning the time that it would take the club going at the speed indicated to cover that small distance, we have the fact that the duration of impact is only about 1/7000th of a second, and that that is the whole time that the golfer has for the guiding of the ball! As the Professor said, “the ball has, in fact, left the club behind before it has been moved through more than a fraction of its diameter”; and in the case of the gutta, with the smaller extent to which it flattened on the club, he came to the conclusion that the duration of impact was far less than that which has just been mentioned.

Incidentally in this connection he took occasion to expose another of the golfer’s fallacies as to the effect of wind on the flight of the ball, in the following words: “It is well to call attention to a singularly erroneous notion very prevalent among golfers, namely, that a following wind carries a ball onwards! Such an idea is, of course, altogether absurd, except in the extremely improbable case of wind moving faster than the initial speed of the ball. The true way of regarding matters of this kind is to remember that there is always resistance while there is relative motion of the ball and the air, and that it is less as that relative motion is smaller, so that it is reduced throughout the path (of flight) when there is a following wind. Another erroneous idea somewhat akin to this is that a ball rises considerably higher when driven against the wind, and lower if with the wind, than it would if there were no wind. The difference (whether it is in excess or deficit will depend on the circumstances of projection, notably on the spin) is in general very small; the often large apparent rise or fall being due mainly to perspective as the vertex of the path is brought considerably nearer to or farther from the player.”

And Professor Tait was led to make a definite pronouncement on the particular kind of weather in which a ball will fly best and farthest. What golfers do not generally realise is that the atmospheric resistance to the flight of their ball is much greater than in simple proportion to its speed; it is as the square of the speed. This is to say, that if one ball is driven twice as fast as another to begin with, the resistance to that ball is four times as great as it is to the slower one. It is this fact which makes it so difficult to get extra length, beyond a good length, on to a ball, no matter what improvements are made in the ball. Therefore, on the weather question the Professor set it down that, “Of course, other circumstances being the same, the only direct effect is on the co-efficient of resistance. If this be taken as proportional (roughly) to the density of the air, it may vary, in this climate, to somewhere about 10 per cent. of its greatest value, and the drive is accordingly shortest on a dry, cold winter day with an exceptionally high barometer. The longest drive will, of course, be when the air is as warm and moist as possible, and the barometer very low.”