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.”
But he probed most deeply into the mysteries of the flight of the golf ball when he came suddenly to understand the rotation which was subjected to it by the club, and it is of interest and importance to every golfer that he should understand it also. The starting-point of the wonderful investigations that he made is contained first in the simple fact that when an object is poised in the air there is equal atmospheric pressure upon it at all points; and second, that, as several of the most eminent scientists before him, from Newton onwards, had found out, when a sphere rotates in a current of air the side of the sphere which is advancing to meet the current is subject to greater pressure than is that which is moving in the direction of the current; and a step further in this argument is that, as the result of this extra pressure, if a spherical ball be rotating, and at the same time advancing in still air, it will deviate from a straight path in the same direction as that in which its front side is being carried by the rotation.
Therefore, when a ball is sliced, it is made to spin round so that its front side moves round constantly to the right, and, in accordance with the law just mentioned, there is a greater atmospheric pressure on the left side than on the right, and, consequently, the ball is pushed away to the right—as we see it. When it is pulled, the spin is in the opposite direction, and the extra pressure is from the right, and so it is sent away to the left. When the ball is topped the spin on the front side is downwards, and the ball ducks—the extra pressure this time being in the same direction as gravity; and when under-cut is applied, and under-spin follows, the front side of the ball is spinning upwards, and the extra pressure is from below and against gravity.
When this conclusion was first briefly stated, golfers resisted the suggestion that when driving they imparted any under-spin to the ball; but the Professor stuck to his point, and proved it beyond doubt, and it is in this way that the ball takes six and a half seconds over its flight instead of the three and a half that it would otherwise do; and he proved, moreover, that if there was no under-spin imparted to it when driving it would only travel about half the distance that it usually does. The greater the under-spin the greater the upward pressure, and this conclusion leads to others very interesting.