The Spirit of the Links

by Henry Leach

In the very earliest days of his investigations upon the flight of the golf ball, Professor Tait thought of the application of this idea to the game. A rotation should be given to the ball to steady its flight and make it longer. A moment’s thought on the part of those whose rudimentary scientific knowledge is a little rusty, will indicate that there are three definite and clearly distinguished axes of rotation. One is a vertical one, and it is chiefly upon that axis that the golf ball rotates when it is pulled or sliced, or upon an axis that has something of the vertical element in it. Then there is the horizontal axis, which is at right angles to the line of flight; and this is the axis upon which it rotates when either under-spin or top has been applied to it. And, thirdly, there is the horizontal axis, which is parallel with the line of flight. This is the axis upon which the rifle bullet spins. At first Professor Tait was inclined to the idea that the last-named would be the ideal axis for the rotation of the golf ball, but it happens to be the one upon which it is impossible to make it rotate when struck by a golf club. However, in this detail of his preliminary theorising he was wrong, due entirely to his not having then investigated the virtues of under-spin as always given to a ball when well driven, and not having come by the great discovery that this under-spin helped the ball to resist gravity and prolong its flight as nothing else could. How exactly under-spin does this, we have just seen, and readers will now have a very definite perception of the qualities of a ball and the importance of rotation, and though the chief advantage of rotation is in resisting gravity, it is an incidental advantage of it, as will now be understood, that the flight of the ball is thereby steadied, and a very slight inaccuracy in centering made of less consequence than it would otherwise be. But remember that a considerable inaccuracy in centering will interfere with the rotation, and therefore the bad flying ball can still be distinguished, because it will fly badly.

VI

Now, in continuation of this brief and simple exposition of some of the points of the Professor’s theorising—backed up by constant practical experiment—upon the merits of under-spin in prolonging and lengthening the flight of the ball which created excited comment in the world of golf at the time, much smaller as that world was then than it is now, it may be mentioned that it was his fair conclusion that good driving lay not in powerful hitting, but in the proper apportionment of good hitting with such a knack as would give the right amount of proper spin to the ball. Thus, while a player who gave no spin to his ball might attain a carry of 136 yards, another one who hit his ball with just the same force, giving it the same initial speed, but also a moderate amount of under-spin, would get a carry of 180 yards. Of course there would be a great difference between the trajectories of the two flights. By an experiment on a small scale he showed very conclusively what under-spin did. By shooting a ball from a very weak bow, but with the string just below the middle of the ball, so as to impart a slight spin, he made the ball fly point blank to a mark thirty yards off. When he drew the string to the same distance, but applied it to the middle of the ball, it fell eight feet short. It had no under-spin the second time.

Another point is extremely interesting. Some golfers no doubt think that in driving they have to cock their balls up in the air, so to speak; that is to say, that they have to aim at an upward trajectory from the beginning. As a matter of fact they have to do nothing of the kind, and as a matter of common knowledge the best balls, as driven by a Vardon or a Braid or any other first-class player, always “start low” and keep a path quite close to the ground for some distance, after which they begin to rise. If there were no under-spin the ball could not keep this horizontal path for the time that it does; still less could it begin to rise afterwards. It is the under-spin that does it, and the theoretically perfect drive is the one that is hit straight forward with practically no initial elevation or incline. The character of the stroke gives to the ball the necessary under-spin and power to rise, and the way in which the club comes on to the ball in a stroke so perfectly executed makes any considerable initial elevation impossible, just as it is not wanted. But mark, that if the golfer has not acquired the proper knack of driving—i.e. the proper knack of imparting just the right kind and right amount of underspin—then he will need some initial elevation in order to keep his ball in the air; and so he has to depart intentionally from the proper principles of driving, and deliberately cock up his ball, even though slightly. How his driving suffers in consequence may be gathered by taking the extreme case of no under-spin at all, upon which Professor Tait says: “When there is no rotation there must be initial elevation, and even if we make it as great as one in four, the requisite speed of projection for a carry of 250 yards would be 1120 feet per second, or about that of sound.” Now, as the actual speed of projection in the case of a fine drive by a first-class player is not more than 350 feet per second, the reader may have some idea as to how hard he would have to hit if he were dispensing with rotation. Of course “a carry of 250 yards” is extremely long, and is rarely if ever done in the absence of a helping wind from behind, but the Professor had just been speaking of the practicability of such a carry “in still air.” Even though it be abnormal, the vast disparity between an initial speed of the ball of 350 feet per second and one of 1120 feet will make the point clear.

VII

The most interesting question arises, that if the well-driven ball starts off almost horizontally and then begins to ascend, what is the line of its flight or its trajectory? Golfers generally have the crudest notions on this point. For the most part they seem to assume that the trajectory is represented by an even segment of a circle, having its vertex or highest point just about half-way along. This is absolutely wrong. Even if there were no spin at all, this would not be the case, the vertex being much nearer the end of the flight than the beginning of it, as in the case of the rifle bullet. On the other hand, many players on seeing a ball well driven constantly remark on what they think is after all a fancy of theirs, that when the ball has gone a long way it suddenly seems to take a new lease of life, and to rise up in the air before moving down towards earth. They will be surprised to know that it is not fancy, that the ball does rise. The fact is that the line of flight of a well-driven ball with under-spin, from its starting to its highest point, is partly concave upwards, and this fact is only evident to the eye when it has travelled some distance. Such a ball is in effect the pull or the slice turned round from the flat in an upward direction. Eventually gravity gets the better of the ball and pulls it down.

With the help of the formulæ that he prepared after several years’ study of the matter, and with the assistance of Mr. Wood, whom he regarded as the quickest and most accurate reckoner of abstruse scientific quantities that he had ever encountered, the professor calculated exactly the trajectories of golf balls driven under many different circumstances. Among them he showed the short line of the flight of a ball to which no initial rotation or under-spin was imparted. While the other balls were started off almost horizontally, it was necessary in this case to give the ball an initial elevation of 15 degrees—that is to deliberately hit it upwards at that angle—in order to make it rise at all. Regarding this trajectory Professor Tait said most significantly that it is “characteristic of a well-known class of drives, usually produced when a too high tee is employed, and the player stands somewhat behind his ball. Notice particularly how much the carry and time of flight are reduced, though the initial speed is the same. The slight under-spin makes an extraordinary difference, producing, as it were, an unbending of the path throughout its whole length, and thus greatly increasing the portion above the horizon.” The run of this ball on alighting is greater than in the other cases, owing to there being no backspin, but it cannot make up for the short flight.

Concerning another short drive of the same class, Professor Tait remarks: “In spite of its 50 per cent. greater angle of initial elevation, the carry of the non-rotating projectile is little more than half that of the other, and it takes only one-third of the time spent by the other in the air. But the contrast shows how much more important (so far as carry is concerned) is a moderate amount of under-spin than large initial elevation. And we can easily see that initial elevation, always undesirable (unless there is a hazard close to the tee), as it exposes the ball too soon to the action of the wind where it is strongest, may be entirely dispensed with.”

A question which may have been in the reader’s mind for some time is as to whether, since the effect of under-spin is to make the trajectory turn upwards as it were, excessive under-spin would not result in the ball taking an absolutely upward trajectory and then curling over and right round. In actual practice so much under-spin could not be put on to a golf ball as would enable it to get the better of gravity and other circumstances to this extent, but theoretically such an evolution would be described if the conditions were equal to it. Professor Tait says: “The kink can be obtained in a striking manner when we use as a projectile one of the large balloons of thin rubber which are so common. We have only to ‘slice’ the balloon sharply downwards in a nearly vertical plane with the flat hand.” It must be remembered that in the case of a very bad slice the ball sometimes does actually curl right round towards the finish of its run.