This really is an extremely simple matter and a very simple explanation. I have taken care to explain it so simply, for swerve is, by a very great number of people, looked upon as an abstruse problem—in fact, my book on Swerve, or the Flight of the Ball, is catalogued as a treatise on applied mathematics, instead of, as I intended it to be, simply a practical application of the ascertained facts to the behaviour of the ball in the air.
Professor Tait's article has enjoyed a wonderful vogue. Although it was published nearly twenty years ago it is quite frequently quoted at the present time. There are, however, in it some errors which one would not have expected to have found in such a scientific article. Speaking of the golf ball shortly after it has left the club, Professor Tait said:
It has a definite speed, in a definite direction, and it may have also a definite amount of rotation about some definite axis. The existence of rotation is manifested at once by the strange effects it produces on the curvature of the path so that the ball may skew to right or left; soar upwards as if in defiance of gravity, or plunge headlong downwards instead of slowly and reluctantly yielding to that steady and persistent pull.
There is, in this statement of Professor Tait's, a fundamental error in so far as regards the flight of the ball. He said: "The existence of rotation is manifested at once by the strange effects it produces on the curvature of the path." This is incorrect from a scientific point of view, and it is also badly stated. The existence of rotation is not manifested "at once"; in very many cases, practically in all, the ball proceeds for quite a long distance before the effect of rotation is seen. This is more particularly so when it is a matter of back-spin, but it is equally true of the pulled ball or the sliced ball. Both of these proceed for a considerable distance before the effect of spin is noticeable. In fact it is well known to all golfers that the spin begins to get to work as the velocity of the ball decreases. Also it seems as though it is incorrect to refer to the strange effects it (rotation) produces on the curvature of the path, for it is the rotation itself which produces the curvature.
Professor Tait then said:
The most cursory observation shows that a ball is hardly ever sent on its course without some spin, so that we may take the fact for granted, even if we cannot fully explain the mode of its production. And the main object of this article is to show that long carry essentially involves under-spin.
I shall deal with these two statements later on.
Professor Tait said:
To find that his magnificent carry was due merely to what is virtually a toeing operation—performed no doubt in a vertical and not in a horizontal plane, is too much for the self-exalting golfer!
The fact, however, is indisputable. When we fasten one end of a long untwisted tape to the ball and the other to the ground and then induce a good player to drive the ball (perpendicularly to the tape) into a stiff clay face a yard or two off, we find that the tape is always twisted in such a way as to show under-spin; no doubt to different amounts by different players, but proving that the ball makes usually from about one to three turns in six feet, say from forty to a hundred and twenty turns per second, this is clearly a circumstance not to be overlooked.
It is wonderful how easily a scientific man, as Professor Tait was, can be led astray when he sets out to find the thing he has imagined. Professor Tait, by a footnote to his article in the Badminton Magazine, to my mind entirely discounts the value of his experiments. His footnote is so important that I must quote it fully. He says: