P G Tait, Freddie Tait and golf
In Douglas Young's book, St Andrews : Town and Gown, Royal and Ancient (Cassell & Company, London, 1969), there is the following description of the golfing exploits of Freddie Tait:-
The thirteenth fairway [of the Old Course, St Andrews] was the scene of a celebrated drive in 1892 by Freddie Tait, son of the Edinburgh professor P G Tait, who used to spend his summers in St Andrews, playing up to five rounds a day, starting at 6 a.m. He once organised a nocturnal match, with the balls painted with phosphorescent paint. It was abandoned at the second hole, when Professor Crum Brown noticed that his glove was on fire. Professor Tait had made many theoretical calculations, and reckoned that no human being could drive a ball so as to carry more than 190 yards. His son Freddie hit a ball at the thirteenth tee that carried for 250 yards, and completed a distance of 341 yards and 9 inches, ending within ten feet of Walkinshaw's grave [a bunker on the thirteenth hole]. Moreover, the ball so driven was of gutta percha: so that the effort was equivalent to driving a modern ball well over 400 yards. Besides winning the Amateur and other competitions in his dashing style, Freddie Tait was a keen player of the bagpipes, even at midnight through the town's streets; and he was universally mourned when he was killed in the Boer war in 1900, as a Lieutenant in the Black Watch.
Douglas Young, in this quote, relates a story which is much repeated, namely that Freddie hit a golf ball further than his father had shown was theoretically possible. Here is an extract of a letter from Freddie Tait about this incident:-
I enclose a cutting from the Daily News of Monday, January 16th, by Andrew Lang, on a drive made by me on my 23rd birthday. No doubt you will say, as the Governor [this is how Freddie referred to his father, P G Tait] said, "Stuff! Humbug!" but the fact still remains. The Governor will be very much annoyed by the article, as he wrote not very long ago an article on golf proving conclusively that it was impossible to carry more than 190 yards on a calm day, unless you exerted about three times more energy.
The reason for the discrepancy in P G Tait's theoretical result and the practical result was due to backspin on the ball. However, Tait was aware of the significance of backspin due to undercutting the ball. Over the years he came to understand more and more how important this was. In his article On the physics of golf (1890) he explicitly states that he is ignoring spin. In fact, by the time Freddie Tait made his drive which carried 250 yards, his father had explained the importance of spin. He wrote in an 1887 article in Nature:-
... in topping, the upper part of the ball is made to move faster than does the centre, consequently the front of the ball descends in virtue of the rotation, and the ball itself skews in that direction. When a ball is undercut it gets the opposite spin to the last, and, in consequence, it tends to deviate upwards instead of downwards. The upward tendency often makes the path of a ball (for part of its course) concave upwards in spite of the effects of gravity ...
P G Tait published another article on golf in Nature in 1891 in which his main concern is the time the ball will spend in flight. He finds that, deliberately ignoring spin, his theoretical conclusions do not match experience and writes:-
The only way of reconciling the results of calculation with the observed data is to assume that for some reason the effects of gravity are at least partially counteracted. This, in still air, can only be a rotation due to undercutting.
He then went on to incorporate the effects of spin caused by undercutting the ball into his calculations and produced a third article On the physics of golf which was published in Nature in 1893. Freddie Tait wrote to a friend in July 1894:-
You might tell the Governor that his article on golf of the other day is being read with great interest by all the people here and at Carnoustie. I have not been able to make any experiments as I cannot find anyone with a stopwatch; but I will have some more trials at St Andrews, when the Governor will be there to superintend.
P G Tait also wrote a popular, non-mathematical, article Long driving which was published by the Badminton Magazine in 1896. The main object of the article is to explain that a golf ball carries much further than one might expect because of backspin produced by undercutting the ball. In it P G Tait writes:-
When the ball parts company with the club ... having by its elasticity just recovered from the flattening which it suffered from the blow, the ball must be moving as a free rigid solid. It has a definite speed, in some 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. 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 UNDERSPIN.
However, P G Tait continued to carry out golfing experiments, often using his son Freddie in these experiments. For example, in a letter written in January 1896 to one of his friends, Freddie writes:-
The Governor and I had a very successful day at college. We think we have arrived at the truth about the velocity of a good drive of about 220 feet per second.
A few days later, Freddie wrote in another letter:-
The Governor has been making a lot of experiments lately at college. He has now finally settled that the velocity of a really good drive of about 240 feet per second. I don't think I'll waste my time explaining how this result was arrived at, as you were never much good at either natural philosophy or mathematics.Because of Freddie Tait's many associations with St Andrews, the 16th hole on the Jubilee Course at St Andrews is named 'Freddie Tait'. In 1891 Freddie Tait competed in the British Open Golf Championship for the first time. The Championship was played on the Old Course, St Andrews, on a cold, rainy and windy October day; it was played over 36 holes, the two rounds being played on just one day. Freddie, with rounds of 94 and 88, came 14th. The winning score from Hugh Kirkaldy was 166 for the 36 holes.
There are many Freddie Tait golfing stories: for example it is recorded that once he hit his ball through the hat of a spectator. The spectator was uninjured but Freddie had to pay 5 shillings to buy him a new hat. Freddie Tait won the British Amateur Golf Championship in 1896 and 1898 so, in the Amateur Championship of 1899, played at Prestwick, Freddie was the defending champion. He reached the 36-hole final which he played against Alan Ball and was one down with two holes to play. At the 17th hole (of the second and final round) he hit his ball into a bunker, which was full of water, close to the green. In those days golf balls were made of gutta percha and floated. Freddie played a miracle shot hitting his floating ball out of the bunker and close to the hole, sinking the putt. Although he squared the match by the end of the round, he lost to Alan Ball at the first extra hole.