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.