Simple Science in Golf?

Question

Does anyone know what types of forces are in work between the time when the golfer hits his club towards the golf to the end when the golf ball goes into the hole? Thank you.

Answer 1

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The Cause of Spring-loading

The backswing is more important than the downswing to achieve stored energy or spring-loading. The backswing incorporates the properly executed wrist c ock, weight shift and rotational action. When the backswing is executed properly, the downswing will occur almost naturally. The key should be for one to practice the development of a smooth rhythmic transition from backswing to downswing.

Cocking and Un-c ocking

The wrist action is very complex. In golf the wrist has two primary actions: cocking and un-c ocking.

Studies were done by Jorgensen to analyze various wrist-****** angles of 90, 110 and 130 degrees. The findings showed that the larger the wrist c ock angle just prior to the downswing generates the greatest swing velocity. This, of course, assumes good flexibility such that the wrist cocking motion is natural and comfortable. If the wrist c ock angle is not natural or exaggerated, it will be difficult to maintain a good swing tempo.

Physicist Alastair Cochran, the author of Search for the Perfect Swing, found that, as the shoulders and arms are still moving upward to the top of the backswing, the hips actually begin moving forward approximately 0.1 seconds before the club-head reaches its furthest backswing position. This furthest position is the point of greatest coiling power. This principle of the body moving forward as the club is moving backward dramatically improves the ability to store and release this elastic energy. One can visualize this concept in the motion of trying to snap a towel by starting its movement forward and just prior to the towel going all the way back.

Once one masters the backswing skill of cocking, then comes the downswing and un-c ocking. Un-c ocking is the pushing down with the back and wrists through the downswing. As velocity increases during the downswing, there is a natural tendency to un-c ock early due to the increasing pull or torque of the wrist. At the start of the downswing, one feels only 15-20 pounds of pull from the club; however, as one completes the downswing near ball contact with the club moving 80-100 miles per hour, this torque is increased to 70-90 pounds. This significant increase in torque being four-fold encourages the forearm muscles of letting the wrists go and conscious effort should be made in order not to release the wrists.
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Answer 2

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Answer 3

There are but three major forces that combine to yield a net force on a golf ball at any given moment. These are gravity, drag/friction, and impact.

Gravity acts on the ball all the time; no matter where in flight it is found. Thus, w = mg; where m is the ball mass and g = 9.81 m/sec^2 on Earth's surface.

When the club head hits the ball, the momentum you and the club head have Mv is passed on to the ball mV. As the ball's momentum is initially 0 = mV because V = 0, there is a major change in its momentum when that club head hits it. Thus we have dp/dt = m dV/dt = ma = f = impact force due to the change in the ball's momentum over time (dp/dt).

That impact force imparts kinetic energy to the ball; so it has both vertical and horizontal velocity as it travels unerringly towards the green flag. While the ball is flying, gravity continues to pull it back to Earth. So the initial upward velocity slows, reverses, and heads back to the ground.

Meanwhile, drag forces D = 1/2 rho Cd A V(t)^2 slow its horizontal velocity. rho is air density, Cd is the coefficient of drag, A is the ball's cross sectional area, and V(t) is the ball's velocity through air at any given time of travel (t). It also slows the vertical velocity a bit, but not a lot because the vertical velocity is way smaller than the horizontal; so that vertical drag is usually ignored.

When the ball hits ten feet in front of the hole, there is yet another impact and resultant force. This one stops the ball from falling through the ground. But there is still horizontal momentum, from mVx(t), where Vx(t) is the horizontal velocity vector remaining after t time of travel in the air. Thus, your ball continues to roll, again unerringly, to the hole.

As the ball rolls over the smooth green green grass, there is another friction/drag force. This time the force tends to slow the remaining horizontal velocity even further. This force F = kmg cos(theta) depends on the coefficient of rolling friction (k), the weight of the ball (mg), and the angle of green incline (theta) between the ball and the hole.

As the ball rolls up or down the incline on the green, gravity also acts on the ball. If the incline is downward to the hole, gravity will tend to speed up the ball; if it's up, the ball will tend to slow from gravity's force. So we typically have both friction drag and gravity affecting the roll of the ball.

And an undulating green also invokes the force of gravity, which is why balls frequently do not go in a straight path to the hole. That results from multiple inclines, the undulations.

But your shot was a great shot. It's like the hole was a magnet pulling your ball toward's it. And, finally,...a hole in one. Once again gravity pulls at the ball, but this time into the bottom of the cup, where there is one final impact force (maybe a bit of bouncing) before the ball comes to a halt.

As I indicated, gravity, friction/drag, and impact are the major forces. There may be minor forces...like changes in angular momentum on a spinning ball. Or lift forces as the ball travels through the air. (This may be a significant force rather than minor however.)

For example, if your ball is spinning backward (towards you), you might want the ball to hit long on the green so it's spin brings it back to the hole rather than forward. In which case, the angular momentum is changed on impact to impart a force to propel the ball back to the hole. The angular momentum changes because of the friction force of the green slowing the ball's rotation from a fast spin in the air to a slower roll on the green's surface.

There is also a lift force on the surface of the ball as it travels through the air. This lift force is augmented by the ball's dimples, which are there to keep the airflow laminar over its surface. This gives the ball more lift and, thus, a longer travel for a given level of impact force at the tee. The lift force equation looks very much like the drag force equation in that lift also depends on air density, velocity, and such. As the ball gets scarred up and the dimples no longer are intact, the lift forces diminish (which is why it's a good idea to keep changing balls over the course, especially if you rely on a long ball for your game).

Answer 4

Kinetic energy.