# Physics of golf

This is interesting...

How will the length and the mass of a golf club affect how far the ball will travel? What are the governing equations?

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Hi there,

If you are trying to explain the distance travel by a golf ball only from the length and the mass of the golf club, you will have huge difference between your calculations and reality.

There are many other parameters that come into play: the angle of the club's face on the ball, the hardness of the club's surface, the dimples in the ball, the pattern of the dimples in the ball, the hardness of the ball, the whip effect of the shaft, ...

Now, I don't know the equations that are governing this movement by heart. I would say that you will need to look into many different fields of classical mechanics, like fluid dynamic for the movement of the ball in the air.

Cheers

Andrew Mason
Homework Helper
This is interesting...

How will the length and the mass of a golf club affect how far the ball will travel? What are the governing equations?
The ball gets its momentum from the impact of the club head. The governing equation there is: p = Ft or, more precisely:

$$p = \int_{t_0}^{t_f} Fdt$$

where F is the force being applied by the club to the ball, and t (tf - t0) is the time during which they are in contact and p is the momentum of the ball that results (ball mass x velocity).

What you want to do is maximize the ball momentum.

Notice that neither the mass of the club head or the length appear in this equation. However, F and t will depend on the mass and speed (momentum) of the club head. The length of the club will affect the speed of the club head. Assuming the golfer is limited in the angular speed that he can rotate the club, a longer club will give faster club head speed. For a given club speed, a greater club head mass will tend to increase the force and the time over which the force is in contact with the ball. However, the greater mass will also require more effort by the golfer to accelerate to the desired speed, so it is a bit of a trade off.

AM

though it appears that mass and length do not make an appreciable effect
it does as explained by AM
mass will play a huge role as in momentum...

morrobay
Gold Member
From rotational kinematics the linear speed of the club at impact is , v = wr
with w = angular speed = delta theta/delta t
So with r , the radius being roughly equal to the club length + arm length then v is
proportional to club length.

With m1 = club mass
u1 = club vel
m2= mass ball
v2= vel ball
then the velocity of ball after impact is
v2 =(2m1/m1 +m2) u1
The range of the ball = x =vo cos theta ) t
at any time t
At any time t that is < or = 2Vo sin theta/g

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