Scigolf Presents Jack Kuykendall's Myths of Golf - #4 - The Reality versus the Big Muscle Myth

The Reality versus the Big Muscle Myth

The Big Muscle Myth is that club head speed is produced by the muscles that move the arms! Four science books that I have reviewed (Search for the Perfect Swing, The Physics of Golf, The Golfing Machine and The Real Truth About The Golf Swing) all claim that club head speed must come from the body because it takes more horesepower than the arms are capable of generating. All four of these books use a two lever system as their model for the swing. Both the model and their claims of the horsepower the arms are capable of producing are incorrect.

What does science (physics) have to say about where power (club head speed) comes from? This does not require advanced physics. This is high school level physics.

A club head striking a golf ball is a collision between two objects - a club head and a golf ball. In physics, this is called an exchange of energy or momentum. The equations that describes the exchange of momentum

mv = (mass)x(velocity)
correctly describes the interaction between the club head and the ball.

Momentum

The momentum of an object is its mass time its velocity. When two objects collide, the momentum before the collision must equal the momentum after impact (conservation of momentum). Mathematically this is stated as:

m1u1 + m2u2 = m1v1 + m2v2 where u1 and u2 are the velocities before impact and v1 and v2 are the velocities after impact. For the collision between the club head and the ball, we define:

m1 = the mass of the club head.
u1 = the velocity of the club head before impact.
m2 = the mass of the golf ball.
u2 = the velocity of the golf ball before impact.
v1 = the velocity of the club head after impact.
v2 = the velocity of the golf ball after impact.

A term called the "coefficient of restitution (cor)" is used to describe the transfer of energy between the two objects. The cor is defined as:

			v2 - v1
		e   =  ----------------
			u1 - u2

where u1, u2 are the velocities before impact and v1, v2 are the velocities after impact.

In a collision between a golf club head and a golf ball, u2 is zero because the golf ball has no velocity before the collision. This reduces the cor to:

			v2 - v1
		e    = ----------------
			   u1

and the momentum equation to: m1 u1 = m1 v1 + m2 v2

We want to solve the equation for v2, the velocity of the golf ball after impact.

Solving the cor for v1, (v1 = v2 - eu1), and substituting into the momentum equation we have,

	m1 u1  =  m1 v2 -m1 u1 e  +m2 v2
	m1 u1 + m1 u1 e  =  m1 v2 + m2 v2
	m1 u1 ( 1 + e )  =  (m1 +m2) v2
		     m1
	v2 = ----------------  (1 + e)   u1
		m1 + m 2

initial ball velocity = (mass) times (1 + cor) times (velocity of the club head)

What effect does the mass of the player have on the initial velocity of a golf ball? Let's insert some numbers into the equation and observe the results. We'll use a 180 pound person. The velocity of the club head will be100 miles per hour. A golf ball weighs 0.1 pounds and the cor of long hitting golf balls is approximately 0.8.

m1 = 180 lbs,	m2 = 0.1 lbs,	e = 0.8   u1 = 100 mph,

			  m1
	v2 = -----------  	  (1 + e)  u1
			m1 + m 2

			 180 lbs
	v2 = ------------------  (1+0.8)  (100mph) 
		       180 lbs + 0.1 lbs

	v2 =   (0.9994)		  (1.08)   (100mph)= 179.90 mph

For the parameters given, the golf ball will leave the club head at 179.90 miles per hour.

For a human golfer M/ (M + m) is approximately 1. The mass of a golfer has less than 0.1% effect in producing initial ball velocity. From the previous example, we can conclude that once the mass (m1) exceeds 175 ounces (approximately 11 pounds), 99% of the mass is transferred. Less than 1% would be lost in a collision due the mass difference between a golf ball and an object that weighed 11 pounds. This means that once the mass of an object exceeds 11 pounds, the increase in mass has virtually no added effect to the initial velocity of the golf ball.

By simply putting numbers into the simple momentum equation, the equation predicts the following:

The task now becomes very simple. All we have to do is sum all the velocities of the different body parts that produce club head speed. How fast does each body part move and what is its contribution to club head speed?

Velocity can only be produced where there is velocity of a moving part.

The velocities of the various parts and their lever effect can be described by the combining of four basic movements:

What is the contribution of these four movements during a downswing? We will choose the club head speed to be 100 miles per hour at impact. A mathematics equation that we are all familiar with is that velocity is distance divided by time.

					d
				v  =  -----
					t

The following golf stroke is that of Moe Norman (considered to be one of the greatest ball strikers of all times). The numbers 1 to7 represent TV frames. For example, frame 1 indicates the postions of the club head, right hand, etc. at the top of the backswing. These postions were taken from the first video frame, then the same positions were taken from the second video frame, and so on.

Each TV frame is 0.033 seconds. The downstroke is 0.23 seconds.

Frame 1,2,3
(0.099sec) Lateral and rotary body motion and small amount from right triceps (15mph). Like starting a merry-go-round. You use a large body force to get the weight moving. There is very little velocity.
Frame 4
(0.033 sec) Right triceps major - small amount from lateral and rotary body motion. Movement of the right arm away from the right shoulder. club head velocity increases from 15 to 39 mph.
Frame 5
(0.033sec) Right triceps major - small amount from right forearm. Movement of the right arm away from the right shoulder. club head velocity increases to 49 mph.
Frame 6
(0.033sec) Right forearm major, right triceps minor. Physics principal that creates the major increase in club head velocity -
1. shortening the radius of an arc. (centripetal force created by the body and left arm).
2. Torque created when the right forearm muscles contract. club head velocity increases to 99 mph.

Frame 7
(0.033sec) Inertia and right forearm and right triceps. The ball is impacted between the 6th and the 7th frame. The impact slows the club face to 78 mph.

Frame Number:
1, 2, 3
3 x 0.033 sec = .099 sec d = 2.2 ft v = 2.2 ft/0.099sec = 22 ft/sec = 15 mph
4 - .033 sec d = 1.9 ft v = 1.9 ft/0.033sec = 58 ft/sec = 39 mph
5 - .033 sec d = 2.4 ft v = 2.4 ft/0.033sec = 72 ft/sec = 49 mph
6 - .033 sec d = 4.8 ft v = 4.8 ft/0.033sec = 145 ft/sec = 99 mph
7 - .033 sec d = 3.8 ft v = 3.8 ft/0.033sec = 115 ft/sec = 78 mph

For the first 0.132 secs (frames 1,2,3 and 4), the right shoulder and right hip rotate through approximately 45 degrees, and return parallel to the intended line of flight. During this same 0.132 seconds, the hips move laterally about 6 inches. The lateral and rotary body motion, during the initial 0.099 seconds of the downstroke, generate approximately 15% towards the club head velocity at impact. During the next 0.033 seconds, the right triceps, with minor assistance from the small motion of the lateral and rotary motion of the body, contributes the next 24% increase in club head velocity.

From frame 4 to impact, the lateral and rotary body motion is very slow and contributes minimally toward club head velocity. During the next 0.033 sec, the right triceps, with a small contribution from the right forearm, contributes the next 10% increase in club head velocity. During the next 0.033 seconds, the right forearm, with a small contribution from the right triceps, contributes 50% towards club head velocity.

The quantitatively correct percentages of how club head velocity is produced in a golf swing are:

Lateral and Rotary body motion: 15%

Right triceps , Right forearm : 85%