# Hit the golf ball harder – Acceleration Counts

## Why are we so focused on the ‘follow through’ ?

On our OnsongSwing web site we talk a lot about club head acceleration. Acceleration is what builds an effective ‘follow through’ into your golf swing. We designed our golf training aid to record and display club head acceleration, maximum speed and ball impact.

We believe that a consistent follow through is the cornerstone of a great golf swing. And that added club head acceleration will help you hit the golf ball harder and further.

##### If you want to improve something; first you have to be able to measure it.

The OnsongSwing provides a unique insight into what is actually happening as the club head smashes into the ball. By looking at the mechanics of that collision between club head and ball we can easily explain just why some golfers hit the golf ball harder and that much further than others; with the same club, same ball and a similar stature. And why the big hitter’s ball seems to launch with an incredible momentum and energy.

### The takeout message from this blog is that:

• the momentum contributed to the golf ball by accelerating the club head into the ball is more influential than outright club head speed;
• one additional G of acceleration adds as much momentum as 2.2 mph increase in swing speed, either will yield 7 yards extra ball flight off the tee;
• all the momentum from acceleration is invested in the ball before the club head begins to slow;
• with club head speed maintained, the ball stays in contact with the club face for longer and more energy is transferred to the ball;
• it could be worthwhile to lower your  club head speed at impact if it allows you to be accelerating more strongly into the ball.
• if you are not specifically training to increase your acceleration into the ball, you are missing out on your chance to hit the golf ball harder.

## Newton’s Laws of motion

##### The mechanics or physics of the collision between club head and ball are governed by Sir Isaac Newton’s three laws of motion:
• the first law deals with inertia and maintaining motion;
• the second law deals with the forces that causes an object to accelerate or slow down;
• and the third law talks about action and reaction, when two or more objects come into contact.
##### Conservation of Momentum

Newton’s three laws of motion establish the rules for what he called the “Conservation of Momentum” whereby, during a collision between objects, none of the momentum that an object possesses due to its motion can be lost … (sic) it all ends up somewhere.  It is similar to the Conservation of Energy principle which led to Einstein’s E=Mc² and the popular quote that ‘Matter/Energy can neither be created nor destroyed’.

##### There are some conclusions that can be drawn from Sir Isaac Newton’s laws of motion and how those laws apply to the mechanics of a collision between the club head and the ball:
• The club head has a momentum as it approaches the ball, that is to say ‘it is moving in a direction, at a speed and does not want to change anything”. At a constant speed the club head’s momentum (P) is proportional to the mass (M) that is the weight of the club head multiplied by club  head velocity (V) . Momentum is a vector force so it has a heading or direction included. First Law
• If the club head is changing its velocity, either up or down, it also has a value of momentum (F) referred to as force. Force is proportional to club head mass multiplied by the rate at which the club head’s velocity is changing (acceleration) over time (t) . This additional (or subtracting) momentum is also a vector force.  The two values; (P) and (F) share the same vector and therefore can be added together. Second Law
• Some fraction of the total momentum (points 1 & 2 above) invested in the club head before the collision is, for the duration of the collision (t), distributed between the ball and club head in inverse proportion to the mass of each. Third Law
##### Where does all this momentum end up?

The transfer of both forms of momentum can only happen while the ball and club head are in contact (t). A significant part of the available momentum is, for a very short period of time, consumed by overcoming the inertia of the ball. If the ball didn’t have some compression the impact (up to 7,000 kgs) would shatter the club face or the ball or both.

Only a portion of the available momentum will be passed to the ball. Logically, all of the acceleration component of club head momentum will be passed to the ball before the club head begins to slow down. Maintaining club head speed for longer suggests that more of the club head’s momentum can be loaded into the ball. Once the ball is travelling faster than club head the collision has ended.

Most of the other variables like friction, ball oscillation, compression of the club face and the twist and bowing of the shaft are not part of the equation but rather are the results of the collision.

## How is Momentum calculated?

##### The two elements of the club head’s momentum can be calculated or quantified if you like, using Newton’s laws:

First Law:— Momentum (P) equals the club head weight (in kg) multiplied by club head speed (in m/sec) at impact — kg · m/sec

Second Law:—  Force (F) equals the club head mass (in kg) multiplied by club head acceleration/deceleration  (in Newton · seconds) for the duration of the collision (t) (in seconds) — kg * N·sec * t  which resolves to and is measured as kg· m/sec

Because both forms of momentum are expressed in kg· m/sec  and are on the same vector and last for the same period of time, the values simply add together.

Note: the Second Law force (F) can be a negative number, if the club head is decelerating.

### So what do the numbers say?

One extra G of club head acceleration, for your driver for instance; adds the same amount of momentum as does an increase of one m/sec (2.24 mph) in club head speed.

So increasing your acceleration into the ball (AKA releasing the club head more effectively) by just 1G could add  just over 7 yards of carry. (Golf industry data suggests that a 1 mph increase in club head speed for a Driver yields 3.2 yards in carry).

## Conclusions

For me it was at this point that I began to understand why some of my golfing buddies could routinely out drive me by 80 yards using my driver.  All I needed to catch up was 10 Gs extra club head acceleration. But I was trying to swing the club faster instead, with disappointing results.

While there will be finite limits as to how fast you can swing the club through the ball and how much acceleration you can impart to the club head; adding more acceleration with your current swing speed will up your ball carry and the ball speed significantly. In fact it would be advantageous to lower your measured club head speed at impact, if it allows you to be accelerating more strongly into the ball.

## Real life example of the forces in play.

This swing speed graph is from our R&D files and is a very well struck driver from Matt, the PGA professional who helped us with our product development, calibration and destruction testing.

For clarity I have added some metrics (in white) to this screen shot from Matt’s OnsongSwing display:

Matt’s OnsongSwing was set to start recording at a 40kph (11m/sec) threshold swing speed.

Across the 215 millisecond swing duration, the ball impact occurred at 70ms.

So the change in velocity over that 70ms was 147kph (40.8m/sec).

Acceleration (a) = change in velocity over time = (40.8 / 0.07/9.8) = 59.5G.

So we easily calculated the average club head acceleration from Matt’s swing graph.

#### You can calculate acceleration from your OnsongSwing display graphs:

• Start by noting the threshold speed setting used;
• from the max swing speed displayed on screen subtract the threshold speed so you have the change in velocity;
• count the pixels across the LED display to the point of impact;
• take the swing duration in ms from the screen, divide that number by 128 (pixels across the screen) and then multiply by the pixel count to the point of impact; You now have the change is velocity over time (average acceleration).
• Convert the change in velocity into meters/sec and convert the time into seconds.
• Divide the meters/sec by the time and divide the result by 9.8 to give you the Gs of acceleration into the ball.

#### An easy rule of thumb is ‘the steeper the acceleration curve, the sweeter the hit’.

If you see that your swing graph has peaked and is curving down before impact, don’t bother trying to calculate the amount of deceleration over time,  it’s a bit to depressing (see the Pivot Table below).

There are a couple of ways to quantify how Matt’s 59.5G of acceleration (calculated above) added to the momentum of the club head:

Every G of acceleration could be said to multiply the weight of the club head from the balls perspective. In the graph Matt’s 300 gram driver is travelling at 187kph and accelerating at 59.5G’s. To put those three numbers in perspective; the golf ball thought it was hit by a 40 pound cannon ball travelling at 112mph.

or

The force exerted on the ball by Matt’s 59.5 G of acceleration in terms of the effective swing speed can be found using the Pivot Table at the end of this blog.  Matt’s effective swing speed was more than doubled to over 247mph (59G*2.24mph).

#### So is Matt’s graph an extreme example?  No!

Most every time I’ve had a golf pro using the OnsongSwing during my demonstrations, the swing graphs look pretty much the same; big steep accelerations and high club head speeds.

For balance and perspective, here is an example in the negative Gs: If our average mid handicap golfer drags the sole of their 3wood over the grass for 6” before making contact with the ball there might not be a big reduction in swing speed but there sure won’t be much acceleration happening. The impact on their golf shot can be significant.

## The equations that drive the pivot table

First Law of motion as it pertains to ball and club head:

• at impact the ball appears, to the club head, to be very heavy indeed, because it is stationary and resists movement but it actually only weighs around 46 grams (Mb) and because it has zero Velocity (Vb) it has no momentum:- Pb = Mb * Vb = 0
• the club head of a driver weighs in around 300grams (Mc); and if it is moving at a constant 50M/sec>(Vcit has significant momentum:-Pc = Mc ·Vc = 0.3Kg*50m/sec = 13.4kg·m/sec

Third law establishes:

• if the club head is travelling at a constant speed all of the momentum (pc), after the collision, is apportioned between club head and the ball in inverse proportion to their mass, and
• no momentum is lost so after collision pb+pc = 13.4kg·m/sec = Momentum due to velocities = Pv

The ball gains momentum and club head loses momentum.
pb= 13.4Kg m*0.3Kg/(0.3+0.046)Kg = 11.6kg·m/sec

Pc = Pv – pb = 1.8kg·m/sec

So to summarise for a system where the club head is at constant velocity:

• All the energy that was in the club head as it approached the ball was apportioned between the club and the ball in inverse proportion to their mass.
• The exchange of momentum only occurs while the club and ball are in contact (until the ball is travelling faster than the club head).

### Introducing the Second law into the equation

We need to integrate our equation for momentum (pv) due to velocity with our equation for force (Fa) due to acceleration. This is important because a club head will typically carry a force due to acceleration and a force due to its terminal speed. To integrate we can simply add the Force due to acceleration with the momentum due to velocity. (pv + Fa)  The combined momentum is then distribute between the ball and club head in inverse proportion to their mass (ie mass of club Mc over [Mc + mass of ball Mb]).

We can do this integration simply enough because both values are measured in kg·m/sec and both share the same vector heading. Both equations share the same time (collision duration) and the same terminal club head speed.

So for a club head accelerating at 40Gs with a terminal velocity of 50m/sec our integration equation looks like this

Ball momentum = (pv + Fa)*(Mc/[Mc+Mb])

=([Mc * V] + [Mc * a])*(Mc/[Mc+Mb])

=([0.300kg*50m/sec]+[0.300kg*40G])*(0.300kg/[0.300+0.046])kg·m/sec

=23.4kg·m/sec

This new number for the combined momentum of 23.4kg·m/sec, available for distribution into the ball, is almost twice the momentum available from club head speed alone 13.4kg·m/sec. (Also see the pivot table for this new number.)

## Pivot Table.

The Pivot Table below shows both positive and negative influences of acceleration on the available ball momentum.

There will be a point for every individual where they will reach the maximum swing speed they are physically capable of achieving with consistency and stability. If that chosen swing speed is achieved at the ball, the club head will have no acceleration at impact and will be losing speed for the duration of the collision.

Obviously, there are physiological differences between golfers, including differences in the percentage of fast twitch muscles that are available to accelerate the club head. There is also a dynamic limitation on how much acceleration can be invested in the club head from very low swing speeds. And of course there is the broad range of technique and swing dynamics to consider. None the less at Onsong Innovation we believe that acceleration into the ball can be the equaliser for virtually all golfers.

So finally let’s look at the table above to demonstrate how changing the dynamics of your current swing might help increase distance and improve consistency.

Taking a cut in impact speed, that allows you to be accelerating at impact, will let you swing the club with more consistency and repeatability.

Adding 10Gs of acceleration is the equivalent of 22mph of swing speed and a difference of approx. 70 yards of carry off the tee.

##### After doing this modelling,  I am more convinced than ever that most golfers could improve the consistency and power in their golf game by training for increased acceleration into the ball.

Note: in doing the research for this blog I was truly surprised that I could not find a single reference paper that would model the distribution of momentum between club head and ball. From Google, to Wiki, and onto the Physics textbooks in our local University library, nothing found. So if you would like to contribute to the discussion please use the Contact form on onsongswing.com/contact and I will be in touch.