Golf Physics 101

Let's take a glimpse at golf physics...

I'm no rocket scientist but simple internet research will bear me out. Yes, the second law...

Newton's Second Law-The above equation also indicates that a unit of force is equal to a unit of mass times a unit of acceleration.
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So, logically, the greater amount of force we apply to the ball, the
farther it will go. And in the equation Force= mass multiplied by
acceleration, then we can see that acceleration is a vital key indeed.
Especially since we are assuming that in executing the golf swing, mass
will remain constant.

But what does this all mean in practical golf terms? Simple- You must
accelerate through the hitting area, specifically during contact with the
ball.

This, I suspect is why some of the smaller players can out drive others
who are twice their size! It's also why some of the smaller females can
outdrive some of the larger male pros, eh? Yes, technique.

That being said, it must also be considered that given about the same acceleration for any two players, the bigger, taller player with more mass will have more force. Look at the height of the top PGA pros... most of them are above six feet... and don't get me started with those long distance champions...

Now, lag and the wrist surely play an important part here. But what about
weight shift? Disregarding obvious factors such as solid contact, club face and swing path, what other factors can affect this?
Specifically what swing mechanics can be taught for better accelaration?
And can this easily be taught to anyone? Or do we need some sort of
innate physical talent?
Alas, at this point I have more questions than answers and I hope others
can write about this...

__________________
Imagine winning nowadays using rusty old clubs!

I think that you have it round the wrong way.

What you need to consider is that you are trying to accelerate the ball from zero to over 100 mph within 0.02 seconds (rough guess on contact duration between ball and clubhead) so the acceleration component of the 2nd law refers to the ball.

The acceleration of the ball is dependent on the mass of the ball and the force applied to it. With the mass of the ball being the same for everyone, this means that the amount of force applied to the ball by the clubhead is the key, which in this case is the SPEED of the clubhead, not the acceleration of the clubhead. A club head can declerate from 120 down to 110 mph during the hitting zone and still hit the ball further than a club accelerating from 70 mph to 80 mph.

Acceleration is still an important component of a golf swing as you are looking to maximise the clubhead speed from the top of the back swing to the point of impact. How your arms move during the downswing will determine the largest component of the clubhead speed; a stiff, straight armed swing will produce a lower clubhead speed than one that snaps the wrists at impact (hence the importance of lag).

Technique is one of the main prerequisites for clubhead speed although extreme clubhead speed requires great strength. Taller players also have an advantage as they have greater natural leverage from their longer limbs.

__________________
Cleveland Launcher 460 - Aldila NV 65 x-stiff
Callaway Big Bertha 3W - Aldila NV 75 x-stiff
TaylorMade Rescue Dual TP (16°, 19°) stiff
Mizuno MP-32 2-PW Rifle Flighted 6.0
Titleist Vokey Wedges 52°, 56°, 60°
Scotty Cameron Circa 62 #3 35/330

in the golf swing the vast majority of all players, pros included, decelerate through impact. I have heard mike austin actually was faster after impact, dont know if that is true or not, but most tour players like tiger, are not. Speed at seperation is what matters, and mass too. You do try and acclerate your swing through the ball but the clubhead will decelerate Now on chips and pitches you may accelerate but not full shots

Transfer of momentum and colliding bodies. That's all.

There's more energy in a ten ton brick going 1mph than there is in a 200 gram clubhead going 100mph. But it will not propel the ball faster.

Below is the equation we frequently use to determine how fast a ball will go:

v = V * ((1+e)/(1+(m/M)))

v = velocity of the ball immediately after impact
V = velocity of clubhead immediately before impact
m = mass of ball
M = mass of clubhead
e = COR (coefficient of restitution of the clubface)

A ball is usually 45 grams and a driver clubhead is normally 200 grams. Do the math to see what you'd get for ball speed. As a reference, 90mph clubhead speed will get you about 225+ yards, 100mph 250+ yards and 110mph 300+ yards. If contact with the ball is perfect and if the spin and launch angle is perfect as well.

If.

It is not possible to accelerate during impact. The reason is simple: Transfer of momentum. When one object transfers momentum to another, it slows down. When we say to accelerate during impact, we mean to apply more force or to swing through or to not wait for the clubhead or to lead with the hands. All I can think of as a reason for this is to counteract resistance from the grass prior to striking the ball to lose as little momentum as possible and to transfer as much to the ball. In short, it serves to maintain control of the club as we swing it and as we strike the ball with it.

Transfer of momentum is all good but what about colliding bodies? What's that? Two bodies that collide will exert force against one another. The result of the collision will be determined by the center of gravity of both objects. In other words, the efficiency of the transfer of momentum is a direct result of the accuracy of the collision between the two objects. This is where the offset strike gives us problems.

An offset collision will transfer momentum but not use it to accelerate the second object in a straight line. Instead it will use it to twist both objects on their respective center of gravity. Namely, the clubhead will twist around its center of gravity, thereby wasting precious momentum that it could have transfered to the ball instead. The result is reduced ball speed, offset ball spin and offline ball trajectory. All of which are mostly undesirable most of the time compared to the optimum expected result.

You see, transfer of momentum applies not only to velocity but also to the type of motion. Such as rotation. One object could transfer its linear momentum to rotational momentum following an offset collision. You see what that means? Instead of transfering its momentum to the other object, it keeps it but uses it to do something else. That's not what we want, is it.

Alright, I've explaned transfer of momentum, now is time to explain production of this momentum.

A little known fact. As we swing the clubhead, we apply centripetal force. The clubhead wants to go straight but we hold it with our hands so it goes around us. We apply centripetal force. Centripetal: Towards the center, that's what it means. Anyway, the amount of force we must apply to hold the club as we swing it must be equal or superior than the weight it will appear to be. For a 200 gram clubhead going 100mph on a 45in shaft, that will come up to about 60 pounds.

60 pounds!

No wonder it's so hard to accelerate through impact, it weighs a ton! Just kidding. Seriously, can you control that club when it weighs 60 lbs? Can you control the club as you swing it to achieve such a speed so that it will weigh 60lbs then control that and while it's doing all that strike the ball exactly on the sweet spot so that you transfer as much momentum to the ball but also transfer it properly to the ball so it goes straight?

What if you swung the club just a little slower, would you be able to control it? Let's see, to propel an object twice as fast, it takes 4 times the energy. In other words, an object going twice as fast produces twice the energy. So, if I was swinging the club half as fast, it would feel like it weighed only 15lbs. That's better.

Of course I can control 15lbs, I'm sure you can too. But that's not the kind of speed we want. We want 90mph, I do anyway. It's good enough for me. I'm sure the club will feel much lighter than 60lbs but I don't know exactly by how much. What I know is that I have enough strength to control the club at that speed to produce proper contact.

The point is that since the club feels much lighter, I can control it much easier so I can strike the ball much better so I can transfer much more momentum than otherwise. I can do it better with less effort. Come to think of it, I can do it better more often as well.

In other words, I can send the ball to the target using the club more accurately and more frequently than if I went all out with each shot. It's the difference between expecting the ball to go to anywhere and expecting the ball to go to my target.

I see too many people focusing on the production of momentum and not enough on proper transfer of momentum.

This is only my opinion, I'm not a physicist.

What has been quoted is the definition of force.
Force units are described in terms of accelerating
a given mass to a given speed. The standard unit
is measured in grams times meters per second.

The formula is kinetic energy = mass times
the square of the velocity. I think it is kinetic
energy you are wanting to be concerned with
in hitting a ball, not force, although the two
are closely related.

The clubhead does not need to be accelerating to
hit the ball a long way, it just has to be moving
fast. Acceleration is not a key factor, rather a
description of the result.

Note the importance of velocity stems from the
fact it is an exponential factor. Say the club speed
is 100 meters per second. If the clubhead weighs
200 grams, the kinetic generated would lift 1 gram
10,000 meters.
If the club speed increases 1 meter per second to
101 meters per second, the resultant will lift
1 gram 10,201 meters.
To gain that same advantage by increasing
weight, you would have to add 4 grams to the
clubhead weight and still swing the original
100 meters per second.

Errr...

If I remember correctly, Newton's Law's of Motion assumed one thing, everything happens in a vaccuum.

Can't remember ever playing golf in a vaccuum......



Ok, that bad joke out of the way, seeing as this thread has been started, let's run with it...

Newton's First Law is:

Every object in a state of uniform motion tends to remain in that state of motion unless an external force is applied to it.

So, in golfing terms, once you put your ball on the tee peg, it will just bloody well sit there until some external force strong enough to shift it is applied to it. Generally, this is us hitting it... For the moment we will also forget that gravity is acting on the ball (and us). Unless of course we are in a vaccuum...

Easy so far...

Newton's Second Law is:

The relationship between an object's mass m, its acceleration a, and the applied force F is F = ma. Acceleration and force are vectors (as indicated by their symbols being displayed in slant font); in this law the direction of the force vector is the same as the direction of the acceleration vector.

For me, the important thing here is that by definition, acceleration is "change in velocity" So, being stationary one instant before impact and moving at whatever speed one instant after impact, the ball has accelerated for that time...

As noted above, both the applied force and the acceleration are "directional vectors". Years ago, when I slept through Physics class, vectors were arrows where both length and direction told the tale.

Now, Martin mentioned Centripetal motion. Given the clubhead moves in a notionally circular path, technically, it is always accelerating, regardless of its velocity, whether its velocity is fast (100mph) or slow (20mph), getting faster, getting slower or remaining constant. By this I mean given the clubhead is changing straight line direction every instant during the swing, it is accelerating.

To better explain this, an object which moves in a circle is having a constant force applied in a direction perpendicular to its motion at any instant. So, to say at impact, the ball will assume a direction perpendicular to the path of the clubhead is true if both the ball and the clubhead were of similar size and spherical and contact was flush centre to centre. Clearly they are not.

Given the clubhead is larger than the ball and planar (flat), the ball will leave the clubhead perpendicular to the face initially (remember, the more lofted the club, the higher the ball travels...??) and then its flight will be effected by the amount and direction of spin applied as dictated by the swing path of the club head.

Square face, square clubhead path at impact, ball will leave the clubhead along the target line and only be subject to backspin. From there (given any number of external variables) things get exceptionally and exponentially complicated...

For me, we are trying to simplify this game and going in to this level of detail about the physics of the golf swing, whilst interesting in discussion, surely can only hurt in practice...

Well, at least I think so...

Cheers

__________________
Look at the Target, Look at the Ball, Swing... Dr Bob Rotella...

bleedin ell
i thought id entered the NASA website for a minute there

Better the NASA site Slats, than the Royal Society Of Gynecologists Site that cmays took us to last week...



Cheers

ha ha
youre right
takes allsorts i suppose
my neighbour is a gynaecologist he decorated his house the other week painted his hallway through the letterbox!

very nice, must remember that one...



Bottom line, the more I play this game, the more I love it and the less I understand it. But, that said, I am unsure if I need to understand it implicitly in order to enjoy myself playing it...

But, that's another thread right there...

Cheers

well said mate
i love this site but ive improved a lot more since i stopped reading every post,tip theory etc

Geez, if I thought I was going to
contribute to throwing anyone's
game off, I would have kept
quiet. To me, it's no big deal.
I mean, I know how to lap and
set the blades on a Toro greens
mower, too; but that hasn't
affected my putting, as far as
I know.
$10 Nassau, anyone?

And my friends the proctologists are loads of fun at parties when they get together with the Gynecologists and the NASA Rocket Scientists...

I think the only thing I get angry about is that I never get invited to those parties...

But, we digress......



Cheers

Errr...take the stick and hit the little white thing on the tee really hard, then go find it, and do it again....

Incorrect. Gravity still exists.