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A bit of maths...

AndrewG

AndrewG

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This is just a bit of basic trig that I've always wanted to work out, but never taken the time.

When I was a kid, my dad (who never played), got me interested in golf by telling me, while watching grainy Open footage back in the 70s, that golf is one of the most skillful games there is, because a millimetre of difference when you hit the ball, can be 20 yards difference when the ball arrives on the green. This always amazed me, and I've loved the sport ever since (though I've only really taken it up for the last few years).

For some reason, I've never had the inclination to actually work out how accurate the club has to be positioned to hit the perfect shot. Now my maths isn't the best, and I'm assuming the conditions of no wind, and no sidespin at all to shape the shot, but here goes:

For a 150yd shot, hit 5yds left or right of the target, the ball is set off at around 2 degrees from the target line. This seemed quite generous to me, but of course, thats a triangle with a 150 yard 'adjacent' side.

At the club face though, given a 2" sweetspot on the face, the outer left or right edge of that sweetspot is only - 0.03" from perfect !!!

So when you hit that shot into the middle of a green from 150 yards, congratulate yourself - you have just steered a piece of metal at approaching 100mph to a position where the edge of the hitting area is within 0.75mm of where you want it to be.
 
AndrewG said:
This is just a bit of basic trig that I've always wanted to work out, but never taken the time.

When I was a kid, my dad (who never played), got me interested in golf by telling me, while watching grainy Open footage back in the 70s, that golf is one of the most skillful games there is, because a millimetre of difference when you hit the ball, can be 20 yards difference when the ball arrives on the green. This always amazed me, and I've loved the sport ever since (though I've only really taken it up for the last few years).

For some reason, I've never had the inclination to actually work out how accurate the club has to be positioned to hit the perfect shot. Now my maths isn't the best, and I'm assuming the conditions of no wind, and no sidespin at all to shape the shot, but here goes:

For a 150yd shot, hit 5yds left or right of the target, the ball is set off at around 2 degrees from the target line. This seemed quite generous to me, but of course, thats a triangle with a 150 yard 'adjacent' side.

At the club face though, given a 2" sweetspot on the face, the outer left or right edge of that sweetspot is only - 0.03" from perfect !!!

So when you hit that shot into the middle of a green from 150 yards, congratulate yourself - you have just steered a piece of metal at approaching 100mph to a position where the edge of the hitting area is within 0.75mm of where you want it to be.
Click to expand...


Ummmmm.... English please? lol just kidding. That is some amazing math! I couldn't fathom thinking about golf this meticulously while playing. I would go nuts!
 
AndrewG said:
This is just a bit of basic trig that I've always wanted to work out, but never taken the time.

When I was a kid, my dad (who never played), got me interested in golf by telling me, while watching grainy Open footage back in the 70s, that golf is one of the most skillful games there is, because a millimetre of difference when you hit the ball, can be 20 yards difference when the ball arrives on the green. This always amazed me, and I've loved the sport ever since (though I've only really taken it up for the last few years).

For some reason, I've never had the inclination to actually work out how accurate the club has to be positioned to hit the perfect shot. Now my maths isn't the best, and I'm assuming the conditions of no wind, and no sidespin at all to shape the shot, but here goes:

For a 150yd shot, hit 5yds left or right of the target, the ball is set off at around 2 degrees from the target line. This seemed quite generous to me, but of course, thats a triangle with a 150 yard 'adjacent' side.

At the club face though, given a 2" sweetspot on the face, the outer left or right edge of that sweetspot is only - 0.03" from perfect !!!

So when you hit that shot into the middle of a green from 150 yards, congratulate yourself - you have just steered a piece of metal at approaching 100mph to a position where the edge of the hitting area is within 0.75mm of where you want it to be.
Click to expand...

The scary thing is, this runs through my head all the time when I'm playing. I'm always amazed how such little imperfection can have such a big impact. And after I think about it, I generally hit it fat about 30 yards.
 
Now the real question, how much does a driver depend on this?

Assuming a straight drive of 280 yds, if you hit the ball with the face open just slightly to 2*, you are guaranteed to be 10 yards to the right of where you aimed. Increase that angle to 5* and you are now 25 yards right. Now, this is just blocking the ball and hitting it straight. Lets take a look at what happens with an out to in swing on top of that.

Knowing the ball velocity and the circumference of the golf ball the theoretical spin rate can be calculated as:

spin rate in rpm = (bv / c) /60
c = .043m
bv = 5/7 f v sin 0
Both top spin and side spin are used to produce a ratio of the true spin rpm and direction
i.e. if top spin = 3600 rpm at 0* and side spin = 900 rpm at 90* (right) then ratio = 900:3600 = 0.25

Assuming a ratio of 1:1 would result in a spin direction of 45* then spin direction = 45* * 0.25 = 11.25*

So your angle now grows from 5* to 16.25* which results in 82.94 off course.

Gives new meaning to "I hit it 300 yards, 200 straight and 100 right."
 
OK. I didn't understand a thing you just said except for the last line, which is the best way to sum up my driver game, except it's more like 150 straight and 100 right.
 
jefrazie said:
Now the real question, how much does a driver depend on this?

Assuming a straight drive of 280 yds, if you hit the ball with the face open just slightly to 2*, you are guaranteed to be 10 yards to the right of where you aimed. Increase that angle to 5* and you are now 25 yards right. Now, this is just blocking the ball and hitting it straight. Lets take a look at what happens with an out to in swing on top of that.

Knowing the ball velocity and the circumference of the golf ball the theoretical spin rate can be calculated as:

spin rate in rpm = (bv / c) /60
c = .043m
bv = 5/7 f v sin 0
Both top spin and side spin are used to produce a ratio of the true spin rpm and direction
i.e. if top spin = 3600 rpm at 0* and side spin = 900 rpm at 90* (right) then ratio = 900:3600 = 0.25

Assuming a ratio of 1:1 would result in a spin direction of 45* then spin direction = 45* * 0.25 = 11.25*

So your angle now grows from 5* to 16.25* which results in 82.94 off course.

Gives new meaning to "I hit it 300 yards, 200 straight and 100 right."
Click to expand...

sweet lord, I thought I was good in math...not even close....good stuff!
 
I would go insane if I tried to think about all of this while playing. I find it hard enough to play golf my way little on try and do math at the same time.
 
This is the type of stuff I don't want to know! I never should've read this thread.
 
mikedean441 said:
sweet lord, I thought I was good in math...not even close....good stuff!
Click to expand...

Its physics.

Funny thing is, I hated it in college. Seemed to make sense after I graduated. :D
 
Did you account for the gravitational field of the moon or other nearby large objects? **looks down at belly**
 
Great replies guys - I really wanted the OP to be something which showed you how great you are when you hit a shot, even 5-10 yds left or right of where you aim. Its just not possible to hit the target line dead-on for every shot in a round - we sholdn't be trying to - and definitely shouldn't be berating ourselves when we don't!

I think I'm starting to understand that now after slipping from 12.8 to 13.7 in the last 9 months...
 
never actually taught of it from that side before. really interesting to think your working with such small tolerances
 
...oh, just had a thought myself... I wonder how accurate you have to be with the clubhead speed to get exactly the right distance :) I'm guessing the higher the loft, the greater the tolerance to higher or lower clubhead speeds... Hmm - one to ponder :)
 
AndrewG said:
This is just a bit of basic trig that I've always wanted to work out, but never taken the time.

When I was a kid, my dad (who never played), got me interested in golf by telling me, while watching grainy Open footage back in the 70s, that golf is one of the most skillful games there is, because a millimetre of difference when you hit the ball, can be 20 yards difference when the ball arrives on the green. This always amazed me, and I've loved the sport ever since (though I've only really taken it up for the last few years).

For some reason, I've never had the inclination to actually work out how accurate the club has to be positioned to hit the perfect shot. Now my maths isn't the best, and I'm assuming the conditions of no wind, and no sidespin at all to shape the shot, but here goes:

For a 150yd shot, hit 5yds left or right of the target, the ball is set off at around 2 degrees from the target line. This seemed quite generous to me, but of course, thats a triangle with a 150 yard 'adjacent' side.

At the club face though, given a 2" sweetspot on the face, the outer left or right edge of that sweetspot is only - 0.03" from perfect !!!

So when you hit that shot into the middle of a green from 150 yards, congratulate yourself - you have just steered a piece of metal at approaching 100mph to a position where the edge of the hitting area is within 0.75mm of where you want it to be.
Click to expand...


Huh? :confused2:
 
I have enough trouble adding everyone's scores!:D
 
Ole Gray said:
Huh? :confused2:
Click to expand...

I'm awaiting an [activate Ole Gray] moment any minute now.....

but my head hurts too much to think of one, now I've read this thread!
 
AndrewG said:
...oh, just had a thought myself... I wonder how accurate you have to be with the clubhead speed to get exactly the right distance :) I'm guessing the higher the loft, the greater the tolerance to higher or lower clubhead speeds... Hmm - one to ponder :)
Click to expand...
YES PONDER AWAY...lol
 
Swing + curse word = bad shot
Swing + smile = good shot

About all the math I can handle at 8am.
 
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