A hypothetical putting question

[mikpga]

This may not be the response you want to hear...

 

In 2016 on the PGA Tour Daniel Summerhayes lead the field in Total 1 Putts from 15' to 20'...

 

He made a total of 42 from this range out of 586 opportunities...

 

His percentage was 7.2% from this range...

 

Roll the ball approximately 20 feet, tap in, and move on...

 

Avoid OVER ANALYSIS of any putt longer than 10 feet...

[NCHACK85]

This may not be the response you want to hear...

 

In 2016 on the PGA Tour Daniel Summerhayes lead the field in Total 1 Putts from 15' to 20'...

 

He made a total of 42 from this range out of 586 opportunities...

 

His percentage was 7.2% from this range...

 

Roll the ball approximately 20 feet, tap in, and move on...

 

Avoid OVER ANALYSIS of any putt longer than 10 feet...

But it's what we need to hear. With what you showed us. What range should we focus on the most on the putting green?

[Matt J]

8 feet and in is around 50% make correct?

 

I'd guess 4 to 8 feet is where you could excel the most.

 

But, getting those longer putts to tap-in is easier said than done, IMO.

 

Hard to waste time on the putting or chipping green. The range is where most of us spend too much time, myself included.

[NCHACK85]

That chipputt technique for long putts help me, for me it seems to come off the putter pretty hot.

[starsail85]

Hmm, not sure , I usually don't notice there was a slope until I leave the putt short ?

[KMeloney]

This may not be the response you want to hear...

 

In 2016 on the PGA Tour Daniel Summerhayes lead the field in Total 1 Putts from 15' to 20'...

 

He made a total of 42 from this range out of 586 opportunities...

 

His percentage was 7.2% from this range...

 

Roll the ball approximately 20 feet, tap in, and move on...

 

Avoid OVER ANALYSIS of any putt longer than 10 feet...

 

This is a great answer to a question like "Should I spend much time working on putts in the 20' range?" But I think the OP is just wondering about the physics here.

 

If I'm understanding the OP's question correctly, he's simply wondering if it takes the same or different amount of energy to roll the ball to the hole in each of these scenarios.

 

Consider if you rolled the ball to the hole in each case with a pinball machine-style plunger ball-launcher. Would you pull back the plunger the same length (and impart the same energy on the ball) in each scenario? Or, would each scenario require different amounts of energy?

[North Butte]

This may not be the response you want to hear...

 

In 2016 on the PGA Tour Daniel Summerhayes lead the field in Total 1 Putts from 15' to 20'...

 

He made a total of 42 from this range out of 586 opportunities...

 

His percentage was 7.2% from this range...

 

Roll the ball approximately 20 feet, tap in, and move on...

 

Avoid OVER ANALYSIS of any putt longer than 10 feet...

 

That actually takes the prize for the single most bloody-minded and unhelpful answer of 2017. Unless of course you somehow missed the word "hypothetical" in the title of the thread!

[Yrrdead]

I am disappoint. I was expecting some mathlab equations , some symbols I haven't seen or used since NNPTC.

 

The real question is launch and the resulting impact vectors. A putt is no different than any other shot but at these velocities I believe that the friction coefficient will outway the landing slope.

 

 

My reasoning is based on the following

 

1. The force due to kinetic friction is the biggest factor

2. That force is calculated based on slope.

3. Bounce means that #2,3 has less of that force applied to the ball.

 

Now I could also see #2 requiring more than #3 due to the direction of normal force (perpendicular to surface) since I would assume that some vector math would show that force being at a more acute negative angle. That being said the longer a putt the more that kinetic friction wins.

 

 

None of the above has been calculated or verified for accuracy it is just the ramblings of a golf junkie who once took some physics classes (and operated a nuclear reactor :swoon: ). We need a high school physics teacher to give this to their class so we can get some actual calculations done for us :). Oh and we can do some experimental verification. Who has a Perfect Putt machine?

[marte]

All I know is on a 20' putt with a rise of 8" or so and a little drop off behind the hole I'll hit it 6' past and miss the come backer.

[Hstead]

Geoff Mangum explains somewhere on his site why a steep slope immediately between you and the hole requires more force. I will have to look for it. I can't recall his break down, but the important take away is that you have to hit putts harder when you have a steep hill immediately in front of you vs closer to the target,

[AlecEmersonGolf]

I am disappoint. I was expecting some mathlab equations , some symbols I haven't seen or used since NNPTC.

 

The real question is launch and the resulting impact vectors. A putt is no different than any other shot but at these velocities I believe that the friction coefficient will outway the landing slope.

 

 

My reasoning is based on the following

 

1. The force due to kinetic friction is the biggest factor

2. That force is calculated based on slope.

3. Bounce means that #2,3 has less of that force applied to the ball.

 

Now I could also see #2 requiring more than #3 due to the direction of normal force (perpendicular to surface) since I would assume that some vector math would show that force being at a more acute negative angle. That being said the longer a putt the more that kinetic friction wins.

 

 

None of the above has been calculated or verified for accuracy it is just the ramblings of a golf junkie who once took some physics classes (and operated a nuclear reactor :swoon: ). We need a high school physics teacher to give this to their class so we can get some actual calculations done for us :). Oh and we can do some experimental verification. Who has a Perfect Putt machine?

I am an AP Physics student right now lol

[Matt J]

For me, I keep grinding back to the fact that if it's a 5% grade than it's the equivalent of 3 degrees of slope. If the average putter has between 2.5 to 4 degrees of loft then perhaps we shouldn't be trying to hit a putt that faces a slope with more force, but simply try and change the vector upwards to gain more loft due to the slope negating the loft of the putter?

[mikpga]

This may not be the response you want to hear...

 

In 2016 on the PGA Tour Daniel Summerhayes lead the field in Total 1 Putts from 15' to 20'...

 

He made a total of 42 from this range out of 586 opportunities...

 

His percentage was 7.2% from this range...

 

Roll the ball approximately 20 feet, tap in, and move on...

 

Avoid OVER ANALYSIS of any putt longer than 10 feet...

 

That actually takes the prize for the single most bloody-minded and unhelpful answer of 2017. Unless of course you somehow missed the word "hypothetical" in the title of the thread!

 

Ooh! Is there a trophy for this?

 

I did preface my post in my first sentence however!

 

Hypothetical is an interesting word.

[North Butte]

Trophy awarded at the end of the year. I'm sure there will be some real doozies between now and then somewhere or another.

[dlam]

Putt #1 borders on being against the rules in golf for pin placement unless you playing mini golf as there should be an flat part around the hole.

[Matt J]

Putt #1 borders on being against the rules in golf for pin placement unless you playing mini golf as there should be an flat part around the hole.

 

Not actually a rule, but rather a suggestion. One that few of the courses I play heed. The USGA sends out an official and marks the pins every time we have a State or National association tournament. In those cases I'd say 90% of the holes are cut with the 2 foot doughnut of flat or little grade immediately around the placement.

[NCHACK85]

Putt #1 borders on being against the rules in golf for pin placement unless you playing mini golf as there should be an flat part around the hole.

 

Nothing like a foot and a half tap in when you can tell the ball is definitely higher than your feet.

[Patrick_O]

Ok assuming the same elevation difference for all three and the steeper portions for 1 and 2 are the same slope: ignoring friction they would all be the same since W=F*D. However in the real world friction would come into play and since 3 is the closest to being a straight line this one would require the least force to overcome the friction. 2 and 3 would be the same. However I agree that it is better to be long for the one with the slope nearest the hole.

[DaveLeeNC]

If you were going to analyze this problem you would probably do it on an energy balance basis. The difference between the speed (kinetic energy) at the start and end of each path is all due to losses:

 

1) Rolling friction

2) Gravity

3) Aerodynamic losses (air friction)

 

Fortunately #3 is probably ignore-able which simplifies things. Aerodynamic resistance is proportional to the square of velocity which makes calculations a bit messy.

 

The losses in #2 are the same in all 3 cases. So throw that one out. I have already decided to ignore #3, so #1 is all that is left.

 

For cases of "true rolling" (like a wheel on a road surface) the rolling frictional force is a constant (over a pretty wide range of velocities). I am an avid cyclist so am pretty familiar with this problem. IF a golf ball was truly rolling on a surface you have the following variables.

 

The constant slope path is the shortest path. Energy loss is F*D so this favors the constant slope path. Additionally rolling resistance is directly proportional to the force perpendicular to the surface (grass in this case). So in the constant slope case the perpendicular force is (slightly) less than the other two cases (except for the short rises in putts 1 and 2 where the perpendicular force is actually less). Can't really analyze this without more numbers than were given, but probably favors the constant slope case.

 

However, as others have pointed out a golf ball bounces a good bit (particularly early in a putt). So all bets are off WRT the analysis I presented.

 

dave

[GeoffDickson]

Geoff Mangum explains somewhere on his site why a steep slope immediately between you and the hole requires more force. I will have to look for it. I can't recall his break down, but the important take away is that you have to hit putts harder when you have a steep hill immediately in front of you vs closer to the target,

 

My best guess is his argument is that the early deceleration of the ball means that is has longer to travel at a much-reduced speed.

[596]

Putt #1 borders on being against the rules in golf for pin placement unless you playing mini golf as there should be an flat part around the hole.

 

Not actually a rule, but rather a suggestion. One that few of the courses I play heed. The USGA sends out an official and marks the pins every time we have a State or National association tournament. In those cases I'd say 90% of the holes are cut with the 2 foot doughnut of flat or little grade immediately around the placement.

 

The rules don't even state that the hole must be cut on the green. It is suggested as such, but you can really cut a hole in a bunker, on the fringe, in the fairway or in the rough and still be completely legal. The rules of golf are stupid.

[vtnerf]

I would say that #1 would need to be hit the hardest. All three have to rise the same amount. However, during the roll, all of them slow while proceeding along the path. During that, there is less force moving towards the hole. If all 3 were hit at the same pace, or with the same force, #2 would roll out the most since it will climb and complete the work required the soonest, then have a flat surface to continue on its path. #3 will gradually slow, just at a higher rate due to the incline. #1 will decline, but will have less horizontal momentum to climb the hill at the end of it's run, thus requiring more effort from the jump to ensure it will climb the hill.

 

That being said, if you were to play #2 to roll out 18inches past the hole, there's a chance that all of them actually get to the hole.

[JustTheTips]

I would say that #1 would need to be hit the hardest. All three have to rise the same amount. However, during the roll, all of them slow while proceeding along the path. During that, there is less force moving towards the hole. If all 3 were hit at the same pace, or with the same force, #2 would roll out the most since it will climb and complete the work required the soonest, then have a flat surface to continue on its path. #3 will gradually slow, just at a higher rate due to the incline. #1 will decline, but will have less horizontal momentum to climb the hill at the end of it's run, thus requiring more effort from the jump to ensure it will climb the hill.

 

That being said, if you were to play #2 to roll out 18inches past the hole, there's a chance that all of them actually get to the hole.

 

Is there any math behind this or is it just a wild guess? Without friction/air resistance or bouncing, you are basically translating kinetic energy to potential energy

a) Ball 1 rolls fast and then slows down close to the hole as it climbs the hill

b) Ball 2 climbs the hill and then rolls slowly towards the hole (i.e. it lost all its speed going up the hill)

c) Ball 3 just steadily loses speed.

 

Rolling resistance is pretty independent of speed. Air resistance goes with the square so 2s lower speed (i.e. it rolls fast up the hill while the first putt rolls fast all the way to the hill), might allow you to hit it softer but at the speeds we are talking about it might be an unmeasurable difference

 

And in the real world, I am not sure how close grass is to a perfect surface for friction simulation.:)

 

As far as bouncing, buy one of those true roll putters:)

[Forward Observer]

They will all require the same force. Consider a level putt: let's say the force required to roll the ball so that it falls over the front lip is x. Now let's say the additional force necessary to overcome a 6 inch rise is x+y. Let's say that extra force 5%, so on a level putt, the ball will roll 105%, or 21 feet. The angle of the slope doesn't matter, because it will bleed off the faster speed over a shorter distance (#1, #3) or over a longer distance (#2) using the same amount of energy.

[JustTheTips]

They will all require the same force. Consider a level putt: let's say the force required to roll the ball so that it falls over the front lip is x. Now let's say the additional force necessary to overcome a 6 inch rise is x+y. Let's say that extra force 5%, so on a level putt, the ball will roll 105%, or 21 feet. The angle of the slope doesn't matter, because it will bleed off the faster speed over a shorter distance (#1, #3) or over a longer distance (#2) using the same amount of energy.

 

You are making the assumption that the force isn't effected by the speed of the ball. That isn't true. Granted at golf ball speeds we might be talking about differences on the order of fraction of centimeters (i.e. aero drag isn't much at golf ball speed).

[skraly]

Let's say you have three 20-foot putts. Same stimp. Let's say in all cases, the green is flat after the hole. I.e. don't worry about things like the ball running away or anything.

 

Putt 1 travels flat and then shortly before the hole, it rises 6 inches.

 

Putt 2 has an rise of 6 inches right after you hit it, and then travels flat to the hole the rest of the way.

 

Put 3 rises 6 inches gently from the ball to the hole at a constant angle.

 

Question : Do you hit all three putts the same initial speed?

 

Follow up question : What if you have the same 20 foot putt but halfway to the hole the ground rises 8 inches, and then drops 2 inches and then flattens out the rest of the way to the hole. . .same speed?

 

Here's a picture for the "visually inclined". Pretend the "flat lines" are actually flat.

 

 

 

I would say the order from hardest stroke to easiest would be 3:1:2. This is strictly from a stand point of how long gravity has to affect the putt. With #3 gravity is slowing the putt from the beginning. With #1 gravity is affecting the putt only for the last few feet but this is at the same time that the putt is beginning to slow notably so would spend more time climbing that last incline unless hit with more speed at the beginning. With #2 the incline is at the very beginning while the putt is still traveling it's fastest and so would spend less time on the incline and so gravity would have less time to cause it to slow. This is assuming all surfaces have the same rolling resistance and all putts are hit squarely with minimal bounce or hop. Someone had mentioned air resistance as a possible factor. I don't believe that the velocity required for a 20 foot putt is enough that air resistance really comes into play. Several have mentioned the ball bouncing after being putted. That may be a factor as any putt of more and a foot or two spends some brief time airborne after being struck. But unless the green speed is very slow and thus requiring a much more forceful strike or the putt is struck improperly, I don't think that a putt of only 20 feet would have enough bounce to make that a factor. At any rate the exact distance from the starting point of the 2 abrupt rises is not stated with any exactness so we don't really know just how close the abrupt rise for #2 is. It may not be close enough to be a factor for a bouncing putt as any putt of only 20 feet that is struck squarely will only take a couple of small bounces before beginning a true roll. Unless green speeds are quite slow you just don't have to hit a 20 foot putt that hard. Any way, that's my take.

[DaveLeeNC]

They will all require the same force. Consider a level putt: let's say the force required to roll the ball so that it falls over the front lip is x. Now let's say the additional force necessary to overcome a 6 inch rise is x+y. Let's say that extra force 5%, so on a level putt, the ball will roll 105%, or 21 feet. The angle of the slope doesn't matter, because it will bleed off the faster speed over a shorter distance (#1, #3) or over a longer distance (#2) using the same amount of energy.

 

You are making the assumption that the force isn't effected by the speed of the ball. That isn't true. Granted at golf ball speeds we might be talking about differences on the order of fraction of centimeters (i.e. aero drag isn't much at golf ball speed).

 

Rolling friction is a constant over a quite range wide of velocities (assuming rolling rather than a combination of bouncing and rolling).

 

dave

[pingfool]

This may not be the response you want to hear...

 

In 2016 on the PGA Tour Daniel Summerhayes lead the field in Total 1 Putts from 15' to 20'...

 

He made a total of 42 from this range out of 586 opportunities...

 

His percentage was 7.2% from this range...

 

Roll the ball approximately 20 feet, tap in, and move on...

 

Avoid OVER ANALYSIS of any putt longer than 10 feet...

 

this ABSOLUTELY is the right answer - naysayers should listen up

 

the best putter in the world isnt "expecting" to make 20'

 

give it a run...tap it in...and get it closer on the next green

[North Butte]

This may not be the response you want to hear...

 

In 2016 on the PGA Tour Daniel Summerhayes lead the field in Total 1 Putts from 15' to 20'...

 

He made a total of 42 from this range out of 586 opportunities...

 

His percentage was 7.2% from this range...

 

Roll the ball approximately 20 feet, tap in, and move on...

 

Avoid OVER ANALYSIS of any putt longer than 10 feet...

 

this ABSOLUTELY is the right answer - naysayers should listen up

 

the best putter in the world isnt "expecting" to make 20'

 

give it a run...tap it in...and get it closer on the next green

 

Except the original poster did not ask about expecting to make anything or about the best putters in the world or about what he should be thinking when he putts. He asked a hypothetical question about how balls roll over various slopes. Did you not bother to read what he wrote?

[Stuart_G]

You are making the assumption that the force isn't effected by the speed of the ball. That isn't true. Granted at golf ball speeds we might be talking about differences on the order of fraction of centimeters (i.e. aero drag isn't much at golf ball speed).

 

Rolling friction is a constant over a quite range wide of velocities (assuming rolling rather than a combination of bouncing and rolling).

 

dave

 

On a solid surface that's true but grass changes that a little bit. Rolling friction increases as the speed slows down. Now it's apparently been found to only be about a 10% variation in the coeff of friction (in the context of a 15 ft putt) so certainly not a major factor. I would assume the faster the greens, the less the variation, the slower the greens the more it might vary.