A Physics Puzzle - Uphill vs. Downhill Putts

So I was thinking about the difference between uphill, level, and downhill putts. I found this paper , and decided to make a quick simulation. You give it stimp, grade, and putt speed, and it finds the rollout of your putt.

Here's the puzzle:

I'm on a green where my level putt rolls 12ft, and my 4% grade uphill putt rolls 7.5 ft. How far does the same putt go if it's hit down the 4% grade???

Hint: the stimp is 12 (Augusta National?).

Any guesses?

19.5 feet

It's all about gravity, size of ball, friction of the grass, temperature and humidity, angle of the dangle, and so forth. And about 11 feet past the hole, there you will find the ball.

Too lazy to look it up.....can you show your work?  Thks!

College physics was a loooooong time ago.

12ft + 7.5ft = 19.5ft

No idea what the answer is, just trying to throw out what seems to me a logical possible answer to the question.  The uphill putt stopped 4.5 feet short of the hole.  So I assumed the downhill putt wouldn't stop 4.5 feet past the hole, it must be more because of the downhill.  I didn't think it would go double the distance, so I just added the two lengths of the other two putts. IDK

Is there a conveyor belt involved?

How much grain?  Which way is the grain?  Most of the time the grain will lean downhill, thus increasing the speed of the downhill putt even as it kills the pace on the uphill putt.

If a putt goes 7.5 feet uphill, and goes 12 feet on level ground. Then that is a 4.5 feet difference. Since potential energy is the same, downhill versus uphill, if you hit the same initial speed, your looking at the putt going 16.5 feet.

Hmmm...4% grade. 12 on the Stimp. Hit the putt with the same force as a 12 foot level putt.

Answer: Until it hits the fringe or the rough on the other side of the green (however far away that might be). Ha ha!

Calculated from hole number 4 at the course in Trenton Ga. Probably about a 4% grade that if you hit the ball hard enough to go a foot on level ground you might as well go back to the bag and get your wedge for the next shot, because you're not going to be putting. If you just touch the ball enough to move it an inch you might get lucky and only have a 5 footer back up the hill for the next putt.

Uphill you have two things stopping the ball. Gravity and Friction. Without friction it would eventually stop and come back the other way.

Downhill only friction is acting on it. Obviously without friction it would roll forever much as it does at the Masters at times.

The point is it will not roll past the hole downhill the same distance it stopped short uphill.

Don't have the exact numbers right now. I'd have to dust off my slide rule. Who am I kidding, I mean my TI-86.

29 feet

Stimpmeter downhill, St(dn)

St(dn) = 0.82 ft / (CF - sin Φ cos Φ)

12ft St CF = 0.82 / 12

You say that jokingly, however, I don't think you are that far off.  When I took my Aimpoint class I learned that 4% is basically the steepest a green can be where a ball will sit.  Anything steeper than that and you have "rolloff."  I have no idea what the actual answer is, but I would suspect it is way higher than any of the answers given so far.

I also think that there is not enough info to get the answer.  Like Hendog said, gravity and friction are the only outside forces acting on it after the putter hits it.  I think we need to know the friction factor of the green to figure it out.

My wild guess ... 45 feet.

How close are we to Lake Merced?

Seems like we should be able to calculate friction since it's the only unknown in the uphill putt scenario. I.e., gravity is a constant, % grade is a constant (at least we're assuming it is), and we know initial speed and total distance - so we have an algebra equation with friction as the only unknown. Also, friction is basically stimp, which has been given.

Interesting... we have answers ranging from 16.5 ft to ball-rolls-forever.

I had this idea because I recently realized how I always go long on downhill putts, but I'm rarely short on uphill putts. It not obvious to me how much I need to change my stroke for an uphill putt vs a downhill putt, as compared to a straight putt of the same length.

I posted this as a fun experiment so people could give a general guess as to what as to what an steep-ish Augusta green might do. I linked the paper, so anyone could work it out if they really wanted to, but that wasn't really the intent. Maybe I'll wait til tonight to post the simulation result.

Why, yes. Actually I forgot to mention this "green" is inside the cabin of a lifting off 747!

The equations assume grain has no effect...I'm just going by what the simulation spits out.

Like sacm3bill said, everything you need to know about friction should be wrapped up in stimp. When you roll the ball down the stimpmeter on flat ground, it goes 12 feet. That tells you how much friction there is.