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*This post continues our discussion of the mathematics and mechanics of lining up a putt. This post covers some additional considerations: how green speed impacts the results of misalignment; some three dimensional graphs to give better intuitive feel for the effects of gravity and speed on putt alignment. To preview, our next post will cover the final subject — the practicalities of alignment and how math and mechanics helps us understand what might work best and why.*

*Why faster green speeds can compound misalignment*

It may be obvious. Our goal however is to put down solid building blocks and to articulate what seems, in some cases, the obvious.

Let us distinguish between green speed and slope (or gravity) and start with a hypothetical green. I will suppose it is an Alistair MacKenzie designed green, like one that would appear at Augusta National or the University of Michigan golf course. You will note the false front on the right side of the green.

If a green is flat, gravity has no influence. If a green has any slope, there will be a pull of the ball in the downward direction of the slope. It will be in a direction exactly perpindicular to the line of the slope. This has a fancy name in math, called the gradient. Its name transfers over to common usage as the grade of a slope. Here is a good explanation with addition diagrams:

http://en.wikipedia.org/wiki/Grade_(slope). Thank you, Wikipedia.

We are used to reading greens for their grade. In the diagram above, you see some lines. These lines are what are called “level curves.” They are the places on the green where, if one were to walk along the line, one would stay at the same height. It is not difficult to see that the grade is perpindicular to these “level curves.” Our eye tries to estimate the grade at each point on the path of a putt by determining the level curves and then the direction of the grade. Experience in everyday life teaches this. Maybe we learned it trying to pull a sled up a hill in snow in winter. Maybe we learned it climbing up a mountain path, where the path is made to minimize the steepness of the walk one has to take.

Grade, gravity, slope — they are all in some sense the same thing. As we saw in the previous part of this lesson, the steeper the grade – the greater the effect of gravity – the more misalignment can affect our putt. That’s why “sliders” are so dangerous. At the course I play most, the fourth hole is treachorous in that way. Almost any putt has to be a lag.

The graph below shows a couple places where gravity pulls the ball. Note that it pulls it in that direction, but if the ball has momentum in a different direction the ball’s path will be somewhere in between the direction of the pull of gravity and direction of its (forward, if you like) momentum. One can see places on the green where one imagine a ball would not stop if it were going with the grade, and places where the slope of the green is gentle.

*The Role of Green Speed*

Putting on a green without friction is, however, a very different matter than putting on a real green. And this is where we begin to distinguish slope from speed. Sometimes they are confused. Why? The greater the slope, the more a ball speeds up in the direction of the slope. But that depends upon the resistance the ball gets from friction – and it is the green’s friction that slows the ball down – even on a flat green. If there were no friction, you would putt a ball on a completely flat green and it would roll forever unless it hit the hole (yep, forever).

Sometimes we hit putts that seem to roll forever, usually on fast greens. Sometimes we hit putts that seem stuck in molasses, usually on slow greens.

It is a matter of friction. Friction has two affects: it retards the role of gravity and it slows the ball on its current path.

We know all this intuitively – most of us usually don’t separate the two effects out.

One reason is that, in general, courses with “fast” greens also tend to have some “slopier” greens. Courses with slow greens tend to be flatter. Hence, we are confused. The two effects tend to appear to us at the same time, on real life courses.

Friction is increased by moisture (wet or dewy grass); by longer grass; by softer greens (the ground); and it is decreased by dryness; shorter grass; and harder ground. Most are now familiar with the stimpmeter, which attempts to calibrate the speed, not the slope, of a green.

Note one important fact – if one is on high stimpmeter greens, the effects are compounded by slope. No slope or slow greens, either one, will make it easier to putt. Indeed, I prefer fast greens because they tend to be very smooth and easier to roll the ball on. I find I can read and judge putts better. This of course is offset by the fact that these greens tend to be slopier. I still, however, prefer the ability to roll the ball better – I personally tend to be relatively good at reading greens and “ok” at lining them up. (I rush a bit too much often.)

Because friction tends to retard the effect of gravity, it reduces the effects of misalignment (a good thing). Or, to some on difficult courses, the absence of much friction leaves little impediment to the effects of gravity, maximizing the affect of misalignment. In short, the faster your greens, the more careful you have to be in lining up your putts; the slower your greens, the more likely you are to make or miss by a small amount a putt that wasn’t aligned well.

*Illustrative Graphs: Riemann Surfaces for Golfers Aren’t So Hard*

We will close out this post with a discussion of a somewhat more complicated version of the hypothetical green above.

Riemann Surfaces? Are you serious? Hey, it’s an “A. Einstein” post. But read on….

Here is a topological map:

This completes the picture. The picture above is just an overhead view of the three-dimensional view (the Riemann surface in math terms) we had above of our Alistair MacKenzie green (which mathematicians, with a bit of work, call a Riemann surface in complex analysis – but let’s not go there — the editors might delete the post, and we can’t have that, can we?)

Added to the standard topological map are some arrows. These arrows show the direction of gravity’s pull. Note that they are always at a right angle to the direction of the slope of the green. The length of the arrow shows how “hard” gravity pulls – that is, how steep the green is at that point.

A stimpmeter tells one how far a ball will roll from an inclined plane of a certain length (defined by the USGA – hey, if you think Riemann Surfaces are tough, try convincing the USGA that they’ve made a mistake …. now that’s tough! …. beyond my ability to even comprehend!!) Golf courses have noted that one difficulty with a stimpmeter is find a level surface on a course. Another is find a “representative” level surface – because we’ve seen that many things effect golf.

A better approach, as this post’s foundations show, would be — given that the stimpmeter was invented 80 years ago and we’ve learned a lot since then, I think — to measure the roll of the ball from a stimpmeter, in feet, from several places on the;greens of a golf course. Make it a “sampling.” (Hasn’t the USGA heard of polling?) If one took five places on the course where the green was flat, using a surveyor’s tools; five places where the incline was about 4 degrees; five places where it was 8 degrees; five places where it was 12 degrees; five places where it was 16 degrees; and, if extant, five places where it was 20 degrees; one would get a very accurate picture of the “speed” of the greens on a course, as the golfer experiences those speeds during the course of a normal round.

I will put the USGA’s address below for anyone who wishes to attempt to contact them. [1] What comes to my mind: wise men fear to tread … Fair warning.

*A. Einstein*

References:

[1]

The United States Golf Association

P.O. Box 708

Far Hills, N.J. 07931

908-234-2300

Fax: 908-234-9687

While it’s certainly true that the 17th green is treachery, and it’s overshadowed by the other traps for the unwary golfer (and even the wary golfer), your picture is not that of the Road Hole, and it looks nothing like the Road Hole, other than the dogleg right.

Interesting. If wrong, I’d better correct it. It was so labeled. Thank you.

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Sure looks like the famous Road Hole bunker to me. By the way, the Road Hole is a dogleg LEFT.

Mark, Would you kindly withdraw your comment. I don’t mean to be rude and reject it, but I think you are confused – I am not sure how. The road runs along the right side of the hole, as the hole dog legs left, deep. The bunker is on the left side of the green, leaving a short-sided shot with a pin placement as pictured. This is exactly what the picture shows. It is what it says it is. I am a bit unsure what you are therefore trying to say.

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Love the Ryder Cup. Wish I could be there. Will watch. I had planned to attend, but can’t it turns out.

“One reason is that, in general, courses with “fast” greens also tend to have some “slopier” greens. Courses with slow greens tend to be flatter.”

This comment is false.

Greens are maintained to provide the best experience to the golfer. This means that all agronomic and playability factors are considered. There are no “in general” rules in terms of slope and speed to be applied.

In fact, many older courses were designed with slopier greens because turf maintenance practices of the day resulted in what we consider today as slow greens. If you employ modern techniques on those greens, the combination of slope and speed make them practically un-puttable. Therefore, the superintendent is forced to “back off” and slow his greens to allow a better golfing experience and pace of play.

In contrast, you can find many modern courses built with less slope anticipating that the variety of turf planted will be a modern variety more tolerant of lower mowing heights. It will also be maintained at a much greater intensity resulting in higher speeds. Thus making the more moderate slope have an proportionally larger effect on the putt due to the speed.

A golf course having fast or slow greens is more a factor of the budget and or expectations of their membership than the relative slope of their greens. A “mom and pop” golf course, regardless of the slope of their greens, simply cannot afford the maintenance practices required for fast greens. Conversely, a high end private club can afford to have fast greens and they often do so independent of the slopiness of their greens. Fast greens are incorrectly considered “better”.

The best golf courses are those that value playability over any perceived “fast’ or “slow” green. They take into account all their agronomic and design factors to give the golfer an honest test of their golfing abilities.

Additionally, the proper method for using a Stimpmeter is to not only roll balls in one direction but to then reverse and go in the exact opposite direction on the same line. Then you take an average of the distances rolled. This effectively accounts for any slope of the green. You still want to find a surface that is as flat as possible but even if it is a little sloped in one direction by rolling both “uphill” and “downhill” you can measure the green speed.

I think I gave a lengthier reply.

Your comment as a whole is a good one; your initial sentence is itself demonstrably false.

In addition I note that your very last paragraph is not accurate either. It does not “effecitvely account[] for any slope of the green.” I have no idea who developed the protocol, but the protocol is a bit like measuring, twice, the wind speed at the time of a lull and then reporting to metereological services that the average wind speed in your area is the average of the two measures. It is misleading at best, and very poor science.

As I’ve said, the golf community lacks a rigorous, yet simple, group of people to add light to these problems. That is part of the goal here. When folk write down things that are simply misguided, no offense, we will point that out with appropriate strong words.

Some of what you say is very interesting factual background; your conclusions are so far off base as to be “part of the problem,” not “part of the solution.” But then we don’t expect those who have vested interests, like the USGA, to like what we say here.

Rather, we are trying to help teaching pros, touring pros, serious amateurs, and most of the rest of us.

By the way, I don’t consider fast or slow greens better for that reason, myself. I like greens where the ball rolls smoothly and which are fairly fast. That is my personal taste. There are limits to that taste. As you note, I’ve played some courses built around 1900 or 1910. The slope is steep. When the greens are fast, some putts even from 6 feet, have to be lagged. In general I just accept what I, myself, am given.

The post however focuses on how green speed (different than green slope) affects alignment.

I do appreciate the comment. It is a very detailed and informative one. I do not think we have different views except that you took issue with a generalization – which is just about averages, not particular cases. My experience tells me that. Until they begin to employ the stimpmeter in the way I suggest, there will be no good way to compare courses.