You’ve just got one problem. You stand too close to the ball after you’ve hit it.
– Sam Snead
This post is an addendum to the post “The Faster You Putt, the Smaller the Hole.” We explain lip outs. It is a somewhat obscure topic itself but it does help shed light on whether it is better to attempt to die a putt at the hole or, as one learned golf expert suggests, intend to putt it 17 inches past should it not drop. At the end of this post, we will show some calculations that give one some idea of how fast a ball needs to be going, if heading for the dead center of the cup, to end up bouncing over the cup.
The first picture shows a ball near the lip. As subsequent pictures will show, it looks like it hangs over the lip more than it does. What would cause this putt to drop to the bottom of the cup, or leave it on the green?
If we know the ball is where it is in the picture, not surprisingly, two variables will determine whether it falls into the cup. One is its direction (in mathematical terms, the direction of its velocity vector), and the other is its speed (the magnitude of its velocity vector, in mathematical terms).
We have discussed in the main lesson how, if the ball has lost all velocity at the point that we see it in the picture, then it will fall if (as is barely true but may be hard to see), its center of mass is over the edge of the lip of the cup.
A Moving Ball
Example 1: As most of these things go, it is easiest to see what will happen by taking an extreme case. For direction, we have three consecutive pictures below, taken from directly overhead. If the golf ball is moving at an angle away from the cup, it won’t drop. Momentarily passing over the edge of a cup is not enough time for gravity to pull the ball into the cup … and that is what is happening when a ball drops … gravity is accelerating it downward at that (familiar to physics students) 32 ft per second per second.
Example 2: If as in the second picture, the ball is headed directly for the center of the cup, and it is moving just ever so slightly, its center of mass will move farther over the edge of the cup and gravity will pull it down to the bottom of the cup. This is no surprise, but we often miss the obvious when trying to understand a more difficult example.
Example 3: If as in the third picture, the ball is headed at an angle just slightly inside a tangent to the lip of the cup, the speed of the ball will determine if it falls. True enough, the center of mass will move farther over the edge of cup then as pictured. However, the edge of the cup is circular. As a result, the ball will want to continue to move in that direction and might again find itself on terra firma. Whether it makes it to terra firma depends upon whether its downward velocity is sufficient to pull the ball down enough that, together with hitting the edge of the cup (because the ball has been pulled down a little below the level of the putting surface), it will be stopped and drop into the cup. (Each overhead shot is from exactly the same perspective; the angle at which it is shown differs.)
If the length of the arrows represents the speed of the ball — longer meaning faster, shorter meaning slower — it is fairly easy to see that the first two balls will not drop, and it is harder to see what will happen in the third example. Will the speed of the ball along the surface of the green be great enough to overcome the pull of gravity and the ‘speed bump’ that the lip will create when the ball, having been pulled down a bit below green level, hits it as it attempts to move in the direction of the arrow in Example 3.
Why do putts “lip out”?
We have technically described why a putt may not drop even though its center of gravity passes over the cup. Obviously, if it is moving too fast for its center of gravity to be over the “cup” for long enough to pull it down, it will not fall to the bottom of the cup. A more interesting question is why does a ball putted in one direction rotate around the cup and seemingly come back at you? An even more difficult question is why does the ball appear to start to drop (go down) and then come back up?
The first question is fairly simple. When the putt in Example 3 strikes the lip, it is like a cue ball striking the edge of a pool table. Its energy, or momentum, will be redirected. One, if one knows pool and how firm the ground is, can figure out the angle at which our ball will bounce off the lip. The way this works in golf, because the ground is a bit softer than the slate of a pool table, and the angle at which it strikes is usually fairly severe (because the edge is curved, and not straight), AND because the ball drops below the lip a bit, hitting the lip will cause it to spin around the edge of the cup. The slower its speed, the more likely it is to drop (since gravity has an opportunity to pull it down for a longer period of time at 32 feet per second per second).
The second question is also not as difficult as it seems. In fact, any time that a ball “lips out” its center of mass will have dropped below the level at which it would be were it sitting on the ground. Some part of the ball will be below the edge of the cup. How much of the ball goes below the edge of the cup will determine how visible that effect is to the eye. In those cases that are most visible, and when the ball does not drop, it is because the speed of the ball coming into the lip of the cup was fairly fast, on a relative basis. (There is in all these cases, something of a sling shot effect. it is just most visible in those cases where it appears the ball was about to drop . . . when our inability to “see” the angular momentum or spinning of the golf ball made us not realize that the ball had not a chance.)
We illustrate in Examples 4a and 4b how the relative speed of the ball versus that created by gravity will determine whether the ball drops.
The ball that bounces over the cup
Finally, let’s try to see how fast a ball must be going, on a flat green, to bounce over the cup. We know the cup is 4 inches wide, the ball is about 1.65 inches in diameter, and acceleration due to gravity is 32 ft/sec/sec. We will make one assumption — that the ball will drop if it strikes the lip on the far side at a point that is 45 degrees below its equator on the theory that this is the point where the amount of the balls momentum that is directed more down/backward than up/forward.
This means that the ball will bounce over the cup if it is going fast enough so that it drops approximately .4124 inches in crossing the 4 inches of the cup. There are equations in standard college physics texts that will tell us how long it takes gravity to pull something down .4124 inches (those equations will also tell us the downward velocity but we are interested in how long it takes).
And the answer is . . . that it takes just a bit over .16 seconds for gravity to “drop” an object by .4124 inches. That means that the ball must travel 4 inches in .16 seconds. That translates into 2.076 feet per second, or just 1.42 miles per hour. Two feet per second sounds pretty quick … you can cover 4 inches in, well, .16 seconds, or a bit less than 1/6th of a second. That’s “green fast” but it’s not very fast at all. (The problem is a bit more complicated than presented. We do not know the elasticity of the dirt that makes up the edge or lip of the cup, which will determine how much of the ball’s momentum it absorbs and how much must be redirected in the ball. We also do not know the rate at which the ball is spinning (or rolling) — that is its angular velocity, rather than just its linear velocity. This will also affect the answer. I mention these factors for those ‘purists’ who are reading this more as math and physics than as golf.)
Moral of the story: it doesn’t take a lot of speed when the ball gets near the cup for it to lip out or bounce right over it.
We are getting closer, bit-by-bit, to the question: to die the ball at the hole or to give it enough to go 17 inches by the cup?