Entering the ‘Drop Zone’
Dr Paul Hurrion

We hear it all the time, don’t we… As a player prepares to roll a birdie putt from mid-to-long range (10 feet and out), the commentator reminds all of us at home that in order to have the best chance of making the putt it has to be rolling at a speed that would see the ball finish 18 inches beyond the hole should it miss.

Well, maybe this is not entirely true… I have been recently been conducting new research into this theory, in part due to the new developments of the Quintic Overhead Putt Tracker.   The software tracks the complete path of the golf ball throughout its journey, measuring parameters such as ball speed, aim location, start direction, apex, point of true roll, total distance and the all-important ball entry speed.

In order for a player to hole a successful putt they must understand the various factors which alter the deceleration rate of the ball. Based on the understanding that the ball-surface relationship is what provides the frictional properties, it is critical for a player to understand how the various types of playing surface may affect this ball-surface relationship. For example, a grainy green may have a higher coefficient of friction than a non-grainy green. Different types of grass (Bent, Fescue, Ryegrass, Bermuda, Zoysia, Poa Annua…) will also have various frictional properties, such as coarser fibres, leading to an alteration in ball behaviour.  The length at which a particular type of grass is cut and the density of the grass will also influence the ball-surface relationship. In addition, the slope, moisture levels and even wind strength and direction can alter the ball-surface relationship and should be considered by the golfer before committing to a line.

The optimum entry speed of a putt is often significantly slower than we are all led to believe, and largely dependent on the amount of break. The reasoning is simple: the faster a ball is travelling, the smaller the effective size of the hole becomes and so the more accurate you need to be to set the ball on the perfect line. Given that it is easier to control the speed of a rolling ball than the precise angle of the putter-face at the moment of impact, one such method of putting is to focus on ‘dying’ the ball into the hole, therefore reading maximum break. One of my long-time students, Padraig Harrington, has always been one to die the ball into the cup (for mid to long-range putting) and much of the time we have spent on the putting green revolves around adjusting the ‘reading’ of the putt to maximise the effective size of the hole as the ball approaches. As a result, the entry point of the hole moves around the clock face according to the severity of the slope. At drop-in speed the ball is obviously going to take more borrow than a ball entering the hole at 2 mph. Visualisation of the balls path and entering the hole from the higher side due to its dead weight speed is a skill that requires practice.

Choosing the correct speed is vital in order to work out your intended line. Where does the ball enter the hole? To help with the visualisation of the true break of the putt, I would always encourage a player to visualise a clock face – at which point does the golf ball enter the hole? A key point here is to not stop visualising at the front lip of the hole – continue through and even out of the back of the hole! This is one reason why I love to use ghost / phantom holes (plastic disks that replicate the size of a golf hole that you can move around the green surface) because you see the entirety of the putt, unlike a real hole, where, although you have the satisfaction of seeing the ball drop, you don’t get to view the end position of the ball.

In the example above (Captured from Quintic Overhead Putt Tracker www.quinticballroll.com), the ball is entering the hole at 7:00 (212°) and speed of 1.46 mph, but how far past would it have gone?

In the example 12 putt shown above, (Putt 17) the ball enters the ghost hole at 7:00 (207°) with a ball speed of 1.08 mph. Note the green line that depicts the ball’s trajectory and how it changes abruptly after passing through the ghost hole. It follows the slope of the putting surface as indicated by the small green arrows (3% Left to Right, 1% Uphill).  The ball finishes 7” away from the middle of the hole.

In a subsequent putt (same start putt location – Putt 18), the ball enters the hole at 6:30 (200°) with a speed of 1.29 mph (An increase of 0.21 mph). Note the subtle difference in the trajectory. The ball has finished 15” away from the middle of the hole, despite having a lower impact ball speed.

The above image has both putts displayed simultaneously. There is only 0.13mph difference in impact ball speed. It is interesting to note that Putt 18 (Orange trajectory) was hit with the lower impact ball speed, (5.78mph), but is actually going faster at the hole, as a difference of 1.46 degrees or 3” higher in the start line, means the ball is travelling up the slope for longer. The ball with the higher start line  (-22”) has an apex of 10” compared to the lower start line (-19”) of 7”. Ball speed influences the line required to make a successful putt. As both putts were holed, it is interesting to note how just 0.13mph impact ball speed and a 3” difference in start line can affect the ball’s path, ball entry speed and finish position.

On a 15-foot putt, a deviation of less than 0.5° in the angle of the putter-face is all that’s required for you to miss your line and the hole – you’d have to be a robot to believe you could consistently keep the face dead square to your starting line! What’s more, if you are someone who likes to roll the ball at pace (the “18 inches beyond the hole” approach), you are effectively shrinking the hole to less than a third of its actual size! You can read more on this previous research at the following webpage: https://www.paulhurrion.com/tuition/an-investigation-into-golf-ball-speed-at-hole-entry/

Therefore, it would suggest that the odds of success are considerably greater if you focus on rolling the ball at a speed that would see it travel perhaps just three or four inches beyond the hole (should you miss), provided you read the full extent of the break.

The above image is taken from Quintic Ball Roll v4.4. The putter face angle was measured at 0.59° open at impact. 15ft is the maximum distance the ball has the possibility of being holed at dead weight.

The science proves the argument. For example, if you are facing a 10-footer on a 3% uphill slope – for the ball to finish 30cm (12 inches) past the hole, the speed of the ball at the point of entry is 180% faster than the pace of the corresponding putt downhill.  At this entry speed the hole is effectively three quarters of its actual size, and that’s a lot to give away.

The diagram above highlights the effective size of the hole for the “30cm or 12” past the hole for both uphill (6 o’clock entry) and downhill (12 o’clock entry). The hole is a lot bigger when coming downhill as the ball is moving slowly! You effectively have 96% of the hole to play with on a putt that is travelling so much more slowly.  Interestingly, on a FLAT putt, to finish 30cm past the hole (Stimp 10) you only have 87% of the hole size available.

If you are 5 feet away and a little unsure of the break, then you might decide to take the risk and stroke the putt a little more firmly. But be aware that the harder you hit it, the smaller the effective hole becomes. The ball won’t drop in even if rolls over the perfect centre of the hole above 3.64 mph (1.63 m/sec), The Physics of Putting, A.R. Penner (February 2002) Canadian Journal of Physics 80(2): 83-96.  There may be a chance it hits the pin dead centre and drops in, but you would have to leave the flag in for that… and that’s a different debate entirely.

The image below is from R. Chiono, (www.roechigolf.it) and gives a fantastic visual description of the how different entry ball speeds behave as they reach the hole.  Above 2.90 mph or 1.3 m/sec the ball doesn’t have time to drop sufficiently under gravity. The equator of the golf ball hits the opposite side of the hole. At 3.64 mph (1.6 m/sec) the ball may still potentially have a chance, but a very slim with no flag present.

Ok, now for flip side of the argument, because I would argue statistically, we don’t hole more downhill putts? If anything, if you had to choose a spot on the clock face to hole an 8ft putt for a tournament win, most players would choose an uphill, slightly breaking (inside the cup) putt. Hopefully, the next part of the article may explain why they do this…

There are four phases to the ball’s speed during a putt: Launch, Sliding, Rolling and Decay.

Phase 1 – Launch: (Smallest Distance covered by the ball). Projectile equations of motion can be used when a ball is in flight. Quintic Ball Roll measures each individual frame, calculating both the Ball Launch angle and the Flight angle. Anything more than 1 degree difference would indicate surface interaction and the ball being trapped into the surface. During the ‘Launch Phase’ essentially there is little or no change in ball speed. In the example below you can see for the first 3” the ball speed is constant (4.65 mph). The ball is airborne (no contact with the surface to slow it down) as a result of a positive 3.00° launch angle. However, on landing, the ball speed typically takes a significant drop, before entering the sliding/skidding phase.

Phase 2 – Sliding / Skidding Phase: This phase is a combination of sliding and rolling. Remember the ball doesn’t suddenly go from 0% rotation to 100%. As the ball is increasing in angular rotation (forward spin) caused by the friction and interaction with the putting surface, its linear (horizontal) speed is decreasing. The point at which the rotational speed and linear speed are equal is the point when the skidding (slipping) stops. At this moment, the sliding frictional force disappears and the third phase begins: Rolling. The sliding frictional force is different to that of rolling friction. We know that a golf ball will decelerate at the quickest rate during the sliding / skidding phase.

Phase 3 – Rolling: This is the largest % of the ball’s journey. The Rolling resistive force is a constant force which is determined by the deformation of the surface, but independent of the velocity of the ball. An example of the deformation of the putting surface would be the grass height. Energy is lost due to the rolling friction (essentially the ball flattening the blades of grass).

Phase 4 – Decay Phase (Unpredictable Rolling): As the angular rotation of the golf ball begins to slow down, so does the linear velocity. There comes a point (depending on the surface, gradient) where the ball no longer has the momentum to continue and flatten the blades of grass. At this point, the ball has a sudden drop in speed. During the ‘Decay Phase’ the golf ball is very unpredictable – you can often see marked deviations in the ball’s path using the Quintic Overhead Putt Tracker. We have all played golf and had a putt tracking to the hole, only at the last second to deviate unexpectedly as the ball runs out of pace. It is interesting to note that the ball speed when this ‘Decay Phase’ begins is approximately 1mph across numerous types of putting surfaces.

Example Putts:

1) Dead Weight (Ball finishes on top of the ghost hole)

In the example above of a dead weight putt, the ball comes to rest directly on top of the ghost hole. The images highlight the position of the golf ball when the start of the ‘Decay Phase’ begins. The Ball Speed is 1.12mph at the start of this phase, but there is still 12” of the ball’s journey to go. The last 12” of the ball’s final journey is unpredictable and at the mercy of any green imperfections, especially evident on poor, bumpy, grainy greens…

2) Ball finishes 10” away from the ghost hole

The images highlight the position of the golf ball at the start of the ‘Decay Phase’. The ball is going to miss on the low side, but interestingly the Ball Speed at the start of the Decay Phase is 1.12 mph. There is still 12” of the ball’s journey to go. The ball finished 10” from the hole.

3) Ball finishes 34” away from the ghost hole

The images highlight the position of the golf ball at the start of the ‘Decay Phase’. The Ball Speed is 1.11mph at the start of this phase. However, in this example the ball has already passed the hole. The ball was still in the rolling phase as it passed the hole and ultimately finished 34” away from the hole.

4) Ball finishes 52” away from the ghost hole

The golf ball has not reached the start of the ‘Decay Phase’.   In the example above the ball speed at the hole is 1.94 mph. The ball disappears out of shot still at 1.27 mph. The final end position was 52” away from the hole. (This was measured manually as the ball disappeared out of the camera view)

5) Ball finishes 10” away from the ghost hole: In this example, the start of ‘Decay Phase’ occurs just as the ball is entering the hole. The golf ball is still in a predictable phase of its rolling and is maximising the size of the hole.

Is this the optimal ball speed to enter the hole for this particular putt?

6) Maximum possible slope. In the following example using an indoor Zen Green Stage (https://www.zengreenstage.com/) the angle of the stage is set to a 4.5° Right-to-Left planar slope. Any greater than this and the ball would not come to rest (this is known as the ‘angle of repose’, the steepest angle at which a sloping surface formed of loose material is stable). In practical terms, if you increased the slope of the platform to 5.0° it wouldn’t be possible to place the ball still on the surface – once you let go it would begin to roll away… The ‘Decay Phase’ in this example begins at 0.91 mph. Notice how the gradient shallows out on the ball speed graph at this point as the ball is slowly trickling down towards the hole. The ball still has an unpredictable path, even on an indoor artificial carpet, for the final 3’ 8” of its journey. Eventually, the ball comes to rest 13” past the hole. The ball was moving for a total of 8.31 seconds for a 12ft putt. Interestingly, 4.7 seconds of the putt’s journey occurred when in the decay phase (57% of the time taken).

Summary:

• Ball speed is a key component in order to putt successfully. Pelz, (2000) suggested that 80% of putts were missed due to poor speed control, highlighting the importance of understanding this relationship for any golfer.
• Rojas, 2004 stated the ball decelerates linearly until a threshold is reached, and the ball stops dead. Rojas & Simon, (2014), state that once kinetic friction disappears (when the ball begins rolling) there is a linear deceleration until the ball reaches a threshold, where it ceases to travel. However, research provided by the Overhead Putt Tracker would suggest the ball speed is not linear.
• Aiming to leave the ball ‘dying’ in the front edge vs 1 foot or even 2 feet past the hole has a marked effect on the required ball speed, start line and effective hole size, particularly when putting on a slope.
• Entry speed and direction needs to be specific to distance, slope & stimp and may also vary depending on a person’s preference and style of putting (dead weight, 12”, 18″ or even 36″ past the hole)
• Remember, once the ball drops below 1 mph it becomes very unstable and unpredictable. The speed drop off is significant. The ball no longer has the angular momentum and energy to stay on top of the surface. It is at the mercy of any imperfections in the putting surface.
• Future research is going to focus on different slopes, grass types, moisture, grain and length of grass to measure ball speed at the start of the decay phase.
• Moving to the real world and how to implement this into practice and coaching: What is 1 mph on the putt you are facing? Should you be aiming to achieve 1 mph just as the ball enters the hole rather than a set distance past the hole? 1 mph ensures the ball is still in true roll and maximises the hole size.
• However, at 1 mph on stimp 12 with a 3% downhill, the ball could easily run 4ft by the hole! Do you want to have a 4ft return putt? Especially if there is a degree of break on the return putt? Therefore, in order to finish 12” past the hole, the golf ball will be in the unpredictable ‘Decay Phase’ prior to reaching the hole. There is now a trade off! Predictable roll vs distance past the hole – the player must decide…
• 1 mph ball speed on my indoor surface (Level) in the putting studio travelled 0.65m (26”) Stimp 15.
• 1 mph ball speed on an outdoor putting green (Bent Grass, Level) travelled 0.3m (12”) Stimp 9.5.
• 1 mph ball speed on an outdoor putting green (Bent Grass, 3% Uphill) travelled 0.15m (6”) Stimp 9.5.
• Golfers should be encouraged to visualise the curve of the putt and how their speed will affect that curve. Optimise the effective size of the hole and entry point in order to give the best chance of holing the putt.
• Don’t always try to finish a set distance past the hole – work out what 1 mph ball speed will do to the distance travelled for the putt you are facing!

If you have any questions or would like to add your input to the article, please email info@paulhurrion.com  Thank you.