How predictable are sloping lies?

This report will outline how this study came about, how it was conducted and an analysis of the findings from the four slopes; the two side slopes, the uphill slope and the downhill slope.

Reasons My reasoning for making this study is: I knew the effect that the various slopes had on the both the ball flight and trajectory; I also knew the ways in which I needed to adjust my setup to get the best possible results from them. However, I wanted to know, if each of the slopes had the same degree of tilt, would the difference in the flight or the trajectory change by the same amount for each slope. Procedure To make this study it was vital that the four slopes were the same. The only way to guarantee this was by having one slope and using it in all four directions, and I chose to use 7° tilt (7.2° to be exact) as I felt that this was a slope of medium severity. There was however one exception, the downhill slope. For this series of shots this one slope was used to stand on to play the shots but the ball was not placed on it. The reason being that because the slope was solid, TrackMan could see the flight of the ball without any problems but not the impact and therefore could not give most or any of the club data. I solved this problem by building a second slope, to the same specifications (0.25° more) out of PVC plastic, which allowed TrackMan to see through the slope and for it to give all club and ball data. I followed the setup procedure as TrackMan recommends, the TrackMan was placed at the Height of the ball in each situation and each time the TrackMan was level to the horizon. This means that the TrackMan was never level to the slope, this allowed me to see the difference in the data between the slopes and the flat. For all the shots, I used new out of the box Callaway Chrome Soft balls and the same three clubs: an 8-iron, a 6-iron and a 4-iron from the same set and were checked to have standard lie and loft.

Method To begin I hit ten balls from the flat with the 8-iron, 6-iron, and 4-iron, and these would serve to be my baseline throughout the study. I then proceeded to hit thirty shots from each slope, ten with each club, the only exception was the downhill slope. When hitting from the PVC slope I needed to hit more than the thirty shots as all the data didn’t arrive every time, whether it was because the slope bounced with the impact of the shot or whether it was because TrackMan didn’t believe the numbers and so it didn’t report them. I made a conscious effort to swing comfortably and in the same way each time. I felt that this was important to the study as I wanted to see what the true effect of the slopes are and by swinging at my normal speed I felt that it would allow for my hands and body to make corrections and compensations, making the data inconsistent and void. Analysis For the analysis, I have removed the bad shots and I will discuss them separately. I will also make two groups for the slopes, one with the two Side slopes and one with the uphill and downhill slopes. I will do this so that a comparison can be made between the slopes that relate to each other. Normalization Throughout this study normalization has been used, and when it has been used it is clearly marked. The settings are as follows: 0 meters of altitude and 25°C.

Side slopes The key numbers here are: Launch Direction, Spin Axis & Side. Flat I feel that it is important to begin with the numbers from the flat, as this is the baseline for all the other numbers to come. When we look at the averages of the three clubs, the balls are launching less than half a degree left of the Target Line, have a very small amount of Spin Axis and are finishing less than two and half meters from the Target Line. This is however only part of the story; we can see from the photo to the right there were shots that landed both left and right of the Target Line. When we look at the individual shots there was only three out of twenty-six shots (11.54%) that launched more than 1.5° from the Target Line; there was only three shots (11.54%) that had more than 3.5° of Spin Axis; and only four shots (15.38%) that finished more than 7.5 meters from the Target Line.

Side Slope – Ball Below Feet

If we start by looking at the beginning of the balls journey, the Launch Direction, we see that the balls are launching on average between 1.6°-2.0° to the right of the Target Line, which is more than 88% of the shots from the flat. In fact, only 21% of the shots selected started less than 1° to the right of the Target and more than half of the shots started more than 1.5° to the right of the Target Line.

	Flat Launch Direction	Ball Below Feet Launch Direction	Difference
4 Iron	-0.4°	1.6°	2.0° More Right
6 Iron	-0.1°	2.0°	2.1° More Right
8 Iron	-0.1°	1.7°	1.8° More Right

Then when we look at the second part of the flight we can see that the averages of all three clubs have a positive Spin Axis: 4.6°, 1.9° and 2.2°. Nearly 74% of these shots had positive Spin Axis whereas there was less than 46% of the shots from the flat that had positive Spin Axis and when we look at the Face-to Path, every shot played from the slope had a positive Face-to Path so we could say that the shots that didn’t have the positive Spin Axis were the result of a non-centered strike and in these cases, they were struck slightly on the toe.

	Flat Spin Axis	Ball Below Feet Spin Axis	Difference
4 Iron	-2.1°	4.6°	6.7° More Positive
6 Iron	-0.7°	1.9°	2.6° More Positive
8 Iron	0.7°	2.2°	1.5° More Positive

The third and final part to the flight is to see how far did the shots land from the Target Line. The average Side with the Non-Normalized data from the three clubs was between 9.9 and 15 meters to the right of the Target Line, the smallest amount was + 3.4 meters and the most was +25.4 meters. However, when we Normalize the data we see that the Side averages drop to 6.8, 7.3 and 11.1 meters to the right, with the furthest shot to the right finishing 17 meters right of the Target Line.

	Flat Side(m) Non-Normalized	Ball Below Feet Side(m) Non-Normalized	Difference Side(m) Non-Normalized	Flat Side(m) Normalized	Ball Below Feet Side(m) Normalized	Difference Side(m) Normalized
4 Iron	2.3 L	15.0 R	17.3 More Right	4.6 L	11.1 R	15.7 More Right
6 Iron	1.9 R	12.8 R	10.9 More Right	1.3 L	7.3 R	6.0 More Right
8 Iron	1.3 R	9.9 R	8.6 More Right	0.6 R	6.8 R	6.2 More Right

Side Slope – Ball above feet

With the second slope in this group we will also start by looking at the beginning of the flight, Launch Direction, and working forward. We can see that with all three clubs the balls are launching to the left of the Target Line, their averages are: -1.1°, -2.1° and -2.6°. What is interesting is that 100% of the shots played from this slope had a negative Launch Angle, whereas from the flat there was less than 54% that had a negative Launch Angle. With the 4-iron from the flat there was only one ball (14.29%) that launched more than -2°, whereas more than 83% of the shots from the slope did. With the 6-Iron from the flat none of the shots launched -2°, whereas more than 57% of the shots from the slope did. With the 8-iron from the flat only one ball (11.11%) launched more than -1°, whereas more than 57% of the shots from the slope did.

	Flat Launch Direction	Ball Above Feet Launch Direction	Difference
4 Iron	-0.4°	-2.6°	2.2° More Left
6 Iron	-0.1°	-2.1°	2.0° More Left
8 Iron	-0.1°	-1.1°	1.0° More Left

With the second part of the flight, the Spin Axis, we can see that all the averages of the three clubs have a negative Spin Axis: -6.3°, -2.2° and -5.4°. The amount of shots with negative Spin Axis increased from nearly 58% from the flat compared to 85% from the slope, and only one of the three shots that had positive Spin Axis was due to a positive Face-to Path ratio, the other two were due to an off-center contact, and in these cases towards the heel. Where there is, a big change is the amount of Spin Axis that the shots from the slope had, more than 76% (13/17) had more than 5° of tilt, compared to less than 7% (1/15) from the flat.

	Flat Spin Axis	Ball Above Feet Spin Axis	Difference
4 Iron	-2.1°	-6.3°	-4.2° More Left
6 Iron	-0.7°	-2.2°	-1.5° More Left
8 Iron	0.7°	-5.4°	-6.1° More Left

With the final part to the flight, the Side, all the shots finished to the left of the Target Line: 9.1 meters, 10.1 meters and 14.3 meters for the Non-Normalized data. The smallest amount that any of these shots finished left was 2.6 meters and the largest was 20.3 meters. When Normalized, the numbers changed slightly to: 8.8 meters left, 8.6 meters left and 16.8 meters left. There were two shots that finished to the right of the Target Line, the most being 1.4 meters right; these are the two shots with heel contacts mentioned before.

	Flat Side(m) Non-Normalized	Ball Above Feet Side(m) Non-Normalized	Difference Side(m) Non-Normalized	Flat Side(m) Normalized	Ball Above Feet Side(m) Normalized	Difference Side(m) Normalized
4 Iron	2.3 L	14.3 L	12.0 More Left	4.6 L	16.8 L	12.2 More Left
6 Iron	1.9 R	10.1 L	12.0 More Left	1.3 L	8.6 L	7.3 More Left
8 Iron	1.3 R	9.1 L	10.4 More Left	0.6 R	8.8 L	9.4 More Left

Comparison

When we look at these two slopes Side by Side we can see that they are producing the same results, the only real difference being that one produces positive numbers and the other produces negative numbers, but have the numbers moved a comparable amount?

In the Launch Direction, the slope with the ball below the feet the 4-iron launched 2° more to the right than the flat and from the slope with the ball above the feet launched 2.2° more to the left than the flat. The 6-iron with the ball below the feet launched 2.1° more to the right and with the ball above the feet launched 2° more to the left than from the flat. With the 8-iron the ball launched 1.4° more to the right when the ball was below the feet and 1° more to the left when the ball was above the feet when compared to the flat. A maximum of 0.4° of difference in change, incredibly consistent, will the same be true for the other key numbers?

	Ball Below Feet Launch Direction	Difference	Flat Launch Direction	Difference	Ball Above Feet Launch Direction
4 Iron	1.6°	2.0°	-0.4°	-2.2°	-2.6°
6 Iron	2.0°	2.1°	-0.1°	-2.0°	-2.1°
8 Iron	1.3°	1.4°	-0.1°	-1.0°	-1.1°

For the Spin Axis, the numbers are quite similar but due to the horizontal gear effect there are some discrepancies. In the 4-iron, there was a +6.7° change with the ball below the feet and a change of -4.2° with the ball above the feet, so a 2.5° difference of variance. For the 6-iron with the ball below the feet there was a +2.6° change and with the ball above the feet there was a -1.5° change, so only a 1.1° of variance.

For the 8-iron, with the ball below the feet there was a +1.5° change whereas there was a -6.1° of change with the ball above the feet, so a rather large 4.6° of variance. If we looked at each of the shots individually, none of the shots had a very similar Spin Axis, all in the right area but all different. This is of course due to the slightly different points of contact that each shot had, some center, some slightly towards the toe and some slightly towards the heel. With a contact, just 1 centimeter from the center of the face could affect the Spin Axis by up to 6°, so the only way for these numbers to be very similar would to have the same point of contact for each of the shots.

	Ball Below Feet Spin Axis	Difference	Flat Spin Axis	Difference	Ball Above Feet Spin Axis
4 Iron	4.6	6.7	-2.1	-4.2	-6.3
6 Iron	1.9	2.6	-0.7	-1.5	-2.2
8 Iron	2.2	1.5	0.7	-6.1	-5.4

When we look at Side we have two groups of numbers, Normalized and the Non-Normalized. If we start by looking at Non-Normalized numbers we can see that the averages of balls played from the slope with the ball below the feet landed: 8.6, 10.9 and 17.3 meters further to the right than the flat and the averages with the slope with the ball above the feet, the balls finished: 12, 12 and 10.4 meters further to the left than from the flat.

Even though the amount the shots landed from the Target Line varied, what is interesting is that the average change from both slopes is very similar, with the ball below the feet the mean of the change is 12.3 meters and with the ball above the feet the mean of the change is 11.5 meters, so only a difference of 0.8 meters which is quite consistent. When we look at the Normalized numbers, the same is true. The mean of the increase in change with the ball below the feet is 10.2 meters and with the ball above the feet the mean of the increase in change is 9.6 meters, a 0.6 of difference.

	Ball Below Feet Side(m) Non-Normalized	Difference	Flat Side(m) Non-Normalized	Difference	Ball Above Feet Side(m) Non-Normalized
4 Iron	15.0 R	17.3 More Right	2.3 L	12.0 More Left	14.3 L
6 Iron	12.8 R	10.9 More Right	1.9 R	12.0 More Left	10.1 L
8 Iron	9.9 R	8.6 More Right	1.3 R	10.4 More Left	9.1 L

	Ball Below Feet Side(m) Normalized	Difference	Flat Side(m) Normalized	Difference	Ball Above Feet Side(m) Normalized
4 Iron	11.1 R	6.5 More Right	4.6 L	21.4 More Left	16.8 L
6 Iron	7.3 R	8.6 More Right	1.3 L	7.3 More Left	8.6 L
8 Iron	6.8 R	6.2 More Right	0.6 R	9.4 More Left	8.8 L

Reasons The reason why the slopes have had these effects on the shots is quite simple, the slopes have required the player to stand and swing in a certain way to make solid contact with the ball. With the ball below the feet the player will have more forward lean of the upper body so that he will be able to reach the ball, as the player leans forward they will also steepen the shaft angle at address and conversely at impact. This steepening of the shaft will change the way that the club sits on the ground and even though the leading edge is 90° to the Target Line the Face Angle will point to the right, this will cause the change in Launch Direction. Another effect of having the club more upright it will also steepen the Swing Plane which will cause the Path to be closer to the Swing Direction, this will be minimal but will never the less help to produce more positive Spin Axis. With the ball above the feet the player will have less forward lean of the upper body to reach the ball, and as the player is standing more upright the shaft angle at address and impact will be flatter. This flattening of the shaft will change the way the club sits and will cause the Face Angle to point more to the left even if the leading edge is 90° to the Target Line, this will cause the balls to launch more to the left. The second effect of this posture and flattening of the shaft will be to also flatten the Swing Plane, this will push the Club Path further from the Swing Direction this will be slight but will never the less cause more negative Spin Axis.

Straight Shot We have seen that the mean change in the amount of Side was between 9.6 and 10.2 meters, so it would be easy to aim this amount right or left of the Target and simply let the ball curve towards the Target, however, what if we wanted to play a straighter shot or the situation wouldn’t allow for the curvature? Well we can see that the average Face Angles on the both slopes are, for the ball below the feet: 1.9°, 2.4° and 2.5°, and for the ball above the feet: -3.0°, -2.4° and -1.3°. The mean number for the both are: 2.3° and 2.2° respectively. So therefore, all we would need to do is to open or close the face at address about 2° and we would be able to neutralize the effect that the change in shaft plane has had on the Face Angle and we would see shots that launch straighter and fly straighter. Bad shots On both slopes, there were two types of bad shots, ones that flew straight and ones that curved too much, both could get us into trouble. On the slope with the ball below the feet there were four shots that landed more than 20 meters from the Target Line, which is just over 13% of the Total shots from the slope, there was however the same percentage of shots that launched straight and flew straight. This happened when the heel of the club dug into the ground at impact and closed the clubface, but even though the club was closed the Face Angle was square to the Target Line, this produced the straighter launch and straighter flight. Other notable factors in the bad shots were that the contacts were thinner than normal. On the slope with the ball above the feet there were five shots that landed more than 20 meters from the Target Line, which is nearly 17% of the Total shots played from the slope. On this slope, there were four shots that landed right of the Target Line, one was due to a severe off-center strike in the heel of the clubface and the other three were due to the toe of the club digging into the ground at impact which caused the Face Angle to point to the right and the balls launched right and curved further right.

Uphill & Downhill The key numbers on these slopes are: Launch Angle, Height, Landing Angle, Carry, Total/Bounce and Roll & Side. Flat We begin by looking at the key numbers from the flat as these will serve as the baseline for the numbers from the two slopes to come. If we start again by looking at the start of the flight, the Launch Angle, the numbers are higher than the PGA Tour averages but are nevertheless quite consistent with 100% of the twenty-four shots having no more than 2° of difference to the averages of each club. The next part of the flight is the Apex, and again these numbers are higher than the PGA Tour averages but again quite consistent with only 25% having more than a 2 meter of difference to the averages. As the other two numbers were higher than the PGA Tour averages it is no surprise that the Landing Angle is also higher, but again there is consistency in the numbers with less than 9% of the shots having more than a 2° of variance from the averages of each club. I will not mention the Carry numbers as they are only interesting when being discussed with the slope as to the increase or loss in distance, I will however mention the Bounce and Roll for each club and here are the averages both Normalized and Non-Normalized.

	Bounce and Roll Non-Normalized	Bounce and Roll Normalized	Difference
4 Iron	4.7m	7.9m	3.2m
6 Iron	2.8m	4.7m	1.9m
8 Iron	1.7m	3.0m	1.3m

Uphill

As with the previous slopes we will begin by looking at the start of the flight and working forward. For the Launch Angle, we can see that there has been a significant increase in the averages of the three clubs; the 4-iron has 7.1° more, the 6-iron has 5.9° more and the 8-iron has 4.4° more. So, the longer the club, the more it follows the slope. However, what is impressive is the consistency to these numbers. Less than 6% (1 shot) of the shots from the uphill slope had more than a 1° of variance from the averages, when more than 29% of the shots from the flat did. What is even more impressive is that with the 6-iron every shot was less than 0.3° of the average!

	Flat Launch Angle	Uphill Launch Angle	Difference
4 Iron	13.1	20.2	7.1° Increase
6 Iron	17.2	23.1	5.9° Increase
8 Iron	23.3	27.7	4.4° Increase

For the Height, we again see an increase in the numbers and again the increase is substantial. For the 4-iron the average apex is 10.4 meters higher (37.4%) than from the flat, the 6-iron had an apex 8.3 meters (27.2%) higher and the 8-iron had an apex 6.2 meters (19.4%) higher. For each club, there was always a shot that flew much lower than the rest but the lowest shot with each club from the slope still apexes higher than the highest shot from the flat. What stands out to me when looking at these numbers is that the apexes from the uphill slope are almost identical: 38.2°, 38.8° and 38.2°, again consistency from this slope and this is after all what this case study is looking for evidence of.

	Flat Height (m)	Uphill Height (m)	Difference
4 Iron	27.8	38.2	10.4m Increase
6 Iron	30.5	38.8	8.3m Increase
8 Iron	32.0	38.2	6.2m Increase

For the Landing Angle, we see a severe steepening for each club from the slope, which comes as no surprise because of the increased Height in which the shots were flying. With the 4-iron, there was an increase of 5.3°, bringing the Landing Angle to 57.5°; the 6-iron increased by 6.5°, bringing the Landing Angle to 60.1°; and the 8-iron increased by 7.8°, bringing the Landing Angle to 63.8°. The mean of these numbers is a little over 6.5° and just half a degree from the value of the slope. When we look at the individual shots of each club, the flattest Landing Angle from the slope was as steep or steeper than the steepest Landing Angle from the flat. These Landing Angles from the uphill slope are what we would expect to see when playing into wind.

	Flat Landing Angle	Uphill Landing Angle	Difference
4 Iron	52.2°	57.5°	5.3° Increase
6 Iron	53.6°	60.1°	6.5° Increase
8 Iron	56.0°	63.8°	7.8° Increase

As the balls were flying higher and landing steeper I would expect that the shots would Carry shorter, and two out of the three clubs when Non-Normalized did and only one of the three Normalized clubs did. Let’s start by looking at the Non-Normalized. The 4-iron was the odd one out and carried the same (0.3 meters further), and what stood out with this club is that not only were the average carries the same but so too were the shortest and longest shots: 150 .5 and 157.5 meters from the flat compared to 150.6 and 157.6 meters from the uphill slope. The 6-iron and the 8-iron did lose distance, 5.4 and 10.5 meters respectively.

It is however the difference in the increase that I find interesting. The 6-iron loses 5.7 meters compared to the 4-iron and the 8-iron loses 5.1 meters compared to the 6-iron. One of the many patterns starting to arise. For the Normalized, the 4-iron and the 6-iron had slight gains in distance; 5.3 and 0.3 meters respectively, whereas the 8-iron lost a small amount of 4.7 meters. With these amounts of difference to the standard shot from the flat there should be little fear in playing this shot if the Height and curvature are not a problem.

	Flat Carry(m) Non-Normalized	Uphill Slope Carry(m) Non-Normalized	Difference Carry(m) Non-Normalized	Flat Carry(m) Normalized	Uphill Slope Carry(m) Normalized	Difference Carry(m) Normalized
4 Iron	154.1	154.4	0.3 Increase	164.5	169.8	5.3 Increase
6 Iron	138.0	132.6	5.4 Decrease	149.5	149.8	0.3 Increase
8 Iron	119.2	108.7	10.5 Decrease	132.4	127.7	4.7 Decrease

Although the Total distance that any shot has in golf is incredibly important, what I want to see here is the difference between the Carry and the Total, which will give us the amount of Bounce and Roll of the shot. If we begin to look at the Total, all three clubs, when Non-Normalized are shorter than from the flat but when Normalized only two of the three Totals from the uphill slope are shorter than the flat. Not surprising that their Total was shorter as they had a higher Apex and a steeper Landing Angle, but maybe a surprise that the 4-iron from the uphill slope had a longer Total than from the flat.

For the Bounce and Roll with the Non-Normalized data, the 4-iron lost 0.5 meters, the 6-iron lost 6.2 meters and the 8-iron lost 13 meters. Then when we look at the Normalized data difference between the Carry and the Total to find the Bounce and Roll there is also a decrease in the amount of Bounce and Roll with the shots from the uphill slope. There though only a small amount of change with the 4-iron and 6-iron averages where the drop-in Bounce and Roll was less than one meter and the averages held true for the individual shots.

However, with the 8-iron there was a 2.5 meter drop in bounce and roll and 71% of the shots had negative Bounce and Roll. Meaning that they had enough backspin to make the balls zip back and have a shorter Total than the Carry, this is a huge shift as 0% of the 8-irons from the flat did. With the Normalized data, the amount was almost the same, they all had a slight decrease in the amount in the bounce and roll of -0.5 meters (4-iron), -0.8 meters (6-iron) and -2.5 meters (8-iron).

	Uphill Slope Bounce and Roll Non-Normalized	Uphill Slope Bounce and Roll Normalized	Difference
4 Iron	4.2m	7.2m	3.0m
6 Iron	2.0m	4.3m	2.3m
8 Iron	-0.8m	1.3m	2.1m

The last part to this slope is Side, and when we look at the Side there are two sets of numbers: Non-Normalized and Normalized. When we look at the Non-Normalized data 100% of the shots from the slope finished left of the Target Line compared to 54% of the shots from the flat. The 4-iron finished the furthest left at 17.2 meters, followed by the 6-iron at 14.8 meters and the 8-iron the least with 11.6 meters. With the normalized data, the numbers were similar with again 100% of the shots from the slope finishing left of Target compared to 58% from the flat. The 4-iron was still the furthest left with 17.6 meters, the 6-iron with 12.5 meters and the 8-iron with 10.1 meters. These numbers are very close to what we saw from the previous two slopes, will the downhill be the same?

	Flat Side(m) Non-Normalized	Uphill Slope Side(m) Non-Normalized	Difference Side(m) Non-Normalized	Flat Side(m) Normalized	Uphill Slope Side(m) Normalized	Difference Side(m) Normalized
4 Iron	0.5 L	17.2 L	16.7m More Left	3.5 L	17.6 L	14.1m More Left
6 Iron	0.7 R	14.8 L	15.5m More Left	2.1 L	12.5 L	10.4m More Left
8 Iron	1.3 R	11.6 L	12.9m More Left	0.6 R	10.1 L	10.7m More Left

Reasons The classic way of playing shots from an uphill slope is to position the body perpendicular to the slope and to have the weight on the lower foot. These adjustments will allow the player to swing up the slope and contact the ball in a similar way to how they would from a flat lie. The drawback of this address position is the shaft will be leaning away from the Target at address and at impact. This leaning of the club away from the Target will increase the Dynamic Loft and cause the higher Launch Angle, the higher Launch Angle coupled with similar Ball Speed and Spin Rate cause the higher ball flight. The higher ball flight leads to the steeper Landing Angle and the steeper Landing Angle with similar Spin Rate will produce less Bounce and Roll.

Another problem playing shots from the slope is weight transfer. With the weight, so much on the lower foot it is very difficult to transfer the weight to the leading foot and the effect is twofold. Firstly, with less weight transfer and body action through the impact there will be a drop in clubhead speed: the 4-iron lost 2.4mph, the 6-iron lost 1.5mph and the 8-iron lost 1.7mph on the averages for the shots. Secondly, as the body is hanging back on the back foot the club is more likely to pass the hands and close the clubface at impact, each Face Angle was exactly 1.5° more closed from the slope compared to from the flat. These two points explain the loss in distance and why the shots started and finished left of the Target.

	Flat Club Speed	Uphill Slope Club Speed	Difference
4 Iron	91.6 mph	89.2 mph	2.4 mph Slower
6 Iron	88.4 mph	86.9 mph	1.5 mph Slower
8 Iron	85.5 mph	83.8 mph	1.7 mph Slower

The numbers didn’t move exactly 7.2°, like the slope, but the adjustments in the setup did produce similar numbers to the flat. The Attack Angle was steeper from the slope, the 4-iron was 1.4° steeper, the 6-iron was 2.7° steeper and the 8-iron was 2.6° steeper but from the slope the Attack Angle was very consistent, with a maximum of 1.1 of variance, true for all three clubs. The Dynamic Loft was more because of the negative shaft lean but the Spin Loft for all three clubs from the flat and the slope was near identical, with a difference of 0.2°, 0.3° and 0.3° of difference, so the adjustments were effective.

	Flat Attack Angle	Uphill Slope Attack Angle	Difference	Uphill Slope Equivalent AoA
4 Iron	-4.6°	1.2°	5.8° More Positive	-6.0°
6 Iron	-4.9°	-0.4°	4.5° More Positive	-7.6°
8 Iron	-5.9°	-1.3°	4.6° More Positive	-8.5°

Lean in What if the situation does not allow or you simply don’t want to play a high soft landing shot, is it possible to play a near normal trajectory from the uphill slope? Well the answer is yes, but we need to make some different adjustments to the setup. Instead of positioning the body perpendicular to the slope and having the weight on the lower foot we would need to lean into the slope and the weight would be more on the leading foot. These changes to the setup would remove the negative shaft lean and produce a more positive shaft lean and bring the Dynamic Loft closer to what we see from the flat. This proved to be a very effective way of playing this shot and when we look at the key numbers the results are excellent: The 4-iron had a Launch Angle that averaged only 1.2° higher than from the flat and 5.9° lower than with the traditional method, the balls had an Apex that was only 2.8 meters higher than the flat, had a Landing Angle that was only 0.8° steeper, carried 1.5 meters further, had the same amount of Bounce and Roll and finished 3 meters further to the right. The 6-iron had a Launch Angle that averaged 1.4° lower than from the flat and 7.3° lower than the traditional method, the balls had an Apex 2.6 meters lower, had a Landing Angle that was 2.4° flatter, carried 4.8 meters further, had 3.3 meters more Bounce and Roll and finished 5 meters further to the right. The 8-iron had a Launch Angle that averaged 2.4° lower than from the flat and 7.7° lower than with the traditional method, had an apex 1.5 meters lower, had a steeper Landing Angle of 2.9°, carried 3.5 meters shorter, had 1.5 meters less bounce and roll and finished only 2.9 meters further to the right. If we look at the dispersion chart to the right, we can see that achieved the same results as the shots from the flat lie, except for one rogue shot that made the averages seem worse than the reality. Even though these numbers are so like the flat numbers and the shot dispersion was so small it is a difficult way of playing the shot because of the severity of the impact and this approach is only suitable for the better player.

Downhill

We have arrived to the final slope of this study, and as with the previous three slopes, we will start by looking at the start of the flight. Launch Angle, there was a huge drop in the angle in which the balls were launching from the downhill slope. With the 4-iron the average launch dropped to 1.9°, which is a 11.2° change, the 6-iron’s average dropped to 8.7°, an 8.5° change, and the 8-iron’s average was 14.3°, a 9° change. These are all extreme changes and this slope has had a much greater effect than the previous three. 100% of the shots from the slope launched lower than from the flat, and by quite some amount, the highest Launch Angle from the downhill slope was considerably lower than the lowest Launch Angle from the flat.

	Flat Launch Angle	Downhill Slope Launch Angle	Difference
4 Iron	13.1°	1.9°	11.2° Decrease
6 Iron	17.2°	8.7°	8.5° Decrease
8 Iron	23.3°	14.3°	9.0° Decrease

	Flat Lowest Launch Angle	Downhill Slope Highest Launch Angle	Difference
4 Iron	11.1°	5.5°	5.6° Lower
6 Iron	16.0°	10.1°	5.9° Lower
8 Iron	21.9°	15.4°	6.5° Lower

Height, was considerably lower from the downhill slope. The average of the 4-iron had an apex of 10.3 meters which is nearly 63% lower than from the flat, the 6-iron had an average apex of 15 meters which is nearly 51% lower and the 8-iron had an average apex of 16.3 meters which is 49% lower. From what we saw with the uphill slope, we would expect these changes but the degree of change is huge. When we look at the highest apex from the downhill slope and the lowest apex from the flat with each club the severity of change still holds true.

	Flat Height	Downhill Slope Height	Difference
4 Iron	27.8m	10.3m	17.5m Lower
6 Iron	30.5m	15.0m	15.5m Lower
8 Iron	32.0m	16.3m	15.7m Lower

	Flat Lowest Apex	Downhill Slope Highest Apex	Difference	%
4 Iron	23.4m	11.1m	12.3m Lower	52.56% Lower
6 Iron	27.7m	16.8m	10.9m Lower	39.35% Lower
8 Iron	30.9m	18.7m	12.2m Lower	39.48% Lower

Landing Angle, as we would expect from shots that are flying lower, the Landing Angles from the downhill slope are flatter than from the flat lie. With the 4-iron the balls are landing nearly 20° (37.93%) flatter, the 6-iron is landing a little over 13° (24.44%) flatter and the 8-iron is landing nearly 12° (20.54%) flatter when compared to the flat. Once again, we see that this slope has caused a big change in the way the balls are flying and far away from the 7.45° of the slope. When we look at the flattest Landing Angle from the flat and the steepest Landing Angle from the slope there is still a large difference and still more than the 7.45° of the slope in two of the three clubs.

	Flat Landing Angle	Downhill Slope Landing Angle	Difference
4 Iron	52.2°	32.4°	19.8° Flatter
6 Iron	53.6°	40.5°	13.1° Flatter
8 Iron	56.0°	44.2°	11.8° Flatter

	Flat Flattest Landing Angle	Downhill Slope Steepest Landing Angle	Difference	%
4 Iron	49.2°	35.1°	14.1° Flatter	28.66% Flatter
6 Iron	51.7°	43.1°	8.6° Flatter	16.63% Flatter
8 Iron	54.8°	48.0°	6.8° Flatter	12.41% Flatter

Carry, 100% of the shots, Non-Normalized or normalized, played from the downhill slope Carried shorter than from the flat with the same club. When we look at the Non-Normalized data there is a big drop in the average distance for one club and an above average amount for the other 2 clubs, the 4-iron lost 28 meters (18.7%), the 6-iron lost 11.6 meters (8.41%) and the 8-iron lost 11.6 meters (9.73%).

However, when we look at the Normalized data the three clubs lose a much more substantial amount, the 6-iron lost 16.4 meters (10.97%) and the 8-iron lost 17.4 meters (13.14%) on the average carries. Yet the 4-iron still lost a whopping 40.8 meters (24.8%) on its average Carry, it even Carried shorter than the 6-iron! When we look at the shortest Carry from the flat and the longest Carry from the slope with each club with the normalized data, there is still a big difference. What is interesting is that 70% of the 6-iron shots carried as far or further than the longest Carry with the 4-iron.

	Flat Carry(m) Non-Normalized	Downhill Slope Carry(m) Non-Normalized	Difference Carry(m) Non-Normalized	Flat Carry(m) Normalized	Downhill Slope Carry(m) Normalized	Difference Carry(m) Normalized
4 Iron	154.1m	126.1m	28m Shorter	164.5m	123.7m	40.8m Shorter
6 Iron	138.0m	126.4m	11.6m Shorter	149.5m	133.1m	16.4m Shorter
8 Iron	119.2m	107.6m	11.6m Shorter	132.4m	115.0m	17.4m Shorter

	Flat Shortest Carry Normalized	Downhill Slope Longest Carry Normalized	Difference	%
4 Iron	162.2m	133.5m	28.7m Shorter	17.69% Shorter
6 Iron	144.8m	136.3m	8.5m Shorter	5.87% Shorter
8 Iron	127.5m	122.0m	5.5m Shorter	4.31% Shorter

Bounce and Roll, it comes as no surprise that the shots played from the slope had more Bounce and Roll than the shots played from the flat seeing that the Landing Angle was a great deal flatter. With the Non-Normalized data, the amount of Bounce and Roll with all three clubs more than tripled, the 4-iron increased by 9.6 meters to 14.3 meters, the 6-iron increased by 6 meters to 8.8 meters and the 8-iron increased by 3.7 meters to 5.4 meters. With the Normalized data, the same holds true, the amount of Bounce and Roll more than tripled. The 4-iron increased by 17.9 meters to 25.8 meters, the 6-iron increased by 10.3 meters to 15 meters and the 8-iron increased by 7.3 meters to 10.3 meters. In both instances the 6-iron and the 8-iron and have increased their amount of Bounce and Roll by controllable amounts but the increase in the 4-iron’s bounce and roll is becoming uncontrollable.

	Bounce and Roll Non-Normalized	Bounce and Roll Normalized	Difference
4 Iron	14.3m	25.8m	11.5m More
6 Iron	8.8m	15.0m	6.2m More
8 Iron	5.4m	10.3m	4.9m More

Side, maybe surprisingly the balls flew quite straight. In the Non-Normalized data, the 4-iron landed 9.2 meters to the right of the Target, which was 9.7 meters more to the right from the flat number, the 6-iron landed 1.5 meters to the right, which was 2.2 meters more to the right than the flat number and the 8-iron landed 0.8 meters to the right, which was 0.5 meters more to the left than the flat number. When Normalized, the shots finished closer to the Target Line, but the difference was like the Non-Normalized data. The 4-iron landed 5.2 meters to the right, the 6-iron 0.0 meters and the 8-iron 0.4 to the right. More than 70% of the shots from the slope finished to the right of the Target Line compared to less than 46% from the flat, showing consistent and playable numbers.

	Flat Side(m) Non-Normalized	Downhill Slope Side(m) Non-Normalized	Difference Side(m) Non-Normalized	Flat Side(m) Normalized	Downhill Slope Side(m) Normalized	Difference Side(m) Normalized
4 Iron	0.5 L	9.2 R	9.7m More Right	3.5 L	5.2 R	8.7m More Right
6 Iron	0.7 R	1.5 R	0.8m More Right	2.1 L	0.0	2.1m More Right
8 Iron	1.3 R	0.8 R	0.5m More Left	0.6 R	1.0 R	0.4m More Right

Reasons The traditional way of playing this slope is to position the body perpendicular to the slope, to have the weight more on the lower foot and to have the ball closer to middle of the stance. These adjustments are to allow the player to swing down the slope and contact the ball in a similar way as they would from the flat. The effect that these modifications will have on the club is that it will have an excessive forward shaft lean at both address and at impact. This forward shaft lean at impact will reduce the Dynamic Loft and cause the lower Launch Angle, the lower launch combined with lower Ball Speed and similar Spin Rate will cause the lower Apex, the lower flight will give the flatter Landing Angle and the flatter Landing Angle with the similar Spin Rate will produce more Bounce and Roll. Another problem that this setup will produce is, little to no weight transfer, as the body is basically pivoting on the leading leg. The effect that this had was twofold. Firstly, because of the reduced weight transfer and body action through the impact there was a drop in clubhead speed. The 4-iron lost 9 mph, the 6-iron lost 7.4 mph and the 8-iron lost 8.6 mph on the averages of the shots, the mean loss in clubhead speed was 8.3 mph; quite a lot compared to the other slopes. Secondly, with the forward shaft lean it will be nearly impossible for the clubhead to pass the hands at impact with a good shot, so most of the impacts from this slope will have positive Face Angle. In fact, only three shots (11.1%) had a negative Face Angle and of those three only one had more than -0.2°. The drop-in Club Speed will account for a large amount of the loss in distance but because the balls flew so low they had no time to Carry before hitting the ground and the more positive Face-to Path will account for the balls finishing more to the right of the Target Line.

	Flat Club Speed	Downhill Slope Club Speed	Difference
4 Iron	91.5 mph	82.5 mph	9.0 mph Slower
6 Iron	88.4 mph	81.0 mph	7.4 mph Slower
8 Iron	85.5 mph	76.9 mph	8.6 mph Slower

Even with all the changes in the numbers, the changes to the setup did their job well and produced similar results to from the flat. The Attack Angle changed very slightly with two of the three clubs: the 4-iron had a slight increase of 0.4° and the 6-iron had a slight decrease of 0.3°. The 8-iron had a slightly larger decrease of 1.7° but that was due to one freak shot where the Attack Angle was 10.3° less than the average as well as having other numbers that were quite different the other shots in the group. The result was however, just like the rest of the other shots in the group.

If we remove this shot from the list, the difference in the Attack Angle was only 0.6° less than the average from the flat. As the Attack Angle didn’t change much but the Dynamic Loft did, there was a change in the Spin Loft, -3.3° with the 4-iron, -2.2° with the 6-iron and -3.2° with the 8-iron, so there was a drop in the Spin Rate of 441rpm and 532rpm with the 4-iron and 8-iron respectively, but with the 6-iron there was a drop of 1220rpm which is an excessive drop and can only be due to the contact slightly higher on the clubface due to the severity of the Attack Angle and as a result of the vertical gear effect they lost Spin.

	Flat Attack Angle	Downhill Slope Attack Angle	Difference	Downhill Slope Equivalent AoA
4 Iron	-4.6°	-12.2°	7.6° More Negative	-4.8°
6 Iron	-4.9°	-11.8°	6.9° More Negative	-4.4°
8 Iron	-5.9°	-11.4°	5.5° More Negative	-4.0°

	Flat Spin Loft	Downhill Slope Spin Loft	Difference
4 Iron	22.6°	19.3°	3.3° Less Spin Loft
6 Iron	28.4°	26.2°	2.2° Less Spin Loft
8 Iron	36.4°	33.2°	3.2° Less Spin Loft

Comparison

When we look at these slopes Side by Side we can see that they are producing the opposite of each other, the uphill slope was flying higher and the downhill slope was flying lower than the flat. The question is however; have they changed by a similar amount?
Launch Angle, there appears to be quite a difference in the change between the two slopes. For the 4-iron, between the flat and the uphill slope there a difference of 7.1°, consistent with the slope, whereas on the downhill slope there was a difference of 11.2°, a difference of nearly 4° from the slope.

With the 6-iron, between the flat and the uphill slope there was a difference of 5.9°, 1.3° less than the slope, whereas from the downhill slope there was a difference of 8.5°, 1.3° more than the slope. For the 8-iron, between the flat and the uphill slope there was a difference of 4.4°, again a difference of 2.6° less than the slope, whereas from the downhill slope there was a difference of 9°, 1.8° more than the slope. What we see here is that the effect of the slopes is much greater with the 4-iron. While with the 6-iron and 8-iron even though at first glance they appear to be very different they have in fact increased/decreased by a similar amount, 1.3° of difference between the 6-irons and 0.8° of difference between the 8-irons.

	Uphill Slope Launch Angle	Difference	Flat Launch Angle	Difference	Downhill Slope Launch Angle
4 Iron	20.2°	7.1° More	13.1°	11.2° Less	1.9°
6 Iron	23.1°	5.9° More	17.2°	8.5° Less	8.7°
8 Iron	27.7°	4.4° More	23.3°	9.0° Less	14.3°

Height, there was a big difference in the change of the two slopes. For the 4-iron on the uphill slope the Apex increased by 10.4 meters but from the downhill slope the Apex decreased by 17.5 meters. For the 6-iron on the uphill slope the apex increased by 8.3 meters but decreased by 15.5 meters on the downhill slope. The 8-iron from the uphill slope the apex increased by 6.2 meters but decreased by 15.7 meters. There was another difference, whereas on the uphill slope the apex of the three clubs was within 0.6 meters of each other on the downhill slope there was 6 meters of difference between the highest and lowest.

	Uphill Slope Height	Difference	Flat Height	Difference	Downhill Slope Height
4 Iron	38.2m	10.4m Higher	27.8m	17.5m Lower	10.3m
6 Iron	38.8m	8.3m Higher	30.5m	15.5m Lower	15.0m
8 Iron	38.2m	6.2m Higher	32.0m	15.7m Lower	16.3m

Landing Angle, again a big difference between the two slopes. The 4-iron from the uphill slope had a steeper Landing Angle of 5.3° whereas from the downhill slope the Landing Angle flattened by 19.8°, a 14.5° difference. The 6-iron, from the uphill slope had a steeper Landing Angle of 6.5° whereas from the downhill slope it had a flatter Landing Angle of 13.1°, a 6.6° of difference. The 8-iron, from the uphill slope had a steeper Landing Angle of 7.8° whereas from the downhill slope it had a flatter Landing Angle of 11.8°, a 4° of difference. Again, we see that the downhill slope has had more effect on the flight of the ball than the uphill slope, particularly with the 4-iron.

	Uphill Slope Landing Angle	Difference	Flat Landing Angle	Difference	Downhill Slope Landing Angle
4 Iron	57.5°	5.3° Steeper	52.2°	19.8° Flatter	32.4°
6 Iron	60.1°	6.5° Steeper	53.6°	13.1° Flatter	40.5°
8 Iron	63.8°	7.8° Steeper	56.0°	11.8° Flatter	44.2°

Carry, two out of the three clubs had a big difference. For the Non-Normalized numbers, the 4-iron, on the uphill slope the Carry increased very slightly by 0.3 meters but from the downhill slope it lost 28 meters (18.17%). The 6-iron, from the uphill slope lost 5.4 meters and on the downhill slope lost 11.6 meters and for the 8-iron, on the uphill slope it lost 10.5 meters and from the downhill slope it lost 11.6 meters. For the Normalized numbers, there were huge differences.

For the 4-iron on the uphill slope it gained 5.3 meters yet it lost 40.8 meters from the downhill slope, the 6-iron from the uphill slope carried the same amount (0.3 meters gain) but lost 16.4 meters from the downhill slope and the 8-iron lost 4.7 meters from the uphill slope and lost 17.4 meters from the downhill slope. From the uphill slope, there was a change in Carry with but no more than a club of difference however with the downhill slope it was always more than a club of difference and in most cases, closer to two or more clubs of difference.

	Uphill Slope Carry Non-Normalized	Difference	Flat Carry Non-Normalized	Difference	Downhill Slope Carry Non-Normalized
4 Iron	154.4m	0.3m Longer	154.1m	28.0m Shorter	126.1m
6 Iron	132.6m	5.4m Shorter	138.0m	11.6m Shorter	126.4m
8 Iron	108.7m	10.5m Shorter	119.2m	11.6m Shorter	107.6m

	Uphill Slope Carry Normalized	Difference	Flat Carry Normalized	Difference	Downhill Slope Carry Normalized
4 Iron	169.8m	5.3m Longer	164.5m	40.8m Shorter	123.7m
6 Iron	149.8m	0.3m Longer	149.5m	16.4m Shorter	133.1m
8 Iron	127.7m	4.7m Shorter	132.4m	17.4m Shorter	115.0m

Bounce and Roll, two out of the three clubs have a notable difference when Non-Normalized and all three have a notable difference when Normalized. If we start with the Non-Normalized, the 4-iron from the uphill slope only had 0.5 meters less bounce and roll but from the downhill slope the amount increased by 9.6 meters. With the 6-iron from the uphill slope the amount decreased by 0.8 but increased by 6 meters from the downhill slope. The 8-iron the amount decreased by 2.5 meters, having a shorter Total than Carry, but increased by 2.7 meters on the downhill slope, so only a 0.2 meter of difference in the change. With the Normalized, the 4-iron from the uphill slope lost 0.7 meters and increased 17.9 meters from the downhill slope. The 6-iron from the uphill slope lost 0.4 meters but increased by 10.3 meters from the downhill slope, and finally the 8-iron lost 1.7 meters from the uphill slope but increased by 7.3 meters from the downhill slope.

	Uphill Slope Bounce and Roll Non-Normalized	Difference	Flat Bounce and Roll Non-Normalized	Difference	Downhill Slope Bounce and Roll Non-Normalized
4 Iron	4.2m	0.5m Less	4.7m	9.6m More	14.3m
6 Iron	2.0m	0.8m Less	2.8m	6.0m More	8.8m
8 Iron	-0.8m	2.5m Less	1.7m	2.7m More	4.4m

	Uphill Slope Bounce and Roll Normalized	Difference	Flat Bounce and Roll Normalized	Difference	Downhill Slope Bounce and Roll Normalized
4 Iron	7.2m	0.7m Less	7.9m	17.9m More	25.8m
6 Iron	4.3m	0.4m Less	4.7m	10.3m More	15.0m
8 Iron	1.3m	1.7m Less	3.0m	7.3m More	10.3m

Side, the only result where the downhill slope was desirable. For the non-normalized shots, the 4-iron on the uphill slope landed 16.7 meters more to the left but only landed 9.7 meters more to the right from the downhill slope. The 6-iron from the uphill slope landed 15.5 meters more to the left but only 0.8 meters more to the right from the downhill slope and the 8-iron from the uphill slope landed 12.9 meters more to the left but only 0.5 meters more to the right from the downhill slope.

For the normalized data, the 4-iron from the uphill slope landed 14.1 meters more to the left and 8.7 meters more to the right from the downhill slope, the 6-iron landed 10.4 meters more to the left from the uphill slope but only 2.1 meters more to the right from the downhill slope and the 8-iron landed 10.7 meters more to the left from the uphill slope but only 0.4 more to the right from the downhill slope. This is the only part of the key numbers where the downhill slope appears to be more under control than the uphill slope.

	Uphill Slope Side(m) Non-Normalized	Difference	Flat Side(m) Non-Normalized	Difference	Downhill Slope Side(m) Non-Normalized
4 Iron	17.2 L	16.7m More Left	0.5 L	9.7m More Right	9.2 R
6 Iron	14.8 L	15.5m More Left	0.7 R	0.8m More Right	1.5 R
8 Iron	11.6 L	12.9m More Left	1.3 R	0.5m More Right	0.8 R

	Uphill Slope Side(m) Normalized	Difference	Flat Side(m) Normalized	Difference	Downhill Slope Side(m) Normalized
4 Iron	17.6 L	14.1m More Left	3.5 L	8.7m More Right	5.2 R
6 Iron	12.5 L	10.4m More Left	2.1 L	2.1m More Right	0.0
8 Iron	10.1 L	10.7m More Left	0.6 R	0.4m More Right	1.0 R

Overall, apart from the Height of the shot, the uphill slope which might cause some problems in certain situations on the course it is very playable and even offers a way to produce straighter shots that fly in a very similar way to from a flat lie. The downhill lie doesn’t offer any versatility; it is a difficult shot; it must be treated with respect and played accordingly. Its only saving grace is that it flies quite straight, so accept its limitations and play the shot accordingly.

Thoughts

All four slopes were consistent in the results that they produced and we saw that the Side slopes produced incredibly similar results to one another, however in most cases the uphill and the downhill did not. The fact that the downhill slope was the only one of the four slopes that didn’t offer an alternative to the traditional way of playing the shot shows just how difficult this shot is, and the reason that it doesn’t offer a variation is due to the way you must attack the ball.

I believe that for this very same reason, it is the odd one out in the numbers. As the club is approaching the ball from a very steep angle, a mean Attack Angle of -11.8°, there is only the top third of the ball exposed to the club which takes away any possibility of approaching the ball in a different way. Whereas from the other three slopes, particularly the uphill slope, all the back of the ball is exposed to the club allowing for some margin of error or manipulation of the impact, depending on the level of the player.

Answer

The answer to my first question is; yes, they are predictable. In fact, I would go as far as to say very predictable. From this study, I have also more confidence in the way in which I play these slopes as the data has proved that the changes to the setup do exactly what they were supposed to do. The study has however raised a few more questions for me though:

• If the slope is halved or doubled, will the numbers do the same?
• What effect would the roll on the clubface of a hybrid or fairway-wood have when played from these four slopes?

So as much as this study on slopes is over, understanding the slopes is just beginning.

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