Ball Flight Laws
The Secret of the `Straight Shot´ I
The horizontal launch angle is determined by only two parameters,the club path and the face angle. As a rule of thumb, the horizontallaunch angle is 15% determined by the club path and 85%determined by the face angle.
-by Trackman (http://www.trackman.dk/download/newsletter/newsletter4.pdf)
[ame="http://www.youtube.com/watch?v=eEHiY5iv5u4"]http://www.youtube.com/watch?v=eEHiY5iv5u4[/ame]
http://thesandtrap.com/b/playing_tips/ball_flight_laws
For decades, golf instructors have been teaching the ball flight laws incorrectly. Many blame the PGA Teaching Manual, and have said that it has contained some incorrect or incomplete information pertaining to a golf ball's flight. Many pros - from Butch Harmon to Nick Faldo - sum up the ball flight laws as follows: "The golf ball starts on the direction of the swing path and curves back to where the clubface was aimed at impact."
Put another way, many instructors and famous golfers have stated that the swing path is the primary, over-riding determinant in the golf ball's initial starting direction. This information is wrong. This information is slowly coming to be understood as wrong in recent years, yet many golfers - famous or otherwise - and instructors - famous or otherwise - still believe it.
http://www.youtube.com/watch?feature=player_embedded&v=5AlFVMmBLcQ
Mike Bennett and Andy Plummer discuss the ball flight laws on Charlie Rose on December 23, 2009.
The (Non-)Debate
The debate over the nature of a golf ball's initial direction of flight is, unfortunately for generations of golfers, a relatively recent one in golf. Only within the past few years have instruments which can measure the moment of impact in precise detail been developed, and those instruments have just recently started to see data that contradicts the decades-old (incorrect) information about what governs a golf ball's launch and flight.
When I first started playing golf, I never considered the possibility that the ball could come off the clubface in any direction other than nearly perpendicular. It seemed like common sense. Though I realized a golf ball-golf club collision was not elastic, I didn't think that a ball could be "carried" very much in the .000045 seconds the ball is compressed on the face - not enough to determine where the ball went, anyway.
Eventually I changed my mind. I'm sad to say that this change was not based on science but rather the fact that awesome instructors and world-renowned players all seemed to say the same thing. "I aim my feet where I want to start the ball and I aim my clubface where I want the ball to go, then swing along the line of my feet" they'd say. During this phase I even went so far as to point out that pool balls, collisions between which are almost as elastic as we see in real life, can be "thrown" off-line due to friction between colliding balls.
It turns out I should have trusted what I felt was common sense in the beginning: that the clubface has a much larger effect on the ball's initial path than any amount of "carrying" on the clubface by the swing path. Even though it's in another plane (vertical rather than horizontal), consider which direction a ball travels when you properly strike it with a descending blow: upward, because the loft of the clubface is pointing that way.
The Science
Though [ame="http://www.amazon.com/Physics-Golf-Theodore-P-Jorgensen/dp/038798691X"]The Physics of Golf[/ame] shared the information years ago (the second edition is dated 1999). The information is available elsewhere too (like [ame="http://books.google.com/books?id=MnC60GN8PJ4C&pg=PA535"]here[/ame] and [ame="http://books.google.com/books?id=bmVk8BkOLH4C&pg=PA490"]here[/ame] - thanks to [ame="http://richie3jack.proboards.com/index.cgi?action=display&board=general&thread=91&page=1#540"]John Graham[/ame] at Richie3Jack's for those links). All of those works are fairly scientific, and though widely read and understood among the scientific component of the golf industry, the average golfer (and golf instructor) remained unaware.
One year ago marked a turning point in the battle of current, correct information versus "the way we've always told people to do it." In January, 2009 Trackman - makers of a popular launch monitor - publicly released information in their newsletter which shared the information in an accessible, easy to understand format. Again, while the scientific community - and a few instructors and golfers - knew this already, the Trackman newsletter was significant simply because of the easy digestibility.
From the January newsletter's article "The Secret of the Straight Shot" here (emphasis added):
These numbers vary little. You might think long drivers, who compress the bejeezus out of the golf ball, flip the ratio, but they don't even get out of the 80s, reaching roughly an 80/20 ratio at best. In fact, the ratio is much more easily pushed in the other direction: a putter, swung at a relatively slow swing speed, can generate ratios approaching nearly 100% clubface oriented.
So How'd They Do It?
During a recent telecast at the Sony Open, Nick Faldo - a six-time major winner and one of the best golfers in the history of the game - shared this advice, captured in the screen shot you see here:
Nick Faldo in the process of giving advice that's clearly based on the old - and very much wrong - ball flight laws.
So how on earth did Nick Faldo shape the ball - and break par let alone win six majors - if he had the wrong information? The power of his subconscious mind. Science tells us that if Nick Faldo set up with his clubface at the tree in the picture above and his shoulders aimed just to the right at the escape route, he would either:
If Nick subconsciously manipulated both the clubface angle and the swing path to produce #2, he'd start the ball to the right of the tree and hook it back towards the target - the shot he wants to play.
What are you going to believe - science or Nick Faldo's feel? Even Nick Faldo's subconscious mind didn't trust his feel, favoring the reality of science (or the instincts of having been a great golfer for a long time) instead!
Ball Flight Laws and Their Effects on Teaching
Consider a student who's hitting a straight-fade or a straight-slice. A straight-fade starts straight at the target and then, for a right-handed golfer, peels off to the right.
If this golfer visits an instructor who believes the old ball flight laws, he's going to have the student trying to square up the clubface. After all, the instructor believes that the ball starts on the swing path, and then reacts based on the face. So the instructor will believe that the student's swing path is fine and that his clubface is open.
This instructor will spend a lot of time trying to get the student to "square up the club at impact" when he's already doing so! Best case scenario? The student starts hitting pulls. Hey, at least they won't slice…
The reality is that this student needs to work on his swing path. His clubface is already awfully close to square at impact - the ball is starting at the target. It's purely his outside-in swing path that's causing the fades or slices.
During the Bob Hope Classic, Michael Breed used what appeared to be the old ball flight laws in helping actor Michael Peña. Peña was hitting a pull-fade - not a bad shot if you can hit it repeatedly because the fade works back to the target - and Breed gave him the advice to swing more from the inside (which is fine if you want to hit a draw) and to release the clubface (oof).
http://www.youtube.com/watch?v=M5oBwzTLBJc&feature=player_embedded
True Ball Flight Laws
One thing is not up for debate and never has been: a ball curves based on the clubface angle at impact relative to the swing path. A closed clubface relative to the swing path always draws/hooks and an open clubface relative to the swing path always fades/slices:
With arrows representing the swing path, the balls in these images will fade/slice, travel straight, or draw/hook from top to bottom.
You can combine these three basic clubface positions with the three basic swing paths:
The combination of the two triplets result in a combination of nine possible ball flights:
This diagram demonstrates every possible shape a well-struck golf ball (we're not talking about tops and shanks here, people!) can have. The true ball flight laws tell us that a pull (B) is a combination of an over-the-top (outside-in) move with a closed clubface that matches the amount of outside-in swing path.
The true ball flight laws tell us that a push-draw (G) is a result of an open clubface with a swing path that's more inside-out than the clubface is open. For example, if the clubface is 3° open at impact but the swing path is 6° inside-out, the ball will start right (open clubface relative to the target) and curve left (closed clubface relative to the swing path).
How would the old ball flight laws tell us to hit a push-draw (G)? They'd tell us to swing in-to-out while keeping the clubface square to the target. Basically, they'd tell us to hit shot D. Ouch.
In the chart above you'll notice that the straight shots - B, E, and H - are italicized. These shots are each hit with a clubface square to the swing path and are the only shots on which the "old" and "true" ball flight laws agree.
I've also marked in bold the "good" shots: a pull-fade, a straight shot, and a push-draw. The straight shot is good for obvious reasons, but as you can see the pull-fade (C) and the push-draw (G) work because, though they start away from the target, they curve towards the target.
(Side note: That's not to say the other shots aren't good. Lee Trevino and Jack Nicklaus both played a push-fade. On my graph, that's shot (I), the farthest right. How could they win majors or even break par hitting that shot? Take the whole graph above and rotate it counter-clockwise (to the left). Imagine Lee Trevino: he aims his feet and swings his club 20° left, pushes the ball 10° right, and lets his fade take the ball the remaining 10° back to the target. That's how shot (I) can win a major - when you play for it.)
Where Do we Go from Here?
If you're like most golfers, having toiled under the old, incorrect ball flight laws, you may feel energized reading this. Perhaps you've been battling a persistent slice by trying to "release the club." It's a common suggestion, but if your ball starts at the target before slicing, you should have gathered that you need to work on your swing path, not your clubface angle at impact. That's even more important if the ball starts left before slicing two fairways over.
Armed with the proper knowledge, you're going to be amazed at how often you hear advice based on the old, incorrect ball flight laws, and from whom you hear it. Magazines, television, respected teachers, and accomplished players will all dish out advice that's potentially damaging to your golf game because it's based on the "old" laws.
The ball flight doesn't lie. Now that you know how to read it, you can spend your time working on the right things.
Example:
Consider the ball flight control method a golfer should use to bypass an obstruction (eg. tree alongside the fairway).
Ball flight predicament
Consider the predicament of the golfer in image 1. His ball has landed at point X - just off the right side of the fairway, about 180 yards from the green, which is surrounded on the left-and-right by two bunkers. There is a large tree (colored in dark green) about 40 yards in front of him obstructing his view of the center of the green and the hole, which is in the middle of the green. The tree is too high for him to consider the optional choice of hitting a straight shot over the top of the tree. There is a lake (colored in blue) on the right side of the rough and alongside the right side of the right bunker.
What can the golfer do to get the ball to land on the green near the hole? Image 2 shows that he has two ball flight options - he can either try to hit a pull-slice shot (yellow curved arrow) or he can try to hit a push-draw shot (orange curved arrow). The major problem associated with trying to hit a push-draw shot is that it is a very risky endeavour, because of the presence of the lake on the right side - he could easily land in the lake if he doesn't successfully draw the ball enough. So, his best option is to try and hit a pull-slice shot. At the worst, if he doesn't curve the ball back enough towards the center, it will either land in the bunker to the left of the green or in the left rough.
How should he execute this pull-slice shot?
Image 3 shows the approach recommended by the "old" ball flight laws. The clubface (short black line) should be aimed towards the center of the green (orange arrow) and his clubhead path should be directed left of the tree (yellow arrow). Theoretically, according to the tenets of the "old" ball flight laws, the ball should start along the direction of the clubhead path, and skirt the tree, before slicing to the right (secondary to the presence of slice spin due to the fact that the clubface is open to his clubhead path). However, that "imagined" ball flight will not happen in "reality" if he adopts that particular choice of clubface orientation and clubhead path. Image 4 shows what will happen in "reality". The ball will start off just to the left of the clubface orientation (85% in the direction of the clubface orientation relative to the clubhead path) and curve to the right (red dotted arrow) into the tree.
The correct approach should follow the tenets of the "new" ball flight laws - see image 5. The clubface (short black line) should be angled to the left of the tree (orange arrow). The clubhead path should be directed even further left (yellow arrow). If the swing is executed correctly, then the ball will start off 85% in the direction of the clubface orientation and curve to the right (due to the fact that the clubface is open to the clubhead path). The ball should then follow the red dotted arrow path to the center of the green.
The golfer needs to ensure that the degree of divergence between the clubhead path angle and the clubface orientation angle is appropriate - so that the ball acquires the "correct" amount of slice spin in order that it can curve rightwards towards the center of the green. If the ball is 40 yards from the tree, rather than 80 yards from the tree, then the golfer will need to curve the ball more to the right. To acquire a greater amount of slice spin, he needs to increase the magnitude of the divergent angle between the clubhead path and the clubface orientation - while keeping the clubface pointing just to the left of the tree. In other words, he will have to swing his club more leftwards if he wants to produce a greater degree of slice spin. It is only through repeated practice that a golfer can learn how to vary the magnitude of the divergent angle between the clubface orientation and the clubhead path to produce a certain finite amount of slice spin that is optimal for this particular ball flight predicament.
http://perfectgolfswingreview.net/ballflight.htm
http://perfectgolfswingreview.net/index.html
The Secret of the `Straight Shot´ I
The horizontal launch angle is determined by only two parameters,the club path and the face angle. As a rule of thumb, the horizontallaunch angle is 15% determined by the club path and 85%determined by the face angle.
-by Trackman (http://www.trackman.dk/download/newsletter/newsletter4.pdf)
[ame="http://www.youtube.com/watch?v=eEHiY5iv5u4"]http://www.youtube.com/watch?v=eEHiY5iv5u4[/ame]
http://thesandtrap.com/b/playing_tips/ball_flight_laws
For decades, golf instructors have been teaching the ball flight laws incorrectly. Many blame the PGA Teaching Manual, and have said that it has contained some incorrect or incomplete information pertaining to a golf ball's flight. Many pros - from Butch Harmon to Nick Faldo - sum up the ball flight laws as follows: "The golf ball starts on the direction of the swing path and curves back to where the clubface was aimed at impact."
Put another way, many instructors and famous golfers have stated that the swing path is the primary, over-riding determinant in the golf ball's initial starting direction. This information is wrong. This information is slowly coming to be understood as wrong in recent years, yet many golfers - famous or otherwise - and instructors - famous or otherwise - still believe it.
http://www.youtube.com/watch?feature=player_embedded&v=5AlFVMmBLcQ
Mike Bennett and Andy Plummer discuss the ball flight laws on Charlie Rose on December 23, 2009.
The (Non-)Debate
The debate over the nature of a golf ball's initial direction of flight is, unfortunately for generations of golfers, a relatively recent one in golf. Only within the past few years have instruments which can measure the moment of impact in precise detail been developed, and those instruments have just recently started to see data that contradicts the decades-old (incorrect) information about what governs a golf ball's launch and flight.
When I first started playing golf, I never considered the possibility that the ball could come off the clubface in any direction other than nearly perpendicular. It seemed like common sense. Though I realized a golf ball-golf club collision was not elastic, I didn't think that a ball could be "carried" very much in the .000045 seconds the ball is compressed on the face - not enough to determine where the ball went, anyway.
Eventually I changed my mind. I'm sad to say that this change was not based on science but rather the fact that awesome instructors and world-renowned players all seemed to say the same thing. "I aim my feet where I want to start the ball and I aim my clubface where I want the ball to go, then swing along the line of my feet" they'd say. During this phase I even went so far as to point out that pool balls, collisions between which are almost as elastic as we see in real life, can be "thrown" off-line due to friction between colliding balls.
It turns out I should have trusted what I felt was common sense in the beginning: that the clubface has a much larger effect on the ball's initial path than any amount of "carrying" on the clubface by the swing path. Even though it's in another plane (vertical rather than horizontal), consider which direction a ball travels when you properly strike it with a descending blow: upward, because the loft of the clubface is pointing that way.
The Science
Though [ame="http://www.amazon.com/Physics-Golf-Theodore-P-Jorgensen/dp/038798691X"]The Physics of Golf[/ame] shared the information years ago (the second edition is dated 1999). The information is available elsewhere too (like [ame="http://books.google.com/books?id=MnC60GN8PJ4C&pg=PA535"]here[/ame] and [ame="http://books.google.com/books?id=bmVk8BkOLH4C&pg=PA490"]here[/ame] - thanks to [ame="http://richie3jack.proboards.com/index.cgi?action=display&board=general&thread=91&page=1#540"]John Graham[/ame] at Richie3Jack's for those links). All of those works are fairly scientific, and though widely read and understood among the scientific component of the golf industry, the average golfer (and golf instructor) remained unaware.
One year ago marked a turning point in the battle of current, correct information versus "the way we've always told people to do it." In January, 2009 Trackman - makers of a popular launch monitor - publicly released information in their newsletter which shared the information in an accessible, easy to understand format. Again, while the scientific community - and a few instructors and golfers - knew this already, the Trackman newsletter was significant simply because of the easy digestibility.
From the January newsletter's article "The Secret of the Straight Shot" here (emphasis added):
The horizontal launch angle is determined by only two parameters, the club path and the face angle. As a rule of thumb, the horizontal launch angle is 15% determined by the club path and 85% determined by the face angle. For example, assume a club path of +6.7 degrees (6.7 degrees inside-out for a right-handed player) and a face angle of -1 degree (1 degree closed for a right-handed player). This would result in a horizontal launch angle of 0 degrees (ball starting at the target line).
In other words, you are saying that the face angle is by far the most dominating factor for the initial direction of the ball. Is this not in direct contradiction with the "Ball Flight Laws"?
Yes it is. According to the "old" ball flight laws, the initial direction of the ball (HLA) is 100% dictated by the club path. All the scientific people in the golf industry know that this is wrong, yet still a lot of PGA professionals use the incorrect 'old' ball flight laws in teaching. And many PGA organizations around the world do not teach their apprentice and member professionals according to the 'true' ball flight laws.
Fredrik Tuxen, Trackman January 2009 Newsletter
The science gets a bit headier beyond that - the downward angle of attack and its effect on the "true swing path" is considered - but the key piece is fairly clear: 85% of the ball's initial direction is determined by the clubface angle and only 15% of the ball flight is determined by the path.In other words, you are saying that the face angle is by far the most dominating factor for the initial direction of the ball. Is this not in direct contradiction with the "Ball Flight Laws"?
Yes it is. According to the "old" ball flight laws, the initial direction of the ball (HLA) is 100% dictated by the club path. All the scientific people in the golf industry know that this is wrong, yet still a lot of PGA professionals use the incorrect 'old' ball flight laws in teaching. And many PGA organizations around the world do not teach their apprentice and member professionals according to the 'true' ball flight laws.
Fredrik Tuxen, Trackman January 2009 Newsletter
These numbers vary little. You might think long drivers, who compress the bejeezus out of the golf ball, flip the ratio, but they don't even get out of the 80s, reaching roughly an 80/20 ratio at best. In fact, the ratio is much more easily pushed in the other direction: a putter, swung at a relatively slow swing speed, can generate ratios approaching nearly 100% clubface oriented.
So How'd They Do It?
During a recent telecast at the Sony Open, Nick Faldo - a six-time major winner and one of the best golfers in the history of the game - shared this advice, captured in the screen shot you see here:
Nick Faldo in the process of giving advice that's clearly based on the old - and very much wrong - ball flight laws.
So how on earth did Nick Faldo shape the ball - and break par let alone win six majors - if he had the wrong information? The power of his subconscious mind. Science tells us that if Nick Faldo set up with his clubface at the tree in the picture above and his shoulders aimed just to the right at the escape route, he would either:
- return his clubface to the same angle as it was at address and swing along his shoulder line.
- subconsciously return the clubface open to (right of) where it was at address and swing even more inside-out than his shoulder alignment.
If Nick subconsciously manipulated both the clubface angle and the swing path to produce #2, he'd start the ball to the right of the tree and hook it back towards the target - the shot he wants to play.
What are you going to believe - science or Nick Faldo's feel? Even Nick Faldo's subconscious mind didn't trust his feel, favoring the reality of science (or the instincts of having been a great golfer for a long time) instead!
Ball Flight Laws and Their Effects on Teaching
Consider a student who's hitting a straight-fade or a straight-slice. A straight-fade starts straight at the target and then, for a right-handed golfer, peels off to the right.
If this golfer visits an instructor who believes the old ball flight laws, he's going to have the student trying to square up the clubface. After all, the instructor believes that the ball starts on the swing path, and then reacts based on the face. So the instructor will believe that the student's swing path is fine and that his clubface is open.
This instructor will spend a lot of time trying to get the student to "square up the club at impact" when he's already doing so! Best case scenario? The student starts hitting pulls. Hey, at least they won't slice…
The reality is that this student needs to work on his swing path. His clubface is already awfully close to square at impact - the ball is starting at the target. It's purely his outside-in swing path that's causing the fades or slices.
During the Bob Hope Classic, Michael Breed used what appeared to be the old ball flight laws in helping actor Michael Peña. Peña was hitting a pull-fade - not a bad shot if you can hit it repeatedly because the fade works back to the target - and Breed gave him the advice to swing more from the inside (which is fine if you want to hit a draw) and to release the clubface (oof).
http://www.youtube.com/watch?v=M5oBwzTLBJc&feature=player_embedded
True Ball Flight Laws
One thing is not up for debate and never has been: a ball curves based on the clubface angle at impact relative to the swing path. A closed clubface relative to the swing path always draws/hooks and an open clubface relative to the swing path always fades/slices:
With arrows representing the swing path, the balls in these images will fade/slice, travel straight, or draw/hook from top to bottom.
You can combine these three basic clubface positions with the three basic swing paths:
The combination of the two triplets result in a combination of nine possible ball flights:
This diagram demonstrates every possible shape a well-struck golf ball (we're not talking about tops and shanks here, people!) can have. The true ball flight laws tell us that a pull (B) is a combination of an over-the-top (outside-in) move with a closed clubface that matches the amount of outside-in swing path.
The true ball flight laws tell us that a push-draw (G) is a result of an open clubface with a swing path that's more inside-out than the clubface is open. For example, if the clubface is 3° open at impact but the swing path is 6° inside-out, the ball will start right (open clubface relative to the target) and curve left (closed clubface relative to the swing path).
How would the old ball flight laws tell us to hit a push-draw (G)? They'd tell us to swing in-to-out while keeping the clubface square to the target. Basically, they'd tell us to hit shot D. Ouch.
In the chart above you'll notice that the straight shots - B, E, and H - are italicized. These shots are each hit with a clubface square to the swing path and are the only shots on which the "old" and "true" ball flight laws agree.
I've also marked in bold the "good" shots: a pull-fade, a straight shot, and a push-draw. The straight shot is good for obvious reasons, but as you can see the pull-fade (C) and the push-draw (G) work because, though they start away from the target, they curve towards the target.
(Side note: That's not to say the other shots aren't good. Lee Trevino and Jack Nicklaus both played a push-fade. On my graph, that's shot (I), the farthest right. How could they win majors or even break par hitting that shot? Take the whole graph above and rotate it counter-clockwise (to the left). Imagine Lee Trevino: he aims his feet and swings his club 20° left, pushes the ball 10° right, and lets his fade take the ball the remaining 10° back to the target. That's how shot (I) can win a major - when you play for it.)
Where Do we Go from Here?
If you're like most golfers, having toiled under the old, incorrect ball flight laws, you may feel energized reading this. Perhaps you've been battling a persistent slice by trying to "release the club." It's a common suggestion, but if your ball starts at the target before slicing, you should have gathered that you need to work on your swing path, not your clubface angle at impact. That's even more important if the ball starts left before slicing two fairways over.
Armed with the proper knowledge, you're going to be amazed at how often you hear advice based on the old, incorrect ball flight laws, and from whom you hear it. Magazines, television, respected teachers, and accomplished players will all dish out advice that's potentially damaging to your golf game because it's based on the "old" laws.
The ball flight doesn't lie. Now that you know how to read it, you can spend your time working on the right things.
Example:
Consider the ball flight control method a golfer should use to bypass an obstruction (eg. tree alongside the fairway).
Ball flight predicament
Consider the predicament of the golfer in image 1. His ball has landed at point X - just off the right side of the fairway, about 180 yards from the green, which is surrounded on the left-and-right by two bunkers. There is a large tree (colored in dark green) about 40 yards in front of him obstructing his view of the center of the green and the hole, which is in the middle of the green. The tree is too high for him to consider the optional choice of hitting a straight shot over the top of the tree. There is a lake (colored in blue) on the right side of the rough and alongside the right side of the right bunker.
What can the golfer do to get the ball to land on the green near the hole? Image 2 shows that he has two ball flight options - he can either try to hit a pull-slice shot (yellow curved arrow) or he can try to hit a push-draw shot (orange curved arrow). The major problem associated with trying to hit a push-draw shot is that it is a very risky endeavour, because of the presence of the lake on the right side - he could easily land in the lake if he doesn't successfully draw the ball enough. So, his best option is to try and hit a pull-slice shot. At the worst, if he doesn't curve the ball back enough towards the center, it will either land in the bunker to the left of the green or in the left rough.
How should he execute this pull-slice shot?
Image 3 shows the approach recommended by the "old" ball flight laws. The clubface (short black line) should be aimed towards the center of the green (orange arrow) and his clubhead path should be directed left of the tree (yellow arrow). Theoretically, according to the tenets of the "old" ball flight laws, the ball should start along the direction of the clubhead path, and skirt the tree, before slicing to the right (secondary to the presence of slice spin due to the fact that the clubface is open to his clubhead path). However, that "imagined" ball flight will not happen in "reality" if he adopts that particular choice of clubface orientation and clubhead path. Image 4 shows what will happen in "reality". The ball will start off just to the left of the clubface orientation (85% in the direction of the clubface orientation relative to the clubhead path) and curve to the right (red dotted arrow) into the tree.
The correct approach should follow the tenets of the "new" ball flight laws - see image 5. The clubface (short black line) should be angled to the left of the tree (orange arrow). The clubhead path should be directed even further left (yellow arrow). If the swing is executed correctly, then the ball will start off 85% in the direction of the clubface orientation and curve to the right (due to the fact that the clubface is open to the clubhead path). The ball should then follow the red dotted arrow path to the center of the green.
The golfer needs to ensure that the degree of divergence between the clubhead path angle and the clubface orientation angle is appropriate - so that the ball acquires the "correct" amount of slice spin in order that it can curve rightwards towards the center of the green. If the ball is 40 yards from the tree, rather than 80 yards from the tree, then the golfer will need to curve the ball more to the right. To acquire a greater amount of slice spin, he needs to increase the magnitude of the divergent angle between the clubhead path and the clubface orientation - while keeping the clubface pointing just to the left of the tree. In other words, he will have to swing his club more leftwards if he wants to produce a greater degree of slice spin. It is only through repeated practice that a golfer can learn how to vary the magnitude of the divergent angle between the clubface orientation and the clubhead path to produce a certain finite amount of slice spin that is optimal for this particular ball flight predicament.
http://perfectgolfswingreview.net/ballflight.htm
http://perfectgolfswingreview.net/index.html