Power: The Geometry of Acceleration (Lesson 6, Part 2)

Some holes require all you have.

Some holes require all you have.

About this site: Golf as God Gave It To Us

[Note:  This an “Albert Einstein” post.  The ideas here are a bit harder than in most posts.  On the other hand, they are well worth taking the time to understand, to obtain a clearer picture of the overall swing.  I suggest reading it over several times if it doesn’t make sense.*]

In the prior lesson on Power, we said that we’d discuss a few aspects of this part of the downswing, building up energy, that need more detailed discussion. The first is what most people describe as “extension” or some call “width.” Before you read the lesson, I encourage you to watch this video, which contains several shorts of Jack Nicklaus’ swing: controlled aggression “crashing into the ball.”

*A couple notes follow this post, which clarify certain points as  noted in the text. This post is indirectly related to this lesson.

Extension

A common aphorism is that one should attempt to get maximum width in the swing.  The explanation is that “width” increases the radius of the path traveled by the clubhead; therefore, so the reasoning goes, one can generate more power.  Larger radius implies more power, is the syllogism (or logical link).

Not true.

Not true at all.

Maximizing the Ability to Build Up Energy

Radii

We’re going to start by simplifying the problem a bit, removing a “hinge” from the swing.  Suppose you were to swing a rope or string with a weight at the end of it around your head, or, if you like, around the center of your chest at a 45 degree to the body (to make it seem more like the movement of the clubhead around the body).  One knows intuitively that if one makes the rope very short, one can increase the speed by letting out a little more rope.  One might be able to spin faster with a shorter rope, but the number of rotations to make the weight travel a given distance have to make up for the shorter rope.  That’s why, up to a point, we sense that letting out more rope will allow us to make it swing faster.

So you say, “aha! A larger radius does mean more power!!”

To which we tell you “to a point.”

One should likewise realize that at some point letting out more rope will make it harder to rotate the weight around one’s head.  (One can imagine trying to rotate a weight around one’s head with any appreciable speed with a 20 foot rope.  It’s not going to go very fast, if you can get it rotating at all.)

There is actually an optimal radius or length of the rope, if you like.  The optimal radius will depend upon two factors:  (a) the power with which you can apply to the rope with your hand/arm, and (b) the mass (or weight) of the weight at the end of the rope.  What this says is that in swinging the club, for the sole purpose of power, added extension away from the body will not enable the golfer to move the clubhead faster around his body.  In fact, it will move slower at some point.  Yes, extension at a point is counter-productive.

Let’s try a couple, perhaps three, ways of seeing this.

The first way is to give a different example than the rope with the weight.  It is one example of rotational velocity but not the only.  A more common example is one you can try at home.  Go to a door, preferably of some weight.  If you try to close the door by pushing at a point very near the hinge, you will see that it requires a tremendous amount of effort.  Now if one goes to the end of the door, it is pretty easy to push it closed.  However, try to barely push it.  Just a small bit of force.  If you keep moving your finger closer to the hinge (but not past the middle of the door) from the end of the door, you will find that you can close the door with a very small force applied in the center of the door that would not close it if applied all the way at the end of the door.  Another way to get the idea about the end of the door is to imagine a very, very large door — perhaps 10 ten feet wide from the hinge.  If that door has any weight – for example it is steel, a couple inches thick – it will not be so easy to close the door by pushing it at its end.  You don’t see people trying to close bank safe vaults by pushing near the end of the door.  They push right in the middle of door.  Because it’s not so easy, and you have to take care to maximize (or optimize) the energy that is available to you.

Too much of a good thing is in fact bad.  Extending the radius of the swing too far will actually diminish the energy that can be given to the clubhead.  (Some call getting too far away from the body “becoming disconnected.”)

Teaching professional Ed Oldfield, Sr., describes the golf swing as “tight, rigid, compact.” (This year’s winner of the Memorial Golf Tournament, Matt Kuchar, tells us that he is working on keeping a tight swing radius in the Golf Digest swing sequence featuring his swing. He calls it a “basic tenet.” Too bad no one ever tells most golfers that.)  The trick is to have it be tight enough so you can effectively accelerate the clubhead around your body.  One cannot not let it get so loose that one loses the ability to accelerate the clubhead.

Now, before ending this section of the post, I will point out that there is something that human beings do not like in general.  Most people dislike gray areas.  And this smacks of finding a point “in a gray area.”   I could put this in fancy math terms, but the fact is that one wants to find the place where one can move the club head around the body as fast as possible, it will be neither as close to the body as possible, nor as far as the arm and shoulder muscles and tendons might allow one to extend.  One is looking to find a kind of “golden mean.”  How far depends upon the strength of the golfer and the weight of the clubhead.  Thus, for any individual golfer, there is an optimal radius, or “golden mean,” at which to have the club head extended away from the body.

Right angle of hinge

You may have noted, or you should have noted, that in the prior part of this lesson, all the great athletes were fully loaded at a point when there appeared to be a right angle. It is worth returning to these photographs, which appear here.  In soccer, there was a right angle between the upper leg and the lower leg, at the end of which was the part of the body (the foot) which would strike the ball.

Tim Lincecum, loaded.

Tim Lincecum, getting loaded.

In tennis, there was a right angle between the upper arm and the lower arm, at the end of which was the part of the body that would propel the racket (the hand).  In baseball, there was also a right angle between the upper and lower parts of the arm, at the end of which is the hand, which is the final connection of the body to the baseball (the hand).  In golf, there is a right angle between the left arm and the club shaft, at the end of which is that which will propel the ball (the clubhead).

Why all these right angles (sometimes called, in a slightly different way, “lag” in golf)?

Imagine trying to accelerate the clubhead, at an extreme, by having the clubhead stuck straight out from the left arm.  One can see (very similar to the point about our long steel door above) that it would be very difficult to accelerate any sort of weight at that distance from the body, particularly if the club were a driver.  As one reduces the angle between the left arm and the club to 90 degrees, one will find that one can gradually improve the velocity (mathematically) that can be achieved with a given amount of energy applied, until one reaches an optimal point, which is the right angle between the shaft and the left arm.

Nicklaus at transition with four clubs, D, 2, 5, and 9 irons.

Nicklaus at transition with four clubs, D, 2, 5, and 9 irons.

As one can see from this still of Nicklaus’ swing with four different clubs, he creates a right angle between his left arm and the shaft in all four swings.  The super-imposed right angles in two of the stills appears to show slightly different from a right angle, unless one looks closely — because the plane of the camera (face on) differs from the plane of swing, it appears that there is not a right angle.  In the photograph below, we see the same right angle mid-way into the down swing.  (Again, any difference is mostly attributable to a difference between the camera plane and the swing plane.)

Nicklaus in downswing.

Nicklaus in downswing.

(Note: we will leave aside several complexities that come into play if one allows the left arm to break, in effect putting two hinges in the swing.  Take on faith for now that any added power that might theoretically be obtained by allowing the left-arm to create a third hinge, and how, will be offset more by a loss of accuracy – applying the clubhead squarely to the ball.  If someone wishes to send in a question, I can discuss this in great depth, but it can get confusing without a blackboard in place.)

And that is why the best golfers “happen” to all have that right angle.  It is the best way to pull the club around the body. [1]

Applications:  “Casting” and “Lag”

There are two familiar points that arise in discussing this aspect of generating power.

One is “casting.”  I note this every so slightly in the start of Luke Donald’s swing.  As he starts his downswing, he ever so slightly casts the clubhead, which in the terms we have been discussing, means he is increasing the angle between the left arm and the club shaft.  It is impossible to reverse this effect, or practically impossible, to reverse this effect.  Once you have cast a bit, you have limited your ability to generate as much power as you are capable of.  If you keep on “casting” or allowing the angle between the shaft and the left arm to open up, it will become progressively harder to accelerate the clubhead.  (There is another problem that “casting” introduces at about the time of release, but we will leave this for a later discussion.) It is not surprising to me that Luke Donald does not hit it as far as some tour players who are no larger.

Another is “lag.”  In the part of the swing where we seek to generate power, having the wrists hinged (but not cupped) allows the rotating body to accelerate the clubhead in its circular arc as fast as possible.

What about “Hogan’s lag” or “Sergio’s lag” in which there appears to be an angle smaller than 90 degrees between the left arm and shaft?  There are two answers to this question.

SergioAngle

One can see from the swing sequence above that Sergio clearly has established a right angle.  In the fourth still, Golf Digest says there is an “acute” angle between the shaft and arm (that is, less than 90 degrees).  But the writer is clearly not taking into account the plane of swing.  Yes, there appears to be a right angle when his swing is turned into a two-dimensional image and projected onto a plane (the plane of the photograph) that is not parallel to the plan of his swing.  To notice this more easily, note the club face, which is roughly parallel to this plane.  If there is the type of “acute angle” lag that they are supposing, it is at best tiny — as suggested by the fifth frame.  It is true — in a very different sense — that his plane of attack has the club head lag behind his body more than someone who has a different angle of attack.  However, this is not the sense in which commentators on his swing have supposed that he is “lagging” the club.  (Having studied pictures of Hogan, given photographic quality and the clubs he was swinging, it is harder to discern whether there was such a “lag” — meaning more than a slight difference from a 90 degree angle.)

Aren’t they losing some of their ability to most efficiently generate energy, or maximize the energy they can generate or build up, prior to the point of release, if there is an acute angle? That is a good question.  The answer gets technical.  If in fact the angle is less than 90 degrees, they are losing some ability to accelerate the clubhead with a caveat.  A slightly smaller angle than 90 degrees at some point in the downswing may allow these golfers to ensure that they never exceed 90 degrees in pulling the club around their bodies.

Ernie Els

Ernie Els

However, once one has passed the point of 90 degrees, if too early in the downswing, the results will be deadly.  It is very important not to allow this angle to become “obtuse” prior to the point of intended “release” of the club head into the ball.  This right angle is lag itself.   The ability to accelerate rapidly disappears (in effect because one can no longer pull the club along a series of straight, ever-changing paths, in a motion that is pointed in the same direction as the butt of the club), and, equally unfortunate, as we shall discuss in the part of “Power” where we discuss the release and points after, it becomes very difficult to apply that built up energy in an ideal fashion.  In short, better to be slightly too tight (or hinged) than too much (Please note:  In both cases, without “cupping ones wrist, which leads off into a separate subject having to do with the geometry of the swing and getting the clubhead to meet the ball “squarely”).

What, then, does ‘Extension’ Mean, on the Backswing?

So why do teaching pros emphasize extension on the backswing, and what sense can we make of it?

In the course of answering this question, a hint:  we will also cover what it means to “go past parallel.”

On the downswing, we want to have a right angle between the club head and the left arm (if a right-handed golfer).  If the angle is larger, we lose our ability to accelerate the club head at our maximum.  Too much energy gets spent in making the head come back to the ball, without being technical, than on our circular path.  If the angle is smaller, our energy starts to move the club head more out than it goes around.  Which puts us in the casting position. It also reduces are ability to accelerate the club head for a given distance of the hands away from the relaxed left shoulder.  Even if we don’t do that we reduce the radius by which we can accelerate the club around our body.

At the top we want to be parallel, if the left arm is pointing up or its line is parallel to the body.  This establishes the right angle.

One can get “false extension” by pulling the hands away so that the arm pulls the shoulder in and away from the body. This is what most golfers are led to believe is “extension” on the back swing. Once those hands go farther away from the body than the extended left arm at its maximum extension, one loses the body’s ability to power the clubhead – try it – a tighter swing with a straight left arm will given you the sensation that the clubhead is rotating around your body at a much faster rate, or should — it can feel quite powerful.

Golfers “who pick the club up”  [2] are prone to getting too much hinge, and going past parallel — which means that they reduce the right angle to a smaller angle.  To counter-act this tendency, golf professionals will advise students to work on extension — which really means keeping the angle greater than 90 degrees on the backswing until it reaches 90 degrees at the top of the swing.

Bubba Watson goes long past parallel and has all the wrong angles but he manages to work himself into near perfect position at impact -- no easy feat.

Bubba Watson goes long past parallel and has all the wrong angles but he manages to work himself into near perfect position at impact — no easy feat.

Now, from this, it should be clear that the object is not to extend away from the body.  How far the club head is away from the  body on the downswing should depend upon what arc or radius will allow a particular golfer to accelerate the clubhead fastest.  For any given arc, or radius, the optimal angle between left-arm and shaft on the downswing (up to release) is a right angle.  Therefore, one could swing back with less “extension” as long as one does not “go past parallel.”

To bring the terms home into everyday “golf” language, this is the difference between an “early set” and a late “set.”  Whether a golfer, say Sergio who “sets late,” gets an early or late set, they seek the same optimal arc or extension for their power to accelerate the club head.  It tends to be that the shorter the backswing, the earlier set makes it easiest to transition to the downswing at the right angles.  On the other hand, the longer the backswing (either because a physical characteristics or because one is taking back a longer club), the later one can “set” the club (at a right angle).

Sergio is an interesting example.  It appears from a straight-on picture that his angle on the downswing is less than 90 degrees (“the lag”).  However, if one views video of him at the transition from the top to downswing which is at a 45 degree angle to straight on, one sees that the club on that plane moves from more than 90 degrees to a 90 degree angle — just on a different plane than one can see with a straight on camera shot.  Likewise, there are great videos of Nicklaus in the series “Golf My Way,” where he is shown swinging in slow motion a number of different clubs from pitching wedge to driver.  It is useful to take the time to watch the angle of the arm/shaft as he gets to the top of his backswing, and then as he starts down.

In short, the object of “extension” on the back swing is not to get the clubhead as far away from the body as possible, but to make sure that the angle between arm and shaft does not go past parallel to less than 90 degrees, which, in most golfers, is likely to lead to casting as the body tries to undo “the fault” or less than optimal placement of the arm/shaft for speeding up the club head as fast as possible.

This is extension on the back swing.  Watch the videos of Jack and Sergio near the top – who most people would say have very different swing types.  [3]  They get into a common position.  This is no accident.  One can’t produce all that power without making full use of the geometry of body and club that will allow for greatest club head acceleration to the point of “release” (a term we shall fine tune eventually, so people better understand what it means).

Take-Aways

Clear as mud?

I hope not.

It’s a lot to take in, but a knowledgeable enough professional, carefully selected, should be able to help you to put it together — and if he or she can’t, you have to ask whether you are with the right teaching professional.

He long ago stopped caring about right angles, and perhaps became unhinged.

He long ago stopped caring about right angles, and perhaps became unhinged.

There are two take-aways, to summarize.

From the first part of this post, you should take away that when you swing the club, you should feel like the swing is “optimally” tight and compact.  You should feel that the clubhead is a distance away from your body that allows it to be accelerated with the greatest force you can apply, and achieving the greatest velocity just before you get to release.  This is neither too close to the body, nor too far from the body.  It is not at a place that can easily be defined.  It is likely that it will be different, not only depending on a person’s body geometry (relationship of arm length to shaft length, arm length to height, arm length to width of shoulders and so one), but also importantly to one’s overall strength.  There is no doubt that a stronger person will be able to achieve a faster clubhead speed with a wider arc (greater extension) than a weaker person with the same arc.  But the reverse is not true.  A weaker person cannot build up more energy (achieve more power) simply by extending to the same arc as the stronger person.  The weaker person has to have a shorter optimal arc.  (Think this thought:  You might be able to push a door closed by pushing very near its hinge, but it may be impossible for a two-year old to do so by pushing at the same point — unless of course the two-year-old falls into the door when trying to push near the hinge.)

Many golfers have been confused for decades by this first take away.  They hear “extension” and think “extend” forever.  In fact, Jack Nicklaus contributes to this misunderstanding in his book, “Jack Nicklaus’ Lesson Tee,” when he tells people to “reach for the sky”.  If he means stretch the hands as far away from the body as possible, as opposed to – say – have the hands as upright as possible for a given fixed distance from the body, he is definitely ruining your swing, and the swings of many other golfers, causing them to lose, not gain power.  Exaggerate the motion someday on the range, and you will see he can’t possibly mean what he says, in the way he says it.  It creates all kinds of unnecessary confusion, and frankly, much as admire the man’s golf, is a short-hand that is deadly to distance.   [4]

The second relationship concerns the optimal angle to try to maintain between the left arm (for right-handed golfers) and shaft on the part of the downswing where one accelerates the clubhead.  That angle is ideally a perfect right angle.

That right angle seems to appear in all activities where human beings 'whack' something.

That right angle seems to appear in all activities where human beings ‘whack’ something.

As one can see, this very fundamental relationship — a right angle — is one that appears in the pictures we have appended from several sports, including golf.  It has everything to do with generating the most energy to transmit to that thing we seek to propel (a golf ball, a tennis ball, a baseball, and a soccer ball).  Moreover, what we have seen, is that a common swing fault (“casting”) is a variation of not replicating this optimal angle and that an attribute of some of the game’s best strikers of the ball (“lag”) is a variation of accentuating the positions that will ensure an optimal angle throughout the swing.

Conclusion

We have discussed a lot of “old wives tales” in golf, or short-hands, and tried to put them in a more sensible context. As the pictures show in the prior part of this lesson, the positions one hopes to achieve are not so complicated — really quite natural and intuitive — and now you know why those positions are optimal.

A. Einstein

A. Einstein

A. Einstein

[1] The right angle in a swinging motion. For one familiar with the mathematics of angular velocity and angular acceleration, the mathematics to show that the right angle is optimal are not difficult. It however is well beyond this blog and, if one takes it one faith, not necessary for our purposes. Even what mathematicians would call a ‘heuristic’ discussion of the proof requires a great deal of mathematical intuition, though if one has that background it is not a very difficult notion at all. We will try to leave the equations to universities and blackboards. Take it on faith that keeping a right angle between the left arm and shaft, for right-handed golfers, allows one to pull the club head (accelerate it) around the body as fast as possible, and that a greater or smaller angle (obtuse or acute) will lead to results that one could improve on.

[2] An “early set” and “extension.” It is easy to mix up two related swing faults. Often golfers who “set” the club early do so by a form of cheating. They allow the left wrist to cup, rather than to hinge. Once that “cupping” of the left wrist occurs, one is going to destroy the optimal radius one can achieve, though it really creates different more serious issues in the swing. Some great golfers play that way, but that is not to say that it is optimal — they make it work. As we say in the “About” section, we are never doctrinaire and anything read here to the contrary is a mistake. Rather the idea is to give a clear picture of why something works best, so one can compare what is best. In this respect, for swing radius, the idea is to neither extend too far nor too little — but both must be in the context of not allowing the left wrist to cup. For those curious about the proper left wrist movement (one what plane it should, or should not break), the book “Search for the Perfect Swing” discusses it fairly well. Watching the left wrist of Dustin Johnson or Sergio Garcia at the top — both of whom over-emphasize “not cupping” also gives one an idea of the best position.

Dustin Johnson actually pronates at the top, which is a very powerful position.

Dustin Johnson actually pronates at the top, which is a very powerful position.

At any point in the back swing, when the left wrist cups, it becomes very hard to put a good swing on the ball. Very hard. One can, but it requires all kinds of compensation factors that are difficult for most golfers to learn.

[3] Going past parallel. It is noteworthy that some very good golfers – Fred Couples and John Daly in particular – go quite a bit past parallel and they cup their left wrists. First note that both men are very, very strong. The other thing to note is that they make moves at the start of and into their downswings to get the club back into optimal position. They likely do not correct their “faults” because it would throw off the timing of their release. As we said at the outset, one size does not fit all — at the same time — we want to understand what might be optimal so we have some idea if we are doing something that is less than optimal why it may, or may not, work for us. The teen-age Nicklaus also had something of a breakdown of the left wrist at the top, allowing it to cup, which one can see from videos 25 years later he had corrected.

[4] “Reaching for the sky.” I do not mean to do injustice to Nicklaus by picking on his book, “Jack Nicklaus’ Lesson Tee.” If one reads his follow-up book, “My Golden Lessons,” he notes that by 1979 this swing thought had produced too upright a swing and that Jack Grout and he had to rework his swing so that he “went deep” rather than “went high.” He describes it best in “My Golden Lessons” himself. It is likewise noteworthy that his performance fell off by 1979 and it was the was the first time he did not play on a U.S. Ryder Cup team.

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