# Low point and Parametric Acceleration

## Low point and Parametric Acceleration

This post includes a lot more technical detail than I normally talk about. I am going to discuss a topic that will hopefully spark some good quality discussions which can further our understanding of the golf swing, and specifically impact. I am also going to, in this and future articles, suggest the practical implications of this information.

Full credit goes to Chris Como for this information. He is currently doing ground-breaking research on this topic and was kind enough to share information with me, which I hope can help some players and teachers. Also, Sasho Mackenzie has done some modeling on this topic and, as I understand, has worked with Chris on proving this theory.

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If you look at the below picture, it shows a pendulum swinging back and forth. Just like any circle with a fixed hub, it will have a very small ‘low point’, marked out in green (the reality is the lowest point of the swing is infinitely small). Hopefully, this is simple to understand.

If a pendulum (or club) is swinging from left to right across the screen, we could speed up the pendulum by pulling the end of the string (or club) in the direction of the green Arrow. Forces want to line up in the direction of the pull, so the bottom end of the pendulum will try and line up with the dotted line by speeding up towards it. This has been coined ‘parametric acceleration’.

If we are pulling the top of the pendulum in the direction of the green arrow, not only does it speed the bottom of the pendulum up, but it will raise the overall height of the pendulum (as it is being pulled upwards).
But the act of pulling upwards whilst the pendulum head is still moving downwards neutralizes each other. The result is a flatter ‘low point’ in the arc of the pendulum swing. This is highlighted in red.
handle moving up, clubhead moving down = flatter/wider ‘low point’
If we are to apply this to the golf swing, look at the below picture. The pendulum is being swung along the hand path, which is moving down and forwards, before moving forwards and upwards. This dramatically increases the speed of the clubhead, and also creates a much longer and shallower low point.

## What are the advantages of this?

### 1. A longer and shallower low point

It can offer a larger margin for error. If the first point of contact with the ground is too far behind the ball, it will have less of an effect on the ball flight and control. Conversely, a swing which doesn’t include this pull in the direction of the green arrow will continue to descend. This will mean that the control of the first point of contact with the ground will need to be much more precise.

### 2. More speed.

The pull in the direction of the green arrow will speed up the clubhead, offering a mechanical advantage (much more speed with for the amount of physical effort applied).

### 3.   More compression.

The player will be able to hit the ball with a more forward leaning shaft position (relative to swing direction), allowing the club to be delofted, hence lowering spinloft and helping the player hit the ball further for the same swing speed.

Without this pull away from the ball, the player could only achieve this decreased loft by having the ball further back in the swing circle. The problem with this is that the player will have an increased angle of attack (steeper) and so spin loft (and hence compression) may not be improved. Also, the player may hit massive divots which need to contact the ground in the right place more precisely, lowering margin for error.

### 4.   Longer line of compression

with these moves, the angle of attack and dynamic loft through the impact interval will remain more constant (than without), offering a longer line of compression. I am not sure we fully understand what this means yet, in practical terms. But it could offer potential benefits to consistency of distance control.

## So, is there evidence of professionals doing this?

Whilst 2D is not the best at looking at these types of things (due to something called parallax, on top of the fact that the swing is a 3D motion), we can see, in the below image, a visual representation of this movement from front on. Please understand, there will also be an inward component to this move (as in the grip of the club being pulled away from the ball to target line).
You can see clearly the hands raising through the hitting zone. Even more so if you look at the coupling point (the point where the two hands meet).

## Practical implications

So, if an optimal hand path moves up and inwards (towards the golfer), we need to understand how to do this – or what are our options?

The first thing to realize is that, if we are going to be pulling upwards, at some point we have to get the coupling point low enough so that we have ROOM to pull up without topping the ball or missing it altogether. Where beginners go wrong is that their hand path through impact is usually too high to begin with, so any pulling up and in would result in a top shot. So usually, they don’t (or do and top it). Or, they move the hands down towards the ball through impact and have major struggles with low point control/consistency.

In the above picture, the red and blue lines represent hand path through the hitting area. The red line is that of an amateur, with the lowest point of the hand path being much further back (opposite right foot) and also being too high through impact. The blue line is more that of a better player, with the hand path being lower down. It also has its lowest point more opposite the right leg, and raises more sharply. This is a good visual to imagine when working on this concept.

## Squat

Why is the professional’s hand path lower down? In almost all professionals, you will see what we call in the industry a ‘power squat’. This is where the player will drop in height. Often, this occurs during the transition between backswing and downswing, but some players do it earlier (during the backswing) and some do it a fraction later.
Take a look at the pictures of Tiger below

We can see in the above picture (pre transition) that Tiger’s head has already significantly dropped in height.
Wow. That’s a foot of height loss as he is coming into impact.
Also, see the below video of Mcilroy for the same basic movement pattern.

This drop in height is created by a drop in hip height, and usually an increase in forward flexion of the spine.
the decrease in sternum height is clearly seen here (from yellow line to red line)

## The raise

Now we have the hand path low enough, we have to raise it through the hitting area. For the best players in the world, the hand path is at its lowest point around the area of the right thigh, before it moves up and in. So, how do we get the hands to move up and in? We have a few options
1. Get the sternum further away from the ball
2. Scapular retraction (left shoulder)
3. Allowing left shoulder to raise through impact through the body rotation
4. Shorten the radius of the swing (bending arms)
Out of our 4 options, with tour players, we more commonly see 1 and 2. However, This below video of Jamie Sadlowski shows him exhibiting all 4. For those of you who don’t know, Sadlowski is a World Long drive champion who has hit the ball 445 yards.
Through the hitting area, he demonstrates his sternum getting further away from the ball by going both upwards and backwards. With a driver, this movement will produce a more upward angle of attack on the ball, allowing for maximum distance, as well as the benefits described from moving the hand path up and in. The backward component (if excessive) may lead to problems with iron strikes, depending upon several other variables. Jamie also achieves moving the sternum further away from the ball via his hip height increasing through impact, created by literally jumping off the ground through leg extension.

Jamie also demonstrates his left shoulder moving dramatically upwards through impact. Moving the head backwards has helped create room for this, and so has having his spine tilted away from the target.
Point 4 is easy to see. Look how much his lead arm has bent through the hitting zone. This has helped Jamie to raise the handle away from the ball even more, allowing him to release his insane amount of lag right around impact – creating insane amounts of speed and distance.

## The irony

The irony of most of this is that, the movements which produce a good hand path have often been frowned upon. Dropping your height and jumping up through impact, for example. The theory has been that, the less moving parts we have, the more consistent we can make the movement.

Whilst this may be true logically, in a biological system which requires ‘margin for error’, more moving parts and more degrees of freedom may offer several benefits over something which looks prettier, more symmetrical and ‘tidy’. It is no surprise that Tiger Woods exhibits a lot of the traits described, and that he has also been one of the best (if not THE best) iron players in the  world over the course of his career, as well as a long hitter of the ball. Again, ironically, these good traits he has were almost taught out of him. Luckily for him, his body never really listened to his training, and he continued with what he did naturally.

I recently added a whole module of drills, exercises and added information regarding this topic on my signature program – Next Level Golf. Make sure you check it out – click the image link below to learn more.

## Take home notes

So, in summary, if you provide an upward pulling force through the hitting area, you can not only create speed through parametric acceleration, but you create a longer low point (for more consistency) and the ability to hit the ball with a lower spinloft (more compression). You will also create a longer line of compression. All of these are good things.

Also, more degrees of freedom and more moving parts can actually be a good thing. Most teachers try to be too restrictive. Whilst this can work, and there are often times I do it myself (if I deem necessary), the idea that less moving parts = more consistency can be taken too far.

What amazes me the most is how our bodies are so intelligent. Tour pro’s have found these macro movements without being told about them, and often in spite of being taught the complete opposite. It also amazes me how the human body can organise so many moving pieces, all moving in different planes of motion, at different speeds, rates of acceleration etc, yet combine them all to produce the impossible; a ball which flies 300 yards down the fairway. Just a couple of degrees out and the ball is offline, yet we manage to do it on (almost) regular occasion. Without going too much into the theory of the uncontrolled manifold hypothesis, it is safe to say that we, as humans, are pretty damn amazing at organising all of these complex movements into one harmonious symphony. We should try and tap into our self-organising skills more often.

### Acknowledgements

I must mention Jon Hardesty for our discussions on this topic. It is also right of me to mention Chris Como and Sasho Mckenzie for their information on hand path, and also Brian Manzella for consistently bringing hand path to my attention. And also to Jeffygolf for the use of the parametric acceleration video.

• #### Andy Laird

Fascinating subject Adam, and a very nice explanation as to how and why it works.

Do you post on GOLFWRX because this would make an excellent discussion thread on there.

Thanks Andy, I wouldnt be able to post my own blog, it gets blocked. but if someone else does it, it can work. Let me know if a convo starts going 🙂 I am a member of that site

• #### Ron Bowers

I would like to see a discussion of the backswing counterpart to this, which is rarely discussed anywhere. the pros or noted to have “great lag”. I do not think can can teach this by static positions i.e. “holding the lag” on the downswing. Lag will occur naturally if
this is enough momentum at the top of the backswing to pull against. This happens “automatically” as you say about the downswing. Kids, since they are usually swinging a club that is heavy relative to their size leave the wrists cocked a long time in the downswing because they do not have the strength to cast the clubbed.

Like parametric acceleration, This is poorly appreciated in teaching, in my opinion.

Players like Bubba(who says he has never had a lesson) show this in the extreme.

Also if you notice Jordan’s pre-swing preparation he starts the cub from a position in the forward swing to feel the momentum at the to.

Your comment has many merits. We are only recently (as golf instructors) discovering the differences between kinetics and kinematics. The example you used – it can be detrimental to try to “hold” lag – but using momentum and other forces in the swing (or lines of forces), we can achieve lag via proper kinetics. It’s not just about how it looks – it’s also about the underlying forces which we cannot always see.

• #### Jasper7

If only it was that easy to do. My brain scrambles just trying to imagine it.

It's something I've seen Rory Di, that rise at impact

• #### Anonymous

Question is – is it worth doing considering the manipulation required ?

the real question is – When most good players automatically do these moves without any conscious thought, effort or direct learning of them, is it worth trying to make their body positions more stable given the manipulation required?

• #### Robert Saunders

Adam. Along these lines, what do you think about deliberately slowing the hands down near release, causing a whiplash effect on the clubhead? Thanks,

Hi Robert

view my article on correlation and causation. Needless to say, I would prefer you accelerate the hands through impact and/or increase the radial pull (pull the club more towards your body and upwards) which would serve to slow the hands down and speed the club up.

• #### andy

what an interesting article, steve elkinton and a golf pro called paul koop made a video called the sequence, not only does paul talk about pulling the left shoulder back through impact but he also pulls the right shoulder back in the backswing. it seems to me that you are talking about similar things

• #### Franklin

Easiest way to do this is, after the transition has allowed the lead leg to push against the ground, to push up. The Squat and Spring. The push up will continue to rotate the hips. The upper body parts, hands, sternum and shoulders, will go up and back accordingly. Any focus or effort to bring about parametric acceleration via upper body action will not work as well.

Hi Franklin – great comment. I agree that the moves should come from the ground, as this creates certain forces and anatomical positions which allow the body to rotate better. However, some people do need more of an upper body move. The feeling of the left shoulder moving up and back away from the ball as the upper body rotates open can help some people. It all has to be done on an individual basis.

Typically, I don’t work on these moves directly with students, they re just things I look out for. I tend to improve the dynamics through other thought processes, and wrote the article to potentially avoid un-teaching these moves, should a teacher see them in a player.

• #### Franklin

Parametric acceleration (P.A.), via ground reaction force and vertical forces, is the most important concept I have come across in twenty five years of playing golf and reading about the swing. It has taken awhile for me to get used to the motion of pushing up with my lead leg. But doing it correctly has allowed me to hit my irons farther and higher as P.A. says it would. I try to focus on a correct transition, of being able to feel that I am in position to push up with the lead leg. When I push up, the hips continue to rotate. A corollary benefit has been straighter shots as well. By focusing on the transition and pushing up with the lead leg, I am not doing other things that would ruin the swing, i.e., (1) rushing or hitting from the top and (2) spinning out with the hips. I have less risk of a pull with my irons.

• #### Lam

Where would be a good place to start studying P.A.?

• #### Kiran Kanwar

Think of the issue of creating parametric acceleration in a 180 degree opposite manner. If you stand as upright as possible to start with, keep the trail trunk lower than the lead during the backswing, have a purely horizontal plane hip rotation during the downswing, have the arms and club arriving from the inside for a shallower-than-typical impact so as to connect the inside trail-side quadrant of the ball, and have hips rotating ahead of shoulders, with the head staying back, you cannot help put get the lead side to rise through impact as the clubhead goes lower.

• #### John

I tried adjusting my hand path so my hands travel up and to the left after impact and I noticed an instant increase in distance and trajectory height w/ the ball ending up the right side of the fairway.

Normally I have a low draw, sometimes a hook. So finding the right side of the fairway is a strange feeling, but it is a god send considering the low hooks are my nemesis.

Just changing the hand path seems to cure the hook?
I think my old hand path goes left, but not sure that I used to have the “upward” motion.

Is that upward motion causing the clubface to not close as quickly.

Just trying to understand why my hook has disappeared.

It will either have changed your path (made it more to the left) or limited face closure for sure. One of those will have to have changed. Without seeing, I wouldn’t like to guess.

• #### Bob

I learned this about 15 years ago looking at pictures of Jack Nicklaus and Laura Davies at impact. Laura Davies on her toes and Jack’s bent back had to mean something, and I started thinking of it as pulling on a rope instead of swinging the club down the line. It works and I have become a pretty good golfer as a result – low index of .5, but running about 4 right now after injury. It could be the most important thing to learn. I also twist (supinate) my left hand a little, making it very easy to square the club face. Note that your swing path needs to be about 10 degrees to the right of the target line. Excellent power and control even as I near age 60. The angle you pull at also becomes critical. If you pull back more, “under” your starting plane, the ball goes left and a hook often results, the opposite is true if you pull more upward “above your plane” – higher fade.

A word of warning – it takes practice, and if you start doing this all the time it is 1) physically demanding on your back, so overuse is an issue, and 2) you’ll outdrive all your friends, making you want to do it even more – go back to 1). On slow swings, like half wedges and such, it is very, very subtle. Keeping your upper arm near your chest is critical, notwithstanding what Jamie Sadlowski does with his elbow bend. That takes a lot of something that apparently most of us don’t have.

• #### Mike

We covered this concept last night in Kung Fu class. We were talking about delivering max power and focus with hand foot and sword strikes. It was great to watch Shifu doing a golf swing with his sword. Talk about a nasty slice. 🙂

• #### Kirk Junge

This is great work Adam!! I currently teach people how to achieve a longer flat spot and have recently been experimenting with a couple of ideas. Besides the flat spot, it seems that there will also be little to no clubhead rotation through impact, and little to no swing arc. Seems impossible that you can have flat, square, and straight line at impact, but as the grip is being pulled up it is also pulled to the inside stopping the club from moving outside, but rather keeping it straight.

I have seen a few postings somewhere on this, but cannot locate them now.

Keep up the great work!!

Kirk Junge
learninggolf.tv

• #### Michael

I use to do this and got talked out of “too many moving parts”. It turns out I was playing with the wrong equipment. Shafts too weak and grips too small. This was the cause of over swinging and mishits. The clubs were not stable enough to through transition and impact. I use to have a very long swing. People told me to shorten it. I couldn’t because now I know the shafts were too weak so I had to swing long to give the shaft enough time to catch up. Got into x stiff shafts and my swing auto corrected to parallel or just short of at the top. I can actually swing the club faster now with center strikes. I went to teaching pros and they always would try to correct the swing without inspecting the clubs. I mean they do but never put enough effort into making sure they are spot on. Swing weight for instance is a major factor. Too heavy and the club can get laid off if and only if for that reason alone. Too light and it can come out and over all by itself. Which in essence is not a swing flaw but a club flaw for a players swing profile. I see plus 6 handicap players playing swing weights that are too light. So being good ball strikers they manipulate the club to a stuck behind position and hit big draws then hold it off to hit a baby fade. If they didn’t drop the club in the swing weight of the club being light would throw the club out over plane. The opposite being swing weight too heavy. Good players would throw the club out and more from the outside to prevent a laid off too high handle too soon fat miss. It’s getting that swing weight correct that will get the swing in the plane window that allows for a much better margin of error. And thus allow the golfer to focus more of parametric acceleration as a key move through the ball creating an even better margin of error! The fat flyer is a good example of this. It was hit fat but low point continuance allows for a decent miss even though a fat shot is much worse than a thin one. So point being: Get your clubs on point first. Err towards lighter than heavier. Always easier to hit from the inside and shallower if you’re going to manipulate somewhere in the transition. Plus it’s always easier to add weight to the club than it is to subtract if the club dynamics are too far off

Boy do I ramble. Any how….

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