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#1 ThanksForAllTheFish

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Posted 13 December 2011 - 06:36 AM

This a thread I proposed in the Looking at Graphs thread. The purpose is to do an analysis of the following graph using agreed principles. Contributions are welcome from all who either know or want to know the principles of v-t graphs.
Just to make it clear, this thread will not help anybody to play better golf. Except for the pursuit of pure knowledge the thread will be a complete waste of time. If highly technical discussions aren't your thing, you will be better off finding another thread to post in.
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#2 ThanksForAllTheFish

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Posted 13 December 2011 - 07:47 AM

The principles are those used in kinematics. These are that the slope is a measure of the acceleration and the area under the curve measures displacement from time to time. Note: edited to correct arithmetic For example, the red curve from t=14 to t=16 (on the horizontal axis) is steady at approximately 196 (on the vertical axis). That is an area with a width of 2 and a height of 196. The area is 392. Counting rectangles gives an estimate of the whole area between the red curve and the axis of 20 by 196. That gives a total area of 3920. As a first estimate, for a top player a downswing takes around 0.250 seconds. That would make the units on the horizontal scale approximately one hundredth of a second per frame. If the vertical scale is degrees, then the area of 392 above corresponds to a rotation of 3.92 degrees and the total rotation of the hips from start of downswing to impact of 39.2 degrees. That sounds about right. A hip rotation of 39.2 degrees over a period of about 0.25 seconds. What say you Weetbix? Close enough to proceed?

#3 Weetbix

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Posted 13 December 2011 - 09:11 AM

Close enough, although I would estimate the hip movement at much closer to 45 degrees (based on averaging around 196 dps over .25 seconds). But close enough. What say you?

#4 ThanksForAllTheFish

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Posted 13 December 2011 - 04:26 PM

Close enough, although I would estimate the hip movement at much closer to 45 degrees (based on averaging around 196 dps over .25 seconds). But close enough.

There are two issues intermingled. The first is the scale. The second is the area under the curve. How confident are you about the scales? I'm pretty confident that the vertical scale is degrees per second. I'm less confident about the horizontal scale. The red curve crosses the horizontal axis at about t=5 and impact is marked at t=23.5. That would make the duration of the downswing about 0.185 seconds which seems a bit quick. We may have to revisit the hundred frames per second estimate later. I think 45 degrees for the area under the curve is a bit high because of the 0.185 figure above. Calculating by eye is always subjective, but between t=5 and t=23.5 the red line looks to have about the same area above the 196 as it does below. That would give us 36.3 degrees. We've currently got estimates between 36.3 and 45. Would you be happy to work with say 38 to 40 degrees as an estimated range for now? If so, over to you to calculate the area under the blue curve (shoulders?).

#5 Weetbix

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Posted 14 December 2011 - 03:02 AM

What are you trying to learn from the graphs though Hermit? Why are we guestimating the total amount of movement of each body segment?

#6 ThanksForAllTheFish

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Posted 14 December 2011 - 05:16 AM

Weetbix, as you know, you can tell three things from a v-t graph. First and most obviously the velocity at any time. Second the acceleration at any time. Third the displacement over any period. My aim in this thread the aim is to extract as much information as possible from the graph. If anybody then wants to carry on and discuss swing theories later on, they will then have a solid set of numbers to work from. What is your aim in participating?

#7 Weetbix

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Posted 14 December 2011 - 07:11 AM

Was just continuing the discussion from earlier, which was more about what the data is saying about the golfer's movements. Given that the diagram is difficult to analyse mathematically because as you've noted we don't have exact values for the X axis I doubt we'll get anything revealing from trying to work out the values for displacement. Happy for you to do it of course. And then we can discuss the conclusions?

#8 ThanksForAllTheFish

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Posted 14 December 2011 - 07:53 AM

Good to hear. We can run a range of scenarios for the x-axis so I don't think it is too much of a problem. I'm happy to discuss the conclusions, but it probably needs to be in another thread (not lead by me) and I'd like to get all the numbers in place first. Counting squares to get displacements is easier than talking about velocities and accelerations so I'd like to do those first. Do you still have a copy of the graph to do the numbers on the shoulders?

#9 Weetbix

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Posted 15 December 2011 - 07:46 AM

No, no access to the graph any more. But to be honest the mathematical numbers aren't that interesting to me. It's what the graph represents. And also, when I compare that to my own graphs, what it says about my action.

#10 ThanksForAllTheFish

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Posted 15 December 2011 - 08:15 AM

Oh well. Never mind. How do you know what the graph represents if you don't know the numbers?

#11 Zenstb

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Posted 15 December 2011 - 03:16 PM

Quite simple if you understand what the graph truly represents. The numbers aren't the primary focus,the pattern and sequence of how the body is moving is what the graph is about. You can cover the numbers so I don't see them and I can tell you exactly what that graph is tell us and what sequence the body is moving in. To be honest we never look at the numbers on this graph, we look at the pattern. Weeties made a great point in his post, he is right and he doesn't need to look at the numbers either, all he needs to know is what pattern the graph is indicating. If anyone wants to know why I had the graph removed I explained in ISG feedback Copy right thread.

#12 ThanksForAllTheFish

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Posted 15 December 2011 - 04:06 PM

Zen, as I've said on many occasions, I'm interested in your work. In this thread I'm only going to discuss the numbers. A couple of numbers of interest to me are about the motion of the club. Assuming 100 frames per second, the graph shows a negative rotation of 24 degrees then a positive rotation of 82 degrees. Overall that is a positive rotation of 58 degrees. If you want to discuss what the graph truly represents please do it in another thread.

#13 Weetbix

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Posted 15 December 2011 - 05:10 PM

Positive of 58 degrees in the time period that the graph actually represents. Which is the last bit of the backswing and the downswing and just past impact. Which is why I don't see how understanding the actual values will help because it is a slice of time, not the complete action.

#14 ThanksForAllTheFish

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Posted 15 December 2011 - 06:09 PM

Weetbix, in this thread I'm only going to talk about the numbers. If there is to be interpretation of the numbers then I've said what I wanted to say in the Looking at Graphs thread. You or somebody else may want to start another interpretation thread. I won't.

#15 Weetbix

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Posted 15 December 2011 - 07:33 PM

Ok.




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