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November 26th, 2011, 05:37 PM   #1
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Measuring central angle of a curve given arc and chord lengt

Hello math experts, thanks for giving me the opportunity to post here.

My maths education is limited to a 16 yr old's so your help is much appreciated.

In my attachment, I have measured A, B and C in 112 different subjects. Using these measurements, I hope to come up with an approximate index that can be used to compare between subjects.

To approximate the arc length, I am going to average A and B. C will be the chord length of that curve. My question is: how can I measure the central angle of that curve given these values? It does not have to be exact, just an estimation that can be used to subjectively describe if one subject is more curved than the other.

In fact, it doesn't even have to be the central angle. Just a discrete value of some sort. Even something as simple as a ratio?

Please help! Thank you.

Jason
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November 26th, 2011, 06:04 PM   #2
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Re: Measuring central angle of a curve given arc and chord l

I have a thought on this that may help you eliminate the need of making those types of calculations. Construct a line that is even with the straightest part of the structure and use the distance from the tip of the curve to that line as the desired value.

To clarify, the desired value would be the length of the green line in the image below. The red line is the line that is even with the straightest part of the structure. I hope I have understood you correctly.

[attachment=0:21okf6qd]sacrum_edit.jpg[/attachment:21okf6qd]
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November 26th, 2011, 08:10 PM   #3
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Re: Measuring central angle of a curve given arc and chord l

hi Greg thanks for your reply and illustration! that is an idea. but that would mean I'll have to take more measurements. it took me 3 whole days to take the ones i've got...would like to use them if possible. but will keep this in mind.

ps just to further clarify my post

B is the outer trace and A the inner trace. C is the linear distance between the midpoints of the straight segments, and the straight segments are NOT included in neither A nor B.
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