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Clicking through this year's top sports pictures, I stumbled upon this one. I was wondering about the shape the baseball is leaving on the wall.

diamond shaped pattern

What phenomenon causes this peculiar shape? Why is it not radially symmetric? My intuition also tells me that the shape should be the solution of some special sort of wave equation (that takes into account the wall's material etc.). But, it looks like something substantially different...

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Hi Begeist. Please have in mind that images should be uploaded via imgur.com file-hosting :-) – Ϛѓăʑɏ βµԂԃϔ Dec 27 '12 at 10:13
I bet the people who study meteor impacts might know the answer. Great question! – ja72 Dec 28 '12 at 7:09

2 Answers

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The fabric covering the foam pad has a warp and weave (we can assume.) The fabric can stretch with the warp or the weave but not at a 45 degree angle, called the bias direction in sewing. So, when the ball hits the fabric it causes a wave in the fabric which begins to travel outward like a ripple in water. The wave causes distortion of the fabric as it moves, stretching the fabric if it can. The diamond shape is a map of the speed away from impact that the wave can travel through the fabric. Faster in directions the fabric can be stretched and slower in the directions it cant be. The longer dimension of the diamond is due either to differential in the tension of the fabric in the up and down as opposed to the right to left direction or because the warp direction can stretch more or less than the weave direction. It is a beautiful photo.

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Thank you for your answer! Why can we assume that the wall consists of foam covered with warp and weave fabric? According to Wikipedia a fabric is more elastic in the bias direction than in the warp or weave directions. – begeistzwerst Dec 28 '12 at 12:19
I did not really think it would be possible to confirm the construction of the fence so I guessed based on personal knowledge. I did get the fact of stretchiness backwards with regards to bias. I would re-guess to say that the wave travels better without stretch than with stretch. – timquinn Dec 28 '12 at 17:58
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the main point of my post was the difference in stretch between bias and non bias direction. I guess my mistake was in trying to flesh out the physics. I would have left the fact as a comment but I could not because I had no rep. – timquinn Dec 28 '12 at 18:02
up vote 1 down vote

I guess the shape is defined to a great extent by the structure of the wall, which can be quite complex - for example, the wall can be anisotropic. Another, related guess, which can be more plausible, - the shape can be defined by the vertical and horizontal dimensions of the component of the wall (the boundaries of the components are seen as dark vertical lines and the horizontal edge at the bottom) - the wall is less rigid in the vertical direction, as the external tissue is longer in this direction (it is probably fastened to a frame). So the shape is defined by the solution of a wave equation, but this solution strongly depends on the boundary conditions, on the position of the point of impact with respect to the boundaries, and the tension of the tissue in two directions.

EDIT(12/27/2012) The following article seems extremely relevant: Int'l J. of Solids and Structures 40 (2003) 6723–6765 , 144.206.159.178/ft/521/198702/5066699.pdf

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You are right. Trying to find an answer without knowing how those walls are built is probably futile. Maybe there is a baseball aficionado around here who knows more about that :) – begeistzwerst Dec 27 '12 at 11:27
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I don't think the boundary conditions are important actually, because it doesn't look to me as if the wave has had time to reach the walls and bounce back. I agree that the tension is probably different in the vertical and horizontal directions though. – Nathaniel Dec 27 '12 at 16:18
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@Nathaniel: Not sure I agree. Two different velocities are relevant: the "tensile wave speed" and the "transverse wave speed of the growing deformation cone from impact", and the former is greater (Int'l J. of Solids and Structures 40 (2003) 6723–6765 , 144.206.159.178/ft/521/198702/5066699.pdf ). In the picture in the question, the ripple (apparently caused by buckling under compression) propagates faster than the "cone" to the left of the baseball, so I believe the lack of ripple to the right of the (right lobe of the) "cone" is due to an underlying board the tissue is fastened to. – akhmeteli Dec 28 '12 at 3:31
Ok, fair enough, I didn't consider that there might be tensile waves as well as transverse ones. BTW, you should edit that link into your answer - it looks like it contains a lot of information that's relevant. – Nathaniel Dec 28 '12 at 3:40
@Nathaniel: Thank you, I did that. – akhmeteli Dec 28 '12 at 4:28

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