Baseball geekiness

So looking at this photo from yesterday got me wondering: can I calculate how fast that ball is going?

Foul Ball

Sure, piece of cake.

First we need some way to get a distance calibration. Jared tells me that a regulation baseball is 3" (76.2 mm) in diameter so if I measure the width of the baseball track from the image, I can get a mm/pixel calibration. I got 5.4 mm/pixel.

Then the length of the baseball track needs to be measured. Since part of it blends into the concrete of the dugout, measuring the track is only approximate, but I got 144 pixels. Using the previous pixel calibration this gives me a track length of 0.78 m.

The EXIF information stored with the photo tells me the exposure time was 1/49 s which gives the baseball a velocity of 38.4 m/s (86 mph for you non-metric people out there).

Extending this a little further, I think I can also calculate how much time there was between when the ball was hit and when the picture was taken.

If I draw a line from where the ball track starts back to where the bat would have been at impact, I get about 68 pixels. If an exposure time of 1/49 s (0.02 s) results in a track length of 144 pixels, then 68 pixels should correspond to a time of 0.02s*(68/144) or 0.0096 s. In other words, this picture was taken a mere 9.6 ms (millisecond) after the ball was hit (give or take a few 0.1 ms), assuming no significant change in ball speed between impact and when the picture was taken.

Of course this depends on where the estimated point of impact is placed, but should at least be within a couple of milliseconds.