Serve speed calibration -
1) To check that the scale is not changing between the frames on my computer screen of the frames to be used, I measured the distance between the two fence posts at the top of the white fence. I was getting two frames at 79 mm and one at 81 mm (OP arm in way) as displayed on my screen. The magnification does not appear to have changed between the frames.
2) The video shows that the camera was hand held and the camera pans to the right.
3) Because the camera pans we will measure from background objects, the downspout is good.
4) Motion blur smears the object edges in the direction of motion but not in the direction perpendicular to the motion.
5) The average tennis ball diameter is known, 2.57-2.70 inches or 6.54-6.86 cm and we can use it as a reference for length. Take average ball to be 2.63". In the frame before the ball is hit it measures 3.8 mm +/- 0.3 mm perpendicular to travel direction and more like 5 mm in the direction of travel with the motion blur added.
A mm scale is convenient for screen measurements.
Using the ball diameter to calibrate length on the screen at the location of the ball
2.63" / 3.8 mm = 0.69 "/ mm. (" abbreviation for inches)
In other words, 1 mm on my screen equals 0.69" in real space as recorded. Wide angle lens may vary magnification across the image, calibrate near the measurement. (The ball's image may be used if it is clear and has distinct edges, even a motion blurred image......)
6) Now we want to measure the distance between two frames.
Using your pictures #2 & #3 and using the down spout for "0" mm
Frame #2
The front blur is about 4 mm +/- 1 mm from the downspout (scale aligned with the ball's trajectory, slightly down).
Frame #3
The front blur is about 15 mm +/- 1 mm from the downspout (scale aligned with the ball's trajectory).
There is a problem in that when I look at the grey blur trying to get a measurement my eye play tricks with the grey level and they move. I estimated that uncertainty at +/- 1 mm. That estimate of the front edge could be much improved with better lighting.
The ball moved
15-4 mm = 11 mm between frame #2 and #3.
Using the screen calibration to get real space travel distance in inches
11mm X 0.69" / mm = 7.59" between frames #2 and #3.
7) The time between frame at 240 fps is
1sec / 240 f/ses = 0.0042 sec or 4.2 milliseconds
8) Velocity
7.59" / 0.0042 sec = 1810 " / second
One hundred miles per hour is 1760 " / second - a good conversion factor to remember for MPH.
1810"/sec / 1760"/sec X 100 MPH = 103 MPH
In this set up, since the ball goes away from the camera at a small angle the real distance traveled would always be greater than measured in 6) and the speed would always be higher from this correction. It is easier than correcting to move the camera to view more perpendicular to the ball's trajectory where you want to measure. First estimate is that if the trajectory goes away from the camera at 10 degrees the correction is to add cos 10 d to the measured length, or +2%. That would make the final measurement in this case, 105 MPH.
The edges of motion blur become smaller as the shutter speed becomes shorter in higher light levels. Better videos would increase accuracy.
The ball is a convenient length calibration but it has to be large enough and in good focus for accuracy.
[Conversions - if you type "X inches per second convert to MPH" or similar in the Google search box, Google performs and displays the conversion.]
