Reading several threads discussing the iphone app "Serve Speed" got me very curious. So I did some research into how to calculate the initial speed, which takes into account the air resistance.
The best website I found that discusses the math behind this is http://www.donthireddy.us/tennis/speed.html
. It even has a calculator that calculates the speed for you. All you need is the frame rate of your camera and the number of frames it takes from the time the ball leaves the racket and the time it hits the ground.
Based on that calculator, I have prepared the following chart for various number of frames and time duration. The three columns are in order 1) number of frames, 2) time spent between ball hitting and ball landing, and 3) calculated speed in mph. The calculated speed assumes a 30 fps camera if you are using the frame method.
The chart may be useful if you just want a rough calculation using a stop watch. These any phone should have a stop watch to record the time duration. This may be a good approximation if your serve speed is less than about 90 mph.
Just to be sure that these numbers are relatively accurate, I have tested them against radar gun speeds from the recent Australian Open and they match up pretty closely although at over 120 mph, the accuracy goes down due to the limitation of the camera speed. At that speed, you really need at least a 60 fps camera.
Frames (30 fps) Seconds Initial Serve Speed (mph)
30 1.0 48.2
28 0.93 51.65
26 0.87 55.62
24 0.80 60.26
22 0.73 65.73
20 0.67 72.31
19 0.63 76.11
18 0.60 80.34
17 0.57 85.07
16 0.53 90.38
15 0.50 96.41
14 0.47 103.29
13 0.43 111.24
12 0.40 120.51
11 0.37 131.47
10 0.33 144.61
I hope you guys find this useful.