Calculating serve speed from frame count in digital video from an Andy Roddick Serve at the 2007 AO.
Serve used in this example shows the radar gun reading of 137mph and it looked like the court display said 221 k/hr (137.323mph).

With the raw video 30fps converted to 59.94 fps it looked like between 20 to 20.5 frames. It is very hard to tell for sure. Then right after that they showed a slow motion of that serve and that calculated 61 frames.

I have no way to be sure, but it appears that it was being showed at 180 (179.82)fps. That is about the only thing that makes since. Doing the math to find the distance, it comes out to 58.84' from racquet contact to ground contact with assumptions of:

  1. hitting the ball 2' (24") inside court and 9'(108") high
  2. camera directly behind the court
  3. objects in the same geometric plane are linear (linked to assumption 2)

Data for Calculation

The other distances were calculated using interpolations of court dimensions and a ruler measuring the distances on the screen. Image below used to calculate distance from center line: Speed Calculator Result: 139.04 MPH

Using 180fps and a distance of 58.84', the result is 139.04mph. If you assume 60' the readings goes up to 142mph, but the distance is not 60' The discrepancy is from errors in the assumptions. Error from Roddick may have been inside the court more than two feet, measuring pixels, camera not directly behind court or objects not the same geometric plane. Just a small error in distance can make a significant difference in initial serve speed. Here are speed readings with slightly different distance readings:

  • 58.84 == 139.04mph
  • 58.50 == 138.10mph
  • 58.25 == 137.41mph
  • 58.00 == 136.73mph
Notice the difference between 58.84 and 58.50 is only 4.
    For those who would like to view the video and verify themselves, the video can be viewed here Roddick Serve.

    If you can not view the video, you will need to install the Codec here Xvid.

    Comments about this method compared to using a consumer Radar gun

    Compared to using a radar gun, this method requires several extra steps.

    There are several sources of error, such as estimating the number of frames and the actual distance, but they are all manageable and in your control( you can minimize them by being careful). A consumer Radar can give significantly wrong speeds depending on how far the ball traveled before entering the range of the radar and the angle between direction of the ball and the Radar's line of sight at the instant it "sees" the ball. Also, once in a while, Radars give you totally wild numbers. If you suddenly hit one serve that is 5mph mpre than every other serve, you will never know if it was an erroneous reading or if you actually did something very right. That will never happen with Video method. If your serve took 0.5 secs to bounce, it is going to be 15 frames in the video. If you serve 5 mph faster, it will be a whole frame quicker and impossible to miss. Even better, you can replay the video and study what you did differently and try to incorporate that permanently into your service motion.

    This method gives you very visual proof that anyone can see. They don't have to take your word.

    You can tape someone while they are playing a match and estimate their speed. You can walk around your club with a camcorder and measure the pace of anyone's serve or groundstrokes. OTOH, A consumer radar can never be used in a match because it need to be placed on the court.