Measure your vertical jump using physics and your iPhone

Have you ever seen the Slo-Mo Video option on your iPhone and wondered ”What is that good for?”
Well, of course you can make great a great video of your latest cannonball dive, showing the splashing water in all it’s slo-motion greatness, but there are many other use cases!

In this article I want to show you, how you can use high frame rate video of the iPhone camera as well as some simple laws of physics to measure your vertical jump.

The vertical jump is a very interesting athletic movement, combining speed and power to beat the gravity of earth, even if it is only for a very brief period of time. As such, there are a lot of studies done by sports scientists where they need to accurately measure vertical jump height.

Most of the time, this is done by very expensive force platforms which record the forces the athlete exerts on the ground during the vertical jump. This recorded data allows at least two different options of measuring the vertical jump

Numerical integration of the area under the recorded force-time graph during takeoff allows to calculate the impulse and the initial speed of the athlete, which is enough data to solve for vertical jump height. You can read more about this method here: The Physics of the vertical jump!

By measuring the time during which the force platform does not record any forces (the time the jumper is in the air) we can also calculate the vertical jump height because gravity on earth is known and (mostly) constant.

The “What’s my Vertical” app takes advantage of the second method. You just shoot a video of a jump, and by tagging the takeoff and landing you are allowing the app to calculate the exact hang time of the jumper.

But if we know the hang time, how exactly do we calculate vertical jump height from that?

Every vertical jump has two phases: An ascending phase that occurs until the athlete reaches the peak of the jump, and a descending phase after that. These two phases have the exact same duration because vertical velocity is being decelerated linearly by the gravity of earth.

So, if we want to find the vertical jump height for a jump with hang time t, we just have to calculate the distance that an object which get’s accelerated by 9.81m/s^2 per second covers in exactly half that time (t/2).

At that point it is pretty simple:

We are now able to calculate the vertical jump height using video analysis. And this analysis is accurate enough to be used in scientific research!

Current iPhones feature 240fps slo-mo video, which means there are 240 unique images takes during a second of video. So if we select a frame to early (or late) as the takeoff we make an error of 1/240 second in estimating hang time.

If we look at a vertical jump of 70cm for example, then this difference leads to an error of less than 0.8cm. If we were to make the same mistake with a regular 30fps video, we would make an error of over 6cm!

There has even been a scientific study to prove the accuracy of this methodology

If you want to test this practical application of the laws of physics yourself, you can get the “What’s my Vertical” app from the app store here: What’s my Vertical iPhone app

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