A Force Plate in Your Phone? The Same Maths, Run Backwards
Summary
AI apps now claim ground reaction force from a phone video. Force equals mass times acceleration, and the maths behind every force number runs one of two ways. Here is where each one goes wrong, and three questions to ask of any force number.
Measured, Derived, Modelled: part 1 of a series on what sports tech numbers really mean.
Two things landed on my desk this week. One was an email from a software house offering ready-made "sports AI": video analysis, pose tracking, performance insights, all prebuilt and waiting for a logo. The other was an ad in my Facebook feed for an app that says it can give you ground reaction force from a single video of an athlete. No force plate. No lab. Just a phone.
It's a gold rush, and a race to the bottom on price. AI has made a lot of things possible that weren't five years ago, and some of them are genuinely good. But a force number is a claim about physics, and physics doesn't care how good the marketing is.
I've spent more than thirty years building timing and force instruments. I'm a firm believer in first principles. They play out in everything. So this is the first of a series where I take these claims apart the way an engineer would. We start with the arithmetic that sits underneath every one of them.
One law, two directions
Force equals mass times acceleration. That's it. Every device that hands you a force number either measures force directly, or it measures something else and walks its way to force through that one equation.
There are two common starting points, and they walk in opposite directions.
An accelerometer, the inertial sensor in most wearables and in plenty of sports equipment, measures acceleration. To get speed you integrate once. To get distance you integrate twice.
A camera measures position. To get speed you differentiate once. To get acceleration, and so force, you differentiate twice.
Same maths, run backwards. And each direction has its own way of going wrong.
Integrate, and errors pile up
Integrating is adding up. Every tiny error in the acceleration reading gets added in, sample after sample, and it never cancels out.
Here's what that looks like. Say the sensor is off by a hundredth of a metre per second squared. That's about a thousandth of the pull of gravity, which is a very good sensor. Over a five second sprint that becomes 0.05 m/s of error in speed and about 0.13 m of error in distance. Over ten seconds it's 0.1 m/s and half a metre. The error in distance grows with the square of time. Real sensors also drift with temperature and knocks, so in practice it's worse.
That is why DynaSled doesn't declare accuracy on distance. We know it's affected by drift, so we don't put a number on it. Acceleration, yes: that's what the sensor reads. Velocity needs correcting, and we do that. Force we don't calculate at all. The load cell reads it, directly, in two dimensions. We covered that difference in an earlier piece, Measured, Not Inferred.
I'd rather tell you what we don't know than sell you a number I can't stand behind.
Differentiate, and noise explodes
The camera goes the other way, and it has the opposite problem.
Differentiating is dividing small differences by a small time step. A phone filming slow motion at 240 frames a second has about 4 milliseconds between frames. Pose estimation software finds a hip or a knee in each frame, but not perfectly. The point it picks wobbles a little from frame to frame. Say it's out by one centimetre.
Divide that one centimetre wobble by 4 milliseconds and you get noise in speed of a couple of metres a second. Do it again to get acceleration and you're dividing by 4 milliseconds twice. The noise in acceleration comes out at hundreds of metres per second squared. That's tens of times the pull of gravity, from a one centimetre wobble.
So every one of these systems has to filter the signal, hard [4]. And this is the catch.
An elite sprinter at top speed is on the ground for about 0.08 to 0.10 seconds a step [1]. At 240 frames a second that's roughly 20 to 24 frames. The force you want rises and falls inside those frames. A filter strong enough to kill the noise is strong enough to flatten the peak. That's not a software bug you can fix in the next update. It's arithmetic. And shooting at a higher frame rate doesn't get you out of it on its own, because the time step you divide by gets smaller too.
Wearables have the same trouble running in the other direction. Integrating a noisy acceleration signal smooths it nicely, then drifts.
What the best evidence says
To be fair, people have done this properly, and some of the results are good.
The best I've seen comes from Glen Lichtwark's group here in Brisbane. They used eight calibrated high resolution cameras around a force instrumented treadmill and in-ground force plates. Across walking, running, jumping and cutting the average error was 0.75 newtons per kilogram of body weight. The worst case was running vertical force, at 1.85 N/kg, about 8 percent of the peak [2]. That's a serious lab doing serious work, and it's a good result.
But look at what it took: eight cameras, all calibrated to each other, and a lab. It's also vertical force, the big, easy component.
A study published this year tested OpenCap, a well regarded open source system that works from smartphone video, normally from two or more phones [5], against force plates in jumping and landing [3]. Timing and impulse were within 5 percent. Peak landing force was underestimated by more than 40 percent. That fits the arithmetic exactly. The average survives the filter. The peak doesn't.
Now take that to a sprint track. One phone. No calibration. An athlete moving at ten metres a second. And the force that actually wins races, the horizontal push in acceleration, is the smallest part of the total.
Three questions to ask of any force number
You don't need to be an engineer to protect yourself here. Ask three things.
Was it measured, or calculated? A load cell or a force plate measures force. Everything else calculates it from something else.
Which way did the maths run, and how many steps? One step of integration or differentiation is manageable. Two steps is where the trouble starts. Ask which direction, and what they did about drift or noise.
Where's the agreement data? Not a correlation. A correlation tells you two numbers go up and down together, not that they agree. Ask for the error in newtons, on the movement you care about, against a direct measurement. If they can't show you, that's your answer.
None of this means video is useless. A good camera, and a good eye behind it, picks up movement patterns no load cell ever will. That's a strength in its own right, and we'll get to it later in the series. But it's a different job from measuring force.
Next in the series: Twenty Frames, a closer look at what a phone actually sees of a ground contact.
Compiled by the Swift Performance team with AI assistance, edited by Mark Fisher.
References
- Murphy A, et al. (2021). Relationship between anthropometric and kinematic measures to practice velocity in elite American 100 m sprinters. Journal of Clinical and Translational Research, 7(5). doi:10.18053/jctres.07.202105.006
- Lichtwark GA, Schuster RW, Kelly LA, Trost SG, Bialkowski A (2024). Markerless motion capture provides accurate predictions of ground reaction forces across a range of movement tasks. Journal of Biomechanics, 166.
- You J, Lin Z, Zhang B (2026). Feasibility of a markerless motion capture system for estimating ground reaction forces during vertical jump and landing tasks. Journal of Education, Health and Sport, 93, 73559. doi:10.12775/JEHS.2026.93.73559
- Winter DA (2009). Biomechanics and Motor Control of Human Movement, 4th ed. Wiley. (On noise amplification in differentiated kinematic data and filtering.)
- Uhlrich SD, Falisse A, Kidziński Ł, et al. (2023). OpenCap: human movement dynamics from smartphone videos. PLOS Computational Biology, 19(10), e1011462.
Mark Fisher
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