Impulse-Momentum vs Flight-Time: How Jump Height Is Calculated

Run the same countermovement jump through two different pieces of force-plate software and don't be surprised when the jump-height fields disagree. One report reads 38.7 cm off the flight-time column. Export the same trial with the impulse-momentum setting turned on and the number drops to 36.9 cm. Nothing about the athlete's jump changed between those two readouts — only the formula did, and a 1.8 cm gap is enough to flip a weekly monitoring dashboard from 'holding steady' to 'flag for fatigue.'

This isn't a software bug or a bad calibration. It's two legitimate ways of interrogating the same force-time curve, built on different physical assumptions that don't always agree. If your jump-height numbers have ever shifted after a firmware update, a software migration, or simply because someone on staff changed a dropdown menu, this is almost always why.

Two Formulas, One Force Plate

Unlike the jump-mat-versus-force-plate question, this isn't a story about cheap equipment versus lab equipment. Both numbers below can come off the exact same trial, recorded on the exact same platform, in the same tenth of a second.

Flight-time method. The plate detects the moment vertical ground reaction force (GRF) drops below a small threshold — commonly 10-20 N — and calls that takeoff. It detects the moment GRF rises back above that threshold and calls that landing. The interval between the two is flight time (t), and jump height follows the standard projectile equation: h = g × t² / 8, where g = 9.81 m/s².

Impulse-momentum method. Instead of watching for airtime, this method looks only at the propulsive (concentric push-off) phase. It subtracts the athlete's own bodyweight from every force sample recorded during that phase, integrates the remainder over time to get net vertical impulse in newton-seconds, and divides by body mass to get takeoff velocity: v = impulse ÷ mass. Jump height then comes from basic kinematics: h = v² / (2g).

Two formulas, one signal, two different physical questions: how long was the athlete in the air, versus how fast were they moving the instant their feet left the ground.

Where the Numbers Actually Split

Flight-time measured on a force plate inherits the same weakness that limits jump mats: it assumes the athlete lands with the same joint angles they had at takeoff. Almost nobody does. Landing with slightly more hip and knee flexion than at takeoff extends the time the plate reads zero load, which pads flight time and inflates calculated height — regardless of whether that zero-load reading came from a $400 mat or a $30,000 plate. Moir (2008), comparing flight-time, impulse-momentum, and double-integration methods on the same countermovement jump trials in recreationally trained men and women, found flight-time produced significantly greater jump-height values than either of the other two methods, while impulse-momentum and double integration tracked each other closely — because both derive height from takeoff velocity rather than airtime, and neither cares what the athlete's knees do on the way down. The limitation worth flagging: the sample performed instructed, technically clean jumps, so the gap between methods can run even wider in fatigued or technically inconsistent athletes, where landing mechanics deteriorate the most.

Impulse-momentum sidesteps the landing artifact entirely, but trades it for a different vulnerability: everything depends on correctly identifying two things before the jump even starts — true bodyweight, and the exact sample where the countermovement begins. Street, McMillan, Board, Rasmussen, and Heneghan (2001) examined exactly this in the Journal of Applied Biomechanics and found that the threshold used to flag movement onset was a major, controllable source of error in impulse-momentum jump-height calculations — large enough to matter for research-grade comparisons between labs. Their recommended fix, now widely adopted in force-plate protocols, is to sample a genuine quiet-standing baseline of at least one second and define onset as a statistical departure from that baseline (commonly 5 standard deviations) rather than an arbitrary fixed force value. The catch: that threshold was validated on deliberate, unhurried jump attempts — rushed field testing with athletes who shift their weight before the countermovement makes clean baseline capture harder to guarantee.

A Worked Example: Same Trial, Two Answers

Take a 78 kg athlete standing on a force plate. Bodyweight force = 78 kg × 9.81 m/s² = 765 N. During the concentric push-off phase, the plate records a net vertical impulse — force above 765 N, integrated over the push-off duration — of 210 N·s.

Impulse-momentum: takeoff velocity = 210 N·s ÷ 78 kg = 2.69 m/s. Jump height = 2.69² ÷ (2 × 9.81) = 0.369 m = 36.9 cm.

Flight-time, same trial: the force trace shows 0.562 seconds between the GRF drop below 15 N and its return above 15 N. Jump height = 9.81 × 0.562² ÷ 8 = 0.387 m = 38.7 cm.

A 1.8 cm gap, from one jump, on one plate, in one session. Multiply that inconsistency across a 25-athlete squad tested weekly and it becomes impossible to tell a genuine 2 cm improvement from a method artifact unless you know which formula generated each number.

Getting the Impulse-Momentum Number Right

If you're choosing impulse-momentum as your primary metric — and for fatigue and readiness monitoring, most sports scientists do, precisely because it ignores landing technique — a few field habits protect the number from the errors Street et al. flagged.

Capture at least one full second of quiet standing before every trial, at a sampling rate of 1,000 Hz or higher where the hardware supports it (500 Hz is workable but adds noise to the baseline estimate). Define takeoff and movement-onset thresholds statistically — bodyweight mean ± 5 standard deviations from that quiet period — rather than a flat number like '20 N for everyone,' because a fixed absolute threshold behaves very differently for a 55 kg gymnast than for a 115 kg lineman. And before comparing this month's numbers to last season's, check what your software's jump-height field is actually reporting: a firmware update or a platform migration can silently swap which formula populates that default field.

The baseline window matters more than most staff realize. A truncated 0.3-second quiet period produces a noisier bodyweight estimate, which tends to delay onset detection and can underestimate calculated height by roughly 1-3 cm relative to a properly captured 1-second window — enough, again, to be mistaken for a real change in athlete readiness.

Which Number Should You Actually Trust?

For week-to-week fatigue and readiness monitoring, impulse-momentum is the safer default. A fatigued athlete's landing technique degrades before their concentric output does, which means flight-time numbers can hold steady or even climb — a false-reassurance signal — right as impulse-momentum height is already sliding.

For comparing against historical benchmarks or older published norms, flight-time may still be the right lens, simply because most jump-mat literature from the 1990s and 2000s used it by necessity. Just build in the roughly 2 cm upward bias when lining those numbers up against impulse-momentum data from your current system.

Whichever method you settle on, the non-negotiable rule is consistency: pick one, document it, and never let a software update or staff turnover silently switch it under you. If a transition is unavoidable, run both methods in parallel for at least two full weeks before retiring the old one — exactly as you would when swapping a jump mat for a force plate.