Two calculations use the same jump trace and report different heights. Before concluding that one athlete performed better, inspect the baseline, the integration interval and the definition of height. A small force error can accumulate over time.
This guide follows a fictional force record from external force to momentum and then to take-off-to-apex height. All quantities are supplied teaching data. The purpose is to read and check a calculation, rather than to prescribe a jump test or assess an individual.
Continue from The Gold Standard of Biomechanics, within The Gold Standard of Education: learning that transfers into life and How X Works.
Choose the question you need to resolve
Build the explanation · Chapters 1–2. Define the quantities and read the measurement chain.
Work through the changing case · Chapters 3–5. Calculate, compare and identify what the result leaves unresolved.
Check and continue · Chapters 6–8. Try new conditions, read the FAQs and choose connected guides.
Chapter contents · Transfer checks with explained answers · Return to the Biomechanics subject guide
Chapter contents
Build the explanation
Work through the changing case
3. Calculate a complete fictional contact interval
Check and continue
6. Test transfer with new force and timing conditions
7. Questions about force and jump height
8. Read the next movement claim with its references attached
Treat the jumper as one system of constant mass m. Choose upward as positive. During contact, assume that the only important external vertical forces are the platform’s ground-reaction force Fz and weight mg. The vertical net force is Fz − mg.
A force plate measures a contact interaction. It does not separately measure every muscle or joint force inside the body. For whole-body vertical momentum, those internal forces do not replace the external-force account.
We will calculate the centre of mass’s rise from take-off to its apex. That is different from its rise from quiet standing to the apex, because the centre of mass may already have moved upward before take-off. State the reference height before comparing methods.
After take-off, neglect air resistance and use constant gravitational acceleration g. The flight rise is h = v²/(2g), where v is upward centre-of-mass velocity at take-off. This relation does not convert a peak contact force directly into height.
Impulse is the integral of net force over time. For this vertical system, J = ∫(Fz − mg)dt = m(vtakeoff − vstart). The force must be in newtons, time in seconds and impulse in newton-seconds. Dividing by mass gives a velocity change.
If integration begins during genuine quiet standing, vstart can be taken as zero within the model. If it starts after movement has begun, that initial-velocity assumption needs independent support. Setting an unknown velocity to zero changes the problem.
The area below body weight counts negatively. During the initial downward movement of a countermovement jump, support force can be less than weight. Removing negative portions would discard part of the momentum history.
Body weight is not the unloaded instrument zero. An unloaded platform should represent zero contact load after appropriate correction. A stationary person still applies a nonzero load to the platform. Confusing those two reference states corrupts the force balance.
Let m = 60.0 kg and g = 9.81 m/s², so weight is 588.6 N. Begin at rest. For transparent arithmetic, divide the 0.60-second contact interval into three 0.20-second segments and use the supplied average force in each segment.
The signed impulses are −20, +100 and +70 N·s. Their sum is 150 N·s. Take-off velocity is therefore 150/60 = 2.50 m/s, and take-off-to-apex rise is 2.50²/(2 × 9.81) ≈ 0.319 m.
Using segment averages makes the integral exact for this constructed table. Real sampled data require justified sampling, filtering, event detection and numerical integration; the table is not a recommendation for reducing an actual jump to three samples.
Notice what supplied the answer: the whole signed area. The largest listed average force alone would not determine the result. A different force–time history can produce the same net impulse.
| Segment duration | Mean Fz | Mean net force | Net impulse |
|---|---|---|---|
| 0.20 s | 488.6 N | −100 N | −20 N·s |
| 0.20 s | 1088.6 N | +500 N | +100 N·s |
| 0.20 s | 938.6 N | +350 N | +70 N·s |
First keep the independently known mass and weight fixed, but add an uncorrected +10 N offset to every contact-force value. The extra impulse is 10 × 0.60 = 6 N·s. Reported velocity becomes 156/60 = 2.60 m/s; height becomes about 0.345 m. That is roughly 8.2% above the original 0.319 m.
Now change the processing chain. Suppose the same stable +10 N offset is present both in the quiet-standing estimate of body weight and in every force value. Subtracting the measured standing baseline cancels that constant offset in the impulse numerator: (Fz + 10) − (mg + 10) = Fz − mg.
But if mass is also inferred from that biased standing baseline, it becomes 598.6/9.81 ≈ 61.019 kg. Dividing the correct 150 N·s numerator by this mass gives about 2.458 m/s and a height of 0.308 m. The numerator cancellation did not repair the mass estimate.
If the true mass is known independently and the identical constant offset cancels in the baseline subtraction, this particular error can cancel completely within the simplified model. Drift, gain errors and changing offsets need a different analysis. “Offsets cancel” is a statement about a processing chain and its assumptions, rather than a universal rule.
Return to the unbiased contact forces, but overestimate the weight subtracted by 20 N while holding mass at 60 kg. Over 0.60 s the impulse loses 12 N·s. The resulting velocity is 138/60 = 2.30 m/s and height is about 0.270 m. This is a separate constructed error, not an expected error rate for a real platform.
A constant net-force error δF adds δF × T to impulse. A longer interval accumulates more error. Starting earlier is helpful only when the starting conditions and baseline are credible; adding an arbitrary long baseline region does not guarantee accuracy.
The bounds of integration also matter. A take-off threshold, a missed sample or filtering can change which area is included. A jump involving a handrail, another contact surface or an external load needs the system boundary and external forces revisited.
Primary research on impulse-method errors provides a reason to preserve processing details. Its study-specific findings should not become universal cutoffs for every device, movement or sampling system. A calculation can be internally tidy while its input definition is unsuitable.
A. Double the integration duration
Keep an uncompensated +10 N error, an independently known 60 kg mass and a valid 1.20-second integration interval. The velocity error is 10 × 1.20/60 = +0.20 m/s. The height error still depends on the underlying take-off velocity; +0.20 m/s is not a fixed percentage of height.
B. Begin while moving downward
Suppose vstart = −0.30 m/s and the correctly measured impulse is 150 N·s for a 60 kg person. Take-off velocity is −0.30 + 150/60 = 2.20 m/s, giving about 0.247 m of flight rise. Assuming a zero initial velocity would instead reproduce 0.319 m.
C. Keep the impulse, change the shape
Two fictional traces have equal signed net impulse and equal mass, and both begin at rest. Their take-off velocities and flight rises match in this model. Their peak forces, loading histories and possible internal loads need not match.
Evidence to retain
Preserve unloaded checks, the standing interval, the mass source, axis convention, sampling and filtering, integration bounds, event rules and original trace. Examine sensitivity to defensible alternatives. A repeatable number is easier to trust when its reference states are also repeatable.
Should body weight be subtracted?
For the stated whole-body vertical momentum calculation, yes: the net external force is ground reaction minus weight. Ground-reaction impulse alone includes support against gravity.
Does zeroing the unloaded plate remove body weight?
No. Instrument zero and a standing person’s load are different states. Both need an appropriate role in the processing chain.
Does twice the impulse mean twice the height?
For equal mass, zero starting velocity and the same model, twice the net impulse gives twice the take-off velocity and four times the take-off-to-apex rise.
Can the result diagnose injury or readiness?
This calculation alone does not establish either. An individual performance or clinical claim needs suitable measurement, context and evidence beyond a fictional impulse example.
Before comparing two heights, write down the system, starting velocity, mass source, force reference and definition of height. Then follow the same assumptions through every step. That habit transfers to gait, impacts and other force-based movement estimates.
Build the movement model
Biomechanics: forces, motion and living bodies — develop the wider body, force and material model.
Sports physics: momentum, energy and motion — connect impulse with other sporting quantities.
Carry the evidence into measurement
Walking biomechanics, forces and joint angles — follow measurement and interpretation through a different movement.
Prosthetic gait analysis and inverse dynamics — distinguish external force from inferred joint-level quantities.
Sports biomechanics: force, leverage and technique — connect calculations with the task being performed.
Sources and the boundary of the examples
All force values, offsets and transfer cases here are original teaching constructions. The algebra isolates particular error pathways and does not estimate the uncertainty of a real device or participant.
OpenStax University Physics: impulse and collisions — publisher explanation of signed impulse and momentum change.
Street and colleagues (2001): Sources of Error in Determining Countermovement Jump Height with the Impulse Method — primary error-analysis paper; its experimental findings remain specific to its methods.
Improving the estimation of countermovement jump height from force plate recordings (2024) — primary study examining interactions between processing choices.
Sources and connected article links checked on 21 October 2026.