Interpreting Ground-Reaction Force Data

Start with the axes and the units

A force plate measures the force exerted on it, conventionally reported as the force applied by the ground to the body: the ground-reaction force. In a laboratory coordinate system, the vertical component is often labelled F_z, with anterior–posterior and mediolateral components labelled F_x and F_y. That convention is not universal. Before interpreting a curve, confirm the plate’s axis labels, positive directions and whether the software has transformed the laboratory coordinates into a participant- or progression-based frame.

Force is measured in newtons (N). A plotted value of 800 N is not the same quantity as 800 N/kg, and neither is the same as a value expressed in body weights. For a participant of mass m, body weight is m × g, where standard gravitational acceleration is approximately 9.81 m/s². A 70 kg participant therefore weighs about 686.7 N, commonly rounded to 687 N. If a peak vertical force is 824 N, its normalized value is:

824 N ÷ 686.7 N ≈ 1.20 body weights (BW)

Normalization can make comparisons between participants of different masses easier, but it does not make every gait difference disappear. Speed, footwear, walking surface, instructions and individual movement strategy can all affect the curve. State the normalization method and retain the original units in analysis records; a percentage or BW value without a clear denominator can be deceptively polished and difficult to reproduce.

Read the walking curve as a sequence, not a silhouette

During ordinary walking, the vertical GRF trace for a single stance phase often has two broad maxima separated by a lower region. The early maximum is associated with accepting and supporting the body after initial contact; the later maximum occurs as the body progresses over the foot and prepares for push-off. Between them, the curve commonly falls as the body’s center of mass passes over the supporting limb. These features are useful landmarks, not a template every person must match.

The first rise begins when the foot contacts the plate and the vertical signal becomes distinguishable from baseline noise. The loading slope describes how quickly vertical force increases, but its numerical value depends on both the movement and the measurement pipeline. A steep slope may reflect a rapid loading strategy; it may also be exaggerated by noise, an abrupt threshold crossing, or filtering choices. Report the definition used—such as the change in force over a specified time interval—rather than treating “loading rate” as a self-explanatory metric.

Likewise, peak force is only one point on a time series. Two trials can share the same maximum yet differ in how quickly the force rises, how long it remains elevated, or how much force is accumulated across stance. A curve’s shape can therefore tell a more complete story than a single peak, provided that its timing and scale are trustworthy.

The mediolateral and anterior–posterior components add context. In a typical forward step, braking and propulsive phases may appear as opposite directions along the progression axis. The exact sign depends on the coordinate convention. A trace that appears to show propulsion before braking may reflect a reversed axis or a transformed reference frame, not an unusual gait pattern. Check the axes before giving the signal a biomechanical narrative.

Worked example: from newtons to a stance measure

Consider a 70 kg participant walking across a force plate. The estimated body weight is:

70 kg × 9.81 m/s² = 686.7 N

Suppose a processed vertical trace reaches 824 N during stance. Dividing by body weight gives 1.20 BW. The number describes the peak vertical force relative to that participant’s weight; it does not, on its own, diagnose a problem or identify a cause. Its meaning depends on the task, walking speed, repeated-trial consistency and comparison being made.

Now suppose stance begins at 0.12 s and ends at 0.78 s, using a defined vertical-force threshold. Stance duration is 0.66 s. At 1,000 Hz, samples are 0.001 s apart, so those event estimates are represented by roughly 660 sampling intervals. This precision is not the same as certainty: the reported times can shift if the threshold, filter, baseline correction or event-detection rule changes.

Impulse provides a useful example of a metric that uses the whole curve. Vertical impulse over stance is the integral of vertical force with respect to time, reported in N·s. In sampled data, it is approximated by summing force values multiplied by the sampling interval:

Vertical impulse ≈ Σ F_z(i) × Δt

At 1,000 Hz, Δt is 0.001 s. The selected integration window matters: including baseline noise before contact or omitting part of late stance changes the result. If the goal is net vertical impulse rather than the integral of the measured ground force, the relevant body-weight contribution and sign convention must also be considered. Name the quantity, window and processing method so that “impulse” does not conceal several possible calculations.

Sampling rate: what 1,000 Hz does—and does not—promise

A sampling rate of 1,000 Hz records one sample every millisecond. That is often sufficient to characterize broad force-time features during walking and to estimate contact events at millisecond-scale intervals. It does not guarantee that every recorded sample represents a distinct feature of the underlying movement. Measurement noise, sensor dynamics, analog conditioning and digital filtering all influence the trace.

Sampling theory sets a basic constraint: a sampled system cannot reliably reconstruct frequency content above half its sampling frequency, the Nyquist frequency. At 1,000 Hz, that limit is 500 Hz, but practical acquisition also requires appropriate analog anti-alias filtering before digitization. A high sampling rate cannot recover frequencies removed by the hardware, and it cannot correct aliasing that has already occurred.

For gait event timing, the difference between a 1 ms sampling interval and a 10 ms interval may matter when a study compares small timing differences. Yet the event rule may introduce a larger shift than the interval itself. One analyst might define contact as the first sample above 20 N; another might use 5% of body weight, or a threshold with a requirement that several consecutive samples exceed it. Those rules can yield different heel-strike estimates, especially when the foot contacts gradually or the baseline is noisy.

Toe-off requires the same care. A threshold crossing near the end of stance may be displaced by filtering or by a low-force tail. Describe the threshold, filter and any persistence rule—for example, whether the signal must remain above threshold for a minimum number of samples. The aim is not to choose a universally perfect rule; it is to choose and document one that suits the question and is applied consistently.

Filtering without editing the biomechanics

Force signals commonly contain high-frequency noise that can make derivatives, such as loading rate, unstable. Filtering can reduce that noise, but a smoothed trace is not an unmediated view of the physical event. A low-pass filter can attenuate rapid changes; depending on its design and application, it can also alter the timing or shape of transients. Filtering the force before identifying contact may therefore move a threshold crossing even when the underlying footfall has not changed.

Document the filter type, cutoff frequency, order and whether filtering was applied forward and backward. A zero-phase forward–backward procedure can avoid net phase delay in the filtered output, but it does not preserve every feature: it changes amplitude and shape according to the filter response, and edge effects remain a concern. The cutoff should be justified for the signal and analysis, not selected merely because it makes a plot look clean.

Keep the raw trace available. Compare it with the processed signal around initial contact, peak force and toe-off, and inspect whether a result—particularly a derivative or threshold-defined event—depends strongly on the processing choice. If the scientific conclusion changes under reasonable settings, that sensitivity belongs in the interpretation rather than being hidden by a single attractive curve.

Center of pressure: a location estimate with conditions

The center of pressure is the point on the plate surface at which the measured resultant force can be represented as acting, given the measured forces and moments and the adopted coordinate convention. It is not the body’s center of mass, nor is it a direct map of pressure under every part of the foot. A force plate’s COP estimate is calculated from its force and moment signals, with equations that depend on the plate’s origin, axis orientation, surface height and sign conventions.

That distinction matters most when vertical force is small. In common COP calculations, the vertical force appears in a denominator. As F_z approaches zero near the beginning or end of contact, even modest moment noise can produce a large apparent COP displacement. A sudden jump at those instants may be a low-load calculation artifact, not a rapid balance correction. Set a justified minimum-load criterion for COP analysis, and do not interpret positions outside that valid interval as though they had the same reliability as mid-stance values.

During stance, a COP path can help describe how the point of application progresses across the support surface. Its shape depends on foot placement, the task and the coordinate frame. A path that runs in an unexpected direction may reflect a sign reversal, a plate rotated relative to the walking direction, or a mismatch between laboratory and participant coordinates. Confirm orientation and transformation before interpreting left–right or forward–backward motion.

COP traces are also sensitive to plate calibration, plate installation and the quality of moment measurements. Check that the active footfall is fully on the plate, that no other contact contaminates the trial and that COP values remain within physically plausible plate boundaries during the valid-load period. A tidy-looking trajectory is not proof of a correct coordinate transformation; pair it with the force and moment channels and the acquisition setup.

Artifacts and biological variation: distinguish before explaining

A surprising peak is a reason to investigate, not an invitation to diagnose. First check whether the signal has the expected sign and units, whether the plate was zeroed appropriately, and whether the participant actually made the intended contact. Then inspect the raw channels, baseline, event window and processing settings. If the trace remains unusual across repeated trials under consistent conditions, a genuine movement difference becomes more plausible—but the force plate alone may not explain its cause.

• Brief spikes: may arise from impact, electrical interference or a contact event. Examine raw data and neighboring samples before treating the maximum as a representative gait feature.
• Baseline offset: a force signal that is not near its expected unloaded baseline can bias threshold timing and impulse calculations. Check zeroing and baseline correction, and avoid correcting away a real pre-contact force.
• Unexpected signs: often point to an axis or transformation convention. Verify the coordinate definition before describing a braking or propulsive phase.
• Erratic COP near contact: can occur as vertical load approaches zero. Apply a minimum-load criterion and interpret COP only in the valid stance interval.
• Inconsistent repeated steps: may reflect targeting, speed changes, missed plate contacts or genuine variability. Report how many valid trials were retained and how they were selected.

In particular, plate targeting can change the movement being measured. Asking someone to land precisely on a small plate may alter step length or foot placement. In overground gait analysis, prioritize natural walking and sufficient valid repetitions; do not silently keep only trials with the most convenient curve. State inclusion criteria, such as complete foot contact on the plate without an additional foot touching it during the analyzed stance.

From curves to gait measures

Stance time is commonly defined as the interval from initial contact to toe-off. Both events need operational definitions. A force threshold is straightforward to implement, but the chosen absolute value may behave differently for participants with different body weights. A relative threshold, such as a proportion of body weight, scales with mass but may be less robust when the signal is noisy or the movement produces small vertical forces. Report the threshold and units rather than giving only the event names.

Peak vertical GRF is usually identified within the stance window, but analysts should state whether the value comes from raw or filtered data and how the stance window was defined. Loading rate requires still more detail because it is derived from changes in force over time. A point-to-point slope, a regression over a specified interval and a force-rise interval between set percentages of peak are different estimands. Their numerical values should not be compared as if they were interchangeable.

For bilateral gait, a single plate typically records the foot that contacts it, not both limbs at once. A series of steps acquired across multiple plates or trials can support comparisons, but the acquisition layout must be understood: a left–right difference can be confounded by plate location, targeting or different walking speeds. When comparing limbs, use matched definitions and consider whether the number and quality of valid steps are sufficient for the intended inference.

Impulse, peak force and stance duration answer different questions. A higher peak can occur without a larger impulse if the force is concentrated over less time; a longer stance can increase accumulated force without a higher maximum. Choose measures that correspond to the research question, and avoid treating a collection of metrics as independent evidence when several are calculated from the same underlying curve.

A practical reading sequence

1. Confirm the measurement frame. Check force axes, positive directions, units and any transformation into a walking-aligned frame.
2. Inspect the baseline and raw signal. Look for offsets, clipping, spikes, contamination and unexpected unloaded values before smoothing or normalizing.
3. Mark the contact window consistently. Record the threshold, filtering approach and event rule used for initial contact and toe-off.
4. Check the curve as a whole. Examine loading, peak timing, mid-stance and late-stance behavior, rather than reporting a maximum in isolation.
5. Assess COP only where load is adequate. Verify plausible plate-surface positions and confirm coordinate orientation.
6. Calculate and label the metric. State whether force is in N, N/kg or BW, and define the integration window for impulse or the interval for loading rate.
7. Compare repeated trials. Check whether the result is consistent and whether trial selection or plate targeting may have influenced the movement.

Reporting that lets another analyst reproduce the result

A useful methods description names the force plate or measurement system, sampling rate, coordinate convention, signal processing and event-detection rule. For example: vertical force was sampled at 1,000 Hz, low-pass filtered using a stated filter and cutoff, and contact events were identified when the processed signal crossed a specified threshold. Include the threshold value in N or as a defined fraction of body weight, and explain how baseline offsets were handled.

For normalized force, report participant mass and the normalization basis. For COP, state the valid-load criterion and coordinate frame. For summary measures, define peak selection, stance window, impulse calculation and any exclusion rules. These details may seem small beside the headline result, yet each can alter a reported value or its timing.

The strongest interpretation is not the most elaborate one. It is the one that connects a measured feature to a defensible physical event while keeping uncertainty visible. A 1.20 BW peak, a 0.66 s stance and a COP path are informative when their units, boundaries and processing history are known. Without those particulars, precision on a graph can outpace precision in the measurement.