Glossary of Key Terms in Force-Plate Measurement

The measured quantities

Ground reaction force (GRF)

The ground reaction force is the force the supporting surface exerts on the body. A three-component force plate reports this vector in newtons (N), commonly as F_x, F_y, and F_z. These components describe forces along the plate’s declared axes, not inherently “forward,” “sideways,” and “up.” Those familiar labels are appropriate only after the axes have been related to the participant or laboratory.

During quiet standing, the vertical component for a stationary person will often sit near body weight. A 70 kg person has a gravitational weight of approximately 686 N using g = 9.81 m/s². That is a useful plausibility check, not a rule that every vertical sample must equal 686 N: movement, acceleration, balance corrections, and the exact measurement interval all matter.

Force component

A component is the projection of a vector onto one coordinate axis. F_z is not a separate kind of physical force from F_x; it is one part of the same resultant force represented in a chosen frame. Components can change when the coordinate frame rotates, even though the underlying physical force does not.

Resultant force

The resultant is the vector sum of the force components. Its magnitude is

|F| = √(F_x² + F_y² + F_z²).

If the measured components are 100 N, 50 N, and 700 N, the resultant magnitude is about 708 N. Magnitude carries no directional sign; retain the components when direction or axis-specific loading is important.

Moment and torque

A moment describes the turning effect of a force about a point or axis. It is reported in newton-metres (N·m), not newtons. In vector form, the moment about an origin is M = r × F, where r is the position vector from the origin to the force’s line of application. The familiar perpendicular-distance form, M = Fd, applies when the force and lever arm are at right angles.

For example, 700 N acting with a perpendicular offset of 0.02 m creates a moment of 14 N·m. The number depends on the axis and reference origin: change either and the reported moment can change. “Torque” is often used informally for a moment, but in reporting force-plate outputs, naming the moment component and its reference point is more exact.

Free moment

The free moment is the component of the resultant moment about the vertical axis that remains after accounting for the moment caused by the center-of-pressure force acting about the plate origin. It represents a turning effect that cannot be described merely by shifting the point of application of the measured force within the contact surface. Its sign and interpretation depend on the coordinate convention and the plate’s output definitions.

Locations, axes, and reference frames

Center of pressure (CoP)

The center of pressure is the point on the contact surface at which the measured resultant force can be represented as acting, subject to the plate’s measurement model and the assumptions used in the calculation. It is a location on the plate surface, usually expressed in metres or millimetres relative to a stated origin. It is not a sensor’s physical location and it is not the body’s center of mass.

In a common plate convention, with the surface in the x-y plane and F_z normal to that surface, CoP coordinates are calculated from the horizontal-axis moments and vertical force. A frequently encountered form is x_CoP = −M_y/F_z and y_CoP = M_x/F_z, with signs dependent on the chosen right-handed axes, moment definitions, and origin. These equations are not universal sign instructions: verify the manufacturer’s convention before applying them.

CoP becomes unstable or undefined when the normal force approaches zero, because its calculation divides by that force. During flight phases or before foot contact, small force noise can therefore produce implausibly large CoP excursions. Analysts commonly use a declared force threshold to exclude such samples, and report that threshold with the processing method.

Center of mass (CoM)

The center of mass is the weighted average location of a body’s mass. It is a property of the body’s mass distribution, typically estimated from a biomechanical model or motion-capture data; a standard force plate does not directly measure it. During quiet stance, CoP movement and CoM movement are related through balance dynamics, but they are not interchangeable positions. A participant can shift pressure under the feet without the CoM moving by the same amount or in the same direction.

Coordinate system

A coordinate system specifies the axes, their positive directions, and the origin used to describe a measurement. A laboratory might define x as forward, y as left, and z as upward, but another setup may choose a different arrangement. A right-handed system follows the right-hand rule: point the index finger along positive x and the middle finger along positive y; the thumb indicates positive z.

Axis labels alone are insufficient documentation. A useful record states the origin location, axis directions, and whether values have been transformed from the plate frame into a laboratory or participant frame. Two datasets can each be correct while showing opposite signs if their coordinate conventions differ.

Global, laboratory, and plate frames

The plate frame is attached to the instrument; its origin and axes are defined by the device or acquisition software. A laboratory frame describes the room’s chosen reference directions. A participant or segment frame follows a person or body segment. Transformations between frames rotate—and sometimes translate—measurements. Force vectors rotate with the axes; moments must also be transformed with attention to their reference point.

Sign convention

A sign convention assigns positive and negative directions to components. It determines whether, for example, a braking force is reported as negative or positive along the chosen travel axis. The sign is a statement about the coordinate system, not a judgment about whether the force is helpful or harmful. State the convention in methods, figure labels, or data dictionaries rather than expecting readers to infer it from a graph.

From sensor output to a usable record

Transducer

A transducer converts a physical input into a measurable signal. Force plates commonly use strain-gauge or piezoelectric sensing elements. Strain-gauge systems detect deformation associated with loading; piezoelectric elements generate electrical charge in response to mechanical stress. The sensing technology influences characteristics such as static response, drift, and frequency response, but does not remove the need to understand the instrument’s calibration and acquisition chain.

Calibration matrix

A calibration matrix maps sensor or amplifier outputs to force and moment components. In a multiaxial plate, loading one direction can affect more than one channel, so calibration accounts for sensitivity and cross-talk among channels. In simplified form, a vector of calibrated outputs is obtained by multiplying the raw channel vector by a calibration matrix, with any required offsets handled separately. The matrix is specific to the instrument and its calibrated configuration.

Cross-talk

Cross-talk is an apparent response in one measurement channel caused by loading in another direction. A vertical load that appears partly as a lateral force, for instance, may reflect cross-talk, alignment, mounting, or a genuine horizontal force. Calibration and validation tests help distinguish these possibilities. It should not be corrected by an undocumented adjustment to a single trial.

Zero offset and baseline

Zero offset is the output present when the plate should be unloaded. An unloaded plate may show small nonzero readings because of electronics, temperature, preload, or noise. Baseline correction subtracts an estimate of this offset from later measurements. Record when the baseline was acquired and whether the plate was unloaded; zeroing while someone is touching or standing on the plate can remove part of the signal of interest.

Sampling rate and sample interval

Sampling rate is the number of recorded samples per second, expressed in hertz (Hz). At 1,000 Hz, the sample interval is 1 ms. A higher rate provides finer temporal sampling, but it does not by itself guarantee more accurate measurements or recover frequencies removed by the sensor, electronics, or filters. The appropriate rate depends on the event and analysis; report it alongside filtering and synchronization details.

Analog-to-digital conversion

An analog-to-digital converter turns a continuous electrical signal into discrete numerical samples. Resolution is often described in bits, but bit depth alone does not specify the force resolution in newtons: gain settings, input range, sensor sensitivity, and the rest of the measurement chain also matter. Saturation occurs when a signal exceeds the available input range and is clipped, flattening peaks and distorting derived quantities.

Aliasing and anti-alias filtering

Aliasing occurs when signal content above the representable frequency range is misrepresented as lower-frequency content after sampling. The Nyquist frequency is half the sampling rate: for 1,000 Hz sampling, it is 500 Hz. A suitable analog anti-alias filter attenuates frequencies before conversion; simply recording at a nominal rate does not prevent aliasing if the acquisition chain is not configured appropriately.

Filtering and cutoff frequency

Filtering attenuates selected frequency components to reduce noise or emphasize a signal’s relevant dynamics. A low-pass filter preserves lower frequencies and attenuates higher ones; its cutoff frequency is a design parameter, not a universal declaration of what counts as noise. Filter type, cutoff, order, and whether processing is forward-only or zero-phase can alter peak amplitude and timing. These choices belong in the methods, especially when comparing peak forces or event timing.

Synchronization

Synchronization aligns force data with another measurement stream, such as motion capture or electromyography. Shared triggers, hardware timing, and known delays can be used to establish alignment. Matching nominal sampling rates is not enough: independently started systems may have an offset or clock drift. State how alignment was achieved when timing across devices affects the analysis.

Derived values and common units

Impulse

Impulse is the time integral of force and equals the change in momentum for the system under the relevant conditions. Its unit is newton-seconds (N·s). For a discrete record, a numerical method such as the trapezoidal rule estimates the area under the force-time curve. If a net impulse is required, specify whether body weight or another baseline has been subtracted; integrating total vertical force answers a different question from integrating vertical force in excess of body weight.

Loading rate

Loading rate describes how quickly force changes over time, with units such as N/s or body weights per second. It may be calculated as a slope across a defined interval or as a peak derivative. Because differentiation amplifies noise, the result depends strongly on sampling, filtering, and the selected time window. “Loading rate” without the calculation interval and method is an incomplete description.

Body-weight normalization

Normalization expresses force relative to a reference, commonly body weight. For a 70 kg participant, body weight is approximately 686 N; a 1,372 N peak vertical force is therefore about 2.0 body weights. Use a consistent gravitational constant, report whether the denominator is measured or estimated, and make clear whether the normalized quantity is a force component or resultant magnitude.

Root mean square (RMS)

RMS summarizes the magnitude of a varying signal over a specified interval. For sampled values, it is the square root of the mean of their squares. Unlike a signed arithmetic mean, RMS does not cancel positive and negative excursions. Its value depends on the interval, preprocessing, and signal component being summarized; it is not a substitute for a peak or a measure of direction.

Threshold and event detection

A threshold is a specified value used to classify a sample or detect an event, such as initial contact. A rule might identify contact when vertical force exceeds a chosen threshold, but the appropriate value depends on noise, the task, and the desired timing precision. Report the threshold, whether it is absolute or relative, and any requirement for consecutive samples. A threshold crossing is an operational event definition, not necessarily the exact instant of physical contact.

Uncertainty and repeatability

Measurement uncertainty describes the range of values reasonably attributable to the quantity being measured, considering relevant sources such as calibration, noise, alignment, and processing. Repeatability describes how closely repeated measurements agree under the same conditions. A signal can be highly repeatable yet systematically biased. Avoid treating displayed decimal places as proof of accuracy: a value printed as 686.2 N may not be known to a tenth of a newton.

A compact worked example

Suppose a plate records F_x = 100 N, F_y = 50 N, and F_z = 700 N at one instant. The resultant force magnitude is approximately 708 N. If the vertical force’s line of action is 0.02 m from a stated horizontal axis and perpendicular to that lever arm, its moment about that axis is 14 N·m. The same vertical force could be associated with a different moment if its line of action were farther from the axis.

That calculation does not, on its own, identify CoP coordinates. To calculate CoP, the relevant moment component, axis orientation, origin, force direction, and sign convention must all be known. Nor does the 700 N value reveal where the person’s CoM is. Each quantity answers a different question, and the distinction is especially important when a report combines force-plate data with motion-capture estimates.

Reporting language that travels well

A clear force-plate report gives the measurement context before presenting a result. Identify the plate and mounting configuration; define the coordinate axes and origin; state force and moment units; and explain how the laboratory frame relates to the plate frame. Include sampling rate, filtering parameters, synchronization method, and any force threshold used to select contact or exclude near-zero-force samples.

Use “vertical ground reaction force” only when the vertical axis has been defined. Name a moment component and reference axis rather than writing “torque” without context. Distinguish an observed force from a normalized value, a filtered signal from a raw signal, and a force-plate CoP estimate from a body CoM estimate. These habits make results easier to reproduce and prevent sign differences or processing choices from masquerading as biological differences.

The most useful vocabulary is not ornamental: it makes the measurement traceable. A force in N, a moment in N·m, a position in metres, and a signal in samples per second describe different dimensions of the same experiment. Keep those dimensions, axes, and assumptions visible, and the data becomes far easier to interpret.