Sway Jerk Horak Calculator

Calculator Inputs

Trial Label

Subject ID

Stance Condition

Input Signal Type

Position Unit

Acceleration Unit

Sample Rate

Smoothing Window

Trim Start Samples

Trim End Samples

Remove Mean Offset

Center AP and ML before derivatives

Notes

AP Samples

ML Samples

Formula Used

For position data, AP and ML traces are converted to meters. The calculator estimates velocity, acceleration, then jerk by finite differences.

For acceleration data, AP and ML acceleration traces are converted to m/s². The calculator estimates jerk with one finite difference.

Resultant jerk at sample i: J_i = √(j_AP,i² + j_ML,i²)

Horak resultant jerk integral: ∑(j_AP,i² + j_ML,i²) × Δt

Mean jerk power: jerk integral ÷ trial duration

How to Use This Calculator

Choose whether your AP and ML values are position traces or acceleration traces.
Select the matching unit and enter the fixed sampling rate.
Paste comma, space, semicolon, or line separated AP and ML samples.
Set trimming and smoothing only when needed.
Press Calculate to show results above the form.
Use CSV for spreadsheet work or PDF for a compact report.

Example Data Table

Case	Input Type	Rate	AP Samples	ML Samples	Use
Quiet stance	Position	50 Hz	0.00, 0.08, 0.18, 0.32...	0.00, 0.05, 0.12, 0.10...	Baseline balance smoothness
Foam stance	Acceleration	100 Hz	0.002, 0.004, 0.001...	0.003, -0.002, -0.004...	Sensor based comparison
Eyes closed	Position	60 Hz	0.10, 0.22, 0.40, 0.31...	-0.04, -0.11, -0.18...	Condition challenge review

Understanding Sway Jerk

Sway jerk describes how quickly body sway acceleration changes. It is useful when balance data looks similar by distance alone. Two trials can have equal sway size. One trial can still include sharper corrections. Jerk helps reveal that hidden roughness.

The Horak style approach often uses AP and ML movement traces. AP means front to back. ML means side to side. The calculator combines both axes. It first prepares the signal. Then it estimates derivatives at each sample. If you enter position data, it differentiates to acceleration. Then it differentiates again to jerk. If you enter acceleration data, it differentiates once to jerk.

Formula Logic

The main result is resultant jerk integral. It sums squared AP jerk plus squared ML jerk across time. A higher value means the sway path changed acceleration more abruptly. The tool also reports mean jerk power. This divides the integral by trial duration. RMS jerk shows typical jerk magnitude. Peak jerk highlights the largest instant correction.

Data Quality

Good data preparation matters. Use a steady sampling rate. Keep units consistent. Remove obvious recording errors before analysis. Use the smoothing window only when the trace contains high frequency noise. Too much smoothing can hide real corrective movement. The trim fields help exclude setup motion at the start and relaxation motion at the end.

This page is designed for research review, teaching, and screening workflows. It is not a medical diagnosis. Compare trials recorded with the same equipment. Keep stance, footwear, vision, and surface conditions consistent. A firm surface with eyes open should not be mixed with foam or eyes closed trials unless the comparison is intended.

Practical Use

The example table shows common inputs and expected outputs. Your own results can be exported for records. The CSV file is best for spreadsheets. The PDF file is best for sharing a compact report. Always store the raw AP and ML data too. Raw data lets you repeat the calculation later.

Use the notes field to document subject posture, sensor placement, and trial condition. These details make the result easier to interpret. They also support careful repeat testing. Over time, consistent sway jerk values can help describe balance smoothness with more precision and less guesswork.

FAQs

What is sway jerk?

Sway jerk measures how rapidly sway acceleration changes. Higher values usually mean more abrupt corrective movement or less smooth postural control during the measured trial.

What does Horak style mean here?

It means the calculator follows the common AP and ML resultant jerk approach used with instrumented sway analysis. It summarizes jerkiness across both horizontal axes.

Can I enter force plate position data?

Yes. Choose position as the input type. Enter AP and ML displacement samples with the correct unit and sampling rate.

Can I enter accelerometer data?

Yes. Choose acceleration as the input type. The calculator will convert the selected unit and estimate jerk directly from acceleration changes.

Why are AP and ML samples required?

Sway is planar. AP and ML values describe front back and side side motion. Combining both axes gives resultant jerkiness.

Should I use smoothing?

Use light smoothing only for noisy traces. Large smoothing windows can reduce real peaks and may lower the calculated jerk value.

What does log10 jerk mean?

It is the base ten logarithm of the jerk integral. It helps compare large ranges of values in reports or analysis tables.

Is this a diagnosis tool?

No. It is a calculation and reporting tool. Clinical interpretation needs proper protocol, repeat testing, and professional judgment.