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Enter values or import telemetry, then run an analysis.
1 Analysis workspace
| # | Time (s) | Ax (m/s²) | Ay (m/s²) | Az (m/s²) | Velocity (m/s) | Position (m) | Distance (m) | Segment | Action |
|---|
Uncertainty analysis
Store the current result as Design A or B, then compare peak, RMS, average, exceedance duration, and sample count.
Design A
Design B
| Metric | Design A | Design B | Difference B − A |
|---|---|---|---|
| Store both designs to compare. | |||
2 Charts and ride timeline
3 Segment analysis
| Segment | Samples | Duration | Average | Peak + | Peak − | RMS | Exceedances |
|---|---|---|---|---|---|---|---|
| No segment results yet. | |||||||
4 Formula used and calculation steps
Formula
Substitution and method
5 Validation, warnings, and assumptions
Included features
Calculation modes
Axes
Geometry
Data tools
Differentiation
Smoothing
Reporting
How to use this calculator
Choose a mode
Use Basic for one interval. Use Telemetry for complete sampled ride data.
Enter or import data
Paste rows, upload CSV or JSON, generate a simulation, or type values.
Configure processing
Choose differentiation, filtering, baseline correction, axes, and comfort limits.
Review and export
Inspect charts, segments, warnings, formulas, uncertainty, then export reports.
Understanding roller coaster jerk
What jerk measures
Jerk measures the rate at which acceleration changes over time. Acceleration describes how quickly velocity changes, while jerk describes how abruptly that acceleration changes. Riders often perceive sudden jerk as a sharp transition, even when the acceleration itself remains within a moderate range.
Roller coaster designers manage jerk through transition curves, banking schedules, launch control, brake modulation, and element geometry. A gradual acceleration change usually feels smoother than an immediate change. The same peak acceleration can therefore create very different rider experiences.
Why three-axis analysis matters
Longitudinal jerk acts forward and backward along the train. Lateral jerk acts from side to side. Vertical jerk acts upward and downward through the seat. Resultant jerk combines all three axes, but each axis should also be reviewed separately because the human body responds differently by direction.
Sensor orientation must remain consistent during analysis. An inertial measurement unit can rotate with the train, seat, or track. Coordinate transformations may be required before direct comparisons are meaningful. Gravity removal also matters when the sensor frame changes orientation.
Filtering measured data
Numerical differentiation amplifies measurement noise. Small acceleration errors can become large jerk spikes after differentiation. Smoothing can reduce this problem, although excessive smoothing can hide real short-duration events. Compare raw and filtered traces before accepting a result.
Central differences often provide a balanced estimate for evenly spaced samples. Forward and backward differences are useful near dataset boundaries. Five-point methods can improve smooth-data estimates, but they require more neighboring samples. Irregular timestamps need careful handling.
Interpreting comfort classifications
The calculator uses user-defined thresholds rather than universal safety limits. Comfort varies with direction, duration, rider position, restraint type, age, health, anticipation, and surrounding motion. A brief peak can feel different from a sustained oscillation with the same numerical maximum.
Use threshold categories for comparison and screening. Never treat them as ride approval or certification. Applicable standards, manufacturer requirements, testing procedures, and qualified engineering judgment must control final decisions.