The Vehicle's Angle, Angular Rate, and Profile Calculator is an essential tool for engineers, enthusiasts, and designers to accurately determine a vehicle's dynamic orientation. Calculate pitch, roll, and yaw angles, angular velocities, and analyze the overall profile for stability, performance, and safety assessments in various driving conditions, including off-road and high-performance scenarios.
Formula:
This calculator estimates a vehicle's pitch, roll, and yaw angles, along with their respective angular rates, based on dimensional measurements and time intervals.
- Pitch Angle (θ): Calculated as the arctangent of the height difference between the rear and front axles, divided by the wheelbase.
- Roll Angle (φ): Calculated as the arctangent of the height difference between the right and left sides, divided by the track width.
- Angular Rates (ω): Estimated as the change in angle over a specified time interval (ΔAngle / ΔTime).
Formulas Used:
Pitch Angle (θ): θ = arctan((HRear - HFront) / LWheelbase)
Roll Angle (φ): φ = arctan((HRight - HLeft) / WTrack)
Pitch Rate (ωθ): ωθ = (θCurrent - θPrevious) / Δt
Roll Rate (ωφ): ωφ = (φCurrent - φPrevious) / Δt
Yaw Rate (ωψ): ωψ = (ψCurrent - ψPrevious) / Δt
Where:
HRear= Current Height at Rear Axle (m)HFront= Current Height at Front Axle (m)HRight= Current Height at Right Side (m)HLeft= Current Height at Left Side (m)LWheelbase= Vehicle Wheelbase (m)WTrack= Vehicle Track Width (m)θCurrent, φCurrent, ψCurrent= Current Pitch, Roll, Yaw Angles (degrees)θPrevious, φPrevious, ψPrevious= Previous Pitch, Roll, Yaw Angles (degrees)Δt= Time Interval (seconds)