# Nature of "damping rate" and "torque curve" and relationship with speed

Hi, I use Unreal Engine to simulate vehicles via PhysX.

I would like to know the nature and the formulas that link several variables with the speed of the vehicle.

• At the wheel there is a “damping rate” parameter expressed in kg.m²/s.

• On the engine setup, there are the parameters “damping rate full throttle”, “damping rate zero throttle clutch engaged” and “damping rate zero throttle clutch disengaged”, which are also expressed in kg.m²/s.

• There is also a “clutch strength” parameter, again expressed in kg.m²/s.

• Finally, there is a “torque curve” which represents the torque versus rotational speed. But I don’t know how this curve is used by PhysX.

Wheel damping works as follows:

newAngularSpeed = oldAngularSpeed - dampingRate x oldAngularSpeed x dt/ wheel moment of inertia

In practice, it all gets wrapped up into a set of implicit equations but the principal holds.

The damping rate of the engine is a function of the throttle. A typical behavour is that an engine that is not driven experiences a higher damping rate than one that is driven. Here’s the physx doxy to describe the parameters involved:

\note If the clutch is engaged (any gear except neutral) then the damping rate applied at run-time is an interpolation
between mDampingRateZeroThrottleClutchEngaged and mDampingRateFullThrottle:
mDampingRateZeroThrottleClutchEngaged + (mDampingRateFullThrottle-mDampingRateZeroThrottleClutchEngaged)*acceleratorPedal;
\note If the clutch is disengaged (in neutral gear) the damping rate applied at run-time is an interpolation
between mDampingRateZeroThrottleClutchDisengaged and mDampingRateFullThrottle:
mDampingRateZeroThrottleClutchDisengaged + (mDampingRateFullThrottle-mDampingRateZeroThrottleClutchDisengaged)*acceleratorPedal;

The clutch strenghth describe the rate at which two spinning plates harmonise their rotational speed. The clutch is modelled as two spinning plates. One is connected to the engine, the other is connected to the wheels. The rotational speed difference between the plates creates a torque that harmonises their speed. The clutch strength is the constant of that linear relationship ie clutch torque = clutch strength * rotational speed difference. The higher the strength, the faster speed discrepancies will diminish.

The amount of torque that the engine can deliver is typically a function of the rotational speed of the engine. It is quite often the case that an engine has a range of rotational speeds where it delivers the highest torque. It’s the goal of a professional race driver to keep the engine in that range. This curve is represented by a maximum of 8 points in physx. PhysX uses normalised units for the axes so the x axis is rotational speed/max rotational speed and the y axis is torque/ peak torque. Editing this curve will give you ranges where there is plenty of torque and ranges where there is less torque.