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How can I calculate the torque that is needed to keep the steering wheel at the same steering angle during turning at given speed?

Example case:

A car with Ackermann steering geometry weights 1000 kg. It is going though a curve - the steering angle is constant 5 degrees. Car's velocity is 10 m/s. Steering ratio is 15:1 (15 degrees on steering wheel means 1 degree of actual steering angle). What torque do I need to apply to the steering wheel to hold those constant 5 degrees on steering?

Reasons:

I need to know the torque because I want to robotize steering of a passenger vehicle and since torque will be applied by human driver's hands I need to supply such torque by an electric motor (probably a stepper with a required "holding torque" specification).

I know the torque could probably somehow measured on the steering wheel (with a torque wrench) with power steering off but it would be nice to be able to at least roughly calculate it. I actually need to know all torques for all car's normal operation scenarios (turning when standing still, when turning in speed, when going through a curve etc.).

EDIT:

I may have forgotten few parameters for the example. Say car's width is 1.5m (tire to tire) and distance between front and read axle is 2m.

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  • $\begingroup$ it depends on details of the steering geometry, you need to know the distance of the axis of steering rotation from the center of effort on the tire contact patch. (This appears to be zero in the pure ackerman cartoon picture, but of course no real vehicle has pure ackerman geometry). I frankly think you are better off to measure it. (aside if you have power steering why not use it on your robotic system?) $\endgroup$ – agentp Aug 4 '16 at 12:27
  • $\begingroup$ I am not sure the original power steering DC motor will be powerful enough when it has no input from a human driver (but maybe it will be). Thus I am thinking of replacing it with a stepper motor with decent holding torque. Also, the original is DC brushed which is driven by proprietary ECU and even if driven properly with custom driver may not give enough steering precision. $\endgroup$ – Kozuch Aug 4 '16 at 12:30
  • $\begingroup$ Turning while standing still - as mentioned in your question - is likely to be the worst case. Why not measure this twice - once on concrete and once in grass or sand - and design for the worst case? (Surface and tyre width are sure to affect the results too.) $\endgroup$ – Andy Aug 4 '16 at 12:31
  • $\begingroup$ @Andy Is still stand on concrete really the worst case? I am afraid rather fast curve may require also decent torque, maybe even more than still stand? $\endgroup$ – Kozuch Aug 4 '16 at 12:34
  • $\begingroup$ i mean why not put your steering actuator on the steering wheel side of the existing power steering box. $\endgroup$ – agentp Aug 4 '16 at 12:41
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Use a hanging scale like the ones in the grocery store and attach it to the steering wheel as a medium to see the pounds of force needed to turn the wheel.

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It heavily depends on the caster that the suspension is set at. Caster makes the wheels go back to neutral position. The more caster, the more torque is needed to keep the wheel at a position. Scrub radius will also make a difference. Google these terms and get familiar with them to get the idea. It will wildly vary per car. Use a scale like Muze mentioned to actualy measure the force needed to keep the steering wheel. Multiply by the radius of the steering wheel to get the needed torque.

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