Let us we are moving in a car. There is a wall in front of us, we need to decide can we go around it or not. It is known that width of the wall is $w$ and our speed is $v = const$.

What is a simple approach to set formally conditions upon which it is safe to go around?

I understand that there are many possible details such as traction, weight of car etc. and will be glad even for the most simplistic analysis. If you can provide a source, that too is great. Thanks.

  • $\begingroup$ compute max turn radius, as function of w and distance. compute centripetal force as function of that radius and v. compare that force to max lateral force on tires before it slips $\endgroup$ – Pete W Mar 8 at 17:29
  • $\begingroup$ If you go around it, you will still have a car. $\endgroup$ – StainlessSteelRat Mar 8 at 18:30
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    $\begingroup$ the calculations for how quickly a car can turn are really too complex unless all you want is a general idea. This would be best accomplished by measuring the car's turning performance empirically. $\endgroup$ – Tiger Guy Mar 8 at 19:19

Each car depending on its handling has a maximum safe turning speed $v_{max}$, and radius $r$. Let us say the current speed $v<v_{max}$, then your turning angular velocity is $$\omega= v/r.$$ We need to go an arc of $\pi/2$ so the time it takes to turn is $$t=\pi/2\omega= \pi r/2v$$ which will give the decision distance $x$ as $x=t\cdot v$.


Above was for a wall wider than the cars cornering turn, if it is less, then the arc is smaller and we have $\theta= arccos(r-\text{car-width})$.


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