# To stop or to go around?

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.

• 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 – Pete W Mar 8 at 17:29
• If you go around it, you will still have a car. – StainlessSteelRat Mar 8 at 18:30
• 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. – 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 $$v, then your turning angular velocity is $$\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})$$.