The coolest number!
Watsisname wrote:That's actually a fairly common experience and I've nearly had an accident that way, myself. It's pretty scary! And it all comes down to physics.
All objects will move in a straight line with constant speed unless acted on by some force. Your car is no different. If you're driving through a curve, a force is necessary to make it follow that curve.
We can consider the curve to be a part of a circle with a radius [math]. To follow that curve, there needs to be a centripetal force [math]. This centripetal force is supplied by friction between the tires and the road surface, and this friction force has a maximum strength of [math], where [math] is the coefficient of friction between the tire and road. m is the mass of your vehicle and g is the gravitational acceleration on Earth.
Equate these to solve for the maximum speed you can have through the curve:
[math]
This tells us the fastest speed we can have for a curve with a given radius of curvature and a coefficient of friction. If we try to drive faster than that, then the tires will not be able to provide enough force to keep us along the curve, and we'll begin to slide. Notice the max speed is slower for a smaller coefficient of friction, a smaller radius of curvature (sharper turn), or if gravity is weaker (harder to drive in low gravity, as anybody who plays with rovers in KSP will know from experience).
Let's apply some numbers:
The coefficient of friction between tires and dry road surface is typically around 0.7. Suppose the curve forms part of a circle with a radius of 25 meters. Then the maximum speed we can safely drive is about 13m/s, or 47km/hr. What if the road is wet? This decreases the coefficient of friction to about 0.4. In that case our max speed for that curve is only 35km/hr! So the road conditions are very important.
It's also very important to note that even at speeds below this theoretical maximum, it is easier to lose control than if you were driving straight, especially if you're also trying to correct your steering or applying the brakes. So we have to be cautious with curves. Apply the brakes before you enter the curve so that you're already at a safe speed, and give yourself an extra margin for safety if the roads are wet.
Salvo wrote:I forgot to mention that the road was uphill, in that case was the coefficient of friction higher because the slope exercised an "additional force"?