The normal force on a level roadway is that due to acceleration by gravity of the mass of the car. The magnitude of the radial force that can be supported without slipping is the product of the normal force and the coefficient of static friction. The magnitude of the radial force required to turn the car is the ratio of the product of the car's mass and the square of its speed to the radius of the curve. That is
kmg = mv²/r
The mass of the car cancels when we solve for v, the maximum speed in the curve:
v = √(kgr)
where k is the friction coefficient, g is the acceleration due to gravity, and r is the radius of the curve.