The relationship between turn radius and velocity

R=(v^2)/a_c, where R is turn radius, v is velocity, and a_c is centripetal acceleration. Turn radius is proportional to the velocity squared.

This means that for a given centripetal acceleration, doubling the speed results in a quadroupling of the turn radius. Therefore, higher speeds require wider turns.

Applied to flight, for a given force of lift, doubling the speed results in 4x the turn radius. This is why you will very occasionally see me use brakes to turn, where the line is too tight to negotiate otherwise.