The Critical Speed     A smooth sphere that is traveling around 250 mph, it has been observed that there is a major change in the drag force.  It is seen that the drag force is reduced with increasing speed and finding the drag force to be reduced roughly 1/3 of its original value at speeds of 300 mph before increasing again. The calculations have been done concerning the drag of the smooth sphere and how it varies with speed and it is shown in figure 1.  By looking at the figure, it appears that the drop of the drag force is irrelevant for golf since the speeds are much higher than a normal golfer would go.  This is where a dimpled golf ball plays a role.                                                                                                                                    It is seen that a dimpled golf ball has a critical speed much lower than that of a smooth sphere.  A modern dimpled golf ball has a critical speed roughly around 30 mph which in turns mean that there is a reduction in the drag of the golf ball immediately after.  By looking at figure 2, we have the dependence of a drag force due to a smooth sphere and a golf ball.  It clearly shows that there is a drop on the drag force at lower speeds for a golf ball than that of a smooth sphere.                                                                                                                                     The changes of the pattern of the airflow causes this drop of the drag force at a critical speed.  The thin boundary layer becomes unstable above the critical speed which welcomes "the faster moving air outside the boundary layer to have a turbulent mixing with the slower air near the surface of the ball and to carry it further towards the back of the ball before separation occurs." (Wesson)  This causes a reduced drag with a smaller wake.     This turbulent mixing really depends on how rough the surface of the sphere is.  Depending on the roughness of the surface, it would give rise to an increase or decrease of the critical speed.  The dimples on the golf ball causes a perturbation of the air flow which brings turbulence at an earlier state in the boundary layer which then reduces the critical speed.  There are many dimples on the golf ball which are of the same order of thickness as the boundary layer and these dimples play a critical role of the drop of the drag force.  A smooth sphere would travel about 100 yards less than that of a golf ball.      We can also see in the next slide the role these dimples have in regards to the spin of the ball.