Sat Nov 02, 2002 11:02 am

Dimples on golf balls. Invented by one of my professors...

The main reasoning for dimples on golf balls is about bluff body aerodynamics and boundary layers. A boundary layer is the air immediately around the object in an airflow - at the surface of the body, the air moves with the body, so the relative airflow velocity is zero (relative to the body!). From there, it increases, so that a few millimetres from the surface, the airflow velocity is almost identical to the airflow velocity infinitely far away from the body.

Now there are two main types of boundary layers: turbulent and laminar. In a laminar layer, the air moves mainly parallel to each other, shearing, but not intermingling. In a turbulent layer (or any turbulent flow), there are significant random movements of air packets (eddies) in all directions, also cross-flow. The end result is that a turbulent boundary layer has much more momentum close to the surface, but takes much more distance (from the body) for the flow to reach the free stream velocity.

Now here comes the crucial part: What does a golf ball do? Imagine it, for a moment, as a circular cylinder, in an airflow. Basically, in 2D, a circle placed in oncoming airstream. What happens to the streamline, the air? It moves around the cylinder. And theoretically, behind the cylinder, it moves back together - potential flow (i.e. ideal, unrealistic) flow does.

But what does real airflow do? It begins to move around the cylinder. If the cylinder has a scale of angles painted on it, with zero facing directly into the airflow, then at 90 degrees, the air has been squeezed together the most, and should be the fastest. So there the pressure is lowest. (Using Bernoulli: Along a stream line, total pressure is constant - total pressure being static pressure plus 1/2 times density times velocity squared. So faster air has lower static pressure). That means up to that point, the air is accelerating, and the pressure gradient moves from higher pressure to lower pressure, pulling the flow (and the boundary layer) along.

But behind that location, at 180 degrees, the flow should - in theory - be back to normal. I.e. back to a higher pressure. So now the flow is fighting against the pressure - it is moving from a low pressure zone to a high pressure zone, decelerating. What does that mean for the boundary layer? At the surface boundary, the velocity is zero, as stated. But a tiny distance from the surface, say half a millimetre, for example, the air is moving at some velocity. So there is a velocity gradient in the boundary layer. If the pressure gradient fights against the velocity gradient, it shifts the velocity gradient, until the velocity changes direction - i.e. the flow actually moves backwards, against the airflow, near the surface! This leads to separation. Separation means a highly chaotic, energetic airflow behind our circular cylinder, and if the air suddenly has all that energy, it needs to come from somewhere. It comes from the force it takes to hold the cylinder still in the airflow - it is drag.

So what is the big difference between turbulent and laminar boundary layers? Turbulent boundary layers have a much higher velocity gradient near the surface, because they have much more momentum (due to the random crossflows). So the adverse pressure gradient needs to fight a lot longer until it manages to turn the boundary layer around and cause separation. So a laminar flow separates near to 90 degrees (actually, even slightly ahead of the 90 degree location in reality), but the turbulent flow clings on to the surface until, say 130 degrees, meaning the separated (drag-inducing) region is much smaller.

If you put dimples on your cylinder, this simulated a rougher surface, and causes the flow to be turbulent. So the most basic and essential result is less drag.

What about the rotating golf ball? Well, any rotating cylinder - even without dimples - will generate lift (if it rotates inside an airflow!), because it induces vorticity. The most basic and simplified formula is Lift equals density times velocity times vorticity. So the dimples can enhance that effect a little, but they do not cause it.

There is one other interesting example: Some balls (for some sport I don't know) have a thick circular leather ridge around them. If you throw them in the air with the ridge at the right angle, it will act as a trip wire (i.e. cause turbulence) on one half of the ball, keeping the flow attached for longer and causing less drag, while on the opposite side, the ridge is so far back that the flow is laminar until the (early) separation point, causing more drag on that side. The end result is a moment on the ball, causing it to fly a curved path! (so you could, with skill, throw a ball into the air that begins climbing more steeply up before losing momentum and tumbling back down)

Now back to the original question: Dimples in golf balls, trip wires and other methods are there to induce turbulent flow and turbulent boundary layers. That makes sense for bluff bodies only. Because sleek, aerodynamic bodies (like an airplane wing for example) keep the flow attached even if it is laminar, by being as gradual as possible in joining the flow back together. And laminar airflow causes less skin friction drag than turbulent one. So an airplane would not benefit from dimples or trip wires.

Main points again:

* turbulence needs energy, causes drag.

* Separated regions are full of giant, strong turbulence.

* Small (dimple-induced) turbulence near the body surface, i.e. a turbulent boundary layer, causes flow to stay attached to the body for longer. So the separated region (with all the giant turbulenc) is smaller, and the energy required is smaller - you have less drag.

I hope this explanation makes any sense without diagrams. It's kinda hard to explain Fluid Dynamics without lots of pretty pictures...