by Sarah Forst

Why does an “illegal” golf ball travel further than a regulation golf ball? Can this effect be applied to cars, for instance to increase down-force on a wing?

I'm not sure my golf game is good enough for me to answer this question.  I prefer 18 holes of drinking and golf cart racing.  But a simple lesson in fluid dynamics – solid objects experience drag due to object traveling through fluid, in this case, air.  There's the drag experienced at the front of the car as it tries to propel forward through the air and there's the drag experienced at the rear of the car. But first, let's play a few holes

The variance between the low and high pressures explains the drag forces and lift that an object experiences.

 In this ideal condition of inviscid (zero viscosity) fluid around an object, the high and low values cancel each other out and there is no drag force.  The flow stays attached as it travels around the body.  The graph at the right indicates the pressure distribution around the sphere.If angle a represents the position along the sphere, the leading edge first encounters a=0 degrees and the trailing edge is a=180 degrees.  The top of the sphere is a=90 degrees while the bottom is a=270 degrees. The air flow is perfectly symmetrical around the sphere in this ideal situation.  The patterns at 0 degrees and 180 degrees match as well as those at 90 degrees and 270 degrees.

 Jean le Rond d'Alembert was the first to discover this conflict between the ideal theory and the drag that a moving sphere experiences in reality (d'Alembert's Paradox) but failed to explain this discrepancy because he disregarded the impact of friction in his research. When an object is exposed to a viscous fluid, the flow separates into erratic vortices that create a wake.  The high pressure on the front face and negative pressure on the rear face exert a drag force on the sphere, evidenced by the pressure distribution on the right.

The boundary layer is the thin layer of fluid (air in our case) that lies very close to the surface of a moving object and where the impact of viscous forces are most obvious. Laminar flow is smooth and steady and the air stream experiences little change in velocity when moving away from the boundary layer while turbulent flow is choppy and creates vortices.  Laminar boundary layers separate more easily than turbulent ones when exposed to pressure gradients. Flow (air or fluid) over a blunt object (sphere or cylinder) experiences massive pressure gradients that cause the air flow to slow down and separate, or lose forward momentum. This separated flow creates an area of low pressure in an object's wake.  We could dig our feet into the technical manure some more and talk about the Reynolds number which indicates the relationship between inertial (resistant to change or motion) and viscous (heavy and sticky) forces in a flow, but it's beyond the scope of this Q&A.  Readers with a far better grasp of this can chime in below.

A golf ball would not travel nearly as far if it were smooth over the entire surface.  A golf ball uses symmetrical dimples of the same size over the entire surface.  The dimples trip the transition causing a laminar boundary layer to become turbulent sooner.  While this causes a slight increase to surface drag, this moves the separation point further back on the golf ball.  The flow on the backside of the ball remains attached longer, creating a much lower pressure drag in its wake. The dimpling on “illegal” golf balls can also sway the ball's direction or speed. Polara's “self-correcting” golf balls have shallower, larger dimples around the equator of the ball which produce a horizontal spin axis, and smaller, deeper dimples on each pole correcting the side spin that results in you hooking or slicing the ball left or right.  Basically, you can drive the ball further and straighter – about a 75% reduction in ending up in the drink or on the beach.  Expect to shell out some good money for these, but if your ass is on the line (like a foursome with your company VP's and a potential promotion sitting out there), they're worth it!

 Air flowing over the smooth sphere becomes separated more quickly. Air stays attached longer with the dimpled golf ball.

Dimples work well on spherical, blunt objects like golf balls for two reasons: their shape lends itself to a separation point closer to the front of the ball which causes the air flow to separate more quickly, causing a thick wake in its path and the resulting pressure drag. And golf balls have no leading edge. A golf ball spins, turns, and isn't always hit in the same spot.  Technically, small bumps on a golf ball would be more beneficial but they would be flattened with each drive until they were useless.

 Many water skis, wakeboards, and snowboards use dimpled surfaces on the bottom though your most effective chance at lowering the drag revolves around a nice coating of wax to slick up that surface finish!