Fluid Flow & Aerodynamics
why things fly, and why the usual explanation is wrong
Concept

Drag crisis — where it appears

The sudden fall in a bluff body's drag coefficient when its boundary layer becomes turbulent and separation moves rearward. It is a factor of about four across a factor of two in speed, and it is why a golf ball is dimpled.

Named by 2 essays across 2 fields — each of them below, with the objects they name alongside it.

The cliff a rough ball reaches sooner. The drag coefficient of a sphere against Reynolds number, on log axes. The smooth curve is Morrison's correlation, which is a fit to measurements and is drawn in the colour this site reserves for a borrowed claim. The other is the same curve shifted along the Reynolds axis by a factor of 6 — a stated model of what roughness does, which is to trip the boundary layer early, and not a measurement of any real ball.

The drag that falls as it speeds up

There is a band of speeds in which a smooth ball experiences less drag the faster it goes. Not a smaller coefficient — a smaller force. Dimples move that band down to where a golf ball actually flies, and they do it by making the friction worse.

applied · Sport ball Two drag laws, one derived and one fitted. Flat-plate drag coefficient against Reynolds number, laminar and turbulent, on log axes. The laminar curve is Blasius' similarity solution, solved by shooting; the turbulent one is the 1/7-power correlation, which was fitted to experiment and is drawn dashed-in-kind to keep the difference visible. Their slopes differ — −1/2 against −1/5 — so the gap between them widens rather than staying put.

The cost of going turbulent

A turbulent boundary layer costs several times the friction of a laminar one, and the multiple is not a constant — it rises with Reynolds number, because the two laws have different exponents. That is why laminar flow is worth more on a long fast surface than on a short slow one.

viscous · Drag budget

Named alongside it

The objects these essays reach for when they reach for this one.

Boundary layerCorrelationReynolds numberSeparationSkin frictionTransitionBlasiusPressure dragRoughnessWake

All concepts