The thread: Taught wrongly, everywhere — page 23
220 essays carry this thread — page 23 of 25.
Fluids at work
A drive's best spin falls where players hit it only because lift tires and drag grows
With lift in proportion to spin and drag fixed, a golf drive keeps gaining from backspin until its best launch has fallen to level, near 4,800 rpm, and past a few thousand more the model flies a ball the length of eight football pitches. Give lift and drag the curves wind tunnels measure — lift growing ever more slowly with the spin ratio, drag rising with it — and the best spin moves to near 2,300 rpm at 70 m/s, with a launch well above level, inside the range launch monitors recommend. Either curve alone leaves it at twice that or more. And along a ridge of best launches the carry hardly moves while the angle falls by ten degrees, which is why the launch angle is the softer of the two numbers.
What is taught wrongly
A swell lifts a ground-effect wing more at its crests than it takes in its troughs
A wing skimming the sea gains its lift from the sea's reflection of it, and the reflection grows sharply as the gap closes. Over a swell the gap opens and closes with every wave, so the lift swings — further up at each crest than down at each trough, which raises the mean lift as well as shaking it. Climbing out of the swing is possible, but the height that calms the lift spends the cushion the craft was built for, and in a sea about two metres high it has spent nearly all of it.
Flows and fields
A cloud folds where a saddle is strong, not when
When every saddle of a lattice strengthens and weakens together, a cloud of heavy particles folds in one step, at the strain's first strong excursion. Give each saddle its own random strength and the folding spreads out into a steady rate — and falls, because a particle now has to be at a saddle while that saddle is strong. The rate follows the Gaussian tail of the strain, at about a tenth of the time the strain spends past its fold condition, and a longer-lived strain helps only up to a few strain times.
Fluids at work
A wand that lags its sea makes flying level the better bet
A foiling dinghy whose height control divides the sea sharply follows the long waves, flies level through the short and beats both pure strategies. Give the division the lag a real wand or filter has and the gain disappears in a moderate sea; in a rough one no crossover both keeps the foil under and spares it from pulling down. A second-order filter, which cuts more sharply, does worse rather than better, because it flies through more of the sea near its crossover than the sea contains.
What is taught wrongly
The side that turns turbulent first decides who arrives first near the wall
Inside a laminar layer the upper parcel's lead over the lower grows with depth. Real wings are not laminar to the trailing edge: one surface's layer turns turbulent first, and a turbulent layer is full almost to the wall. At the incidences a wing flies at, the upper side goes first and the exaggerated lead survives to the trailing edge, smaller than the laminar one and shrinking with the Reynolds number. Below about one degree the lower side goes first, and a tenth of the way into the layer the lower parcel arrives first.
Fluids at work
The run moves the best drive below the ridge that carries furthest
A drive's carry is greatest along a ridge of launches on which more spin trades for a lower angle at almost no cost. Every drive on that ridge lands at about the same steep angle, so the run after landing hardly chooses between them. What the run rewards is leaving the ridge: less spin and a launch several degrees lower, a lower flight that lands flatter, gives up thirteen metres of carry and gets back twenty in the run. On an ordinary fairway the best drive in all lands near thirty-five degrees, at every ball speed; on a firm one the model's ground stops being a turf anybody has measured before the run stops paying.
Ideal flow
Plating that gives way slows the water that slams it, but only on a flat bottom
The slamming pressure on a hull's bottom is a ridge that rides at the edge of the wetted width, and how fast that edge moves depends on how far the water has to climb. A panel of plating that bends inward under the load gives the water further to climb, and while it is moving away it slows the climb itself. Fed back into Wagner's condition, that takes a seventh off the peak stress of a panel on a four-degree bottom loaded to the edge of what aluminium can bear, and almost nothing on a deep V — because what matters is the plating's deflection against the bottom's own rise across the panel.
Compressible flow
A wire sings with the force on it, not the flow round it
A free flow can only radiate as a quadrupole, four sources nearly cancelling, which is why a jet's noise grows as the eighth power of its speed and so little of its power becomes sound. Put a body in the flow and the cancellation is broken: the fluctuating force the body exerts is a dipole, its sound grows as the sixth power, and at the speed of any wind it outshouts the turbulence that made it by a factor of tens of thousands. The whistle of a wire is the force of its own wake, radiated.
What is taught wrongly
Free to rise and fall, a ground-effect craft rides its own cushion over the swell
A wing held still over a swell sees its gap change and its lift swing with it. A real ground-effect craft is not held: its weight sits on that lift, and ground effect, whose lift rises as the gap closes, gives it a height stiffness — a spring made of its own cushion — while its vertical speed changes its angle of attack and damps it. Free in heave it is an oscillator driven through that spring. Over long swells it follows the sea and keeps twice the held wing's clearance; over short ones it flies level and rides a dozen centimetres higher, because the cushion's swing is convex; and it comes closest to the crests over the swells it meets near its own natural frequency, never as close as the held wing does.