Indexing the archive…
Your Universe of Digital Possibilities
Tennekes’s great flight diagram: from a fruit fly to a jumbo jet, wing loading climbs as weight1/3 and cruising speed as weight1/6 — one line through twelve decades. Fly the dial and fit it from your own samples. Then race the power flight needs against the power muscle gives: the line ends, for flapping, where the ratio reaches one — somewhere near the weight of a swan.
In steady level flight the wing’s lift carries the weight: air density, the square of airspeed, wing area and a lift coefficient of order one. Solve it for V and size enters only through W/S.
Geometric similarity for flyers: weight is a volume, wing area a surface. Tennekes’s diagram runs one such line (N/m², W in N, approximate) from insects to airliners.
The lift equation with wing loading ∝ W1/3: cruise speed grows as the sixth root of weight — a jumbo about a hundred times a fruit fly’s speed for 10¹¹ times its weight.
Power to fly grows as weight times speed, W7/6; flight muscle, a fixed share of the body, delivers ∝ We with e ≈ 1. The ratio creeps up as W1/6 and crosses one somewhere among the heaviest flapping birds.
The Lemuel grammar: a quantity as a power of body size. On log–log axes every allometric law is a straight line whose slope is the exponent b — fitted, on every instrument of the edition, from the sizes you visit.
The sixth size takes The Bone’s square–cube law into the air: wings are areas, flyers are volumes, and a jumbo jet is a fruit fly scaled by three powers of size and still on the same line. What does not scale is muscle against the power to stay up — the same budget The Heart counts in watts, and the reason the biggest flyers flap no more. Cayley separated lift from thrust in 1799, Lilienthal measured the bird in 1889, Pennycuick put the power curve on a pigeon in 1968, and Tennekes drew the diagram. The air the flyer moves through is The Fall’s; the flocks it flies in are The Flock’s.