BIRD | 747 | Albatross | |
---|---|---|---|
Designer | Boeing | natural selection | |
Mass (fully-laden) | m | 363 000 kg | 8 kg |
Wingspan | w | 64.4 m | 3.3 m |
Area* | Ap | 180 m2 | 0.09 m2 |
Density | ρ | 0.4 kg/m3 | 1.2 kg/m3 |
Drag coefficient | cd | 0.03 | 0.1 |
Optimum speed | vopt | 220 m/s = 540 mph |
14 m/s = 32 mph |
need to pick one of them and double it:
Let’s define the filling factor fA to be the area ratio:
(Think of fA as the fraction of the square occupied by the plane in figure
C.7.) Then
force = (cdfA)1/2(mg).
Interesting! Independent of the density of the fluid through which the
plane flies, the required thrust (for a plane travelling at the optimal speed)
is just a dimensionless constant (cdfA)1/2 times the weight of the plane.
This constant, by the way, is known as the drag-to-lift ratio of the plane.
(The lift-to-drag ratio has a few other names: the glide number, glide ratio,
aerodynamic efficiency, or finesse; typical values are shown in table C.8.)
Taking the jumbo jet’s figures, cd ≅ 0.03 and fA ≅ 0.04, we find the
required thrust is
(cdfA)1/2 mg = 0.036 mg = 130 kN
How does this agree with the 747’s spec sheets? In fact each of the 4
engines has a maximum thrust of about 250 kN, but this maximum thrust
is used only during take-off. During cruise, the thrust is much smaller:
Airbus A320 | 17 |
Boeing 767-200 | 19 |
Boeing 747-100 | 18 |
Common Tern | 12 |
Albatross | 20 |