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:

(C.17)
(C.18)
(C.19)
(C.20)

Let’s define the filling factor fA to be the area ratio:

(C.21)

(Think of fA as the fraction of the square occupied by the plane in figure
C.7.) Then

force  =  (cdfA)1/2(mg).

(C.22)

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

(C.23)

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:

Table C.6. Estimating the optimal speeds for a jumbo jet and an albatross.
∗ Frontal area estimated for 747 by taking cabin width (6.1 m) times estimated height of body (10 m) and adding double to allow for the frontal area of engines, wings, and tail; for albatross, frontal area of 1 square foot estimated from a photograph.
Figure C.7. Frontal view of a Boeing 747, used to estimate the frontal area Ap of the plane. The square has area As (the square of the wingspan).
Airbus A320 17
Boeing 767-200 19
Boeing 747-100 18
Common Tern 12
Albatross 20
Table C.8. Lift-to-drag ratios.