|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|
|Optimum speed||vopt||220 m/s
= 540 mph
= 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
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: