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* | A_{p} |
180 m^{2} |
0.09 m^{2} |

Density | ρ |
0.4 kg/m^{3} |
1.2 kg/m^{3} |

Drag coefficient | c_{d} |
0.03 | 0.1 |

Optimum speed | v_{opt} |
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 *f*_{A} to be the area ratio:

(C.21)

(Think of *f*_{A} as the fraction of the square occupied by the plane in figure

C.7.) Then

force = (*c*_{d}*f*_{A})^{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 (*c*_{d}*f*_{A})^{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, *c*_{d} ≅ 0.03 and *f*_{A} ≅ 0.04, we find the

required thrust is

(*c*_{d}*f*_{A})^{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:

Airbus A320 | 17 |

Boeing 767-200 | 19 |

Boeing 747-100 | 18 |

Common Tern | 12 |

Albatross | 20 |