its weight mg. The downward momentum of the sausage created in time t

is

mass × velocity = *m*_{sausage}*u* = *ρvtA*_{s}*u*

(C.4)

And by Newton’s laws this must equal the momentum delivered by the

plane’s weight in time *t*, namely,

*mgt*.

(C.5)

Rearranging this equation,

*ρvtA*_{s}*u* = *mgt*,

(C.6)

we can solve for the required downward sausage speed,

Interesting! The sausage speed is inversely related to the plane’s speed *v*.

A slow-moving plane has to throw down air harder than a fast-moving

plane, because it encounters less air per unit time. That’s why landing

planes, travelling slowly, have to extend their flaps: so as to create a larger

and steeper wing that deflects air more.

What’s the energetic cost of pushing the sausage down at the required

speed *u*? The power required is

(C.7)

(C.8)

(C.9)

(C.10)

The total power required to keep the plane going is the sum of the drag

power and the lift power:

(C.11)

(C.12)

where *A*_{p} is the frontal area of the plane and *c*_{d} is its drag coefficient (as

in Chapter A).

The fuel-efficiency of the plane, expressed as the energy per distance

travelled, would be

(C.13)