its weight mg. The downward momentum of the sausage created in time t
mass × velocity = msausageu = ρvtAsu
And by Newton’s laws this must equal the momentum delivered by the
plane’s weight in time t, namely,
Rearranging this equation,
ρvtAsu = mgt,
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
The total power required to keep the plane going is the sum of the drag
power and the lift power:
where Ap is the frontal area of the plane and cd is its drag coefficient (as
in Chapter A).
The fuel-efficiency of the plane, expressed as the energy per distance
travelled, would be