Question

The lightest and heaviest flying birds are the bee hummingbird of Cuba, which weighs about 1.6 grams, and the great bustard of Europe and Asia, which can weigh as much as 21 kilograms. Show that the bee hummingbird produces about 0.016 newton of lift when it flies, whereas the great bustard produces about 205.8 newtons of lift. Which species would you expect to have proportionally larger wings? Why?

Answer 1

for the birds to be able to stay vertical in flight without falling down to earth, they must produce a lift that will counteract their weight

for the small bee humming bird,

mass = 1.6 g = 1.6 x
`10^(-3)` kg

weight of the bird under acceleration due to gravity = mg

where g = acceleration due to gravity = 9.81 m/s^2

weight of the bird = 1.6 x
`10^(-3)` x 9.806 = 0.0156 ≅ 0.016 N

for this bird to maintain flight, the least lift upward, it must generate must be equal to its weight downwards, i.e

lift = weight

therefore,

lift = 0.016 N

For the bustard of Europe and Asia,

mass = 21 kg

weight of the bird under acceleration due to gravity = mg

weight of the bird = 21 x 9.806 = 205.9 N

lift = weight = 205.9 N

lift generated is proportional to the wing surface area according to the lift equation

L = Cs x p x
`(v)/(2)` x S

where L = lift

C = lift coefficient

p = density of air

v = relative velocity of bird and air

S = surface are of the wing.

The great bustard will have a proportionally larger wing area to hold its weight in flight