How many miles can a hungry bird with the total weight of 1 kg fly? The bird lives in Chicago IL USA.? Please specify all of your engineering assumptions.
Question proposed by my Machine Design I.
Solution:
- Bird will weight 1 kg and 5% of its body mass is fat. it makes the weight of the fat 50 grams
- Fat is a fuel and has heating value of 38 Calorie/4.3 grams of fat or 1,848 J
- With 50 grams of fat the amount of energy that fat will burn is = 1,900 J
- Bird will fly with the average constant horizontal speed of 40 km/h equal to 11.1 m/sec
- We will ignore the energy that it require to reach to a comfortable height
- Drag force (N) = 1/2 * density of air at 10,000 feet * Cd * A * V^2
- In Chicago birds will fly up to 10,000 feet in average
- Density of air at 10,000 feet = 1 kg/m^3
- Cd = Drag force coefficient for birds (Average) = 0.3
- A = Cross section area of the bird body = (Bird average diameter 10 cm) = 0.008 m^2
- V^2 = 11.1 ^2 = 123.2 (m/sec)^2
- Fd = Drag force to the bird body = 0.15 N
- Energy comes from burning fat - Energy consumed by Drag Force = Delta (KE)
- 1,900 - Fd x D = 1/2 * ( 1 * 11.1^2)
- D = (1,900 - 62) / 0.15 = 12,253 meters = 12 km = 7.5 miles
