Naked Science Forum
Life Sciences => Plant Sciences, Zoology & Evolution => Topic started by: katieHaylor on 24/05/2018 15:13:33
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Donald says:
What adaptations would be required for a blue whale to fly? For instance wingspan, flap rate, kg of fat burned per second if specifically the body main mass remained constant.
Ignore whatever is impossible, for instance, structural stability, heart size and rate, respiratory rate because, of course, whales will never fly in air. They fly through water!
What do you think?
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From an aerospace engineering perspective, for a whale to fly, or for anything to fly for that matter, its lift must be greater than it's weight, and its thrust must be greater than it's drag. A blue whale is hydrodynamically and aerodynamically shaped, meaning in the air it would have relatively low drag. This is great for flight! The average weight of a blue whale is 100-150 tons, which sounds like a lot, but the maximum takeoff weight of an A380 is about 617 tons. So if an A380 can fly, so can a blue whale. The question is then, what would be the whale's thrust? One could easily say, with enough rocket fuel, anything can fly. But if you want to strictly stick to physiological methods, this is where flapping comes in. For such a dense and heavy creature to fly, the wings need to have an extremely large plan-form area, must be very strong, lightweight and flexible. So this whale would need nature's equivalent of carbon fibre wings.....
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There is a relationship between the weight of a bird and its wingspan. The equation can be expressed as 2.43w0.03326, where the weight "w" is in pounds and the resulting wingspan is in feet. The weight of a typical adult blue whale ranges from about 100,000 to 300,000 pounds, with the record being 380,000 pounds. This equation predicts required wingspans for these three weights, respectively, of 111.8, 161.2 and 174.4 feet.
I'll try to come back to this question later to address the other issues.
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What adaptations would be required for a blue whale to fly?
Loading it into an aeroplane in a big tank of water.
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Loading it into an aeroplane in a big tank of water.
Would it help if we made the tank out of transparent aluminum?
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Wing flap rate is more difficult to calculate. This article describes an equation that can be used to estimate it: http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.530.7390&rep=rep1&type=pdf (http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.530.7390&rep=rep1&type=pdf)
f = 1.08(m(1/3)g(1/2)b-1S(-1/4)ρ(-1/3)), where
f = wing beat frequency (in beats per second)
m = mass (in kilograms)
g = force of gravity (in meters per second squared)
b = wing span (in meters)
S = wing area (in square meters)
ρ = air density (in kilograms per cubic meter)
Unfortunately, we don't know the wing area for this hypothetical flying blue whale. I'll look around to see if any equations are available to help predict it.
EDIT: I found what I was looking for. It's in the very last page of this artlcle: https://ocw.mit.edu/courses/materials-science-and-engineering/3-a26-freshman-seminar-the-nature-of-engineering-fall-2005/projects/flght_of_brdv2ed.pdf (https://ocw.mit.edu/courses/materials-science-and-engineering/3-a26-freshman-seminar-the-nature-of-engineering-fall-2005/projects/flght_of_brdv2ed.pdf)
By using the graph, I estimated that the needed wing loading for an average blue whale is between 151 and 232 kilograms per square meter. This corresponds to wing areas of 301 and 588 square meters. Now let's go back to the original equation. For the 100,000-pound (45,500-kilogram) blue whale at sea level, this yields:
f = 1.08(m(1/3)g(1/2)b(-1)S(-1/4)ρ(-1/3))
f = 1.08(((45,500 kg)(1/3))((9.8 m/s2)(1/2))((34.08 m)(-1))((301 m2)(-1/4))((1.225 kg/m3)(-1/3))
f = 1.08((35.7)(3.13)(0.0293)(0.24)(0.9346))
f = 0.793 beats per second (47.58 beats per minute)