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The more general question would be whether or not one can scale an animal to some other size and preserve its properties. The method of scaling is by volume, scaling all dimensions by the same factor. The mass is scaled so that the mass/body ratio is constant.

Some factors I thought about:

  1. How does muscle strength scale with muscle size?
  2. Could the joints support the new mass?
  3. If ducks rely on aerodynamics/wind to fly, how does the size change influence those factors?
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  • $\begingroup$ You weren't by any chance inspired by this song to ask yourself that question? the-burgenland-bunch.org/Songbook/Fing-mir-eine-Muecke/… $\endgroup$ – skymningen Sep 8 '17 at 7:31
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    $\begingroup$ Why a duck? Is a duck the most aerodynamic bird? $\endgroup$ – anongoodnurse Sep 9 '17 at 3:14
  • $\begingroup$ Horses can only gallop for 15 minutes before being exhausted, and can only canter for fairly short periods of time. It would flap it's wings very slowly and there would be insane energy demands on a single wing flap. to lift and maintain 300 kilos by 10 meters takes horse muscles about 5 minutes at maximum output and then the horse is very exhausted. $\endgroup$ – aliential Dec 29 '17 at 16:59
  • $\begingroup$ I don't know why a duck. $\endgroup$ – iayork Dec 31 '17 at 13:49
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The largest flying bird ever was probably Argentavis, which weighed about 70 kg, far smaller than a horse but still pretty impressive:

enter image description here

A duck scaled even to 70 kg wouldn't be able to fly since it wouldn't have the same relative wingspan. A 1 kg duck has a wingspan less than 100 cm; volume (and weight) increase as the cube of dimensions, so a 70 kg duck would have maybe a 4-meter wingspan, whereas Argentavis was nearly double that (around 7 m).

The largest flying animal we know of was probably Quetzalcoatlus, or perhaps one of the other Azhdarchid pterosaurs, which were definitely horse-sized depending how you measure:

enter image description here

enter image description here

These pterosaurs were comfortably over 250 kg, which puts them into small-horse range, so something that is "horse-sized" could definitely fly. However, these are very differently shaped and scaled from ducks, as you can see.

One important difference is probably that pterosaurs launched from the ground using their wing muscles -- quadrapedal launching -- whereas birds use their legs; heavier leg muscles needed to launch a big bird are wasted weight in flight, while heavier wing muscles needed to launch a big pterosaur remained functional in flight. That re-emphasizes that big things are not just scaled-up small things, but need to reshape their bodies to cope with their size; the square-cube law is just part of it.

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One response to your first question: Muscle strength depends on the cross-sectional area of the muscle, as it depends on the number of fibers. Therefore, it is increased by the square of the muscle diameter. On the other hand, the mass of the muscle increases in the third power when the diameter increases. So, a large muscle has less effect per kg than a small.

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