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Just a A4 paper sheet folded into a plane seems to fly decently. But a model of actual (big) plane made out of paper is only good at falling...

What is different for paper planes? Are there "modern and improved" designs of paper planes?

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do you have pics of the ones you compared? often paper planes have a very thin hull and wings while model aircraft have much thicker hull and wings, often heavier as well –  ratchet freak Jun 28 at 20:48
    
Something like if one tries a Google Image Search of "paper plane model". –  Anonymous Jun 28 at 21:37
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I suspect the answer will have something to do with Reynolds numbers. When you scale down your 747 to A4 size, you are not scaling down the viscosity of the fluid in which the object flies. –  RedGrittyBrick Jun 28 at 22:21
    
The article also mentions them. –  Anonymous Jun 28 at 22:37
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up vote 10 down vote accepted

The reason is really the size! Air molecules have the same size if they flow around a small paper airplane or a big real airplane, but since their relative size is so much smaller when they flow around the real airplane, friction effects are much smaller for the big airplane. When comparing airplanes of different sizes, a dimensionless number first formulated by Osborne Reynolds is most helpful. It is basically the ratio of inertial to viscous forces in the airflow, and the formula is $$Re = \frac{l \cdot v}{\nu}$$ Nomenclature:
$Re\:\:\:$ Reynolds number
$l\:\:\:\:\:\:$ characteristic length, for example wing chord
$v\:\:\:\:\:$ airspeed
$\nu\:\:\:\:\:$ kinematic viscosity of air

Flows with the same Reynolds number behave identically, but your scaled-down aircraft flies at a very different Reynolds number than the original (both speed and characteristic length are a lot lower), so the airflow around it will be very different. For it, the air looks more like a syrup when that around the original is like flowing water! Therefore, lift creation needs different means at this scale (wings with more chord, for example), and the paper airplane is better suited to cope with this particular flow condition.

The next difference is wing loading: The paper airplane is very light; its mass per area is low. Therefore, it can fly at a slower speed than your scaled-down real airplane, and it will be easier for you to launch the paper airplane properly into the air. The scaled-down airplane needs to be thrown harder, but still straight, and this might be another reason for it falling down quickly.

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How will a giant paper (or other material if paper is too weak) plane fly? Will it also sink like a stone? –  Anonymous Jun 28 at 23:36
    
With a bit of cheating, it can be made to work. Look at cardboard, which is essentially glued paper. Smart construction can reinforce paper to be strong enough. You should be able to pull off a 2 meter glider. –  MSalters Jun 28 at 23:54
    
@Anonymous: Increasing size will help, even if the shape of the plane stays identical. But you definitely need something stronger than paper. The plane will fly, but will need more thrust (if engines are installed) or fly less far when launched compared to a plane with conventional shape due to its lower aerodynamic efficiency. –  Peter Kämpf Jun 29 at 5:37
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@MSalters: A 2 meter glider is essentially a model aircraft, and they can be made similar to the real ones. But optimization for this scale will still lead to bigger and stubbier wings and airfoils with less camber and thickness, for example. –  Peter Kämpf Jun 29 at 5:40
    
and at the 2 meter scale you will be using fiberglass or if you have deep pockets carbon –  ratchet freak Jun 29 at 14:06
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