Paper plane dynamics

Rakesh has made a generic paper airplane which when launched perfectly, flies straight and lands smoothly on the ground after a while. He gets bored with it and decides to experiment. He makes one cut each on the bottom of each wing and bends the cut piece up or down. If the piece is bent up, it is shown in red, if it is bent down, it is shown in green. Rakesh tests the nature of the flight trajectory of the plane for different configurations of the wings. He makes perfect launches every time. Each configuration is denoted in the diagram.

Finally, he compares the trajectories of each of the scenarios A , B , C , D A,B,C,D with the generic unmodified paper plane's trajectory. He marks under each letter, the most suitable number according to the following rules:

  1. If the plane deviates left from normal trajectory, mark 1 1 .

  2. If the plane deviates right from normal trajectory, mark 2 2 .

  3. If the plane flies significantly longer than normal, mark 3 3 .

  4. If the plane makes a nose dive, mark 4 4 .

  5. Otherwise, mark 0 0 .

Rakesh now has a four digit number underneath the letters. What is this number?

0430 0210 4231 4003 3214 0120 1423 3004

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3 solutions

Emma McGinty
May 27, 2020

The flaps give more or less lift and unbalanced lift is how airplanes turn so with the different flaps the planes turn

Shashank Gupta
May 23, 2015

Consider the aerodynamics of the wings... Normally the air pressure above the wings is lower than that below, so the airplane tends to rise due to this pressure gradient.. If you make flaps, and fold a flap up, it blocks the air from passing and this increases the pressure, decreasing the pressure gradient. Thus the wing will go down faster than normal. Vice versa happens when you fold it down...

That said

If both are folded up, the plane will do down much faster than normal (nose dive) If one is folded up the other down, the plane dips in the direction of the wing with flap that's folded up this turning towards it... If both are folded down, the plane will be pulled upward by the pressure gradient which is higher than normal, so it status in the air longer...

Nishu Sharma
May 20, 2015

I thought by using energy conservation (Bernoulli principle) ... Am i right ?

I do not know. But the simplest way to solve the problem is by considering the forces acting on the wings due to air hitting the flaps.

Raghav Vaidyanathan - 6 years ago

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Yes , By bernoulli , i mean that velocity of air near wings are lesser than that of opposite (down or up accordingly) wings . So this create pressure difference and we get respective deviations ... something like that .. !

Btw what is source of this question ? is it original ?

Nishu sharma - 6 years ago

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Yes, it is original. I make paper planes as a hobby.

Raghav Vaidyanathan - 6 years ago

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@Raghav Vaidyanathan that's Nice , I used to make paper planes very long time ago.. It is good to see you still love to do it .. :) :)

Nishu sharma - 6 years ago

When considering the planes that had one flap bent up and the other bent downward, I thought that the downward-bent flaps would act similar to a paddle in water, so that the left downward-bent flap would cause a pull to the left and vice versa. Is the opposite actually true, that the upward-bent flaps cause the shift in trajectory? Or is it more complex? I'm not too familiar with aerodynamics.

Tabitha Faber - 6 years ago

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An upward bent flap produces a downward force on the back of the wing, and a downward bent flap produces an upward force on the back of the wing.

When both flaps are up, the back of the wing is pushed down heavily, thus increasing the angle of attack and making the plane glide for longer time. When one is up and the other down, the wing with the upward flap is pushed down and the other is pushed up, thus creating a sort of tilt in the plane which makes it move in the direction of the tilt.

Raghav Vaidyanathan - 6 years ago

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@Raghav Vaidyanathan Okay, that makes sense. Thank you =]

Tabitha Faber - 6 years ago

Your idea of the paddle in water is partly correct. The "paddle" in an actual airplane is in its tail.

Raghav Vaidyanathan - 6 years ago

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