Physics of Paper Airplanes


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Paper Airplanes, flight at its simplest for humans. As kids, we learned how to build paper airplanes and send them soaring into the sky. We didn't stop to think about why the airplanes where able to fly after the initial thrust we gave them or how they were able to glide for so long afterwards. Ignorance was bliss then, but now we strive to understand how things work. Looking back to the childhood past time of flying paper airplanes, I will try to explain some of the parts that make paper airplanes fly.


First off, it should be stated that there are many different designs of paper airplanes and that different designs could affect the physics applied to it. If one paper airplane used a second set of wings or had a tail like a real airplane, those items would have more physics applied to them like extra drag.

Up, Up and Away! So your paper airplane takes to the air and glides gentely to the ground but you still don't understand how it is able to glide. Your paper airplane uses lift to carry it through the air and to its landing area. Now you are interested and want to know how lift works. The lift for your paper airplane doesn't work quite the same as a real airplane but understanding how an airplane maintains lift is useful. Now something important to remember is that lift can only happen when in the pressense of a moving fluid and that air has fluid properties.


The basic concepts of lift for an airplane is seen. The air that is flowing splits to move around a wing. The air that that moves over the wing speeds up creating lower pressure which means that the higher pressure from the air moving slower under the wing pushes up trying to equalize the pressure. The lift generated can be affected by the angle at which the wing is moving into the flowing air. The more surface area of the wing resisting against the flow of air can either generate lift or make the plane dive. This can be easily simulated in everday life. Next time you are riding in a car with someone stick your hand out the window. Have your fingers pointing in the direction of the motion of the vehicle. Now move your hand up and down slightly. You can feel the lift and drag that your hand creates.

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There is an equation to solve for what the force of lift is as seen here:

L = lift
Cl = lift coefficient
(rho) = air density
V = air velocity
A = wing area
If there was not lift created for your paper airplane it would fall pretty fast to the ground and would have to rely on pure thrust to keep it up. It would be like throwing a baseball into the air and hoping to watch it glide. So now you know how lift affects your paper airlplane and you are starting to think of new ways to build that favorite style of yours. Maybe try to make larger wings to increase the lift.


Air Drag

When anything is moving in the air, there is a resistive force of the air pushing back. This is known as Air Drag. On the picture above, air drag is represented by the letter 'D'. Air drag is dependent on a few factors such as the density of air, area of the air plane and the drag coefficient. This is the equation for air drag:
R=(1/2)DpAv^2
For the equation, the different parts are:
R=resistive force
D=drag coefficient
p=density of the air
A=cross sectional area of object
v=velocity
If we crumpled up a paper airplane into a ball and dropped it from the top of a building and there was wind, we could look at the forces on the crumpled airplane as the downward force of gravity and the opposite force of air resistance. Because the force of gravity is equal to the mass times gravity (Fg = mg) we can add the forces on the ball into the equation:
F = mg - (1/2)DpAv^2
Air resistance plays a large part in the flight of paper airplanes by limiting the flight distance. If the air resistance was too high, the paper airplane wouldn't go anywhere. It would be like trying to throw a paper airplane under water. The design of a paper airplane revolves somewhat around the air resistance and the attempt to lessen the cross sectional area of the paper airplane. The less area that is perpendicular to the horizontal path of the airplane the less ressistance will be experienced.


Air,
huh, yea, what is it good for,
pressure and density!


So what does air have to do with paper air planes some might wonder. You may think that air plays close to no roll but with it comes fluid like mechanics such as pressure and density. Density is a part of matter and is the mass per unit volume of a substance. Pressure is the force acting on an object at a perpendicular angle to a specified surface and is in newtons per meters squared.


DENSITY!!!!!
Hey, are you calling me dense? I guess you could say yes because all matter has density and so do I. Density is the amount of mass compacted into an area of an object. Get a glass of water and take a good look at it, it's density is the mass of the water contained in the area bounded by the glass. The equation for density is p=m/V which is density is equal to mass devided by volume. So why is this important you might ask. Well a paper airplane needs to fly does it not? Because of the equation for air resistance under the drag section, air density helps define the resitance the paper airplane is going to experience while in flight. Temperature is also a factor that relates to density. If a substance heats up, its molecules increase in bouncing around so they try to take up more room. That means if you have a container of a substance and you heat it up, it will try to expand which increases the volume. Larger volume equals less density.


PRESSURE!!!!!
Felling pressured to do something that you don't want to? Well that is close to how real pressure works. Pressure is the force diveded by area which is P=F/A. Because pressure is a scalar quantity it acts in all directions. So now you see that pressure acts on a paper airplane by exterting a force over the airplane. If the pressure of our standard atmosphere was higher such as the pressure of deep ocean water then our paper airplane might be crushed before even taking flight. The pressure of air is also dependant on the depth you go. There is a seperate equation that relates pressure to the parts of a fluid such as density, depth and gravitational field strength. This equation is P=pgh where P is pressure, p is density, g is gravitational strength and h is depth. This means that the higher someone goes in the air, the less pressure there is.


Thrust
What gives that paper airplane the long distance flight, the design helps but the intial thrust given by the thrower is mainly where it is at. When looking at the modle of an airplane flying, there are a couple of factors that keep it up in the air and going. One is that the lift has to be greater than the acceleration down due to gravity. The second factor is that lift is dependant on thrust with an airplane (and paper airplanes). If the thrust is equal to the air resistance then the object is stationary. Looking at the modle of the airplane you can see the different forces acting on it:

Because thrust can not be maintained on paper airplanes, they have to come down at some point. Just as an airplane as to come down to refuel, paper airplanes come back down to be picked up again and send soaring into the air. This can be related to Newton's first law stating that in the absence of an external force, a body at rest remains at rest and a body in motion remains in motion. That means that if there were no other forces like gravity, the paper airplane would continue to travel.
To find the thrust that you give your paper airplane you need to find the force that you transfer to the paper airplane when you throw it. Using Newton's second law we find that force is equal to the mass of an object multiplied by the acceleration which is shown in this equation:
F=ma
Force is measure in the SI unit called the newton. A newton is defined as a force that produces as acceleration of 1 m/s^2 when acting on a 1 kg mass, so 1N=1kg*m/s^2.



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