Rubberband Airplanes: Physics for Takeoff, Flight & Range

[vvoo7vv]

I'm working on a project relating to rubberband power airplanes. I need to know the physics related to it. For my project I need to. Sketch two free-body diagrams: one for the plane accelerating on the ground and another one for the plane flying. Show all the forces in each case and write simple equations to show the relations between these forces. Include equations which show the relation between these forces and the acceleration, velocity, and distance your airplane travels on the ground before becoming airborne. Show also equations for the endurance and the range.
- takeoff distance
- takeoff speed
- maximum height attained in flight
- gliding angle from the maximum height to the touch-down point
- time aloft (endurance)
- range (distance traveled)

If you can help me, I would appreciate it. Thanks a lot.

 

[NateTG]

FBD Guide

Perhaps there should be a guide for posting problems to the help section.

Specifically regarding FBD's, if you don't know where to start, try listing all of the forces that are acting on the airplane.

 

[maverick280857]

Well, essentially an aircraft is subject to the following four forces:

1. Thrust
2. Drag
3. Lift
4. Weight (gravity)

During take off, the thrust of the engine causes the aircraft to move forward (thanks to its wheels it really does move). The drag at this point is offset by this large thrust. At the optimum speed (at which the thrust is optimum) the elevators assist in directing a portion of this thrust at an angle with respect to the horizontal, to balance the gravitational force. The aircraft takes off just when the thrust is greater than the weight.

When in air, all the four forces listed above are still acting, though differently depending on the motion of the airplane. With these facts in mind, you should be able to make a FBD for the aircraft. The force equations can be easily written by applying Newton's Second Law (F = ma) once you have convinced yourself about the FBD. Depending on your needs, you might want to consider more complex situations involving center of gravity and center of pressure.

The takeoff distance is the minimum distance required to develop enough lift (or acceleration if you use F = ma, assuming negligible mass change) to counter the weight. You can use kinematics to find this out. The takeoff speed is similarly computed.
Maximum height attained in flight really depends on the net vertical force and parameters such as fuel left, mass, etc.
For other equations you might want to check out some aerospace engineering texts...or do a google search.

Cheers
Vivek