#22c Airplane flight
In aviation it is usually more convenient to consider the motion of air over a wing or over a propeller blade in their own frames of reference. This lesson examines swept-back airliner wings (also at swept-forward and swiveled wings), and at the loss of propeller efficiency when the airplane gains forward speed.
#22d Airplane flight--How High? How Fast?
An optional second unit(added later) on basic aerodynamics--on how lift and drag depend on velocity and altitude, and how airplanes balance high cruising speed against low landing speed.
Part of a high school course on astronomy, Newtonian mechanics and spaceflight
by David P. Stern
This lesson plan supplements: |
#22c "Airplane Flight," Sflight.htm,
on the web http://www.phy6.org/stargaze/Sflight.htm
#22d "Airplane Flight--How High? How Fast?" Sflight2.htm,
on the web http://www.phy6.org/stargaze/Sflight2.htm
Note: All this material may be regarded as is optional. If time is short, the discussion of forces on a propeller (the more difficult part) may be omitted.
This lesson plan does not cover section #22d. A teacher wishing to use that part needs to prepare ahead.
#22c. Airplane Flight
The student will learn:
Stories and side excursions: The wind tunnel of the Wright brothers, the swept-back wing, the X-29 airplane with swept-forward wings and the swivel-wing idea.
#22c. Airplane Flight--How High? How Fast? (Not part of the lesson plan)
The student will learn:
Stories and side excursions: The nonstop round-the-world flight of the "Voyager" airplane.
Starting the lesson
Today we will discuss the application of frames of reference to an airplane flying with a constant velocity v through the air. Viewed in the frame of reference of the ground, in the absence of wind, the airplane is moving through still air.
If on the other hand we prefer to use the airplane as our frame of reference, then the air is what moves, blowing in the opposite direction to the flight and flowing around the wings and the aircraft.
We can look at it either way, but the second way is usually more convenient. In any case, it is the flow of air over the wings of an airplane that supports the airplane in the air, creating an upward force known as lift. Lift increases rapidly with velocity--as a matter of fact, it grows like the velocity squared--so with enough speed, even an airliner weighing 100-200 tons can be supported
We don't have the time here to discuss how lift is generated. Let it just be said, that the cross-section of the wing--flat on the bottom, curved on top--makes air flow faster over the top than over the bottom. This only happens when the front of the wing faces the wind (directly or lifted slightly, at a small "angle of attack").
When the airplane stands on the ground, not moving, air presses on the top and bottom of the wing with equal force. In flight, the faster flow on top of the wing creates lower pressure there, and the extra pressure from below is then what produces the lift.
Another force on the wing and on the airplanes is the drag--that is the name given to the air resistance, and it also grows like the square of the velocity. The drag is overcome by the thrust, the forward pull of the propeller or the push of the jet engine. And finally, the lift is opposed by the weight of the airplane and its cargo.
[As part of this discussion, it may help to draw on the board a side view of an airplane, and each time a force is mentioned, illustrate it by an appropriately directed and labeled arrow.]
Then continue from the text of section #22c, starting at the subhead "Frames of Reference."
Questions and side excursions
What are the 4 forces acting on an airplane in flight, and what are their directions?
Drag--the resistance of the air, opposes the thrust
Lift--the upward force on the wing
Weight--the downward pull of gravity.
What creates the lift on an airplane wing?
Why do jetliners avoid flying above the speed of sound?
Why do jetliners avoid flying faster than even 85% of the speed of sound?
Why do swept-back wings allow an airliner to fly closer to the speed of sound?
However, a component of a velocity is always less than the full velocity. Therefore, in a swept-back wing the speed of the perpendicular flow will be smaller than that of the airplane. This allows the airplane to get closer to the speed of sound before shocks form on top of its wings.
Will wings swept forward have the same effect?
Can the same advantage be obtained from a wing that turns around a swivel after the airplane has attained cruising speed--one wing is swept back, the other forward?
Optional peripheral discussion--or riddle to ponder at home:
In the lobby of the Air and Space Museum in Washington hangs the "Voyager" airplane which flew non-stop around the world, taking more than a week. It took off at 138 miles-per-hour, using two engines, but it came back at only 78 miles per hour, with one engine turned off. Why the difference?
How does an aircraft propeller work?
(The blade ends, which move fastest, produce most of the lift)
Before take-off, when the airplane stands on the end of the runway and the pilot "revs up" the propeller, how does air flow in the frame of a propeller blade?
How does the above flow change when the airplane has appreciable forward speed?
If the propeller blade is viewed like the wing of a flying airplane, the added flow is like an added wind, blowing vertically downward. The combined flow appears to the blade like a head wind slanting downwards.
What is done to remedy this?
What limits the usefulness of this remedy?
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Author and Curator: Dr. David P. Stern
Mail to Dr.Stern: stargaze("at" symbol)phy6.org .
Last updated: 10-24-2004