Lesson Plan #33         http://www.phy6.org/stargaze/Lflight.htm

#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

"From Stargazers to Starships" home page: ....stargaze/Sintro.htm
Lesson plan home page and index:             ....stargaze/Lintro.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:

  • Basic concepts about airplane flight.

  • The reason jetliner wings are swept back.

  • Why jet engines have replaced propellers in high-speed flight

Terms: frame of reference, relative velocity, lift, drag, thrust, angle of attack, wind tunnel, sweepback of wings.

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:

  • About drag D (air resistance) and lift L, both are proportional to the square v2 of the velocity and to the air density d.   In addition, L depends on the "angle of attack" between the wing and the air flow, and of course on the size and design of the wing.

  • In flight L must equal to the weight W of the airplane. To fly at high speed, airliners rise to high altitude. Usually, they fly at about 85% of the speed of sound; once that is exceeded, air resistance and fuel consumption rise steeply.

  • To slow down for landing, the higher air density near the ground is not sufficient, and the wing shape needs to be adjusted, too.

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

Forces on airplane     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?

    Thrust of the engine--pulls the aircraft forward
    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?

    The pattern of air flow over the top and bottom of the wing reduces the air pressure on the wing's top surface.

[Optional discussion:
Can the same lift force be applied to transportation by water?

    A.: Yes! Such wing-like surfaces are known as hydrofoils, a name which is sometimes also applied to boats and ships using them. The hydrofoils extend below the hull and across its width--e.g., one in front and one in the rear. The boat starts moving like an ordinary boat, floating on the water. Then, when an appropriate speed is reached, the hydrofoils lift the hull out of the water, leaving only the propellers and hydrofoils submerged. Such boats are capable of much greater speeds than ordinary motor boats, e.g. 70 mph and more.]

Why do jetliners avoid flying above the speed of sound?

    Because at supersonic speeds, air piles up in front of the aircraft and its wing, forming a compressed layer ("shock"), rather than smoothly flowing around the airplane. Compression heats up the air, and since heat is a form of energy, the process robs energy from the motion and greatly increases the drag force. It also reduces the lift of a wing, which depends on the orderly flow of air around it.

Why do jetliners avoid flying faster than even 85% of the speed of sound?

    Because as part of the lift-generating process, air flows faster over the top of the wing. When the airliner's speed only approaches the speed of sound, the flow over the top of the wing may exceed that speed and form shocks.

Why do swept-back wings allow an airliner to fly closer to the speed of sound?

    Because in a crude approximation, the flow of air over a swept-back wing can be resolved into a component flowing along the wing, not strongly involved in lift and drag, and a component flowing across the wing, perpendicular to it, which acts like the ordinary flow across a wing that is not swept back.

    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?

    Yes, they will, as demonstrated on the X-29 airplane. However, the flexing of wings makes this design less stable.

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?

    Yes it can, and such designs have been tested with a model. The swivel-wing airplane can fly along a straight path, but cannot be safely steered.

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?

    Flying nonstop around the world took a lot of fuel--in fact, fuel weighing many times more than the rest of the airplane. On take-off and in early stages of its flight, Voyager was heavily loaded, and to let its wings create enough lift to hold it aloft, it had to fly fast. Coming home, most of the fuel had been consumed, there was no need for such speed, and one engine could supply all the thrust that was needed.

How does an aircraft propeller work?

    It could be viewed as a small rotating wing, whose lift pulls the airplane forward.
    (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?

    The air flows in a way similar to its flow over an airplane wing.

How does the above flow change when the airplane has appreciable forward speed?

    In addition to the flow experienced by the propeller on the ground before take-off, it now also feels a flow of air from the front, due to the motion of the airplane.

    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?

    The blades of the propeller can be twisted (even in flight), in a way making them face the slanting flow of air.

What limits the usefulness of this remedy?

    The lift force on the propeller is now at an angle. Only part of it pulls the airplane forward, the rest contributes a greater air resistance to the motion of the propeller. The faster the airplane flies, the smaller is the part that pulls and the greater the part that resists and must be overcome.

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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