This section contains examples from aviation, of wing sweep-back and variable propeller pitch, to illustrate frames of reference, vector addition and vector resolution.

Basics of Aviation

  Any object immersed in a fluid (in air or water, for instance) experiences a pressure on all its surfaces, a force on each unit of area due to the weight of air or water stacked up above it (even if that surface faces sideways or down). In the absence of motion--e.g. when the airplane is standing on the runway--a wing experiences equal pressure on its top and bottom, and therefore tends to move neither up nor down.

  With the airplane in flight, an air flow passes over the wing, and the shape of the wing's cross section--curved above, flat or nearly flat below--reduces the pressure on top, causing the extra pressure from below to exert a lifting force ("lift"). The lift increases if the front of the wing is raised slightly, biting into the moving air at a small angle ("angle of attack"), and for a given lifting force, this kind of wing produces much less air resistance ("drag") than a flat kite.

Frames of Reference

      But wait a moment--isn't it the airplane that is moving, not the air?

(In the sections that follow it will be shown one can also extend this to flight in a curved path, as long as one includes the centrifugal and Coriolis forces, "intertial" forces which only appear in calculations in a moving frame.)

  The wind tunnel built by Orville and Wilbur Wright, inventors of the first practical airplane, was not the first--a few others already existed at the time--but it was the first one to be actually used to design a flying machine. The Wrights used small-scale replicas of wings and measured their lift and drag by means of delicate balances (a theory exists on the behavior of scaled models). A reconstruction of their original wind tunnel, as well as displays of the balances with which they measured lift and drag, can be seen at the Franklin Institute museum in Philadelphia.

Swept-back wings

   The wings of small airplanes, whose speed is limited, are generally straight, a design which offers the greatest efficiency. On jet airliners, on the other hand, and on fast military airplanes, wings are often swept back; some military jets can even rotate their wings--straight-out for greatest efficiency when taking off and landing, swept back for flight near the speed of sound.

At the speed of sound, the air resistance ("drag") increases steeply, because air cannot get out of the way fast enough and therefore becomes compressed and heated. Heat is a form of energy, and to produce it, something else has to give up energy--in this case, it is the motion, producing increased drag; the "lift" of the wing also suffers. Actually, those problems begin well before the speed of sound is reached, because part of the flow above a wing has extra speed and can reach that speed even before the airplane does.

  But one can "cheat" to some extent by sweeping the wing backwards, by some angle s. Now, even though the air advances towards the airplane with velocity v, the velocity vector can be resolved into the sum of two perpendicular components--a flow velocity v sin s directed along the wing and a flow velocity v cos s directed perpendicular to it. Both are smaller than v, since both (sin s) and (cos s) are always smaller than 1.

  One can now argue that the flow of air along the wing will not cause any pile-up, nor any lift or drag, and ignore it. Only the perpendicular flow v cos s has such effects, and in a crude theory, the performance of the wing depends only how near the speed of sound that perpendicular component gets. Thus sweepback allows the airplane to fly a little bit closer to the speed of sound, without incurring associated penalties; the Airbus 320, for instance, has a sweepback of about 25 degrees. For a detailed website discussion of swept-back wings, click here

Propellers

  Because of such problems, propeller-driven airplanes have never even approached the speed of the jets. The faster propeller-driven fighter airplanes of World War II flew at about 370-400 mph. The speed record for a purely propeller-driven airplane, 463 mph, was attained in Germany before the war (in 1939) and stood for decades. The current record is 528.33 mph, attained in 1989 by the "Rare Bear", a WW-II US Navy 8F8 "Bearcat" fighter, modified for high-speed racing. The airplane had crashed in 1962 and was lying in an Indiana cornfield, next to a runway, before Lyle Shelton in 1969 found it and restored it. He later replaced its 2400 HP engine with one of 4000 HP (getting less than 1 mile per gallon gas at top speed), replaced its propeller, and trimmed its weight. It is still flying. (Thanks to Dr. Eddie Irani for this information).

And by the way...

 

Tilt-Wing Airplanes

A NASA engineer, Robert T. Jones, has experimented with a related idea--one wing swept forward, the other one back. Such a wing can be attached to the airplane by a pivot. For take-off and landing, the wing is perpendicular to the fuselage, operating at its greatest efficiency and giving the aircraft a conventional appearance. Then at cruising altitude, as the airplane speeds up, the wing is rotated around its pivot--one tip points forward, one back. Would that work?

NASA's model tilt-wing airplane   Click here for color version (136K)

Work with a radio-controlled model has shown that it actually would. That model (on the right) is now in storage among other exhibits of the National Air and Space Museum of the Smithsonian institution. This was followed by a small piloted twin-jet AD-1 airplane (image below), designed by the Rutan Aircraft Factory and flown by NASA 1979-82 from Dryden Flight Research Center at Edwards, California. For further details, see

   Unfortunately, the tilted-wing configuration only flew well in a straight line--attempts at turning the airplane put it in a barrel roll. The benefits did not outweigh the risk of the wing getting stuck and the airplane being unable to land, and the design was not further pursued.