Airplane
Flight
Goals
The student will learn:
Terms: frame of
reference, relative velocity, lift, drag, thrust, angle of attack, wind tunnel,
sweepback of wings.
How High?
How Fast?
Goals
The student will learn:
Engagement + Exploration
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."
Evaluation
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.
Elaboration
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.
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.
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.