Many of us are not equipped to teach physics and engineering of
flight quantitatively. But "flying machines"; are too important to be
ignored. So let me outline an elementary approach which I hope is
not too dangerous (in terms of leading to misconceptions). Would
such approach be acceptable? Why not? What is a better sequence?
It is only a sketch.
1) Free fall in empty space. Call the net force m*g a "thrust".
2) Vertical fall through air. Thrust = m*g- resist = m*g -"lift".
The terminal velocity of a parachute can be controlled by
increasing the lift force (large surface area).
3) A horizontally pushed rock, first without air resistance then
with such resistance. The concept of the range of "flying" is
familiar. The air resistance force has two components, vertical
(lift) and horizontal (drag).
4) A horizontally pushed paper airplane. How does it differ from
a rock? The shape is different but it is still a projectile. It has
wings, stabilizer, fin, etc. They help to increase the lift and to
minimize the drag. The initial speed is no longer the only factor
by which the range can be modified. Larger wings are needed
to keep the range constant when the mass becomes larger.
5) A glider pulled by a long horizontal rope. The speed is adjusted
to make m*g = lift. Stability of orientation is controlled by the
pilot acting on numerous fins (ailerons, elevators, stabilizer,
etc.) Stick a hand out of the window of a moving car to experience
the effect of a relative velocity. [In a wind tunnel the craft is
often suspended while the speed of the wind is changed to
measure the air resistance forces (lift and drag).]
6) We assumed, so far, that air is at rest with respect to the ground,
there is no wind. A glider does not create wind in front of itself.
7) The rope is disconnected from the glider. Same as in 4 above.
8) The rope is disconnected from the glider but the wind is blowing
toward the craft. The wind is deflected down by the body of the
aircraft and this produces an additional lift. This is soaring.
There is even a possibility to increase the horizontal speed here
and to climb, or to soar in directions other than toward the wind.
Things become complicated but at least we can understand why
the elevation does not have to decrease progressively, as in 4
and 7.
8) Self-propelled airplane in steady horizontal flight. Some kind
of a thrust force is needed (instead of the rope). A propeller
pushing air backward (like water is pushed back while rowing
a boat, by spinning its paddle wheel, etc.) is added. Or a jet
engine acting as a "super-fast" machine gun firing "molecular
bullets". Things become more complicated but the basic four
forces are always the same (thrust, drag, weight and lift).
9) A helicopter can be seen as an aircraft with spinning wings. The
role of its spinning blades is to produce both the lift and the
drag (pushing air down and backward). A complication
resulting from the dependence of the relative speed on the
distance from the axis of rotation can be ignored in the
qualitative analysis.
10) This introductory discussion should give you some general
ideas about "flying machines". The mathematical theory of
flight is very complicated but you must know it to become a
designer of real airplanes and helicopters. Words can lead to
mathematics but they can not be used as a substitute for it.
Fortunately, even non specialists can understand general
principles of aeronautics.