I'm sorry to disapoint you, axel, but both hang gliders and paragliders fly using the bernoulli principle which (for our purposes) states that when air moving over a wing moves over the top surface more rapidly than the bottom surface, then there is a net pressure difference, which provides lift.
As for your second paragraph, you are getting slightly confused about relative and absolute velocities. Here's my attempt to put you right:
1. In the limiting stable case (ie all controls centred, flying at constant velocity relative to the air) all gliders move downward through the air.
2. The ratio of the horizontal to vertical velocities is known as the glide angle. (ie 10mph forward to 1mph down = glide angle of 10).
The glide angle (in the steady state case) is equal to the ratio of drag to lift.
MATHEMATICAL DIGRESSION.
For the mathematically minded this can be proved as follows:
consider a glider with a vertical lifting force L and a horizontal drag force D.
Since the glider is moving a constant velocity, it's kinetic energy is constant.
We can then balance energy gains and losses. The glider loses Gravitational potential enegery at a rate MS, where M is the mass of pilot and glider, and S is the sink rate.
(work done = force * distance) (power output = force * velocity)
However, since we are descending at constant velocity, there is no vertical acceleration, and thus M=L (lift = gravitational downward force).
So we lose Gravitational energy at rate LS.
Where does this energy go?
It is transferred to the air as a whole (by various complex mechanisms) this produces drag. (Intuitively, you 'stir up' the air by moving through it, giving it energy, and it provides a retarding force on you).
So... the rate at which energy is lost to the air = VD, where V = horizontal velocity, and D = drag force.
We know that these are the only energy inputs and outputs, and energy is conserved, so,
LS+VD=0 (conservation of energy).
now we can rearrange this as follows:
LS+VD=0
=> LS=-VD.
=> (L/D)S=-V
=> (L/D)=-(V/S)
This shows us that the ratio of lift to drag (L/D) is equal to the negative of the ratio of horizontal velocity to vertical velocity.
Note that the minus sign appears, because vertical velocity is being measured upwards, and we are gliding downwards. The glide angle G is thus -(V/S) and so L/D=G.
QED.
END MATHEMATICAL DIGRESSION.
The only reason gliders go up is because they fly through moving air, and so their net vertical speed is the sink rate + the vertical speed of the air they are moving in.
Powered aircraft fly upwards because they have engines that produce a net thrust. This thrust forces the aircraft forwards. We can increasing the Angle of attack of the wing, so a greater amount of lift (and drag) is generated, and the extra drag is cancelled out by the thrust of the engines, leaving a net lift.
The above paragraph is a gross oversimplification, but it'll do for our purposes... study physics & fluid dynamics to learn more
Does that answer your wuestion about how aircraft fly??
MH.
*********************************************** Martin Harvey Pembroke College, Cambridge University.
Uni web pages:
http://www-stu.pem.cam.ac.uk/~mch24/ ***********************************************