Why does the paraglider fly? The answer is given by the aerodynamics. Every flying apparatus, including the paraglider obeys the laws of aerodynamics.
The earth attracts the glider vertically with force G. G is the gravity of the pilot and all the equipment (hook in weight). It is completely compensated by full streamline force T. It is the resultant of the elevating force and the resistance.

Elevating force
Elevating force A lifts the paraglider up and forward. It works perpendicularly to the direction of the stream. It is the elevating force that makes the difference between a paraglider and a common parachute. The streamline is the basic premise of the elevating force. The air particles and the paraglider glide over each other. The air particles glide in the glider with a certain speed, called air speed.
The formula of the elevating force is:
A = cA.p/2 .v2.F
cA = elevating force coefficient, depending on the form of the section, the form of the wing and the angle of attack.
p = the consistence of the air.
v = own speed.
F = area of the surface

Resistance
Resistance stops the paraglider and lowers the energy. Despite this fact, the resistance is very important for a proper operation and landing. There are three types of resistance: drag (caused by the air particles creating the elevation force), inductive resistance (appearing at the edges of the carrying surfaces) and the resistance caused by the particles that do not take part in the creation of the elevating force (the pilot and the lines, for example).
The formula of the resistance is:

W = cw.p/2.v2.F
cw = resistance force coefficient, depending on the form of the section, the form of the wing and the angle of attack.
p = the consistence of the air.
v = own speed.
F = area of the surface

Controlling the Speed
Pulling the lines pulls the trailing edge towards outer parts of the cupola. Thus the angle is lowered and the section is altered. If the lines are loose the glider flies at its top speed. The angle of attack is small and the elevating force - moderate.
When the lines are slightly pulled the glider slows down. The elevating force and the resistance are in such ratio that the angle of planing is the best. The more the lines are pulled, the more the angle worsens and the resistance increases. The stream slowly starts departing in great surfaces. The speed comes to its lowest. The best speed of flying is from 30 to 40 km/h

Closure of the cupola
If the angle of attack is too small, the leading edge is being streamed from above. The rigidity the wing filled with air is not enough to hold the aerodynamic forces. The canopy turns downwards.

Axes
The paraglider performs all the aerodynamic turnings round the three aerodynamic axes that cross the center of gravity of the wing-pilot system.
· The parachute bends round the cross-axis. The pilot rocks backwards and forwards.
· The parachute turns round the longitudinal axis. The pilot bends left and right.
· The parachute twists round the vertical axis. The pilot spins.

In case of a static turn, it is necessary to define the radius of the curve, the slope, the speed and the weight. In order to go into a turn, the pilot pulls the brake line at the wanted side.