  # TFX: by Digital Image Design ### APPENDIX SIX THE SIMULATION

A simulation is a program which approximates a real situation. In a flight simulation, this is done by setting up the rules of physics and aerodynamics and treating an airplane as a set of key data, such as wing area, mass and so on.

TFX includes a flight model which does this. The main forces acting on the aircraft are calculated, and added together as vectors, producing a resultant force vector. Like normal numbers (called scalars) vectors can be added to each other. They cannot be multiplied by each other in the normal sense, but you can multiply a vector by a scalar, which multiplies its magnitude, keeping its direction the same. Vectors are a way of using maths to apply to the real world, which has three dimensions.

The world works according to certain laws, which were written down first by Sir Isaac Newton (1642-1727). Newton's First Law states that any object will continue travelling with the same speed and in the same direction unless something else changes it. Both speed and direction can be defined by a single vector: a velocity vector.

In TFX, your plane has a velocity vector, which only changes from frame to frame due to the action of the acceleration vector, which changes the velocity vector in the following way:
v = v + a x Dt

Dt ('delta t') is a scalar, the length of time in one frame. Obviously, real life does not work in frames, but the smaller the frame time, the more accurate the calculation will be. The length of the time interval is determined by the speed of your machine. If the acceleration vector is in the same direction as the velocity vector, it will change the size of the velocity. If part or all of the acceleration vector is perpendicular (at right angles) to the velocity, the direction of the velocity vector will also be affected.

To find the acceleration, Newton's Second Law is used:
ACCELERATION = FORCE/MASS

In vector terms:
a = F / m

F is the force vector, found by adding all the force vectors affecting the airplane end to end. There is a force vector for gravitational force (weight), one for aerodynamic force, one for thrust, and so on. A similar, but more complex set of rules are used in determining the angular (rotational) behavior of the aircraft.

AERODYNAMICS

FORCES

The aerodynamic forces are determined by the aircraft speed V, air density r (rho), wing area S, and appropriate coefficients such as, CL or CD.

Lift is the force which keeps an airplane in the air, by acting against gravity. Drag is the force opposite to the direction of travel, which Thrust, the engine force, must overcome. Because drag is inevitable and lift is desirable, these are the main aerodynamic forces.

There is another aerodynamic force, sideforce, but this is usually small, as the aircraft is symmetrical, and sideslip angle b (beta) is mostly small (a few degrees), whereas angle of attack a (alpha) can be as high as 60 degrees in some maneuver.

LIFT L = 1/2rV2 S CL
DRAG D = 1/2rV2 S CD

This is a way of looking at aerodynamic forces which shows the principal factors involved. For example, if everything else is the same, then doubling air density r will double lift and drag.

L = W
D = T
CL depends on wing shape, angle of attack, a, wing cross-section shape, and other factors (see below).

MOMENTS

Moment is the angular equivalent of force. The pitching moment CM determines rotation up or down relative to the aircraft. It is important, because it helps to determine angle of attack.

PITCHING MOMENT M = 1/2rV2 S CM

CM is determined by a, by rate of pitch, q, and by elevator deflection, h (eta). For stability, a positive angle of attack should produce a negative CM to counteract it, so if the pilot does not move the elevators using the joystick, the aircraft will pitch down again.

COEFFICIENTS

Although the equations above show variations of lift, drag and moment with the main factors, the coefficients vary in several ways. In addition to the variation of lift with the square of speed, lift coefficient CL also varies with speed and other factors. You might then ask what the difference is between the V2 factor in the lift equation and the way velocity affects CL. The answer is simply that the coefficient is a useful way of comparing different wings and airplanes. The term (1/2rV2) is called dynamic pressure, and describes the pressure decrease when air travels at a certain speed. Of course, the air at different parts of an aircraft travels at different speeds, but V is the overall airspeed, and describes the general speed for purposes of discussion. "

From the manual