The direction of the Speed Vector can be defined in terms of the Vertical Angle along the Vertical Plane (x-axis) and the Horizontal Angle along the Horizontal Plane (y-axis). The Vertical Angle is plus or minus 90 degrees and the Horizontal Angle is 0 to 360 degrees, starting with 0 degrees pointing north and proceeding in a clockwise direction.

The Module treats Thrust and Drag as Speed modifiers and Lift as a Speed deflector. Gravity can be a Speed modifier or a Speed deflector, depending on the Vertical Angle of the Speed vector. The Gravity deflector equals Gravity X sin(Angle). This deflector always acts downward along the Vertical Plane. The Gravity modifier equals Gravity X cos(Angle). This modifier can either decrease or increase the Speed vector, depending on whether the Speed vector is pointed up or down.

There are two sets of Reference Planes: the World Reference Planes and the Airplane Reference Planes. The World Reference Planes are the Vertical and the Horizontal Planes, discussed above. The Airplane Reference Planes are the Pitch (x-axis), Bank (z-axis) and Yaw Planes (y-axis).

The three primary Planes are the Pitch Plane and the Vertical and Horizontal Planes. Changes along the Airplane Bank Plane do not directly affect the Speed Vector magnitude or direction. Changes along the Airplane Yaw Plane are rarely made.

Lift acts only along the Pitch Plane. These changes along the Pitch Plane result in changes along the Vertical and Horizontal Planes. Gravity acts only along the Vertical Plane. Together, Lift and Gravity can generate changes along the Horizontal Plane (which is how an airplane turns).

This Example 1 shows how changes in Pitch, Bank and Yaw result in changes to the Vertical and Horizontal angles. This example ignores the affect of Gravity. To minimize clutter, the Bank and Yaw Planes are not shown.

An Airplane has directional flight controls which cause rotation along the Pitch, Bank and Yaw Planes. In general, these controls use 3 different control surfaces:

• Elevator - the horizontal control surface at the tail which causes the nose of the airplane to pitch up and down, which increases or decreases Lift.(
• Ailerons - the control surfaces on the wings which cause the airplane to roll left and right.(
• Rudder - the vertical control surface at the tail which causes the airplane to yaw left and right.(

This Example 2 shows the operation of the elevator, ailerons and rudder. Where the airplane is banked, this example shows the airplane in a level turn - we will discuss how that works in more detail later.

In order to fly, an Airplane must generate a Lift deflection that is greater than the Gravity deflection. This means that we must put the Airplane in motion because Speed is required to generate Lift.

To generate Speed, the Airplane must use a method of propulsion that generates Thrust while the Airplane is in the air. The two primary methods of generating Thrust are with a propeller or a jet. This Thrust must be sufficient to overcome drag, which generally increases with Speed.

In addition to Speed, the other factor in generating Lift is the Angle of Attack (AoA). The AoA is roughly the difference between the direction of the Airplane Wing and the Flight Path, along the Pitch Plane. The greater the AoA, the more Lift is produced. However, the maximum AoA is relatively small, generally between plus or minus 16 degrees. If you exceed the AoA, the Wing will not longer produce Lift. AoA also creates a form of Drag, called Induced Drag, which requires additional Thrust to overcome.

The Gravity deflector also changes. In level non-turning flight, the entire Gravity deflects the Speed Vector downward. As the airplane pitches up (or down) along the Pitch Plane, the Gravity deflecting the Speed Vector decreases and the amount of Lift required to offset the Gravity also decreases. The remainder of the Gravity decreases (or increases) the Speed Vector. Thus, to maintain Speed in a climb, the net Thrust must increase enough to offset this increase in Gravity. In a vertical climb, all of the Gravity is reducing the Speed Vector. Thus, the airplane must generate enough Thrust to offset Gravity - Lift is irrelevant.

In a descent, more Gravity is increasing the Speed Vector. At shallow angles of descent, you can offset the increase in the Speed Vector by decreasing net Thrust. If you decrease the engine Power to zero, net Thrust will become negative. However, in a vertical descent Gravity will overwhelm even this negative net Thrust. and Speed will increase.

Example 3 shows how the Lift and Gravity deflectors affect an airplane in non-turning flight. In level or fixed-angle climbing flight, the Lift and Gravity vectors exactly offset each other. The relationship between the Lift and Gravity deflectors can be illustrated by showing how these Vectors affect an airplane in flight. Where the vertical deflections are equal, the Speed Vector vertical direction will remain fixed.

Once the Airplane leaves the ground, the Airplane must also be able to turn horizontally. The Airplane can generate horizontal Lift by banking into the turn. Because Gravity is still trying to deflect the Speed Vector downwards, the Airplane must increase total Lift in order to generate enough vertical Lift to offset Gravity.

This Example 4 shows the interplay between Lift and Gravity.

The maximum bank angle is limited by the amount of Lift the airplane can produce at that speed, as well as the g-forces on the airframe and pilot can tolerate. For example, in a 60 degree bank the airframe and pilot will be subjected to g-forces of 2x the force of gravity. The increase in Lift will also create an increase in Induced Drag which will tend to cause the airplane to slow down. Eventually, the airplane will reach a speed where Thrust = Drag (Parasitic and Induced).

The Angle of Attack (AoA) is also a key component of both Lift and Drag. The AoA is the angle between the Wing Chord and the Direction of Flight, measured along the Pitch Plane. For most airplanes, the AoA can range from roughly -16 to +16 degrees. Beyond that range, the wing will "stall" and no longer produce Lift.

Since airplanes require a positive AoA to fly, most airplane designers tilt the wings back to produce an AoA equal to the AoA required for cruise flight. However, this is not necessarily done for aerobatic airplanes since they are also designed to fly upside down.

In real life, the pilot changes the airplane direction, which changes the AoA, which changes the Coefficient of Lift (CfL). However, this vastly complicates the design of flight simulations because the simulation must keep track of both the airplane direction and the direction of the Speed Vector. Keeping the two correctly aligned can be quite challenging, especially in certain flight regimes (e.g. steep banks). The SVFM simplifies this process by assuming that the pilot is directly changing the direction of the Flight Vector, including the CfL. This is mathematically valid because there is a linear relationship between AoA and the Coefficient of Lift (AoA = CfL/10).

Thus, the SVFM can simply treat AoA as a by-product of pilot induced changes to the Coefficient of Lift.