# Flight Mechanics

##  Referentials

In order to define all the physics that rule a flying machine, we need to define three different referentials.

Let be [itex] \$R_0\$ [/itex] the earth referential. [itex]\$x_0\$[/itex] is pointed towards the geographical North. [itex]z_0[/itex] is pointed towards the center of the earth (i.e. parallel to [itex]g[/itex]). Finally, [itex]y_o[/itex] is such that [itex]\$R_0\$[/itex] is a right handed referential.

Furthermore, let be [itex]R_b[/itex], the body referential. [itex]x_b[/itex] is pointed towards the front of the flying machine. [itex]y_b[/itex] is pointed towards the right hand side of the flying machine. Finally, [itex]z_b[/itex] is pointed such that [itex]R_b[/itex] is a right handed referential.

Finally, let be [itex]R_a[/itex], the aerodynamic referential. [itex]x_a[/itex] has an opposite direction of the relative wind coming towards the flying machine (i.e. direction of flight but not necessarily where the nose is pointing). [itex]y_a[/itex] is generally assumed to be coincident with [itex]y_b[/itex] and [itex]z_a[/itex] is pointed such that [itex]R_a[/itex] is a right handed referential.

# Airframe Configuration

## Variants

###  Airfoil Design and Optimization

The Airfoil is the 2D cross-section of the wing. Generally has a design of 2 parabolic shapes put together in a parametric way for optimization of flight. The Airfoil on the primary wings is one of the larger determinants of governing what the capabilities in flight are for a given aircraft.

## Tail Type

### Fuselage-Mounted Tail & Cruciform Tail: ┴ ┼

The most common tail has a cross section with a flat horizontal stabilizer & elevator on the bottom, and a vertical stabilizer and rudder rising from its center. The creases of this configuration cause some parasitic drag, but it is very easy to make this strong enough structurally to work well. Some planes, especially those designed for tail-down semi-stalled landings, lift the horizontal stabilizer up to 1/4 to 1/2 the height of the vertical stabilizer in order to prevent the edges from clipping the ground or getting caught in the wing's downwash.

### T Tail: T

Some designs lift the horizontal stabilizer all the way up to the top of the vertical stabilizer. This helps reduce the wing's downwash hitting the horizontal stabilizer. A T tail experiences large twisting forces when hit with a crosswind, and often must be made stronger & heavier than other designs.

### V Tail: V

V tails, and the opposite inverted V tails, combine the functions of elevators (1 DoF) and rudders (1 DoF) into two 'ruddervators' (2 DoF) which point outwards and either upward or downward from the aerodynamic center.

### Other Tails

The Pelikan tail is a combination of a traditional horizontal stabilizer and a V tail, creating a 'U' shape.

The Y tail is simply a V tail which places an additional vertical fin in the opposite direction to supplement rudder forces.

# Controllable Elements

## Rudder

The rudder is a movable flap which is located on the vertical stabilizer (tail) of an aircraft.

Like the rudder on a boat, it allows the aircraft to yaw about its axis, and operates in a similar way that an elevator does.

The rudder brings a natural stability effect. Indeed, when a slideslip angle is present, the relative wind creates a lift on the rudder which tends to align the nose of the aircraft with respect to the relative wind.

## Elevators

The evevators are the control surface used to control the pitch axis.

## Ailerons

The ailerons are the control surface around the roll axis. They work in an antisymmetric way.

When the pilot wants to roll to the left, the left aileron will move upwards, decreasing the lift on the left wing. On the contrary, the right aileron will move downwards, increasing the lift on the right wing. The difference of force between the left and the right wing will create a rolling moment. The direction of the lift will have a horizontal component and will tend to turn the aircraft to the left.