Principles of Flight

When an aircraft banks, its lift vector tilts. If total lift were left unchanged, its vertical component would become smaller than the aircraft’s weight and the aircraft would descend.

In a steady, coordinated and level turn:

$L \cos \phi = W$

Therefore:

$L = \frac{W}{\cos \phi}$

where:

• $L$ is total lift,
• $W$ is weight,
• $\phi$ is the bank angle.

Total lift must therefore be greater than weight. At a given airspeed, the pilot increases the angle of attack to generate the additional lift required to keep the vertical component equal to the weight.

The higher lift coefficient and load factor increase induced drag, so additional thrust is normally required to prevent the airspeed from decreasing.

The load factor in a coordinated level turn is:

$n = \frac{1}{\cos \phi}$

This is also why stall speed increases as the bank angle increases during a level turn.

Vectors are shown for explanation and are not necessarily to scale.

Reference: FAA Airplane Flying Handbook — turns and load factor.

$M_{crit}$ (critical Mach number) is the lowest Mach number at which airflow over any part of the aircraft — typically the wing — first reaches Mach 1, leading to the onset of compressibility effects such as shock waves, drag rise, and flow separation.

MMO (Maximum Mach Operating number) is the maximum authorized Mach number for safe operation of the aircraft. It ensures that the aircraft remains below speeds that could cause structural stress, control issues, or high-speed buffet.

In summary:
- $M_{crit}$ marks the start of transonic effects
- MMO is a design limitation to avoid unsafe flight conditions
- $M_{crit}$ is always lower than MMO

Flying beyond MMO may result in loss of control or airframe damage, and must be avoided.

The two primary types of aerodynamic drag acting on an aircraft are:

• Parasite drag: Caused by the aircraft moving through the air. It includes form drag, skin friction, and interference drag. Parasite drag increases with the square of airspeed.
• Induced drag: Also called lift-induced drag, it results from the generation of lift. It is highest at low speeds and decreases as speed increases.

Total drag is the sum of both:
Total Drag = Parasite Drag + Induced Drag

The critical angle of attack is the angle above which aerodynamic stall occurs. At this point, the airflow can no longer remain attached to the upper surface of the wing, leading to a rapid loss of lift.

At the critical angle, the lift coefficient ($C_{L}$) reaches its maximum. Beyond this point, even if the angle of attack increases, the wing can no longer generate sufficient lift to sustain flight.

Note:
- Every aircraft stalls at a specific angle of attack for a given configuration — not at a specific airspeed or attitude.
- The critical angle of attack decreases at high altitude and high Mach numbers due to compressibility effects and aerodynamic limits.
- Airframe icing can also lower the critical angle of attack significantly.
- Wing configuration affects it as well:
- Leading-edge slats and flaps, when extended, tend to increase the critical angle of attack.
- Trailing-edge flaps, on the other hand, generally reduce it.
- For this reason, in most jet aircraft, leading-edge devices extend automatically when trailing-edge flaps are deployed.

Coffin corner, also called Q-corner, describes the high-altitude region in which the usable speed margin between the low-speed buffet boundary and the high-speed Mach-buffet or MMO boundary becomes very small.

• If speed decreases, the angle of attack must increase to maintain lift. This can lead to low-speed buffet and eventually a stall.
• If speed increases, the Mach number approaches its upper limit. Further acceleration may result in an MMO exceedance; shock-wave-induced flow separation can cause Mach buffet and reduced control effectiveness.

It is therefore inaccurate to describe the upper boundary simply as a “high-speed stall.”

At the theoretical aerodynamic ceiling, the low-speed and high-speed boundaries meet. The AFM maximum operating altitude is below this point, and the selected cruising altitude must retain an adequate buffet and manoeuvre margin.

Higher aircraft mass, increased load factor, bank angle, gusts or turbulence can further reduce this margin. Flight crews must therefore respect the aircraft’s buffet limits, maximum operating altitude and procedures.

Conceptual diagram: exact boundaries depend on aircraft type, mass, load factor and configuration.

Reference: FAA AC 61-107B — high-altitude operations and coffin corner.