Flight Envelope, Load Factor and Structural Limitations
The V-n diagram
The flight envelope plots load factor against equivalent airspeed. Its boundaries are the positive and negative limit load factors, the manoeuvring speed, the never-exceed speed and the maximum lift available at low speed. Candidates must be able to identify the corner speed, where maximum lift and maximum structural load coincide, and understand that below it the aircraft stalls before it overstresses, while above it structural failure is possible before the stall.
Limit load is the maximum expected in service; ultimate load is typically 1.5 times limit load, and the structure must withstand it without failure though permanent deformation is permitted. Safety factor and gust load are commonly examined.
Speeds and limitations
Know V_A, V_B, V_C, V_D, V_NE, V_FE, V_LO and V_MO. V_A falls with weight because the lift available at the stall is lower. Gusts raise load factor abruptly, and in turbulence the recommended action is to slow to the design manoeuvring or turbulence penetration speed.
Traps and a worked example
Traps: assuming V_A is constant with weight; confusing limit and ultimate load; and thinking V_NE is a handling speed rather than a structural limit.
Rule of thumb: at the corner speed, load factor equals the limit load factor and the wing is at the critical angle of attack.
Worked example: an aircraft of 1000 kg with a limit load factor of 3.8 and stall speed at 1 g of 60 kt. V_A is 60 × √3.8 ≈ 117 kt. At 90 kt, the maximum load factor before stall is (90/60)² = 2.25, well inside the structural limit.
High-Speed Flight, Mach Effects and Sweep
Compressibility
As speed rises, local airflow over the wing accelerates and may reach the speed of sound while the aircraft itself is still below it. The Mach number at which this first happens is the critical Mach number, and the resulting shock wave causes drag rise, buffet, trim change and possible control reversal. Candidates must distinguish the local Mach number from the flight Mach number and know that the critical Mach number falls as lift coefficient or thickness ratio rises.
Wave drag and sweep
Above the critical Mach number, wave drag grows rapidly and the drag curve rises steeply. Sweep delays the onset of compressibility by reducing the velocity component perpendicular to the leading edge; the effective Mach number is the flight Mach number times the cosine of the sweep angle. Thin sections, supercritical aerofoils and area ruling further delay the drag rise. Above Mach 1, shock waves attach to the nose and the aircraft becomes a supersonic design with different stability characteristics.
Traps and a worked example
Traps: assuming Mach number is constant with altitude for a given true airspeed (it rises as temperature falls); confusing the critical Mach number with the drag divergence Mach number; and forgetting that swept wings have poor low-speed characteristics and tip stall tendencies.
Rule of thumb: the speed of sound is about 340 m/s at sea level and about 295 m/s at 35 000 ft, so a given true airspeed gives a higher Mach number at altitude.
Worked example: at 30° sweep, the effective Mach number for a flight Mach of 0.80 is 0.80 × cos 30° ≈ 0.69, so the wing behaves as if flying at Mach 0.69, delaying the drag rise.
Propellers
Geometry and terminology
A propeller converts shaft power into thrust. Candidates must know blade angle, pitch, geometric pitch, effective pitch, slip and advance per revolution. Blade angle is measured between the blade chord and the plane of rotation; it is large at the root and small at the tip in a twisted blade so that each section operates at a favourable angle of attack. The helical path of the blade through the air explains why the angle of attack of a blade section depends on both rotational speed and forward speed.
Efficiency and limitations
Propeller efficiency is thrust power divided by shaft power, typically 80–85% at design conditions. Efficiency falls at very low and very high speeds, and at high forward speed the blade tips may reach the speed of sound, causing noise and loss of efficiency. Fixed-pitch propellers are a compromise: coarse pitch suits cruise, fine pitch suits climb. Constant-speed units vary blade angle to hold rpm, and feathering reduces drag after engine failure.
Traps and a worked example
Traps: confusing pitch with blade angle; assuming propeller efficiency is constant; and forgetting that at high altitude a fixed-pitch propeller may over-speed in the dive or under-speed in the climb. Another trap is the belief that increasing rpm always increases thrust; beyond a point, blade-tip compressibility and engine limits intervene.
Rule of thumb: geometric pitch in inches times rpm divided by 1056 gives theoretical speed in miles per hour; actual speed is lower because of slip.
Worked example: a propeller of 60 in pitch turning at 2400 rpm has a theoretical advance of 60 × 2400 / 1056 ≈ 136 mph. If the aircraft flies at 120 mph, slip is about 16 mph, roughly 12%, and efficiency is near 88% before other losses.
Asymmetric Flight and Multi-Engine Aerodynamics
The asymmetric case
When one engine fails, the remaining engine produces thrust offset from the centre of gravity, creating a yawing moment toward the failed engine. The rudder must produce an opposing moment, which requires sideslip and hence a rolling moment; aileron is used to hold the wing level, and the resulting combination increases drag and reduces performance. Candidates must know V_MC, V_YSE, V_XSE and the definition of the critical engine, which is the one whose failure produces the greatest control difficulty, normally the engine whose propeller rotates such that its slipstream and P-factor act further from the centre of gravity.
Control and performance
V_MC is the minimum control speed in the air, determined with the critical engine failed, the other at maximum take-off power, gear up, flaps take-off and a bank of not more than 5° toward the live engine. Below V_MC directional control cannot be maintained. Single-engine service ceiling, drift-down and the importance of reducing drag and weight are commonly examined. The four forces on an asymmetric aircraft include a large rudder force, and the ball must be centralised to avoid further yaw and drag.
Traps and a worked example
Traps: assuming V_MC is fixed regardless of weight and altitude (it varies); believing the aircraft can climb on one engine at any altitude; and forgetting that a bank toward the live engine helps control but increases the load on the rudder if overdone.
Rule of thumb: keep the ball centred; a sideslip of a few degrees can cost a significant fraction of single-engine climb performance.
Worked example: if the live engine produces 6000 N of thrust at 3 m from the centreline, the yawing moment is 18 000 N·m. If the rudder arm is 8 m, the rudder must generate 2250 N of side force, which requires substantial rudder deflection and produces significant drag.