Aeronautical Engineering flashcards

32 cards. Read the term and the definition here. The deck at the top of this page is optional.

Euler column buckling load

A slender ideal column buckles at P_cr = π²EI/(KL)², where E is Young's modulus, I the least second moment of area, L the length and K the effective-length factor (1.0 pinned-pinned, 0.5 fixed-fixed, 2.0 cantilever).

Newton–Raphson iteration

The recursion x_{n+1} = x_n − f(x_n)/f′(x_n) converges quadratically near a simple root, but stalls or diverges when the derivative is near zero or the starting guess is poor.

Reynolds number

Re = ρVL/μ = VL/ν measures the ratio of inertial to viscous forces; low values indicate laminar, viscosity-dominated flow, high values indicate turbulent, inertia-dominated flow in geometrically similar cases.

Laplace transform of derivative

L{f′(t)} = sF(s) − f(0⁺); differentiating in time multiplies the transform by s and subtracts the initial value, converting linear differential equations into algebraic ones.

Final value theorem

The limit of f(t) as t tends to infinity equals the limit of sF(s) as s tends to zero, provided all poles of sF(s) lie strictly in the left half-plane; a pole at the origin invalidates it.

Composite Simpson 1/3 rule

Using an even number n of equal subintervals of width h, the rule sums the end values, four times odd-index values and twice even-index values, then multiplies by h/3; error is O(h⁴).

Second-order peak overshoot

For a standard second-order system with damping ratio ζ below one, percentage overshoot equals 100·exp(−ζπ/√(1 − ζ²)); it is 100 percent at zero damping and vanishes as ζ reaches one.

Z-score standardization

z = (x − μ)/σ converts a value into standard deviations from the mean, letting any normal distribution be read from standard normal tables; about 68, 95 and 99.7 percent lie within one, two and three sigma.

Principal stresses in 2D

For plane stress, σ₁,₂ = (σ_x + σ_y)/2 ± √[((σ_x − σ_y)/2)² + τ_xy²]. Principal plane orientation satisfies tan 2θ_p = 2τ_xy/(σ_x − σ_y), and shear stress is zero on those planes.

Parallel axis theorem

I = I_c + A d² gives the second moment of area about any axis parallel to a centroidal axis, where I_c is the centroidal value, A the area and d the perpendicular separation of the axes.

Confidence interval for a mean

With known standard deviation, the interval is x̄ ± z σ/√n, where z is the standard normal quantile: 1.96 for 95 percent and 2.576 for 99 percent confidence.

Lift equation

Steady lift equals ½ρV²S·C_L, where ρ is free-stream density, V true airspeed, S the reference wing area and C_L the lift coefficient; the group ½ρV² is dynamic pressure q.

Induced drag coefficient

C_Di = C_L²/(πAe), with aspect ratio A = b²/S, span b and Oswald efficiency e; induced drag therefore falls as span grows, which explains the long slender wings of gliders.

Maximum lift-to-drag condition

For the polar C_D = C_D0 + K C_L², best L/D occurs at C_L = √(C_D0/K) and equals 1/(2√(C_D0 K)); this optimum is independent of wing loading and altitude.

Speed of sound in gas

For a perfect gas a = √(γRT), with γ the ratio of specific heats, R the gas constant and T absolute temperature; in air at ISA sea level a is about 340.3 m/s, independent of pressure.

Isentropic stagnation temperature ratio

T₀/T = 1 + ((γ − 1)/2)M² gives total temperature from static temperature; in air at M = 1 the ratio is 1.2, and total temperature is conserved along an adiabatic duct with no work transfer.

Prandtl–Glauert correction

In subsonic flow, compressibility raises the section lift coefficient by the factor 1/√(1 − M²); the rule fails near M = 1 and does not apply to supersonic flow, where Ackeret theory is used.

Choked nozzle pressure ratio

A convergent nozzle chokes when p_e/p₀ reaches (2/(γ + 1))^{γ/(γ−1)}, about 0.528 for air with γ = 1.4; beyond that, mass flow stays constant and extra expansion occurs outside the nozzle.

Turbofan bypass ratio

Bypass ratio is the mass flow through the fan duct divided by the mass flow through the core. Increasing it improves propulsive efficiency and reduces jet noise, at the cost of nacelle weight and drag.

Thrust specific fuel consumption

TSFC is fuel mass flow divided by net thrust, commonly expressed in kg/(N·h) or lb/(lbf·h). Lower values mean better fuel economy; high-bypass turbofans beat turbojets in subsonic cruise.

Ideal Brayton thermal efficiency

The ideal cycle efficiency is 1 − 1/π_c^{(γ−1)/γ}, where π_c is compressor pressure ratio; it rises with pressure ratio and specific-heat ratio, while real cycles lose work to component inefficiencies.

Static margin

Static margin is (x_np − x_cg)/c̄, the distance from centre of gravity to the neutral point measured in mean aerodynamic chords; positive values indicate pitch stability but reduced manoeuvrability.

Bredt–Batho shear flow

In a thin-walled closed section carrying torque T, the shear flow is q = T/(2A_m), where A_m is the area enclosed by the mean line; skin shear stress is τ = q/t for wall thickness t.

Goodman fatigue criterion

The line σ_a/S_e + σ_m/S_u = 1 predicts fatigue failure for alternating stress σ_a and mean stress σ_m, using endurance limit S_e and ultimate strength S_u; it is conservative relative to most test data.

Chicago Convention 1944

The Convention on International Civil Aviation established ICAO and set principles of state sovereignty over airspace, aircraft nationality and mutual recognition of certificates, forming the basis for bilateral air service agreements.

ICAO Annex 8

Annex 8, Airworthiness of Aircraft, contains the minimum standards for type certification and continuing airworthiness that member states transpose into national codes such as 14 CFR and EASA Part-21.

Type certificate

A type certificate approves the design of an aircraft, engine or propeller type after showing compliance with the applicable airworthiness standards; each individual unit still needs its own airworthiness certificate.

Fifth freedom of the air

The fifth freedom allows an airline to carry revenue traffic between two foreign states on a route beginning or ending in its home state; it requires explicit bilateral agreement and is politically sensitive.

ITAR versus EAR

In the United States, ITAR controls defense articles and technical data listed on the USML under the State Department, while the EAR controls dual-use items classified by ECCN under the Commerce Department.

Paramountcy of public safety

Professional engineering codes such as NSPE's hold that public safety, health and welfare come first; engineers must not approve designs they cannot justify and must disclose factors endangering life or property.

Just culture

Just culture separates honest error and system-induced slips, which are answered with support and learning, from reckless or deliberate violations, which justify sanction; it underpins confidential reporting systems such as ASRS.

Negligence four elements

A negligence claim requires a duty of care owed, a breach of the applicable standard, actual and proximate causation, and resulting compensable damage; failing to prove any one element defeats the claim.