aerospace-engineering

## What I do - Analyze aerodynamic forces and moments - Design aircraft and spacecraft propulsion systems - Model flight dynamics and stability - Calculate orbital mechanics and trajectories - Perform structural analysis for aerospace structures - Specify materials for aerospace applications - Analyze loads and fatigue for flight vehicles ## When to use me When designing aircraft, spacecraft, propulsion systems, or analyzing aerodynamic and structural performance of aerospace vehicles. ## Core Concepts - Aerodynamics and fluid dynamics - Propulsion systems (jet, rocket, hybrid) - Flight dynamics and control - Orbital mechanics and astrodynamics - Aerospace structures and materials - Load factors and fatigue analysis - Aircraft performance (range, endurance, climb) - Compressible flow and shock waves - Stability and control derivatives - Spacecraft attitude dynamics ## Code Examples ### Aerodynamic Calculations ```python import math from dataclasses import dataclass @dataclass class Atmosphere: altitude: float # ft temperature: float # Rankine pressure: float # psf density: float # slugs/ft³ speed_of_sound: float # ft/s def standard_atmosphere(altitude: float) -> Atmosphere: """Calculate standard atmosphere properties.""" if altitude < 36000: T = 519.67 - 0.00356 * altitude P = 2116.2 * (T / 518.67)**5.256 else: T = 389.97 P = 2116.2 * math.exp(-(altitude - 36000) / 14700) rho = P / (1716 * T) a = math.sqrt(1.4 * 1716 * T) return Atmosphere(altitude, T, P, rho, a) def lift_coefficient( CL: float, rho: float, V: float, S: float ) -> float: """Calculate lift force.""" return 0.5 * rho * V**2 * S * CL def drag_polar( CD0: float, e: float, AR: float, CL: float ) -> float: """Calculate drag coefficient using drag polar.""" return CD0 + CL**2 / (math.pi * e * AR) def mach_number( V: float, a: float ) -> float: """Calculate Mach number.""" return V / a def dynamic_pressure( rho: float, V: float ) -> float: """Calculate dynamic pressure.""" return 0.5 * rho * V**2 # Example: Aircraft performance at 20000 ft alt = 20000 atm = standard_atmosphere(alt) V = 400 # ktas CL = 0.8 S = 500 # ft² q = dynamic_pressure(atm.density, V * 1.688) M = mach_number(V * 1.688, atm.speed_of_sound) print(f"Density: {atm.density:.6f} slugs/ft³") print(f"Dynamic pressure: {q:.1f} psf") print(f"Mach number: {M:.3f}") ``` ### Flight Performance ```python def thrust_available( TSL: float, # sea level thrust altitude: float, velocity: float ) -> float: """Calculate thrust at altitude using Napier's approximation.""" sigma = standard_atmosphere(altitude).density / 0.002377 return TSL * sigma * (1 - velocity**2 / 5e10) def power_available( HP: float, # shaft horsepower prop_efficiency: float, rho: float ) -> float: """Calculate available power.""" return HP * 550 * prop_efficiency / (rho / 0.002377) def range_breguet( R: float, # range nm V: float, # true airspeed L_D: float, # lift-to-drag ratio TSFC: float, # thrust specific fuel consumption /hr W_start: float, W_end: float ) -> float: """Calculate fuel required using Breguet range equation.""" return V * L_D / TSFC * math.log(W_start / W_end) def stall_speed( W: float, # weight lb S: float, # wing area ft² CLmax: float, rho: float ) -> float: """Calculate stall speed.""" Vs = math.sqrt(2 * W / (rho * S * CLmax)) return Vs * 0.5925 # convert to knots def climb_gradient( T_W: float, # thrust-to-weight ratio W_S: float, # wing loading lb/ft² rho: float, CLmax: float ) -> float: """Calculate maximum climb gradient.""" return (T_W - W_S * 0.5 * rho * CLmax / (2 * W_S)) / (W_S * 0.5 / (rho * CLmax)) # Example: Aircraft range calculation W0 = 80000 # lb Wf = 20000 # lb range_nm = 3500 L_D = 18 V = 450 # kts TSFC = 0.5 fuel_required = range_nm * TSFC / (V * L_D) * (W0 - Wf) print(f"Fuel fraction required: {fuel_required:.4f}") ``` ### Rocket Propulsion ```python def rocket_thrust( md: float, # mass flow rate kg/s Ve: float, # exhaust velocity m/s Ae: float, # exit area m² pe: float, # exit pressure Pa pa: float, # ambient pressure Pa ) -> float: """Calculate rocket thrust.""" return md * Ve + (pe - pa) * Ae def specific_impulse( thrust: float, md: float, g0: float = 9.81 ) -> float: """Calculate specific impulse.""" return thrust / (md * g0) def mass_ratio( m_initial: float, m_final: float ) -> float: """Calculate mass ratio.""" return m_initial / m_final def delta_v_rocket( Isp: float, # seconds m_ratio: float, g0: float = 9.81 ) -> float: """Calculate delta-V using rocket equation.""" return Isp * g0 * math.log(m_ratio) def nozzle_expansion_ratio( pe: float, # exit pressure Pa pc: float, # chamber pressure Pa gamma: float = 1.2 ) -> float: """Calculate nozzle area expansion ratio.""" return ((gamma + 1) / 2)**((gamma + 1) / (2 * (gamma - 1))) * math.sqrt(pe / pc) # Example: Rocket calculation m_dot = 250 # kg/s Ve = 3500 # m/s chamber_pressure = 7e6 # Pa Isp = 350 m_ratio = 15 dV = delta_v_rocket(Isp, m_ratio) print(f"Delta-V capability: {dV:.0f} m/s") ``` ### Orbital Mechanics ```python def orbital_velocity( mu: float, # gravitational parameter m³/s² r: float # orbital radius m ) -> float: """Calculate circular orbital velocity.""" return math.sqrt(mu / r) def orbital_period( mu: float, a: float # semi-major axis m ) -> float: """Calculate orbital period.""" return 2 * math.pi * math.sqrt(a**3 / mu) def hohmann_transfer( r1: float, # initial radius m r2: float, # final radius m mu: float ) -> dict: """Calculate Hohmann transfer parameters.""" a_transfer = (r1 + r2) / 2 dv1 = math.sqrt(mu / r1) * (math.sqrt(2 * r2 / (r1 + r2)) - 1) dv2 = math.sqrt(mu / r2) * (1 - math.sqrt(2 * r1 / (r1 + r2))) transfer_time = math.pi * math.sqrt(a_transfer**3 / mu) return { "dv1": dv1, "dv2": dv2, "total_dv": dv1 + dv2, "transfer_time": transfer_time } def escape_velocity( mu: float, r: float ) -> float: """Calculate escape velocity.""" return math.sqrt(2 * mu / r) # Example: GEO transfer r_leo = 6678e3 # m r_geo = 42164e3 # m mu_earth = 3.986e14 # m³/s² transfer = hohmann_transfer(r_leo, r_geo, mu_earth) print(f"Transfer burn: {transfer['dv1']:.0f} m/s") print(f"Insertion burn: {transfer['dv2']:.0f} m/s") print(f"Total delta-V: {transfer['total_dv']:.0f} m/s") ``` ## Best Practices - Use consistent unit systems throughout calculations - Apply appropriate factors of safety for flight hardware - Consider environmental factors (temperature, pressure) in performance - Validate analytical results with CFD and wind tunnel data - Follow aerospace standards (MIL, NASA, FAA, EASA) - Account for structural loads in aerodynamic design - Consider maintainability and inspection requirements - Use margin on critical performance parameters - Consider failure modes and safety margins - Document all assumptions and methods used