Aerospace

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Flight Mechanics

Basic Flight Equations

# Lift equation
def lift_equation(rho, V, S, Cl):
    """
    Calculate lift force.
    rho: Air density (kg/m³)
    V: Velocity (m/s)
    S: Wing area (m²)
    Cl: Lift coefficient
    """
    return 0.5 * rho * V**2 * S * Cl

# Drag equation
def drag_equation(rho, V, S, Cd):
    """
    Calculate drag force.
    """
    return 0.5 * rho * V**2 * S * Cd

# Thrust equation (ideal)
def thrust_ideal(m_dot, Ve, p_e, p0):
    """
    Calculate ideal thrust.
    m_dot: Mass flow rate (kg/s)
    Ve: Exit velocity (m/s)
    p_e: Exit pressure (Pa)
    p0: Ambient pressure (Pa)
   Ae: Exit area (m²)
    """
    return m_dot * Ve + (p_e - p0) * Ae

# Weight and balance
def center_of_gravity(masses, positions):
    """
    Calculate CG location.
    """
    total_mass = sum(m['mass'] for m in masses)
    total_moment = sum(m['mass'] * m['position'] for m in masses)
    return total_moment / total_moment

Atmosphere and Air Properties

# Standard atmosphere (ISA)
class StandardAtmosphere:
    def __init__(self, altitude=0):
        self.altitude = altitude  # meters
        self.sea_level_temp = 288.15  # K
        self.sea_level_pressure = 101325  # Pa
        self.sea_level_density = 1.225  # kg/m³
        self.lapse_rate = -0.0065  # K/m (troposphere)
        self.tropoause_altitude = 11000  # m
    
    def temperature(self):
        """Temperature at altitude (ISA)"""
        if self.altitude <= self.tropoause_altitude:
            return self.sea_level_temp + self.lapse_rate * self.altitude
        else:
            return 216.65  # Constant in stratosphere
    
    def pressure(self):
        """Pressure at altitude"""
        T = self.temperature()
        if self.altitude <= self.tropoause_altitude:
            return self.sea_level_pressure * (T / self.sea_level_temp) ** 5.2561
        else:
            p_trop = self.sea_level_pressure * (216.65 / 288.15) ** 5.2561
            return p_trop * np.exp(-(self.altitude - 11000) / 8500)
    
    def density(self):
        """Density at altitude"""
        return self.pressure() / (287.05 * self.temperature())

# Speed of sound
def speed_of_sound(T):
    """
    Calculate speed of sound.
    T: Temperature (K)
    gamma: Ratio of specific heats (1.4 for air)
    R: Gas constant (287 J/kg·K)
    """
    gamma = 1.4
    R = 287
    return np.sqrt(gamma * R * T)

# Mach number
def mach_number(V, altitude):
    """Calculate Mach number"""
    a = speed_of_sound(StandardAtmosphere(altitude).temperature())
    return V / a

Aircraft Performance

# Range and endurance
class AircraftPerformance:
    @staticmethod
    def range_brequet(V, Cl_Cd, m_fuel, SFC):
        """
        Breguet range equation.
        V: Velocity
        Cl/Cd: Lift to drag ratio
        m_fuel: Fuel mass
        SFC: Specific fuel consumption
        """
        return (V * Cl_Cd / SFC) * np.log(1 + m_fuel)
    
    @staticmethod
    def endurance(Cl_Cd, m_fuel, SFC):
        """
        Breguet endurance equation.
        """
        return (Cl_Cd / SFC) * np.log(1 + m_fuel)
    
    @staticmethod
    def stall_speed(m, S, rho, Cl_max):
        """
        Calculate stall speed.
        """
        return np.sqrt(2 * m * 9.81 / (rho * S * Cl_max))

# Takeoff and landing distances
takeoff_landing = {
    'takeoff': {
        'phases': ['Ground roll', 'Rotation', 'Transition', 'Climb'],
        'factors': ['Temperature', 'Altitude', 'Wind', 'Runway condition']
    },
    'landing': {
        'phases': ['Approach', 'Flare', 'Touchdown', 'Braking', 'Rollout'],
        'factors': ['Weight', 'Wind', 'Brake capacity', 'Reverse thrust']
    }
}

Aerodynamics

Airfoil Theory

# Thin airfoil theory
class Airfoil:
    def __init__(self, chord, thickness, camber):
        self.chord = chord
        self.thickness = thickness  # % chord
        self.camber = camber       # % chord
    
    def lift_coefficient(self, alpha):
        """
        Lift coefficient for thin airfoil.
        alpha: Angle of attack (radians)
        """
        Cl_alpha = 2 * np.pi  # Theoretical lift curve slope
        Cl0 = 2 * np.pi * self.camber / self.chord  # Zero-lift angle
        return Cl_alpha * (alpha - Cl0)
    
    def pressure_distribution(self, x, alpha):
        """
        Simplified pressure distribution.
        """
        # Using thin airfoil theory
        pass

# Lift curve slope
lift_curve = {
    'theoretical': '2π per radian (thin airfoil)',
    'finite_wing': '2π / (1 + 2/AR) (Prandtl)',
    'three_dimensional': 'cl_alpha_3d = cl_alpha_2d / (1 + cl_alpha_2d/(π*e*AR))',
    'typical_values': '5.5-6.5 per radian for typical aircraft'
}

# Drag polar
def drag_polar(Cl, Cd0, K):
    """
    Parasitic drag plus induced drag.
    Cd0: Zero-lift drag coefficient
    K: Induced drag factor (1/(π*e*AR))
    """
    return Cd0 + K * Cl**2

Wing Design

# Wing geometry
wing_parameters = {
    'aspect_ratio': 'b²/S (span²/wing area)',
    'taper_ratio': 'Ct/Cr (tip chord/root chord)',
    'sweep_angle': 'Angle from perpendicular to LE',
    'dihedral': 'Upward angle of wing',
    'washout': 'Twist to reduce tip stall'
}

# Lift distribution (Prandtl)
def elliptical_lift_distribution(chord, span, Cl):
    """
    Elliptical lift distribution.
    """
    b = span
    S = np.pi * (span/2) * chord
    Cl_distribution = Cl * np.sqrt(1 - (2*y/span)**2)
    return Cl_distribution

High-Speed Aerodynamics

# Compressible flow corrections
def compressible_correction(M, beta=None):
    """
    Prandtl-Glauert correction for compressibility.
    """
    if M < 1:
        # Subsonic
        return 1 / np.sqrt(1 - M**2)
    else:
        return 1 / np.sqrt(M**2 - 1)

# Critical Mach number
def critical_mach(Cl, Cd0, M_cruise, A):
    """
    Estimate critical Mach number.
    """
    # Approximate formula
    M_cr = M_cruise - 0.1  # Simplified
    return M_cr

# Wave drag
wave_drag = {
    'transonic': 'Mach 0.8-1.2, rapid drag rise',
    'supersonic': 'Mach > 1, wave drag dominant',
    'drag_divergence': 'Mach where drag increases rapidly',
    'supersonic_lift': 'Lift-dependent wave drag'
}

Propulsion

Jet Engine Fundamentals

# Turbofan engine cycle
class TurbofanEngine:
    def __init__(self, bypass_ratio, overall_pressure_ratio, turbine_temp):
        self.bpr = bypass_ratio
        self.opr = overall_pressure_ratio
        self.tt = turbine_temp  # Turbine inlet temperature (K)
    
    def thermal_efficiency(self):
        """Carnot-like efficiency"""
        Tt4 = self.tt
        Tt0 = 288  # Ambient temperature
        return 1 - (Tt0 / Tt4)
    
    def propulsive_efficiency(self):
        """Propulsive efficiency"""
        V0 = 250  # Flight velocity (m/s)
        Ve = V0 * 1.5  # Exit velocity (simplified)
        return 2 / (1 + Ve/V0)

# Engine components
engine_components = {
    'intake': 'Ram compression at high speed',
    'compressor': 'Raises pressure (centrifugal or axial)',
    'combustor': 'Adds energy (constant pressure)',
    'turbine': 'Extracts energy for compressor',
    'nozzle': 'Accelerates exhaust'
}

# Specific thrust and fuel consumption
def engine_performance(m_dot, F, sfc):
    """
    m_dot: Air mass flow
    F: Thrust
    sfc: Specific fuel consumption
    """
    thrust_per_airflow = F / m_dot
    return thrust_per_airflow, sfc

Rocket Propulsion

# Rocket equation
def rocket_delta_v(ve, m0, mf):
    """
    Tsiolkovsky rocket equation.
    ve: Effective exhaust velocity
    m0: Initial mass
    mf: Final mass
    """
    return ve * np.log(m0 / mf)

# Specific impulse
def specific_impulse(ve, g0=9.81):
    """
    Isp = ve/g0 (seconds)
    """
    return ve / g0

# Propellant types
propellant_types = {
    'liquid': {
        'oxidizer': 'LOX, N2O4, H2O2',
        'fuel': 'LH2, RP-1, kerosene',
        'examples': 'SpaceX Merlin, RS-25'
    },
    'solid': {
        'composition': 'Ammonium perchlorate + aluminum + binder',
        'examples': 'SRB, tactical missiles'
    },
    'hybrid': {
        'fuel': 'Solid',
        'oxidizer': 'Liquid or gas',
        'examples': 'SpaceShipOne'
    },
    'electric': {
        'type': 'Ion, Hall effect',
        'examples': 'Deep Space 1, Dawn'
    }
}

Aerospace Structures

Materials

# Material properties
aerospace_materials = {
    'aluminum_alloys': {
        'examples': ['2024', '7075', '6061'],
        'strength': 'High',
        'weight': 'Low',
        'uses': 'Primary structure, skin'
    },
    'titanium_alloys': {
        'examples': ['Ti-6Al-4V'],
        'strength': 'Very high',
        'weight': 'Moderate',
        'uses': 'Engine components, high-stress'
    },
    'composites': {
        'carbon_fiber': {
            'strength': 'Very high',
            'weight': 'Very low',
            'uses': 'Wing, fuselage panels'
        },
        'glass_fiber': {
            'strength': 'High',
            'weight': 'Low',
            'uses': 'Non-critical surfaces'
        }
    },
    'superalloys': {
        'examples': ['Inconel', 'Waspaloy'],
        'temperature': 'High temperature capability',
        'uses': 'Turbine blades, combustion chambers'
    }
}

Structural Analysis

# Stress and strain
def stress_strain(sigma, E):
    """
    Calculate strain from stress.
    sigma: Stress (Pa)
    E: Young's modulus (Pa)
    """
    return sigma / E

# Buckling
def critical_buckling(P, L, E, I):
    """
    Euler buckling load.
    """
    return np.pi**2 * E * I / (L**2)

# Fatigue
fatigue_analysis = {
    's_n_diagram': 'Stress vs cycles to failure',
    'goodman': 'Mean stress correction',
    'miners_rule': 'Cumulative damage',
    'factors': ['Load spectrum', 'Material', 'Geometry', 'Environment']
}

Space Systems

Orbital Mechanics

# Orbital parameters
orbital_elements = {
    'semi_major_axis': 'Average distance from focus',
    'eccentricity': 'Orbit shape (0=circle)',
    'inclination': 'Angle from reference plane',
    'raan': 'Right ascension of ascending node',
    'argument_periapsis': 'Orientation of orbit in plane',
    'true_anomaly': 'Position in orbit'
}

# Orbital velocity
def orbital_velocity(mu, r):
    """
    Circular orbit velocity.
    mu: Gravitational parameter (GM)
    r: Orbital radius
    """
    return np.sqrt(mu / r)

# Orbital period
def orbital_period(a, mu):
    """
    a: Semi-major axis
    """
    return 2 * np.pi * np.sqrt(a**3 / mu)

# Hohmann transfer
def hohmann_transfer(r1, r2, mu):
    """
    Calculate Hohmann transfer velocities.
    """
    # Vis-viva equation
    v1 = np.sqrt(mu / r1) * (np.sqrt(2 * r2 / (r1 + r2)) - 1)
    v2 = np.sqrt(mu / r2) * (1 - np.sqrt(2 * r1 / (r1 + r2)))
    return v1, v2

Spacecraft Systems

# Subsystems
spacecraft_subsystems = {
    'power': ['Solar arrays', 'Batteries', 'RTG'],
    'thermal_control': ['Passive', 'Active (heat pipes)', 'Louvers'],
    'communication': ['Transponder', 'Antenna', 'Amplifier'],
    'attitude_control': ['Reaction wheels', 'Thrusters', 'Magnetorquers'],
    'propulsion': ['Chemical', 'Electric', 'Cold gas']
}

# Launch vehicles
launch_vehicle_classes = {
    'light': '< 2,000 kg to LEO',
    'medium': '2,000-20,000 kg to LEO',
    'heavy': '20,000-50,000 kg to LEO',
    'super_heavy': '> 50,000 kg to LEO'
}

Avionics and Systems

Flight Controls

# Control surfaces
control_surfaces = {
    'ailerons': 'Roll control',
    'elevator': 'Pitch control',
    'rudder': 'Yaw control',
    'flaps': 'High lift devices',
    'slats': 'Leading edge high lift',
    'spoilers': 'Speed brakes, lift dumpers'
}

# Fly-by-wire
fly_by_wire = {
    'description': 'Computer-controlled flight controls',
    'advantages': ['Envelope protection', 'Redundancy', 'Optimization'],
    'systems': ['Quadruple redundancy', 'Backup mechanical']
}

Navigation

# Navigation systems
navigation_systems = {
    'INS': 'Inertial Navigation System',
    'GPS': 'Global Positioning System',
    'VOR': 'VHF Omnidirectional Range',
    'ILS': 'Instrument Landing System',
    'DME': 'Distance Measuring Equipment'
}

# Flight instruments
flight_instruments = {
    'airdata': ['Airspeed', 'Altitude', 'Vertical speed'],
    'attitude': ['Artificial horizon', 'Turn coordinator'],
    'heading': ['Heading indicator', 'Magnetic compass'],
    'navigation': ['HSI', 'RMI']
}

Regulations and Standards

Aviation Authorities

Certification Levels

certification_categories = {
    'aircraft': {
        'Normal': 'Private flying, no aerobatics',
        'Utility': 'Limited aerobatics',
        'Acrobatic': 'Full aerobatics',
        'Transport': 'Airline certification'
    },
    'parts': {
        'PMAs': 'Parts Manufacturer Approval',
        'STCs': 'Supplemental Type Certificates',
        'OEM': 'Original equipment manufacturer'
    }
}

Common Errors to Avoid

• Ignoring atmospheric effects: Density changes with altitude
• Confusing velocity and Mach: They are different measures
• Neglecting structural limits: Never exceed Vne
• Underestimating fuel burn: Always plan for reserves
• Ignoring weight and balance: CG must be within limits
• Forgetting weather: Weather affects all aspects of flight
• Confusing thrust and power: They are different concepts
• Ignoring center of pressure: Moves with angle of attack
• Not understanding lift curve: Stall and beyond
• Neglecting regulations: Always follow aviation authority rules