ffsshhttiikk 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
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
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
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
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