Aerodynamics Module

The vulcan::aero module provides fundamental aerodynamic calculations for flight mechanics and trajectory optimization. It is designed to work seamlessly with both numeric types (double) and symbolic types (janus::SymbolicScalar) for automatic differentiation.

Overview

The module provides:

• Fundamental Quantities: Dynamic pressure, Mach number, Reynolds number, Airspeed.
• Aerodynamic Angles: Angle of attack (α) and sideslip angle (β).
• Combined State: A struct AeroState containing all key aerodynamic properties.

Basic Usage

Include

#include <vulcan/vulcan.hpp>
// or
#include <vulcan/aerodynamics/Aerodynamics.hpp>

Computing Individual Properties

All functions are templated on Scalar type.

double rho = 1.225;   // kg/m^3
double V = 250.0;     // m/s
double a = 340.3;     // m/s (speed of sound)
double mu = 1.789e-5; // Pa*s (dynamic viscosity)
double L = 2.0;       // m (characteristic length)
 
// Dynamic Pressure (q)
double q = vulcan::aero::dynamic_pressure(rho, V); // 38281.25 Pa
 
// Mach Number (M)
double M = vulcan::aero::mach_number(V, a); // 0.734
 
// Reynolds Number (Re)
double Re = vulcan::aero::reynolds_number(rho, V, L, mu); // 3.42e7

Computing Aerodynamic Angles

aero_angles computes angle of attack (α) and sideslip (β) from the body-frame velocity vector.

vulcan::Vec3<double> v_body;
v_body << 200.0, 10.0, 20.0; // [vx, vy, vz]
 
auto angles = vulcan::aero::aero_angles(v_body);
double alpha = angles(0); // ~0.1 rad (atan2(vz, vx))
double beta = angles(1);  // ~0.05 rad (asin(vy / V))

Combined Aerodynamic State

For efficiency, especially in trajectory optimization, use aero_state to compute everything at once. This effectively combines the atmosphere model outputs with flight conditions.

// 1. Get atmosphere state (e.g. at 10km)
auto atm = vulcan::ussa1976::state(10000.0);
 
// 2. Define flight condition
vulcan::Vec3<double> v_body_10km;
v_body_10km << 250.0, 0.0, 0.0;
double char_len = 5.0;
 
// 3. Compute Aero State
auto state = vulcan::aero::aero_state(
    atm.density,
    atm.speed_of_sound,
    atm.dynamic_viscosity,
    v_body_10km,
    char_len
);
 
// Access results
std::cout << "Mach: " << state.mach << std::endl;
std::cout << "Dyn P: " << state.dynamic_pressure << std::endl;

Symbolic Optimization

The entire module is Janus-compatible. You can use janus::SymbolicScalar to build computational graphs for optimization problems.

// Define symbolic optimization variables
janus::SymbolicScalar alt = janus::sym("h");
janus::SymbolicScalar velocity = janus::sym("v");
 
// Compute atmosphere symbolically
auto atm = vulcan::ussa1976::state(alt);
 
// Compute dynamic pressure symbolically
auto q = vulcan::aero::dynamic_pressure(atm.density, velocity);
 
// 'q' is now a symbolic expression graph that depends on h and v

Note: aero_angles uses janus::atan2 and janus::asin, which are fully differentiable and safe for symbolic use.