Aerodynamics.hpp

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// Vulcan Aerodynamics Module
// Core aerodynamic utility functions for trajectory optimization
#pragma once
 
#include <vulcan/core/VulcanTypes.hpp>
 
#include <janus/math/Linalg.hpp>
#include <janus/math/Logic.hpp>
#include <janus/math/Trig.hpp>
 
namespace vulcan::aero {
 
// =============================================================================
// Fundamental Aerodynamic Quantities
// =============================================================================

template <typename Scalar>
Scalar dynamic_pressure(const Scalar &density, const Scalar &velocity) {
    return Scalar(0.5) * density * velocity * velocity;
}

template <typename Scalar>
Scalar mach_number(const Scalar &velocity, const Scalar &speed_of_sound) {
    return velocity / speed_of_sound;
}

template <typename Scalar>
Scalar reynolds_number(const Scalar &density, const Scalar &velocity,
                       const Scalar &length, const Scalar &viscosity) {
    return density * velocity * length / viscosity;
}

template <typename Scalar>
Scalar airspeed(const Vec3<Scalar> &velocity_ground,
                const Vec3<Scalar> &velocity_wind) {
    Vec3<Scalar> v_air = velocity_ground - velocity_wind;
    return janus::norm(v_air);
}

template <typename Scalar> Scalar airspeed(const Vec3<Scalar> &velocity) {
    return janus::norm(velocity);
}
 
// =============================================================================
// Aerodynamic Angles
// =============================================================================

template <typename Scalar>
Vec2<Scalar> aero_angles(const Vec3<Scalar> &velocity_body) {
    Scalar vx = velocity_body(0); // Forward component
    Scalar vy = velocity_body(1); // Right component
    Scalar vz = velocity_body(2); // Down component
 
    // Total speed
    Scalar v_total = janus::norm(velocity_body);
    Scalar eps = Scalar(1e-10);
    Scalar is_zero = v_total < eps;
 
    // Angle of attack: alpha = atan2(vz, vx)
    // Positive when flow comes from below (nose up relative to velocity)
    Scalar alpha = janus::atan2(vz, vx);
    alpha = janus::where(is_zero, Scalar(0), alpha);
 
    // Sideslip angle: beta = asin(vy / v_total)
    // Positive when flow comes from right
    Scalar beta = janus::asin(vy / v_total);
    beta = janus::where(is_zero, Scalar(0), beta);
 
    Vec2<Scalar> angles;
    angles << alpha, beta;
    return angles;
}
 
// =============================================================================
// Combined Aerodynamic State
// =============================================================================

template <typename Scalar> struct AeroState {
    Scalar dynamic_pressure; 
    Scalar mach;             
    Scalar reynolds;         
    Scalar airspeed;         
    Scalar alpha;            
    Scalar beta;             
};

template <typename Scalar>
AeroState<Scalar>
aero_state(const Scalar &density, const Scalar &speed_of_sound,
           const Scalar &viscosity, const Vec3<Scalar> &velocity_body,
           const Scalar &char_length) {
    Scalar V = airspeed(velocity_body);
    Vec2<Scalar> angles = aero_angles(velocity_body);
 
    return AeroState<Scalar>{
        .dynamic_pressure = dynamic_pressure(density, V),
        .mach = mach_number(V, speed_of_sound),
        .reynolds = reynolds_number(density, V, char_length, viscosity),
        .airspeed = V,
        .alpha = angles(0),
        .beta = angles(1)};
}
 
} // namespace vulcan::aero