Function cone_flow 

pub fn cone_flow(mach: f64, half_angle_rad: f64) -> Result<ConeFlow, AeroError>

The flow over a cone of half-angle half_angle_rad at Mach mach and zero angle of attack: the Taylor–Maccoll equation (NACA Report 1135, 1953, eq. 177, p. 628) integrated from the shock to the surface, the shock angle found so the surface falls on the cone. The weak, attached solution.

In V′ = V/V_max with V_θ = dV_r/dθ: V_r″ = [V_θ² V_r − ((γ − 1)/2)(1 − V_r² − V_θ²)(2V_r + V_θ cot θ)] / [((γ − 1)/2)(1 − V_r² − V_θ²) − V_θ²], started behind the oblique shock (eqs. 148 to 153, p. 623) and stopped where V_θ = 0.

Below SLENDER_CONE_RAD (0.029°) the start behind so weak a shock is too near the equation’s singular line to integrate, and the flow is linearized slender-cone theory’s: C_p = δ²(2 ln(2/(βδ)) − 1), β = √(M² − 1), the shock on the Mach angle and the surface Mach number isentropic from the free stream. From there to twice that angle the two are blended linearly, so the flow is continuous in the half-angle. At a millidegree scale these pressures differ from the free stream’s by under 1e-5. Near Mach 1 (1.01) the integration can still fail just above that angle; it then returns an error.

Errors

• AeroError::Domain for a Mach number that isn’t above 1 or a half-angle outside [0, π/2).
• AeroError::Unsupported where the shock detaches (the half-angle exceeds the steepest cone an attached shock allows at this Mach number), or should the integration fail to reach the cone.