Module nose_drag 

Pressure drag of noses, shoulders and steps at every Mach number: Niskanen’s semi-empirical method (2009 §3.4.3, eq. 3.86–3.87, and appendix B), with Stoney’s measured curves for the shapes that have no closed form.

A nose, or a shoulder (a transition that widens toward the tail), drags on its increase in area with a coefficient (C_D•)_p(M) in three parts:

• At rest, (C_D•)_p,0 = 0.8 sin² φ (eq. 3.86), with φ the joint angle at the aft end (crate::drag::joint_pressure_drag_coefficient): the separation drag of a joint that isn’t smooth.

• From a lower bound M_L, appendix B’s transonic and supersonic value C_T(M), which depends on the shape and the fineness ratio f = l/(d_aft − d_fore) (a nose’s length over its base diameter; a shoulder’s length over its rise in diameter, so a cone and a conical shoulder of the same surface angle drag alike):

  shape	C_T(M)	M_L
  a step (no length), a body’s bare front face	the blunt cylinder, 0.85 q_stag/q (eq. B.2)	0.8
  cone	eq. B.4–B.6, a cubic between Mach 1 and 1.3 (cone_pressure_drag_coefficient)	1
  ogive	the cone of the same length and diameter times 0.72 (κ − ½)² + 0.82 (eq. B.8)	1
  power series, parabolic series, Haack series	Stoney’s fineness-3 curves, scaled to f by eq. B.9	where the curves start
  elliptical	Hoerner’s measured forebody drag below Mach 0.8, Stoney’s ellipsoid scaled by eq. B.9 from Mach 1.2, a straight line between (ellipsoid_subsonic_pressure_drag; ADR-173, a blunt ellipsoid’s measured drag)	0 (its own curve throughout)

• Between Mach 0 and M_L, eq. 3.87: a M^b + (C_D•)_p,0, with a and b fitting the value and slope of C_T at M_L (subsonic_pressure_drag_coefficient).

Niskanen p. 48 treats shoulders “similar to nose cones” at all speeds and calls the result “somewhat dubious at supersonic velocities”; a step is a shoulder of zero length, fineness 0. See Drag through Mach 1 in the guide and the decision record ADR-028.

A 5:1 von Kármán nose at Mach 1.5, the guide’s worked example: Stoney’s 3:1 curve gives 0.0893, scaled by eq. B.9 to 0.0407 on the base area, where a 5:1 cone drags 0.0653.

use hpr_aero::nose_drag::{PressureDragCurve, cone_pressure_drag_coefficient};
use hpr_design::NoseShape;

let von_karman = PressureDragCurve::new(NoseShape::VON_KARMAN, 5.0, 0.0)?;
assert!((von_karman.coefficient(1.5)? - 0.0407).abs() < 5e-5);
assert!((cone_pressure_drag_coefficient(5.0, 1.5)? - 0.0653).abs() < 5e-5);

Structs

PressureDragCurve

A nose’s, shoulder’s or step’s pressure-drag coefficient against Mach number, on its increase in area: the value at rest, eq. 3.87’s fit, and appendix B’s transonic method from M_L (the module docs). It serializes what it was built from, not its internals.

Enums

StoneyNose

A nose shape Stoney measured at fineness 3 (NASA TR R-100, 1961, Figure 12, printed p. 16), whose pressure-drag curve hpr carries as digitized points.

Constants

CONE_SUPERSONIC_MACH

Where eq. B.4 takes over from the cubic join for cones: Mach 1.3 (Niskanen 2009 p. 107, “M ≳ 1.3”).

HEMISPHERE_FOREBODY_PRESSURE_DRAG

The forebody pressure drag of a hemispherical head on a cylinder at low speed, on the cylinder’s area: 0.01 (Hoerner, Fluid-Dynamic Drag, 1965, p. 3-12, Fig. 20, “evaluated from pressure distribution”, from Rouse and McNown’s water-tunnel heads; friction not included).

ROUND_HEAD_FOREBODY_PRESSURE_DRAG

The forebody pressure drag of the round head about one diameter long in the same figure: −0.05, suction on the shoulder outweighing the stagnation pressure at the tip (Hoerner 1965 p. 3-12, Fig. 20). The figure prints no length; the head is drawn about one diameter long.

Functions

cone_pressure_drag_coefficient

The pressure drag of a cone nose of fineness ratio f (length over base diameter) at any Mach number, on its base area (Niskanen 2009 eq. 3.86–3.87 and B.3–B.6):

ellipsoid_subsonic_pressure_drag

An elliptical nose’s (or shoulder’s) pressure drag below Mach 0.8, on its increase in area, interpolated in fineness between the forebody pressure drags Hoerner measured at low speed (1965 p. 3-12, Fig. 20) (ADR-173, a blunt ellipsoid’s measured drag):

fineness_scaled_pressure_drag

Eq. B.9’s fineness-ratio scaling, for shapes measured at fineness 3 (Niskanen 2009 p. 110):

ogive_pressure_drag_factor

Eq. B.8’s ratio of an ogive’s pressure drag to that of the cone with the same length and base diameter, at transonic and supersonic speeds: 0.72 (κ − ½)² + 0.82 (Niskanen 2009 p. 110), with κ = ρ_t/ρ the tangent ogive’s arc radius over the ogive’s (0 for a cone, 1 for a tangent ogive). It is 1 at both ends and 0.82 at κ = ½, after NAVWEPS Report 1488 p. 239: the best ogive drags “consistently 18% less” than the cone at Mach 1.6 to 2.5 and fineness 2 to 3.5.

subsonic_pressure_drag_coefficient

Niskanen’s eq. 3.87 between Mach 0 and the transonic method’s lower bound M_L: (C_D•)_p = a M^b + (C_D•)_p,0, with a and b “computed to fit the drag coefficient and its derivative at the lower bound of the transonic method” (Niskanen 2009 p. 48): b = C_T′(M_L) M_L/Δ and a = Δ/M_L^b, where Δ = C_T(M_L) − (C_D•)_p,0.

takes_cone_formula

Whether a nose or shoulder of shape takes any of Niskanen’s closed-form cone (eq. B.3–B.6, times eq. B.8 for an ogive) in its transonic pressure drag (PressureDragCurve::new): a cone and an ogive wholly; a power series of exponent above ¾ and a parabolic series of parameter below ½ in part, as they blend toward the 3:1 cone. That closed form reads high against measurement from Mach 0.8 (issue #67), so a shape that takes it carries that issue’s warning.