Spin Drift and Aerodynamic Jump

Spin Drift and Aerodynamic Jump

Both are spin-induced corrections that lob models with two fidelity levels — Litz (empirical, needs only Miller stability) and Boatright (needs full geometry + flight history to Mach 1.2). Selection is automatic: try Boatright, fall back to Litz, otherwise zero. Both are built once at Build().

Spin drift

Lateral deflection from gyroscopic precession (yaw of repose), applied post-solve to deflection.

Boatright (source/lob_builder.cpp) when diameter, meplat, base, length, nose, tail, ogiveRtR, velocity, c, mass, twist, stability_factor, BC and wind.z are known:

1. Computes ogive geometry RT, LFN, aspect ratio, Mach, Q, S, CL, CDa, ρ, Iy/Ix, P, R, N, F1+F2, F2, Tn.
2. Short-integrates to v = Mach 1.2·c (60 s timeout → kLobErrorInternalError, temporary guard — revisit when boatright path is optimized) for supersonic time.
3. Forms KV=log(1.2c/v0), Kω, QTS, β(R,Ω), boattail-adjusted CL, CL(T) → spindrift_factor = 0.388132·QTS·β·CL(T)/mass stored in ctx.spindrift_factor. At solve time (source/lob_solve.cpp): deflection += spindrift_factor · |elevation|.

If incomplete, spindrift_factor = NaN and drift falls through to Litz.

Litz (source/litz.hpp): drift = 1.25·sign(sg)·(|sg|+1.2)·TOF^1.83 inches, applied when spindrift_factor is NaN and |sg|>0 (source/lob_solve.cpp). sg is Miller stability (Atmospheric Model). Tests in test/source/lob_spin_drift_test.cpp.

Selection:

if (finite spindrift_factor) use Boatright (factor·|drop|)
else if (|sg|>0)             use Litz (TOF^1.83)
else                         no drift

Limitations: Litz is empirical, not 6-DOF; Boatright's many intermediates are from Boatright & Ruiz papers, not claimed beyond “tests pass”.

Aerodynamic jump

Vertical pitch at the muzzle from crosswind on a spinning projectile, modeled as an angle added to launch:

launch = zero_angle + aerodynamic_jump   (source/lob_solve.cpp, source/solve_angle.hpp)

Computed once and reused for every solve (including zero-finding and inverse).

Boatright when same full inputs present (source/lob_builder.cpp):

γ   = w_z / v0
R   = epicyclic ratio from sg
N   = nutation cycles
CD  = CD0 + γ²·R²/(R−1)²·CDa
pitch = γ·(R²−1)/(2πNR)·(1 − cos(2πN/(R−1)))
Jv  = sign(twist)·N·Tn·Q·S·(CL+CD)·sin(pitch)
jump = −Jv / MOM   (radians → MOA)

Uses same supersonic Tn etc. as drift; stored in ctx.aerodynamic_jump.

Litz if Boatright didn't produce a jump (source/lob_builder.cpp):

• w_z==0 → 0
• else if sg, diameter, length available: jump = sign(sg)·(0.01·|sg| − 0.0024·L/D + 0.032)·w_z_mph MOA (source/litz.hpp, p.422)
• else 0

Both forward (LobSolve) and angle-finding (SolveAngle) add jump before v = v0·(cos launch, sin launch, 0), so zero and inverse share it (Shared Angle Solver). Validated in test/source/lob_cwaj_test.cpp and lob_inverse_test.cpp with non-zero jump.

Limitations: Single scalar added to elevation; no rolling-moment history; zero when inputs missing (deliberate graceful degradation).