Uni‑vector

INPUTS: STW (kn), HDG (°), SOG (kn), COG (°), AWS (kn), AWA (°, +stbd/−port), HEEL (magnitude °, always ≥0), K (always ≥0, default 12.5)

STEP 1 — Leeway & course through water:
  sign = −1 if AWA > 0 (stbd), +1 if AWA < 0 (port), 0 if AWA = 0
  LWY = sign · K · |HEEL| / STW²  [0 if STW = 0 or AWA = 0]
  CTW = HDG + LWY  (set K = 0 to bypass leeway)

STEP 2 — Apparent wind direction (check value):
  AWD = CTW + AWA  (direction wind comes from, compass °)

STEP 3 — Current (C = B − A), flows toward CD:
  Cx = SOG·sin(COG) − STW·sin(CTW)
  Cy = SOG·cos(COG) − STW·cos(CTW)
  CS = √(Cx²+Cy²)  |  CD = atan2(Cx,Cy)

STEP 4 — True wind (AW corrected for boat motion through water):
  TWx = −AWS·sin(AWD) + STW·sin(CTW)
  TWy = −AWS·cos(AWD) + STW·cos(CTW)
  TWS = √(TWx²+TWy²)  |  TWD (from) = atan2(−TWx,−TWy)
  TWA = TWD − CTW  (normalized to ±180°, +stbd/−port)

STEP 5 — Ground wind, standard (AW corrected for boat motion over ground):
  GWx = −AWS·sin(AWD) + SOG·sin(COG)
  GWy = −AWS·cos(AWD) + SOG·cos(COG)
  GWS = √(GWx²+GWy²)  |  GWD (from) = atan2(−GWx,−GWy)

STEP 6 — Ground wind, alternate (TW + current — should equal GW):
  GWqx = TWx + CS·sin(CD) = TWx + Cx
  GWqy = TWy + CS·cos(CD) = TWy + Cy
  GWSq = √(GWqx²+GWqy²)  |  GWDq (from) = atan2(−GWqx,−GWqy)

All directions in degrees true (0–360). Wind directions are where the wind comes FROM. CD is where current flows TOWARD. GWSq and GWDq should equal GWS and GWD to within rounding.