feat: move stuff to numerics

internal/numerics/vec.go

@@ -64,3 +64,26 @@ func LngLerp(a, b, l float64) float64 {
 func Lerp(a, b, l float64) float64 {
 	return (1-l)*a + l*b
 }
+
+// AddGeo returns the component-wise sum a+b without longitude wrapping. Use it
+// to combine derivative (rate) vectors — rates accumulate linearly, unlike
+// positions, which wrap via GeoAdd.
+func AddGeo(a, b GeoVec) GeoVec {
+	return GeoVec{Lat: a.Lat + b.Lat, Lng: a.Lng + b.Lng, Altitude: a.Altitude + b.Altitude}
+}
+
+// EarthRadius is the spherical Earth radius (metres) used for horizontal
+// motion, matching the reference Tawhiri implementation.
+const EarthRadius = 6371009.0
+
+// WindToGeoRate converts eastward (u) and northward (v) wind in m/s at the
+// given latitude (deg) and altitude (m) into the geographic rate in deg/s on a
+// spherical Earth. The returned dLng diverges near the poles as cos(lat) → 0.
+func WindToGeoRate(u, v, lat, alt float64) (dLat, dLng float64) {
+	const degPerRad = 180.0 / math.Pi
+	const piOver180 = math.Pi / 180.0
+	r := EarthRadius + alt
+	dLat = degPerRad * v / r
+	dLng = degPerRad * u / (r * math.Cos(lat*piOver180))
+	return dLat, dLng
+}