feat: move stuff to numerics

internal/numerics/atmosphere.go

@@ -23,3 +23,16 @@ func NasaDensity(alt float64) float64 {
 	}
 	return pressure / (0.2869 * (temp + 273.1))
 }
+
+// DragTerminalVelocity returns the vertical velocity (m/s, negative = downward)
+// of a parachute descent at the given altitude. seaLevelRate is the descent
+// speed at sea level (positive m/s); the rate grows with altitude as the
+// thinner air provides less drag:
+//
+//	v = -k / sqrt(rho(alt)),  k = seaLevelRate * 1.1045
+//
+// Matches Tawhiri's drag_descent.
+func DragTerminalVelocity(seaLevelRate, alt float64) float64 {
+	k := seaLevelRate * 1.1045
+	return -k / math.Sqrt(NasaDensity(alt))
+}

internal/numerics/motion_test.go

@@ -0,0 +1,58 @@
+package numerics
+
+import (
+	"math"
+	"testing"
+)
+
+func TestAddGeo(t *testing.T) {
+	// Rates sum component-wise with no longitude wrapping.
+	got := AddGeo(GeoVec{Lat: 1, Lng: 350, Altitude: 2}, GeoVec{Lat: 3, Lng: 20, Altitude: 4})
+	want := GeoVec{Lat: 4, Lng: 370, Altitude: 6}
+	if got != want {
+		t.Errorf("AddGeo = %+v, want %+v (no wrap on rates)", got, want)
+	}
+}
+
+func TestWindToGeoRate(t *testing.T) {
+	// Pure eastward 10 m/s at the equator, sea level.
+	dLat, dLng := WindToGeoRate(10, 0, 0, 0)
+	wantLng := (180.0 / math.Pi) * 10.0 / EarthRadius
+	if math.Abs(dLat) > 1e-15 {
+		t.Errorf("dLat = %v, want 0", dLat)
+	}
+	if math.Abs(dLng-wantLng) > 1e-15 {
+		t.Errorf("dLng = %v, want %v", dLng, wantLng)
+	}
+
+	// Northward 5 m/s at 60°N: dLat independent of longitude scaling.
+	dLat, _ = WindToGeoRate(0, 5, 60, 0)
+	wantLat := (180.0 / math.Pi) * 5.0 / EarthRadius
+	if math.Abs(dLat-wantLat) > 1e-15 {
+		t.Errorf("dLat at 60N = %v, want %v", dLat, wantLat)
+	}
+
+	// cos(lat) factor makes eastward motion span more degrees nearer the poles.
+	_, dLngEq := WindToGeoRate(10, 0, 0, 0)
+	_, dLng60 := WindToGeoRate(10, 0, 60, 0)
+	if dLng60 <= dLngEq {
+		t.Errorf("eastward deg/s should grow with latitude: eq=%v 60N=%v", dLngEq, dLng60)
+	}
+}
+
+func TestDragTerminalVelocity(t *testing.T) {
+	// Descent is downward (negative) and faster (more negative) at altitude
+	// where the air is thinner.
+	sea := DragTerminalVelocity(5, 0)
+	high := DragTerminalVelocity(5, 20000)
+	if sea >= 0 {
+		t.Errorf("sea-level rate = %v, want negative (downward)", sea)
+	}
+	if high >= sea {
+		t.Errorf("expected faster descent at altitude: sea=%v high=%v", sea, high)
+	}
+	// Sanity: at sea level rho≈1.225, so v ≈ -5*1.1045/sqrt(1.225) ≈ -4.99 m/s.
+	if math.Abs(sea-(-5*1.1045/math.Sqrt(NasaDensity(0)))) > 1e-12 {
+		t.Errorf("sea-level formula mismatch: %v", sea)
+	}
+}

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
+}