package numerics

import "math"

// NasaDensity returns air density in kg/m^3 at the given altitude in metres,
// using the NASA piecewise standard-atmosphere model.
// See https://www.grc.nasa.gov/WWW/K-12/airplane/atmosmet.html.
//
// The model is split into three altitude bands (troposphere, lower
// stratosphere, upper stratosphere); density is pressure / (0.2869 * T_K).
func NasaDensity(alt float64) float64 {
	var temp, pressure float64
	switch {
	case alt > 25000:
		temp = -131.21 + 0.00299*alt
		pressure = 2.488 * math.Pow((temp+273.1)/216.6, -11.388)
	case alt > 11000:
		temp = -56.46
		pressure = 22.65 * math.Exp(1.73-0.000157*alt)
	default:
		temp = 15.04 - 0.00649*alt
		pressure = 101.29 * math.Pow((temp+273.1)/288.08, 5.256)
	}
	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))
}