/** This is a 2-dimensional ballistics / aerospace simulation that attempts
    to model a Mars meteorite re-entry.

    This program can be altered to model many types of impactors.  Some may
    slow down to terminal velocity (which means they probably actually
    burned up.)
*/

use MarsAtmosphere.frink

// h is height above ground (initial height)
h = 14 km

diameter = 1 cm
radius =  diameter/2
volume = 4/3 pi radius^3
density = 7.874 g/cm^3

// m1 is the mass of the projectile
m1 = volume density
println["Mass is $m1"]

// area is area of projectile in direction of travel.
// area of a sphere can be calculated from mass and density as:
// area = (3/4)^(2/3) m1^(2/3) pi^(1/3) density^(-2/3)

//area = (3/4)^(2/3) m1^(2/3) pi^(1/3) density^(-2/3)
area = pi radius^2
println["Area is " + (area->"cm^2")]
//area = 0.7 m^2

// Initial velocity in the x direction (horizontal)
vx = 0 km/s

// Initial velocity in the y direction (vertical, positive is up)
vy = -13 km/s

// mp is mass of planet
mp = marsmass
r = marsradius
gravity = G mp / r^2

// x and y are a cartesian coordinate system with the center of the planet
// at x=0 m, y=0 m.  The projectile typically begins its journey at x=0 and
// at a given height-above-ground.
x = 0 km
y = r + h

initialGeopotentialHeight = (r * h) / (r + h)
//println["Geopotential height = " + (geopotentialHeight -> "ft")]
initialGeopotentialEnergy = m1 gravity initialGeopotentialHeight

initialKineticEnergy = 1/2 m1 (vx^2 + vy^2)

timestep = .005 s

t = 0 s

// Energy lost to drag
Edrag = 0 J

g = new graphics
line = new polyline
height = new polyline

do
{
   // l is distance from center of Mars
   l2 = x^2 + y^2
   l = sqrt[l2]
   h = l - r

   // Angle with respect to center of Mars
   alpha = arctan[x,y]

   // Force due to gravity
   fg = - G m1 mp / l2

   // Acceleration due to gravity
   ag =  fg / m1
   agx = ag sin[alpha]
   agy = ag cos[alpha]

   // Atmospheric drag
   v2 = vx^2 + vy^2
   v = sqrt[v2]

   // Angle of travel (0 is in x direction, 90 degrees in y direction)
   theta = arctan[vy, vx]

   [temp, pressure, adensity] = tpd = MarsAtmosphere.getTPD[h]

   // Calculate drag coefficient as a function of velocity
   Cd = Cd[v]

   fdrag = 1/2 adensity v2 Cd area
//   println["tpd=$tpd, Fdrag = $fdrag"]
   
   adrag =  -fdrag / m1
   adragx = adrag cos[theta]
   adragy = adrag sin[theta]

   t = t + timestep

   // Total acceleration
   axtotal = agx + adragx
   aytotal = agy + adragy
   atotal = sqrt[axtotal^2 + aytotal^2]
   
   dvx = axtotal timestep
   dvy = aytotal timestep
   
   vx = vx + dvx
   vy = vy + dvy

   dx = vx timestep
   dy = vy timestep

   // Power due to drag
   Pdrag = fdrag v
   
   // Energy lost to drag
   // E = f * d = f * v * t
   Edrag = Edrag + Pdrag timestep
   
   x = x + dx
   y = y + dy

   line.addPoint[x/m, -y/m]
   height.addPoint[t, -h/m]

   geopotentialHeight = (r * h) / (r + h)
   geopotentialEnergy = m1 gravity geopotentialHeight

   kineticEnergy = 1/2 m1 (vx^2 + vy^2)

   totalEnergy = geopotentialEnergy + kineticEnergy
//if t mod (1 s) == 0 s
      println[formatFixed[t,"s",3] + "\t" + /*format[x,"m",8] + "\t" + format[y,"m",9] + "\t" + */ format[h,"m",9] + "\t" + /* format[adragx,"gee",4] + "\t" + format[adragy,"gee",4] + "\t" */ format[adrag,"gee",4] + "\t" + format[v,"m/s",7] + "\t" + formatEng[Pdrag, "W", 3]]
} while h >= 0 m

initialEnergy = initialGeopotentialEnergy + initialKineticEnergy
println["Initial potential energy = $initialGeopotentialEnergy"]
println["Initial kinetic energy   = $initialKineticEnergy"]
println["Final kinetic energy     = " + (1/2 m1 v2)]
println["Initial energy           = " + initialEnergy]
println["Energy lost to drag      = $Edrag\t(" + formatEng[Edrag, "tons TNT", 3] + ")"]
println["Fraction of energy lost to drag = " + format[Edrag / initialEnergy, "percent", 4]]

g.add[line]
g.show[]

g2=new graphics
g2.add[height]
g2.show[]

// Drag coefficient equation for a sphere in the subsonic-to-hypersonic environment
// See ESTIMATING THE DRAG COEFFICIENTS OF METEORITES FOR ALL MACH NUMBER REGIMES.
// R. T. Carter, P. S. Jandir, and M. E. Kress,
// 40th Lunar and Planetary Science Conference (2009)
// They don't actually display the "quadratic" behavior which occurs below
// about Mach 0.8, so this is a curve-fit.
// For hypersonic velocities, this is about 0.92, while other authors state that
// a constant 0.7 is okay.
Cd[v] :=
{
   M0 = v/mach
   
   if (M0 >= 0.8)
   {
      // Mach 0.8 and above, use eq. from paper.
      M1 = M0 + 0.35
      return 2.1 e^(-1.2 M1) - 8.9 e^(-2.2 M1) + 0.92
   } else
   {
      // Below Mach 0.8
      // Use "quadratic" range picked off chart and fitted
      return 0.424 + 0.472 M0^2
   }
}