/** This is a 2-dimensional ballistics / aerospace simulation that accurately
    models air resistance (using the U.S. Standard Atmosphere as implemented
    in StandardAtmosphere.frink ) and the curvature of the earth (in 2
    dimensions.)
`
    It can be used to model anything from orbital decay to hypervelocity meteor
    impacts to orbital decay due to atmosphere.

    Using the defaults below, an orbit of a small iron sphere starts
    approximately circularly at an altitude of 180 km above earth's surface
    and decays over the course of several days until reeentry.

    The variant meteorCrater.frink 
    models a hypervelocity impactor for Meteor Crater, Arizona and shows
    the huge amount of energy radiated by pushing through atmosphere.
*/

use StandardAtmosphere.frink

// h0 is height above ground (initial height)
// Highest X-15 flight, flight 149, 22 August 1963
// https://en.wikipedia.org/wiki/List_of_X-15_flights
h0 = 354200. ft
h = h0

// m1 is the mass of the projectile
// https://en.wikipedia.org/wiki/North_American_X-15
//m1 = 33500 lb   // Gross weight
m1 = 14600. lb   // Empty weight

// Cd is drag coefficient of projectile
//
// THERE IS LOTS OF DATA HERE FOR THE X-15
// https://citeseerx.ist.psu.edu/document?repid=rep1&type=pdf&doi=e65b16435676e88edffaaba028ee0d03abc2bd93
Cd = 0.0645

// 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)
//
// https://frinklang.org/fsp/solve2.fsp?equations=area+%3D+pi+radius%5E2%0D%0Avolume+%3D+4%2F3+pi+radius%5E3%0D%0Adiameter+%3D+2+radius%0D%0Amass+%3D+volume+density%0D%0A%0D%0A&solveFor=&f=on&ev=on&sel_area=L&val_area=33+cm%5E2&sel_density=L&val_density=7+water&sel_diameter=S&val_diameter=&sel_mass=L&val_mass=1+kg&sel_pi=L&val_pi=3.141592653589793238&sel_radius=S&val_radius=&sel_volume=S&val_volume=&resultAs=cm&solved=on&showorig=on

//density = 7 g/cm^3
//area = (3/4)^(2/3) m1^(2/3) pi^(1/3) density^(-2/3)

// THERE IS LOTS OF DATA HERE FOR THE X-15
// https://citeseerx.ist.psu.edu/document?repid=rep1&type=pdf&doi=e65b16435676e88edffaaba028ee0d03abc2bd93
area = 13.60 ft^2

//println["Area is " + (area->"cm^2")]
//area = 0.7 m^2

// Initial velocity in the x direction (horizontal)
// (Orbital velocity can be found as v = sqrt[G planetmass / r] )
vx = 3794 mph

// Initial velocity in the y direction (vertical, positive is up)
vy = 0 km/s


planetmass = earthmass
r = earthradius

// 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 m
y = r + h

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

initialKineticEnergy = 1/2 m1 sqrt[vx^2 + vy^2]^2

timestep = .1 s

t = 0 s

// Energy lost to drag
Edrag = 0 J

g = new graphics
p = new polyline

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

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

   // Force due to gravity
   fg = - G m1 planetmass / 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] = StandardAtmosphere.getTemperatureAndPressure[h]
   density = StandardAtmosphere.getDensity[h, temp, pressure]
   fdrag = 1/2 density v2 Cd area

   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

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

   p.addPoint[x/m,-y/m]

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

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

   totalEnergy = geopotentialEnergy + kineticEnergy
//   println["agx=$agx\tagy=$agy"]
//   println["adragx=$adragx\tadragy=$adragy"]
//      println[format[t,"s",3] + "\t" + format[x,"m",3] + "\t" + format[y,"m", 3] + "\t" + format[h,"m",3] + "\t" + format[agx,"gee",3] + "\t" + format[agy,"gee",3]]
   if t mod (1 s) == 0 s
      println[format[t,"s",3] + "\t" + format[x,"m",3] + "\t" + format[y,"m", 3] + "\t" + format[h,"m",3] + "\t" + format[adragx,"gee",8] + "\t" + format[adragy,"gee",8] + "\t" + format[adrag,"gee",8] + "\t" + format[vx,"mph",3] + "\t" + format[vy,"mph",3] + "\t" + format[v,"mph",3] +  "\t" + format[Edrag, "J", 3] + "\t" + format[dragpow,"W", 3]]
} while h >= 0 ft

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

[left, top, right, bottom] = getBoundingBox[p]
g.saveClip[]
g.clipRectSides[left,top,right,bottom]
g.color[0,0,1]
g.fillEllipseCenter[0,0,2 earthradius/m, 2 earthradius/m]
g.color[0,0,0]
g.add[p]
g.restoreClip[]
g.font["SansSerif", 10 km/m]
g.caption[formatFix[x,"miles", 0]]
g.caption[formatFix[h0,"miles", 0], "left", 90 deg]
g.show[]
g.write["X-15.png",400,undef]

// Frink solver:
// https://frinklang.org/fsp/solve2.fsp?equations=E+%3D+mass+gravity+height%0D%0AE+%3D+1%2F2+mass+velocity%5E2%0D%0Adistance+%3D+height+glideslope%0D%0A&solveFor=&f=m&ev=on&sel_distance=S&val_distance=&sel_E=S&val_E=&sel_glideslope=L&val_glideslope=+4&sel_gravity=L&val_gravity=196133%2F20000+m+s%5E-2&sel_height=S&val_height=+&sel_mass=S&val_mass=+&sel_velocity=L&val_velocity=4554.+mph&resultAs=miles&solved=on&showorig=on
glideslope = 4/1
maxdistance = glideslope v^2 / (2 gravity)
println["Maximum distance at glideslope of $glideslope:1 is " + format[maxdistance, "miles", 0]]