--https://www.ltc.lu/enseignants/mike.anen/pdf/dichte_9de.pdf

dichteLuft  = 0.0012041 --g/cm³
dichten={
dichteAlu   = 2.700,
dichteStahl = 7.900,
}

pi = math.pi

print("g to lift")
io.write("> ")
gToLift = tonumber(io.read())
print("dicke der hülle in mm")
io.write("> ")
hullThickness = tonumber(io.read())

i = 0
print("Welches hüllenmaterial soll verwendet werden?")
for k,v in pairs(dichten) do
  i = i + 1
  print(i,k,v.."g/cm3")
end
io.write(">")
number = tonumber(io.read())
i = 0
for k,v in pairs(dichten) do
  i = i + 1
  if i == number then
    dichteHull = v
  end
end

print(dichteHull)

function doTheFancyShit(m,p1,p2,d) -- masse,dichteLuft,dichteHülle,dickeDerHülle
  -- get volume needet to replace enugh air to lift [m]
  Va = m/p1
  -- get radius of said volume
  r = math.pow(Va/(4/3)/pi,1/3)

  -- get volume of hull
  Vh = (4/3*pi*math.pow(r+d,3)-4/3*pi*math.pow(r,3))
  -- get mass of hull
  Mh = Vh * p2
  return r,Mh
end

Mh = 0 -- hull weight is init
rl = 0 -- last radius
repeat
  rl = r
  r,Mh = doTheFancyShit(gToLift+Mh,dichteLuft,dichteHull,hullThickness)
  print(r,Mh)
until rl == r

print("Radius: "..math.floor(r).."mm")