Ballistic rocket passenger transport

bfr.rb

#! /usr/bin/env ruby

require 'rubygems'
require 'quantify'

include Math

# Mission parameters:
# 100 people plus baggage
# from New York City to Shanghai
# on a 100km ballistic trajectory
Dsurf    = 11800.km
Amax     = 100.km
Pax      = 240
Mpayload = 100.kg * Pax

# Facts about Big Momma
Rearth   = 6370.km
GPearth  = (1.km**3 / 1.s**2) * 398_600
Gearth   = 9.807.m / 1.s**2

# delta vee
# see http://www.alternatewars.com/BBOW/ABM/DeltaV_BMs.htm
Rburnout   = Rearth + Amax
GRad       = GPearth / Rburnout
RangeAngle = (Dsurf / Rearth).value
Dv1        = sqrt(((GRad * 2 * sin(RangeAngle)/2) / (1+sin(RangeAngle)/2)).value).km/1.s
Dv2        = Dv1 * 0.20 # wild guess for braking DV
Dv         = Dv1 + Dv2

# BFR ship and engines
# see https://www.youtube.com/watch?v=E4FY894HyF8
# and https://web.archive.org/web/20160928040332/http://www.spacex.com/sites/spacex/files/mars_presentation.pdf
# and https://en.wikipedia.org/wiki/Merlin_(rocket_engine_family)
Mship = 85.t         # cited in 2017 video
Ne    = 12           # need enough engines to get off the ground!
Me    = 750.kg * Ne  # assumed Raptor mass (compare to Merlin mass: 470kg)
F1    = 1_700.kN     # cited in 2017 video
Isp   = 330          # cited at 330-356 in the video; assume all sea level burns
F     = F1*Ne        # combined thrust from all engines
Ve    = Gearth * Isp # exhaust velocity
PCH4  = 0.21         # propellant ratio of methane
PO2   = 0.78         # propellant ratio of O2

# Tsiolkovsky equation; solving for m0
Mdry  = Mship + Me
M0    = (Mdry+Mpayload) * E ** (Dv / Ve).to_si.value
Mprop = M0 - (Mdry+Mpayload)

# Acceleration profile
M   = (Mdry+Mpayload+Mprop)
Acc = (F.to_si / M.to_si) - Gearth

# Fuel parameters
DenCH4 = 0.656.g/1.L # methane density at STP
DenO2  = 1.429.g/1.L # oxygen density at STP

# Cost of CH4 for a given mass of methalox propellant
def costCH4()
  mass = Mprop*PCH4
  # wellhead cost of CH4: approx $4 per 1,000 ft^3
  # see https://www.eia.gov/energyexplained/index.cfm?page=natural_gas_prices
  vol_per_dollar = ((1.ft**3) * 1000).to(Unit.L) / 4
  mass_per_dollar = vol_per_dollar * DenCH4
  (mass / mass_per_dollar).to_si.value
end

# Cost of O2 for a given mass of methalox propellant
def costO2()
  mass = Mprop*PO2
  # $0.16 / kg at 2001 prices
  # see https://www.quora.com/How-much-does-NASA-pay-per-kg-for-hydrogen-and-oxygen-in-rocket-fuel
  dollar_per_kg = 0.25
  dollar_per_kg * mass.to_si.value
end

MoleCH4 = 16.04.g
MoleCO2 = 44.01.g

def co2_footprint()
  (Mprop * PCH4) / MoleCH4 * MoleCO2
end

puts 'Performance'
puts '-----------'
puts 'Net accel:    ' + (Acc / Gearth).value.round(2).to_s + ' g'
puts 'Propellant:   ' + Mprop.round(1).to_s
puts
puts 'Cost per pax'
puts '------------'
puts '  Propellant: $' + ((costCH4 + costO2) / Pax).round(0).to_s
puts '  CO2:        ' + (co2_footprint / Pax).round(3).to_s