Need Help with Triamese Orbital Ascent performance estimates / Ascent Simulation

[CarlKinder]

I'm designing a triamese reusable space-plane for X-plane V10, and I need some help determining performance estimates such as maxQ, staging velocity, and 1st stage burn time.

The vehicle is a stretched lifting body with low-aspect switch-blade wings that retract and stow into the fuselage (tucked in-between the fuel tanks and heat shield). It's inspired by the original triamese / MUSTARD proposals of the 1960s, but with the payload bay replaced with a disposable fairing / load-frame.

I was able to do a crude estimate using the rocket equation, but I'm not sure how to factor in varying ISP with altitude...

Here's what I have so far:

XSR - eXperimental Shuttle Replacement

Vehicle Summary:

Launch Profile: VTHL (Vertical Takeoff / Horizontal Landing) Triamese 1st stage with crossflow - parallel main engine burn.

Wingspan:  125ft

Height (gear to tail):  43.5ft

Length:  171ft

Tailspan:  80ft

Empty Weight:  200,000lb (manned orbiter), 195,000lb (unmanned orbiter), 190,000lb (unmanned booster)

Fuel weight:  1,100,000lb (manned/unmanned orbiter), 1,222,500lb (unmanned booster)

RCS/OMS (ethane+N2O):  20,000lb (manned/unmanned orbiter), 2,000lb (each unmanned booster)

Engine: RS-25 SSME Space Shuttle Main Engine (5 per vehicle) 418,000lb sea level thrust each

Stack total thrust at liftoff:  6,270,000 lb (15 RS-25 engines @104% throttle)

Payload weight:  50,000lb + 10,000lb discarding payload shroud with mounting hardware (load frame) and cross-flow plumbing

Stack total liftoff weight (Triamese launch – 1 orbiter + 2 boosters):  4,204,000lb

Liftoff thrust to weight:  1.49 : 1

Cross range capability estimate:  ~ 800 – 900 miles


Delta-V Performance Estimates:

1st Stage (ISP estimated by average altitude during ascent):

9.81m/s^2*(370s)*ln(4,204,000lb/1,919,000lb) = 2,846.5 m/s

2nd Stage: (Orbiter Thrust to weight – 1.8 : 1)

9.81m/s^2*(420s)*ln(1,375,000lb/275,000lb) = 6,631.2 m/s

Orbiter total = 9,477.7 m/s – 1,850 m/s (Estimated aero & gravity losses)


= 7,627.7 m/s for polar orbit (military payload)

+ 250 m/s boost to ISS inclination = 7,877.7 m/s

+ 400 m/s boost to low inclination eastern orbit = 8,027.7 m/s


Post 2nd Stage booster Delta-V Brake (using reserve fuel – RCS depleted during attitude reverse):

9.81s*(400s)*ln(270,000lb/194,000lb) = 1,297.1 m/s

Orbiter RCS / OMS available Delta-V for orbital maneuvers & inclination changes:

9.81s*(310s)*ln(275,000lb/255,000lb) = 230 m/s (with 50,000lb payload)