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)