Two-Stage Reusable Spaceplane Rough-Size

I did this study without much forethought,  because of all the hypersonic craft and spaceplane stuff I have been seeing on LinkedIn.  Much of that stuff ignores the issues that (1) without a heat protection solution,  there is no credible hypersonic design,  and (2) combined-cycle propulsion is still at the concept and early test stage,  and scramjet s not quite yet truly ready for application. 

What I show here seems to be feasible,  although it is not optimized.  This is a study of a two-stage vertical takeoff,  horizontal landing system,  to be powered by liquid rocket engines approximating the performance of SpaceX’s Raptor-2 designs.  Each stage is a flat-bottomed wave-rider aircraft with a delta wing,  a butterfly tail,  and retractable landing gear.  The second stage mounts on the first stage,  belly-to-belly.  As the vehicle leaves the sensible atmosphere at only Mach 2,  there is no danger from shock impingement heating between the two parallel-mounted airframes. 

The first stage booster aircraft has initial thrust/weight of 1.5,  and flies very nearly vertically to the staging speed,  achieved well exoatmospheric,  then it coasts to a very high altitude (probably beyond orbit altitude),  and finally falls back.  It performs an entry burn to reduce its speed to about Mach 2 at around 130,000 feet,  where the sensible atmosphere begins.  It then belly-flops to subsonic,  goes nose first,  pulls out of the dive,  and glides back to the base from which it was launched.  A short entry transient at only Mach 2 allows the use of organic composites for the bulk of its airframe,  and it needs no heat shield at all.  It retains just enough propellant to make a go-around burn at landing.

The second stage has a similar shape,  just smaller.  It carries 5 metric tons of cargo internally,  for delivery on-orbit.  The system is sized to reach low-inclination low Earth orbit.  It has an ignition thrust/weight of only 1.05,  so that the gravity turn effect has serious effect early in the ascent burn.  It makes that ascent burn,  then coasts to orbit altitude,  where it makes a circularization burn.  End-of-mission,  it makes a de-orbit burn,  then aerobrakes at high angle of attack to about Mach 3 at 13,000 130,000 feet (corrected 9-26-2022).  From there it belly-flops subsonic,  and then glides to an approach to its landing.  It retains a bit of propellant to enable a go-around at that landing.  This sizing includes carrying the entire cargo mass back from orbit.

The basic concept is illustrated in Figures 1 and 2.  As it turns out,  no solid booster rockets were necessary.  Figure 3 illustrates the approximations I used for the go-around capability.  Figure 4 illustrates most of the other assumptions I made.  Figure 5 has the results.  Note that both craft have inert masses that are 15% of their ignition masses!  These craft both have wings and landing gear,  unlike anything else flying into space today.  The second stage orbiter must have a heat shield and largely-metallic construction.  The first stage booster must have the structure and attachments to carry the second stage at some large gee values. 

It would be quite unrealistic to assume anything less than 15% inert fractions for the two stages.  However,  anything significantly larger would render the concept infeasible!  Note that the 5 metric tons of cargo is just about 1% of the cluster gross mass at liftoff.  Expendable and semi-reusable vertical launch rockets carry larger payload fractions than that,  which explains their overall popularity over the decades.  Per flight cost must be lower,  to make the low payload fraction attractive.

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Update 8 Sept 2022:  What this study explores is almost exactly the original design concept for the Space Shuttle, which originally was a 2-stage spaceplane vertically-launched,  with both stages landing horizontally,  using wings.  The Shuttle was fueled with hydrogen,  leading to bulky fuel tanks and sizes,  and the resulting very serious aerodynamic drag problems.  Shuttle stages in that original concept did not have go-around capability at landing.  They were "dead stick" gliders.  (We all know how that concept got changed to the semi-reusable cluster that actually flew,  for budgetary reasons.) 

My study here is methane-fueled,  avoiding most of the bulkiness and drag problems (and the notorious hydrogen leak problems).  I did allow for a minimal go-around capability at landing,  with both stages.  What I noticed was the criticality of selecting the "right" staging speed,  and the very narrow window of feasible inert masses in both stages!  

Most people use too low an inert mass fraction to be realistic,  and the resulting performance results fool them into thinking they have a feasible design with breakthrough performance.  Nothing could be further from the truth.  Even my 15% inert fractions may be too low in terms of realism,  but if any higher,  the feasibility goes away almost immediately as deliverable payload zeroes.  

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While you cannot really do this in the real world,  this study is simple enough that everything (masses and thrusts) scales proportional to delivered payload mass.  Example:  if 10 tons,  double everything.

 

Figure 1 – Basic Two-Stage Spaceplane Flight Plans for Vertical Takeoff,  Horizontal Landing

Figure 2 – Basic Two-Stage Spaceplane Shapes and Inboard Layouts

Figure 3 – Outline of the Go-Around Approximation

Figure 4 – Most of the Remaining Assumptions Illustrated

Figure 5 – Summary of the Results Obtained,  Not Optimized,  Just Feasible

Values Used for Propulsion

The SpaceX Raptor-2 engines provided the Isp ranges used here.  I did not specifically use the SpaceX thrust values,  nor did I size engine counts.  The vacuum and sea level designs share the same power heads,  but with different expansion bells.  The sea level engine has a 40:1 expansion ratio (curved bell).  The vacuum engine has a 150:1 expansion ratio (curved bell).   Performance is listed at full chamber pressure 4400 psia.  It is lower,  if throttled down.  Update 10-5-2022:  had to correct the table --  had the sea level and vacuum numbers swapped for the sea level design.  

References:

#1. G.W. Johnson,  “Rocket Engine Calculations”,  paper yet to be posted here on “exrocketman”,  which shows how to get close estimates of liquid engine performance,  and uses the SpaceX Raptor-2 sea level and vacuum engines as examples.  Update 10-5-2022:  this article now posted as of 10-1-2022,  under the indicated name.  

#2. Pratt & Whitney “Vest-Pocket Aeronautical Handbook”,  12^th edition,  21^st printing,  Dec. 1969,  for the US 1962 standard day atmosphere data within.