Wednesday, April 3, 2019

Pivot-Wing Spaceplane Concept Feasibility

In an earlier posting,  I described a unique folding-wing spaceplane idea and explored its feasibility.  This is described in ref.1 (list at end of article).  The fundamental idea was to move the aerosurfaces into the wake while entering the atmosphere from orbit dead-broadside to simplify the aerodynamics and reduce the number of possible aeroheating failure modes.  By folding the aerosurfaces that way,  the dead-broadside forces that would rip the aerosurfaces off,  could be avoided.  Once subsonic,  these surfaces could more easily be deployed for an airplane-like landing.

This posting describes another way to accomplish the very same goal,  one that avoids the need for complicated fairings and entry-capable streamlining design for the folding-wing hinge joint. The folding butterfly (V) tail is not a problem,  and is retained,  being mounted to the dorsal surface already in the entry wake zone.  Instead of folding wings,  this revised concept uses a pivoting wing,  rather similar to the Russian “Baikal” missile booster seen at multiple recent airshows. 

This article presents nothing but a design concept feasibility analysis.  Only the gross overall dimensions and characteristics get determined.  I look at a ballpark weight statement,  best-estimate wing loading,  and  estimated entry gees and heating for that,  as well as an estimated landing speed.  Not much more.


Figure 1 depicts the vehicle design concept in cartoon form (all figures at end of article).  Figure 2 depicts how this concept might be operated in flying practice.  The craft is a small spaceplane launched with stowed wing using an appropriate two-stage rocket booster.  The entire delta-vee to low Earth orbit (LEO) comes from the booster rocket.  The spaceplane,  to be useful for real missions,  must arrive with significant maneuvering delta-vee (for plane changes,  transfer orbits,  rendezvous,  and the like,  plus including its final small de-orbit burn).

Figure 1 shows the vehicle to be a high-wing airplane with a butterfly tail and a non-circular cross section.  The main heat shield is located on a nearly (but not exactly) flat belly surface.  The figure says its radius of curvature should be about 1.5 times the length (or more) in order to reduce equilibrium stagnation surface temperatures enough to enable use of a low-density alumino-silicate ceramic material.  The actual radius turned out to be 1.55 times the length,  but could just as easily be twice the length.  The noncircular cross-section shape is similar to that of the old Mercury and Gemini capsules,  so that from orbit,  highly-emissive reradiating metal “backshell” surfaces can be used,  hidden from hypersonic scrubbing in the wake,  and with negligible plasma radiation heating effects,  at only 7-8 km/s entry speeds.  The same applies to the stowed wing,  but perhaps not the V-tail.

The cargo bay is near the middle,  with the center of gravity and the wing pivot,  so that changes in payload require minimal trim adjustments. Propellant tankage is disposed ahead and behind this cargo bay.  These can be simple tanks within the mold line,  with some insulation to protect them from the hot reradiating skin.  The propellants are room-temperature storables,  most likely monomethyl hydrazine (MMH),  and nitrogen tetroxide (NTO),  so that the same propellant supply serves both the main engine and the attitude thrusters,  with hypergolic ignition.  Simple is more reliable.

The cockpit is located forward,  and is the only pressurized space,  sized for a crew of two.  Since this craft returns to land while flying like an airplane,   having a second pilot to support the first serves safety and reliability well,  just as in airliner flying.  It is likely this craft will be a challenge to fly,  as the return trajectory in Figure 2 suggests.  That makes two pilots more desirable in any event.

Anticipating high landing speeds because of the geometric limits for the size of the pivot wing,  landings on dry lake beds are presumed,  which makes a landing gear arrangement like that of the X-15 desirable and proven.    There is a steerable nosewheel forward under the pressurized cockpit,  and a pair of main skids near the tail in the engine compartment.

Pitch,  yaw,  and roll are presumed controlled with the V-tail surfaces,  which otherwise also hinge so as to stow vertical in the wake for entry,  and afterward deploy to about 45 degrees off vertical,  for aerodynamic flight.  Pitching tail surface leading edges together up-and-down provides pitch control,  pitching them opposite provides forces that affect both yaw and roll,  requiring different amounts from each fin to properly allocate the yaw and roll effects,  as influenced by the high wing.  The wing can be a subsonic airfoil,  and is a straight wing of fixed geometry,  effectively high-wing-mounted.

Unlike the space shuttle,  but like the other folding wing concept in ref. 1,  this craft enters the atmosphere at essentially 90 degrees angle-of-attack (AOA) and zero roll angle.  The flat shape of its belly provides significant lift with small changes in pitch,  so that aerodynamic lift can be used to fly the desired entry trajectory (a technique well-proven with Apollo and Space Shuttle).  The intent here is to return with little-to-zero payload and near-zero propellants,  having only a small allotment for the attitude thrusters. The heavier the return payload,  the higher the landing speed. 

The craft comes out of hypersonics at about Mach 3 at very high altitude (near or above 100,000 feet) still dead-broadside to the airstream.  Closer to Mach 1,  the V-tail and attitude thrusters put the nose down streamline,  and a drogue chute deploys,  that is sized for about the same drag as that of the entry configuration dead-broadside (both are sufficient to reach subsonic terminal velocities).  Once streamwise and subsonic,  the pivot wing is deployed and the drogue chute discarded.  At this point,  the craft becomes a straight-wing V-tail glider,  handling very much like any subsonic airplane,  just flown dead-stick (with maybe just enough propellant still on board,  to support a go-around on the main rocket engine).


Figure 3 depicts the spreadsheet worksheet used to rough-out the basic weight statement and characteristics of the design,  as a function of overall length and selected “wing loading” values.  User inputs are highlighted yellow.  Most (but not all) significant outputs are highlighted blue or green. 

The first data group is “engine”  and gives delta-vee capability for given specific impulse (Isp) and the mass ratio values that come from the weight statement.   The engine and thrusters should do as well or better than the 300 sec of Isp shown,  and the mass ratio-derived ideal delta-vee value exceeding 2.5 km/s at 300 sec is quite attractive for a variety of possible missions.  One must hold in reserve at least the deorbit burn and an allotment for the attitude thrusters.

The second data group is “inert weight fraction”,  and is just an organized way to guess a realistic inert weight fraction,  based crudely upon what the structure must do.  These methods are described more in ref. 2,   as part of a larger methodology for estimating performance of rocket stages. The result here of 20% should be quite realistic.  Bear in mind that operational military and commercial airplanes here on Earth usually run near 40% inert,  where that category plus propellant fraction,  plus payload fraction,  must sum to 100%.

The third data group is “payload”,  and shows 200 kg for two men,  a quarter ton for their suits and life support,  and 5 tons max in the cargo bay.   The user inputs a payload fraction (in this case 20%),  and the remainder is the propellant load.  That leads immediately to the weight at ignition,  and thus the vehicle weight statement in the fourth data group. 

This spreadsheet analysis simply presumes that the body planform area is 0.8*length,*width,  and that the body cross section area is 0.8*width*height.  It also presumes the chord of the pivot wing is 1/3 the body with,  and that the span of the pivot wing is ¾ the body length.  That leads to a fixed wing area to body planform area ratio of 31.25% or thereabouts.  The user inputs the ratios of body width/length and body height/length,  representing fineness ratio proportions (both 16%,  or 6:1,  here).

There is a user input for the cargo bay length/body length proportion,  that eventually leads to a cargo specific gravity,  under the assumption that cargo fills 100% of the available volume.  I set that for a specific gravity 1/3 that of water,  to represent bulky,  lower-density items.

In the “aerosurfaces” group,  one sets the tail proportion and the entry “wing loading” of burnout weight/body planform area,  along with a hypersonic drag coefficient for the intended shape,  yielding an entry ballistic coefficient.  That gets used in the entry ballistic analysis.

A representative max wing loading for airplane-like flight with the wing deployed,  would be burnout weight divided by the sum of body planform area plus wing planform area.  That is because,  while the body lift curve slope is low,  the body planform is the larger area,  and thus a significant contributor to lift.  This applies,  as a user-input max lift coefficient,  to the landing speed calculation group.

The “proportions” group is where one inputs the body length,  its width and height ratios,  and the cargo bay length fraction.  This is where the various areas and volumes get estimated,  along with the cargo specific gravity,  and the weight/area loadings. 

It is necessary to iterate to closure here.  The weight/area outputs from “proportions” must match those derived from your input weight/area loading in “aerosurfaces”.  You have “body length L, m” and entry loading “Wbo/Abdy,  psf” as your values to change until you achieve convergence.  The higher the Wbo/Abdy figure,  the higher the ballistic coefficient will be,  and the higher the landing speed will be. 

I found that guessing max lift coefficient for landing was too unreliable.  So I added a worksheet to estimate this more explicitly from the “proportions” outputs.  This is the “landing” worksheet,  shown in Figure 5.  That worksheet produces the “right” stall lift coefficient to use in the “landing” group of the “rough-out” worksheet (and then you will see the landing speed estimates agree between the two worksheets).  I also added a worksheet to estimate the size of the drogue chute,  shown in Figure 4.

The landing worksheet estimates lift curve slope for the very low aspect ratio “wing” that is the body,  from an equation obtained from ref. 3,  the Hoerner – Borst lift book that is analogous to Hoerner’s “drag bible” (ref. 4).  This would be equation 9,  located on page 17-3 of chapter 17 in Hoerner and Borst (ref. 3).  Low aspect ratio wings inherently have very low values of lift curve slope. 

The only additional inputs to the “drogue” worksheet,  beyond outputs from “proportions” in the “rough-out” worksheet,  are the parachute subsonic drag coefficient and the end-of-hypersonic (Mach 3) point from the entry trajectory analysis.  The drogue is sized to provide the same drag and subsonic terminal speeds at 60,000 feet and 20,000 feet altitudes,  as the body falling dead broadside with the wing stowed.  The end-of-hypersonics point is just a check:  need 100,000 feet (30 km) or higher.

Entry Analysis

The entry trajectory analysis is a very simplified 2-D Cartesian model from the mid-1950’s that was used for warhead entry analysis.  It is based on a scale-height model of approximating density versus altitude,  and presumes a constant trajectory angle in 2-D Cartesian space.  To use it for estimates here requires that one fly a trajectory always oriented at a constant angle to local horizontal around the Earth. The range wraps around the Earth. The analysis is attributed to H. Julian Allen,  and is described in ref. 5.

In my spreadsheet version of the old model (image given in Figure 6),  there are user inputs for the vehicle model,  the scale height model,  the entry interface conditions,  and the stagnation heating model.  The vehicle model requires a ballistic coefficient and a “nose” radius (really the heat shield radius of curvature).  The entry interface model is altitude (for LEO,  140 km),  velocity (for a surface-grazing ellipse,  7.742 km/s),  and path angle below horizontal (for that same surface-grazing ellipse,  2.35 degrees) at entry interface conditions.  The final vehicle model achieved here has a ballistic coefficient of 439 kg/sq.m,  a length of 17.45 m,  and a heat shield radius of curvature of 27 m. 

Use of this spreadsheet model requires inserting a row of cells to represent the altitude and results for a speed corresponding to Mach 3 end-of-hypersonics (in this case about 1 km/s).  One iteratively adjusts the altitude so that a 1 km/s speed shows in the table.  One uses data from start (at entry interface) to only end-of-hypersonics for creating plots.  The model does not apply once speed is no longer hypersonic.  That is why you stop at the Mach 3 point for bluff bodies.  All of this is shown in Figure 6.

As also shown in Figure 6,  I added two things at the bottom.  One picks off the metric-units peak heating rate (wherever it occurs),  and the integral of heating at end-of-hypersonics,  and inputs them to a US customary units converter.  Next to this,  one uses an input emissivity and the converted peak heating rate to estimate the surface temperature at peak heating,  under the assumption that reradiated cooling power equals the convective heating power.  This would apply to a refractory (non-ablative,  and not-liquid-cooled) heat shield. I converted to US customary,  because that is the units of the radiation constant that I know,  and those are the materials-limitation properties that I know.

It is easy enough to highlight where the instantaneous gees exceed 5,  determine the peak gees,  and use the time scale to estimate how long the high-gee interval is,  that must be endured.  It is also easy to determine whether hypersonics is over at (or above) 100,000 feet (about 30 km),  as it should be for the rest of the concept’s descent sequence.

It is easy to plot the data from the entry spreadsheet analysis.  These are given in Figures 7-10.  Figure 7 is a range versus altitude plot,  illustrating the constant angle trajectory in the 2-D Cartesian model.  Both slant range down the trajectory,  and horizontal range along the ground,  are shown.  At only 2.35 degrees different,  the two curves fall on top of each other in this plot.  Horizontal range wraps around the curvature of the real Earth,  and the constant descent angle must be treated as constant with respect to local horizontal as one proceeds along the trajectory.

Figure 8 shows velocity versus altitude.  It starts at 140 km altitude and orbital speed,  and ends just under 35 km at 1 km/s (just about Mach 3).  Not much deceleration happens at all,  until one descends to about 60-70 km.  From there deceleration quickly grows to high values at about 40-50 km and below.

The two key kinematics results are shown in Figure 9.  These are velocity versus time,  and deceleration gees versus time.  Peak gees is about 6.22,  at 326.9 sec,  where the velocity is 3.820 km/s at 42.5 km/s altitude.  The time above 5 gees is only about 30-40 sec.  The peak and duration of the high-gee exposure is feasible for a seated astronaut,  to be endured in the “eyeballs-down” direction.   

Figure 10 gives the time history of the convective stagnation heating rate as q, W/,  and its time-integral accumulation of energy Q, KJ/  Peak heating rate occurs a little earlier than peak deceleration gees,  being 26.75 W/ at time from entry interface 270.8 seconds,  altitude 55 km,  and velocity 6.824 km/s. 

End of hypersonics (at just about Mach 3) occurs at 412.6 seconds from entry interface,  altitude 34.78 km,  and speed 0.999 km/s. Looking at the heating rates,  a good guess says the plasma-induced radio blackout is about 3 minutes long,  as expected.  The whole entry is a bit over 6 minutes from interface to end-of-hypersonics.  These numbers are very,  very realistic,  despite the oversimplified analysis method.  It looks like my misuse of the old warhead entry analysis is justified for capsule-like entry.


The first time through,  I used a shorter (13.5 m) vehicle with a higher ballistic coefficient (732 kg/sq.m) and a 27 m heat shield radius,  which had an infeasibly-high max-load landing speed near 300 mph,  and came out of hypersonics at about 31 km.   It showed a peak surface temperature of 2541 F,  too high for an alumino-silicate refractory heat shield material (shrinkage cracks form above 2350 F upon cooldown). It was at this point that I added the drogue and landing worksheets to the rough-out worksheet,  in order to better optimize this design concept.

The final form is a 17.45 m long craft,  with a lower ballistic coefficient of 439 kg/sq.m,  and the same 27 m heat shield radius of curvature.  That reduced peak gees and peak heating,  reduced the heat shield temperature to a barely-feasible 2345 F,  raised the end-of-hypersonics to nearly 35 km,  and lowered the max-load landing speed to about 217 mph at sea level stall (under 200 is desired). 

These were computed for the full burnout weight loaded onto the body planform or total planform areas,  meaning flying back with full cargo.  Flying back with reduced cargo will lower heat shield temperature and landing speed.  That improves the feasibility of this roughed-out design.

Having a stagnation-point surface temperature under 2350 F is very important if one wishes to use a low-density alumino-silicate ceramic as a refractory,  re-radiation-cooled heat shield.  This need not be the logistical nightmare that Space Shuttle tiles proved to be.  There are other materials that could be developed with the applicable characteristics,  and providing the redundant retention that shuttle tiles lack.   See Ref. 6 for a very experimental material that was a fabric-reinforced low-density ceramic. 


What this analysis shows,  very much like that in ref. 1,  is that this sort of small spaceplane is within the realm of engineering feasibility.  The pivot-wing design would be easier to implement as entry heat-protected than the folding-wing design of ref. 1.  All-in-all,  borrowing the Russian “Baikal” pivot-wing approach is an improvement,  provided that it is deployed subsonically to reduce aerodynamic deployment loads.  It is limited in how much wing area can be feasibly added in a dorsal-only mount. 

The craft as-sized is 28.5 metric tons at fully-fueled,  fully-loaded ignition.  Its body is 17.45 m long,  and about 2.8 m wide,  and 2.8 m high.  Only the tail fins stick out to the dorsal side.  It might actually fit within the standard payload shroud of a Falcon-Heavy booster rocket,  and certainly falls within the payload weight limit for that rocket to recover its first stage cores.   If SLS ever really flies,  it could certainly carry one (or more) of these craft.

About 2.4 km/s worth of on-orbit delta-vee makes a great many missions possible with a craft like this,  once delivered to eastward LEO by a suitable booster.  That is over 15 degrees worth of plane change,  or very nearly to Earth escape velocity.  Multiple orbit visit locations in one mission become possible,  a very attractive characteristic indeed.

Having a small airplane with an easily-stowed wing as the returning spacecraft,  makes possible picking this up with something like a C-130,  and flying it to any suitable launch site.  Having a low-density alumino-silicate heat shield makes a long service life between repairs feasible,  as long as it does not take the form of bonded tiles,  no two of which are alike,  as with the Space Shuttle.  Thus logistics are greatly simplified.  That makes turnaround time shorter,  and flying costs lower. 

Final Comments

This is not a real design study.  It is only a configuration rough-out and basic feasibility analysis.  It shows that such a design really is feasible,  that much is certain.  Little else.

But,  the reader is cautioned to not take this work to be more than it actually is!  I ran no dimensions other than some overall ones,  selected no materials,  conceived and weighed no structural components,  and I did not do any detailed heat transfer,  air loads,  or stress-strain analysis.  Most of the parts for which those kinds of design analyses are appropriate,  have not been designed at all.

This pivot-wing design approach offers a much easier-to-heat-protect method of mounting the stowable wing for reentry.  It is strongly limited in how large that wing can be,  relative to the rest of the airframe.  Thus it inherently suffers from high landing speeds.

The earlier folding-wing concept can have a much larger wing relative to the rest of the airframe,  which means it can have a much lower landing speed.  That offers any airport as a landing field,  even if the main skid gear is retained (wheels add more weight).  The problem is heat-protecting the hinge joint,  especially if a low-wing design.  That is not impossible,  just quite difficult.


#1.  Johnson,  G. W.,  “A Unique Folding-Wing Spaceplane Concept”,  article posted on,  dated March 2,  2013.

#2. Johnson,  G. W.,  “Back-of-the-Envelope Rocket Propulsion Analysis”,  article posted on,  dated August 23,  2018.

#3. Hoerner,  S. F.,  and Borst,  H. V.,  “Fluid Dynamic Lift”,  published by Mrs. Liselotte A. Hoerner,  1975.

#4. Hoerner,  S. F.,  “Fluid Dynamic Drag”,  self-published by the author,  1965. 

#5. Johnson,  G. W.,  “BOE Entry Model User’s Guide”,  article posted on,  dated January 21,  2013.

#6.  Johnson,  G. W.,  “Low-Density Non-Ablative Ceramic Heat Shields”,  article posted on,  dated March 18,  2013.

 Figure 1 – Vehicle Concept for Pivot-Wing Spaceplane

 Figure 2 – Operations Concept for Pivot-Wing Spaceplane

 Figure 3 – Image of Spreadsheet Worksheet Used For Vehicle Rough-Out Calculations

 Figure 4 – Image of Spreadsheet Worksheet Used to Size the Drogue

 Figure 5 – Image of Spreadsheet Worksheet Used for Landing Speed Calculations

 Figure 6 – Image of “BOE Entry” Spreadsheet Worksheet Used for Entry Estimates

 Figure 7 – Spreadsheet-Generated Plot of Entry Trajectory Shape

 Figure 8 -- Spreadsheet-Generated Plot of Entry Trajectory Deceleration Trend

 Figure 9 -- Spreadsheet-Generated Plot of Entry Trajectory Kinematics

Figure 10 --  Spreadsheet-Generated Plot of Entry Trajectory Heating

Monday, April 1, 2019

Something Added to the House

We recently got a historical marker on our house.

The first photo is of our front porch,  near the front door.  You can see the big metal Texas star,  which matches one on the farm shop across the driveway.  The new historical plaque is on the front wall just left of the metal Texas star.

The second photo is a closeup of that historical marker,  so that you can actually read it.  Enjoy. 

The main takeaway here is that historical and hysterical are spelled (and pronounced) very similarly.