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.**Once subsonic, these surfaces could more easily be deployed for an airplane-like landing.***By folding the aerosurfaces that way, the dead-broadside forces that would rip the aerosurfaces off, could be avoided.***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 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.*
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.

**Concept**

**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 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).**

*The craft is a small spaceplane launched with stowed wing using an appropriate two-stage rocket booster.***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.**

*Figure 1 shows the vehicle to be a high-wing airplane with a butterfly tail and a non-circular cross section.***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 cargo bay is near the middle, with the center of gravity and the wing pivot, so that changes in payload require minimal trim adjustments.***Simple is more reliable.**

*the same propellant supply serves both the main engine and the attitude thrusters,*__with hypergolic ignition__.
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.***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.**

*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 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).

**Sizing**

**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.

**The user inputs the ratios of body width/length and body height/length, representing fineness ratio proportions (both 16%, or 6:1, here).***That leads to a fixed wing area to body planform area ratio of 31.25% or thereabouts.*
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.

**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.**

*It is necessary to iterate to closure here.*

*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 end-of-hypersonics point is just a check: need 100,000 feet (30 km) or higher.***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.**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.**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.***This would apply to a refractory (non-ablative, and not-liquid-cooled) heat shield.*
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/sq.cm, and its time-integral accumulation of energy Q, KJ/sq.cm. Peak heating rate occurs a little earlier than peak deceleration gees, being 26.75 W/sq.cm 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.

**It looks like my misuse of the old warhead entry analysis is justified for capsule-like entry.***These numbers are very, very realistic, despite the oversimplified analysis method.***Feasibility**

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.**This need not be the logistical nightmare that Space Shuttle tiles proved to be.**

*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.***See**

*There are other materials that could be developed with the applicable characteristics, and providing the redundant retention that shuttle tiles lack.***Ref. 6**for a very experimental material that was a fabric-reinforced low-density ceramic.

**Conclusions**

What this analysis shows,
very much like that in ref. 1, is
that

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

**If SLS ever really flies, it could certainly carry one (or more) of these craft.***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.*
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 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.**

*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.***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.

**References**

#1. Johnson,
G. W., “A Unique Folding-Wing Spaceplane
Concept”, article posted on http://exrocketman.blogspot.com, dated March 2, 2013.

#2. Johnson, G. W.,
“Back-of-the-Envelope Rocket Propulsion Analysis”, article posted on http://exrocketman.blogspot.com, 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 http://exrocketman.blogspot.com, dated January 21, 2013.

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

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