The question at hand is: how feasible is a single-stage
spaceplane to orbit and back, that has
airliner-like characteristics in order to lower ticket costs for
passengers, or per-pound costs for cargo
(or any other effectiveness criterion, including the difficulty and cost of
military missions). The notion behind
this question is that until spaceships can be operated like airplanes, costs of access to orbit will simply be too
high to do anything but the most critical tasks there, the ones for which cost is ignored.

To answer the question at hand I did a little approximate
bounding calculation. I used the weight
statement of a well-proven, long-serving
airliner as the weight statement for my spaceplane. I assumed a vertical launch, non-lifting ballistic fast ascent to minimize
gravity and drag losses at about 10% of the orbital speed to be achieved. (If you stay low at very high speed, the drag losses can easily exceed 100%-300%
of orbit speed.) I also assumed
on-orbit, de-orbit, and go-around-at-landing propulsion weights to
be part of the inert weights on ascent (!!!!).

Some may argue with my using the high inert weight fraction
of the airliner for the spaceplane. But
I would remind them that if you want true airliner characteristics, then the vehicle must be able serve for about
half a century and about 40,000 landing/take-off cycles, without a single major airframe rebuild. That’s what airliners do, and their airframes not subjected to the abusive
loads that a spacecraft must endure. We
are talking about an aluminum airframe whose entire exterior must be protected
by some sort of reusable heat shield (which must serve just as long without a
rebuild).

*The 5-10% inert fractions of rocket stages are just entirely inappropriate assumptions to make for a winged spaceplane.*
The analysis uses the rocket equation with a corrected
delta-vee requirement. I used 25,000
ft/sec as the velocity to be achieved (maybe 26,000 is better, but so what?). This is for a low Earth orbit eastward at no
more than about 23 degrees inclination.
Orbital altitude might be around 100-300 statute miles.

I used customary US units for this; metric conversions for mass in lbm (usually
the meaning of weights in lb) are 2.205 lbm = 1.0 kg. Conversions for thrust: 1.0 lb = 4.45 Newtons. Weight (mass) ratios and Isp, sec need no conversion. For lengths,
1.0 meter = 3.2808333 feet. I did
approximate the rocket exhaust velocity as Isp x standard acceleration of
gravity. 1 statute mile = 1.609 km.

The situation and aircraft data that I used are given in
Figure 1. The spaceplane specific
impulse (Isp) requirements shown there are to be interpreted as an average for
the entire ascent trajectory. Note that
the max cargo weight and max fuel capacity of the Boeing 747-100 airplane
cannot both be had, simultaneously. The gross weight limitation restricts the sum
of these to a fixed amount shown in the figure.

I went ahead and used these limitations to figure my
spaceplane at max payload and at max fuel load.
I solved the rocket equation for a given mass ratio and theoretical
delta-vee, for the exhaust velocity
required to accomplish the mission, and
then converted that to a trajectory-averaged specific impulse (Isp)
requirement. At modest
acceleration, you leave the air at about
Mach 2 / 130,000 feet conditions, still
near vertical. The depression to
horizontal and acceleration to high speed occurs exoatmospheric.

There is a thrust greater than weight requirement for
vertical takeoff that combines with a diameter limit, into a frontal thrust density that must be
equaled or exceeded in order to lift off.
Later in the trajectory, because
the ascent is still near-vertical,

__thrust minus drag__and that same diameter combine so that the same frontal__net force__density must still be exceeded in order to continue climbing. Those estimates are also given in the figure.Figure 1 – The Data Used for the Bounding Analysis

I did not even try to estimate drag data. But,
on a frontal cross section area basis (not wing planform area
!!!!), it would be very hard indeed to
imagine any shape with a drag coefficient averaging less than 0.4 across the
speed range from launch to atmospheric exit at around Mach 2-ish. Drag is a very significant force, especially around Mach 0.9 to 1.3
(transonic). At Mach 1 and 45,000 ft
conditions, that would be 5000-6000 lb
of drag at the very least, even without
considering that in the real world very few drag coefficients would be under
1.2 (not 0.4) at Mach 1 speeds.

*The drag could easily be 3-4 times larger than those numbers.*
It is very important to understand that there are

__both__specific impulse__and__frontal thrust density requirements that simultaneously must be met, in order to achieve results in this scenario. These have to be met on a trajectory that begins at zero speed, vertical, at sea level, and that leaves the sensible atmosphere at about Mach 2 (2000 ft/sec), still near-vertical, at around 130,000 feet or so.
Trajectory
averaged Isp, sec

>1469/min
payload

>4002/max payload

Launch
frontal thrust density, psf

>3900/min
payload

>3900/max payload

M=1 @
45 kft net force density, psf

>3900/min
payload

>3900/max payload

So, what are the
possible propulsion concepts, and what
are their characteristics, as expressed
in these terms?

**That excludes “Star Trek” warp and impulse drives, and other similar things, for which there exists no science. The list is:***For my bounding calculation, I looked at technologies we actually have, and at technologies we don’t actually have, but which we could actually develop.*
Chemical
rocket propulsion (as demonstrated, not
theoretical things which proved impossible)

Nuclear-thermal rocket propulsion
(including both solid and gas core concepts)

Chemical
airbreathers (ramjet, gas turbine, and scramjet)

Nuclear
airbreathers (nuclear scramjet)

Nuclear
pulse (explosion) propulsion (included with the rocket data as “rocket-like”)

Figure 2 contains the typical characteristics of three common
chemical rocket systems, the projected
characteristics of multiple nuclear thermal rocket concepts as best we know
them, and the typical characteristics
quoted for nuclear pulse propulsion as it was proposed circa 1959 during
Project Orion. There are all the rocket
reaction propulsion concepts that we have,
aside from the extremely low-thrust electric concepts, which are clearly not candidates for this
application.

The chemical rocket systems have the thrust density to take
off vertically and accelerate upward,
but they lack the required specific impulse capability by a very large
margin. The one nuclear thermal rocket
for which we have real test data likely cannot meet the thrust density
requirement to take off and climb due to its low engine thrust/weight ratio, plus,
it lacks the specific impulse capability to meet the needs of the low
payload fraction case.

The gas core nuclear thermal rocket concepts are exactly
that: concepts. None has ever been built and tested. So the data are just best guesses. These concepts very likely have much better
engine thrust/weight ratios, so that
frontal thrust density requirements might be met, as long as no waste heat radiator is
required. The closed-cycle gas core
“nuclear light bulb” engine comes close to meeting specific impulse
requirements with a clean exhaust for the low payload fraction case. The open-cycle gas core engine definitely
satisfies the impulse for the low payload fraction case, but has a radioactive exhaust plume. None meet requirements for the high payload
fraction case, for which the economics
would be more feasible.

Only nuclear pulse propulsion meets the impulse requirements
and the frontal thrust density requirements,
and for both cases: low and high
payload fraction. There are two very
serious downsides: the vehicle must be
very large (over 5000 tons at launch,
preferably over 10,000 tons), and
the “exhaust stream” is quite literally a series of nuclear explosions in the
atmosphere, starting with a surface
burst. Not only is there radiation
released, there is a very destructive
EMP.

Therefore, of the
rocket and rocket-like concepts, only
the “nuclear lightbulb” engine might possibly serve, and then only if the weight statement can be
adjusted to make 1300 sec Isp feasible.
This will be a difficult design to do,
without a lot of margin, and with
a reduced payload fraction that makes the economics more difficult. Such a weight statement might be ascent
inerts 0.40, ascent propellant
0.50, and payload 0.10, remembering that “ascent inerts” includes
on-orbit, de-orbit, and landing go-around propulsion that is not
the nuclear ascent engine.

The airbreathers are summarized in Figure 3. At first glance, the Isp’s of the ramjet and the gas turbines
looks attractive, but upon further
inspection the frontal thrust densities are clearly not feasible. Further,
the impulses are only attractive in a narrow band of speeds. Variable inlets do not change this.

The ramjet depicted is a supersonic design with a minimum
operating Mach number of 2, which
happens just as the vertically-launched spaceplane is leaving the sensible
atmosphere somewhere above 100,000 feet.
A subsonic design that could ignite somewhere around Mach 0.7 and burn
to about Mach 2-2.5 usefully, but would
have about half to two-thirds the listed impulse capability, which renders it infeasible. At altitude,
the frontal thrust densities are also completely infeasible, unless these were staged-off strap-ons very much
larger than the spaceplane’s fuselage.
It is staging we are trying to get away from here!

Neither gas turbine design has the frontal thrust density to
take off vertically at all, so this kind
of propulsion would also have to be gigantic strap-ons that get staged
off. Not feasible by definition.

**They might well be useful for a horizontal-takeoff, depressed-trajectory design, at the cost of enormous drag losses. But that is a different scenario!**

*The basic message here seems to be that the airbreathers are very probably not very useful for vertically-launched fast ascent trajectories if no staging is allowable.*
Figure 3 – Characteristics of Existing Airbreather Systems
(Ramjet and Gas Turbine)

A nuclear ramjet is no better: although its effective specific impulses are higher
(you need to look at air specific impulse instead of fuel specific impulse to
compare fairly, the fuel air ratio
embodied in the chemical ramjet data is .074),
the frontal thrust density is no better than the chemical ramjet. It may well be worse due to the impact of a
very heavy core on engine sizing.
Plus, its exhaust stream is
intensely radioactive, based upon the
Project Pluto nuclear ramjet ground tests decades ago.

**The impulses look marginally-attractive in a narrow range of speeds, but the frontal thrust densities at stratospheric altitudes are infeasible. Going nuclear does not help the fundamental incompatibility of a very high-speed airbreather on this trajectory. Where the vehicle reaches these speeds, there is no air!**

*These Mach numbers are simply incompatible with the vertical launch scenario.*
Figure 4 – Guessed Data for Supersonic-Combustion Ramjet
(Scramjet) Systems (Chemical and Nuclear)

So, there are only
two known propulsion concepts that could support a vertically-launched single
stage spaceplane with operating characteristics of an airliner. One is the “nuclear light bulb” version of
the gas core nuclear thermal rocket,
which likely could support payload fractions around 5-10%, if it actually existed, which it does not. What that really says is that this “nuclear
light bulb” engine ought to be a major development priority. It is not.

The other is nuclear pulse propulsion, which would only work in vehicle sizes far
beyond anything ever before constructed,
and at the social cost of uncontained nuclear explosions in the
atmosphere. The EMP is probably actually
more dangerous than the radioactivity,
but the radioactivity will be the political killer of this idea.

*So that leaves only the “nuclear light bulb” as a feasible propulsion for this kind of spaceplane. But for vertically-launched fast ascent, this looks to be entirely feasible. Which means that its mythical engine should be a high-priority development.*
The only other approach to a single stage spaceplane to
orbit would be a horizontally-launched craft with a depressed trajectory to
make airbreathers feasible for a small portion of the ascent, trading their impulse advantage against the
enormous drag losses of flying fast down in the atmosphere. The last program to attempt that approach was
X-30, which failed. (It is very difficult to do realistic
estimates for that kind of trajectory,
unlike this scenario.)

PS: The ramjet data were obtained with my latest version of the high-speed range cycle codes for sizing and performance.