A TECHNICAL ANALYSIS OF SSTO VEHICLES
by
Steven S. Pietrobon
Small World Communications
6 First Avenue
Payneham South SA 5070
Australia
steven@sworld.com.au
Submitted to sci.space.tech 7 February 1994
Revised 21 February 1994
ABSTRACT
A technical analysis of rocket based Single Stage to Orbit (SSTO) vehicles is
described in the context of minimising the cost of deploying payloads to low
Earth orbit (LEO) or geosynchronous transfer orbit (GTO). We show that liquid
Hydrogen/liquid Oxygen (H2/O2) appear to be the best propellant combination in
comparison to lesser performing but denser propellants. Also, we show that
there is considerable cost advantages in having the SSTO place its payload into
a trajectory just short of reaching orbit. A very small second stage then
places its payload into the required low Earth orbit (LEO) or a larger second
stage places its payload into geosynchronous transfer orbit (GTO). The SSTO
vehicle makes a single near-orbit around the Earth, landing at the original
launch site after deploying the payload.
1 INTRODUCTION
There has been much discussion about SSTO launch vehicles as the next stage
beyond the current expendable and partly reusable launch vehicles. Their
advantages have been listed as:
Fully reusable
No assembly required
Low infrastructure required for launch
All these factors are expected to lead to lower launch cost per kilogram of
payload into orbit.
In order to develop SSTO several technical factors need to be overcome, namely
low weight structures and high performance and reliable engines that can be
used many times before having to be refurbished.
In this paper we make a simple technical analysis of SSTO. The SSTO vehicle is
designed so as to minimise the costs of delivering a payload to LEO or GTO.
additional missions such as servicing, crew transfer, and payload return are
not considered as priorities. However, the design does not necessarily preclude
these missions (as with any type of launch vehicle). All data that is used
comes from existing published data. In the first section we analyse the
traditional SSTO concept where the SSTO vehicle places its payload into orbit
and then returns to Earth. We do this for a number of propellant combinations.
In the second section we analyse the concept of the SSTO vehicle going into
an orbit with an apogee of 200 km and a perigee close to sea level, a near
Earth orbit (NEO). The SSTO vehicle releases its payload in NEO, re-entering at
the completion of its orbit and landing at the original launch site. A very
small second stage then places its payload into LEO. It is shown that the SSTO
vehicle dry mass is reduced by nearly 44% over a traditional design. We also
study the requirements for placing a payload into GTO with non-high performance
H2/O2 engines. A 29.5% reduction in SSTO vehicle dry mass was found to be
achieved if extenable nozzles are used.
2 TRADITIONAL SSTO ANAYLSES
We have the standard rocket equation
v_d = v_e ln (m_i / m_f)
where
v_d = change in speed (m/s)
v_e = effective exhaust speed (m/s). This is the specific impulse in seconds
times the standard acceleration of gravity at the Earth's surface
(9.80665 m/s). We prefer to use v_e instead of specific impulse as it
gives a better feeling of the performance of a rocket engine (it also is
independent of Earth). v_e is very close to the actual exhaust speed of a
rocket engine.
m_i = initial mass (kg or t (1 t = 1000 kg))
m_f = final mass (kg or t)
We can break m_i and m_f into
m_i = m_p + m_s + m_c
m_f = m_s + m_c
where
m_p = propellant mass
m_s = structural mass (engines, structure, and tanks)
m_c = cargo or payload mass
For each stage i let
r_i = exp[v_d_i / v_e_i]
where
v_d_i = change in speed for stage i
v_e_i = exhaust speed for stage i
There are four stages that we are considering. Launch, orbital maneuvers before
and after cargo release, and a powered landing. For launch we assume that 9300
m/s is required (this includes both gravity and drag losses). For orbital
maneuvers we use 100 m/s before cargo release and 150 m/s after cargo release
(including the deorbit burn). Note that the U.S. space shuttle has a 365 m/s
capability (our 250 m/s is more modest). We have assumed full vacuum exhaust
speeds for orbital operations.
For landing, the terminal speed for a Delta-Clipper style SSTO is about 100
m/s. Deceleration will require a v_d of 150 m/s to kill this speed at 30 m/s^2
(100 m/s for braking and 50 m/s gravity losses). An additional 200 m/s is
required to allow 20 s of hover time. This gives the total landing v_d = 350
m/s. We have assumed sea level exhaust speeds for landing.
The following table summarises these values and gives the r_i's for three types
of propellant combinations
H2/O2 Kero/O2 UDMH/N204
i profile v_d_i (m/s) v_e_i (m/s) r_i v_e_i (m/s) r_i v_e_i (m/s) r_i
-------------------------------------------------------------------------------
1 launch 9300 4286 8.7570 3180 18.6254 2991 22.4060
2 orbital 100 4441 1.0228 3295 1.0303 3099 1.0328
3 deorbit 150 4441 1.0344 3295 1.0466 3099 1.0496
4 landing 350 3677 1.0999 3020 1.1159 2795 1.1334
The vacuum exhaust speeds are taken from [1]. For H2/02 the Space Shuttle Main
Engine (SSME) values are used. For Kero/O2 the RD-170 (from the Zenit first
stage and Energia strap-ons) values are used. For UDMH/N2O4 the RD-253 (from
the Proton first stage) values are used. Each of these engines are the current
highest performing engines known for sea level to vacuum operation. The launch
exhaust speeds are 3.5% less than the vacuum exhaust speeds to take into
account the reduction of exhaust speed at sea level.
It can be shown that
m_c/m_s = (1/gamma - beta_s) / beta_c
where
gamma = m_s/m_p (mass ratio)
beta_c = r_1*r_2 - 1
beta_s = r_1*r_2*r_3*r_4 - 1
We make the assumption that gamma is constant. In reality this is not exactly
true as gamma usually decreases as the propellant mass increases (due to a
proportionally less area required for the increased volume of propellant).
Other parts of the SSTO are proportional to m_p, such as the engine mass (since
the required lift-off thrust is proportional to the launch mass which is mostly
propellant). As shown later, the engine mass is a large fraction (about 30%)
of m_s which offsets somewhat the effect of the tank size. The following table
gives the final performance figures.
Propellant beta_c beta_s gamma (%) m_c/m_s
-----------------------------------------------
H2/O2 7.957 9.190 7.9 0.436
Kero/O2 18.190 21.412 4.5 0.045
UDMH/N2O4 22.141 26.529 5.1 -
The values for gamma are taken from [2] and are the lowest mass ratios known
for each of the propellant combinations. The value for H2/O2 is for the SII,
the second stage of the Saturn V. The value for kero/O2 is for the Atlas
missile. The value for UDMH/N2O4 is for Commercial Titan III. All these values
are from the fifties and sixties and so can be expected to be improved upon
using modern materials. As can be seen, H2/O2 is clearly superior to other
propellant combinations. Despite its low density, the high exhaust speed more
than makes up for this disadvantage.
Let us now say that 7.9% is a bit low, how high can we go? Let us assume that
gamma = 0.1. This is a 26.6% increase over the gamma used above, which should
allow for the increase in mass due to the engines and thermal protection
system as well as provide additional margin for any weight increases (note that
modern materials will compensate for some of these mass increases). We have
that m_c/m_s = 0.1018. For m_c = 10 t, this gives an m_s = 98.2 t and an m_p =
982.3 t. The amount of propellant used in each stage is
m_p_4 = m_s (r_4 - 1) = 9.8 t (v_d_4 = 350 m/s check)
m_p_3 = m_s (r_3 - 1) r_4 = 3.7 t (v_d_3 = 150 m/s check)
m_p_2 = (r_2 - 1) (m_c + m_s r_3 r_4) = 2.8 t (v_d_2 = 101 m/s check)
m_p_1 = m_p - m_p_2 - m_p_3 - m_p_4 = 966.0 t (v_d_1 = 9301 m/s check)
3 NEAR EARTH ORBIT SSTO ANALYSIS
The basic idea behind NEO SSTO is that we try to minimise the delta-v to get
a payload to orbit, while still maintaining the philosophy of SSTO. To do this
the main SSTO vehicle is placed into a NEO of perigee close to sea level and
an apogee of 200 km. The SSTO vehicle does one orbit around the Earth before
re-entering and landing back at the launch site. No orbital maneuvers are
required. This immediately saves us 250 m/s (and as shown in the previous
section about 6.5 t of orbital propellants that need to be lifted).
We can also reduce the required delta-v of the first stage by about 50 m/s
since the SSTO vehicle can go into a lower initial orbit. Appendix 1 gives the
derivation of this. There are now only three stages to be considered (the
wasteful re-entry maneuver not being needed):
i profile v_d_i (m/s) v_e_i (m/s) r_i
-------------------------------------------
1 launch 9250 4286 8.6555
2 orbital 160 3060 1.0537
4 landing 350 3677 1.0999
We increase the required orbital velocity by 60 m/s to make up the shortfall
of the first stage with a 10 m/s margin (100+50+10 = 160 m/s). We will assume
that the Marquardt R-4D with a thrust of 490 N (MMH/N2O4 as propellants) is
used in the second stage [1]. We have that
m_c/m_s = (1/gamma - beta_s) / beta_c
where
gamma = m_s/m_p (mass ratio of SSTO)
m_s = structural mass of SSTO vehicle
m_p = m_p_1 + m_p_4 (propellant mass of SSTO vehicle)
r_2 (r_1 - 1)
beta_c = ---------------------
1 - (r_2 - 1) gamma_2
beta_s = r_1*r_4 - 1
gamma_2 = m_s_2/m_p_2 (mass ratio of second stage)
We shall assume that gamma_2 = 0.16 (a fairly large value for MMH/N2O4 since
the required amount of propellant is small). We will let gamma = 0.1 for the
SSTO. We thus have beta_c = 8.1365 and beta_s = 8.5202. Therefore m_c/m_s =
0.1819. This indicates that the structural mass of the SSTO vehicle can be
reduced by 44%! The propellant and structural masses are for an m_c = 10 t, m_s
= 55 t, and m_p = 549.8 t are
m_p_4 = m_s (r_4 - 1) = 5.5 t (v_d_4 = 350 m/s check)
m_c (r_2 - 1)
m_p_2 = --------------------- = 0.6 t (v_d_2 = 177 m/s check)
1 - (r_2 - 1) gamma_2
m_s_2 = gamma_2 m_p_2 = 0.1 t
m_p_1 = m_p - m_p_2 = 544.3 t (v_d_1 = 9245 m/c check)
As can be seen, the second stage is very small and gives much greater
flexibility in reaching higher orbits than a traditional SSTO vehicle can.
The total vehicle mass is 615.5 t (with weight of 6036 kN at sea level). This
requires at least five SSME's (1668 kN thust at 100% at sea level) for a
thrust to weight ratio of 1.38 (single engine out capability at sea level).
For landing the minimum thust required is 539 kN which is 32% of maximum
thrust of a single engine. The current minimum thrust for an SSME is 65%. Thus,
the SSME would need to be modified to operate at the smaller thrust level.
The mass of the five SSME's is 15.9 t, 29% of the mass of the SSTO dry mass!
A problem with the NEO trajectory is that the Earth moves by about 22 degrees
(about 2400 km at the equator) during one orbit. If the payload is launched
from an equatorial launch site into a 0 degree inclination only the range is
increased. The vehicle only has to travel a little further than if the Earth
wasn't moving. For payloads into a polar orbit, the vehicle has to deviate
to the east by 2400 km in order to reach the launch site. One solution to polar
launches is to launch at very high lattitudes. The distance moved on the
surface of the Earth is less during one orbit, decreasing the cross-range
requirement. Another way is to simply land 22 degrees west (or as close as you
can get to the launch site), and then make a short hop after refueling. Ideally
though, the full cross range ability would be best. The McDonnell Douglas
Delta Clipper SSTO [3] is specified to have a cross-range ability of 2575 km,
which is within the required cross-range for a NEO trajectory, indicating that
this is possible.
3.1 Geosynchronous Transfer Orbit
If the second stage is used to put a satellite into geosynchronous transfer
orbit (GTO) then v_d_2 = 2500 m/s (see Appendix). For m = m_c + m_s_2 + m_p_2
= 10.7 t we have
m_p_2 = m (1 - 1/r_2)
For the RL-10 H2/O2 engine we have v_e_2 = 4358 m/s and gamma_2 = 0.2 (say).
Then r_2 = 1.7747, m_p_2 = 4.7 t, m_s_2 = 0.9 t, and m_c = 5.1 t. This is more
than Ariane 4 (4.4 t), but less than Ariane 5 (6.8 t).
3.2 SSTO using Ariane 4 and 5 engines.
The above has assumed the use of SSME's which currently require refurbishment
after every flight. Less stressful engines are required to reduce the amount
of maintenance that needs to be performed after every flight. However, these
engines have a smaller exhaust speed. To compensate for this, the mass ratio
(gamma) has to be reduced (otherwise m_c/m_s becomes too small). If we reduce
gamma to 0.09 (from gamma = 0.1 used in the previous section) we can obtain a
reasonable m_c/m_s as will be shown. Compared to the S-II the increase in gamma
is now only by 13.9% (almost half of the 26.6% increase of the previous
sections). This implies that less mass margin is available in constructing the
SSTO vehicle.
i profile v_d_i (m/s) v_e_i (m/s) r_i
-------------------------------------------
1 launch 9250 4090 9.5986
2 orbital 2500 4372 1.7715
4 landing 350 3184 1.1162
The SSTO uses the HM-60 H2/O2 Vulcain engine (v_e = 4238 m/s reduced by 3.5%)
and the second stage uses the HM-7B H2/O2 third stage Ariane 4 engine. We assume
gamma_2 = 0.2. Thus beta_c = 18.0116, beta_s = 9.7140, m_c/m_s = 0.0776. For
m_c = 5 t, m_s = 64.5 t, and m_p = 716.2 t. We have
m_p_4 = 7.5 t (v_d_4 = 350 m/s check)
m_p_2 = 4.6 t (v_d_2 = 2520 m/s check)
m_s_2 = 0.9 t
m_p_1 = 708.7 t (v_d_1 = 9246 m/s check)
For 4.6 t of H2/O2 propellant (320 kg/m^3 density), a volume of 14.4 m^3 is
required which needs to be accounted for if the payload is placed between the
propellant tanks. Denser propellants could be used using the L7 MMH/N2O4 engine
from the second stage of Ariane V. This engine has a thrust of 27.5 kN, a mass
of 110 kg, and an exhaust speed of 3138 m/s (tests in 1988 indicate a potential
of 3246 m/s). The total mass into NEO is m = 10.5 t. The lower value gives r_2
= 2.218. From the previous section equation we have m_p_2 = 5.8 t. Assuming
gamma_2 = 0.15 (the same as for Ariane V), we have m_s_2 = 0.9 t and m_c = 3.8
t. This payload mass is probably not large enough for commercial operations. If
the better exhaust speed is used then r_2 = 2.1602, m_p_2 = 5.6 t, m_s_2 = 0.9 t
and m_c = 4.0 t. Again, this is probably not satisfactory. The alternative is
to increase the SSTO vehicle mass by 25% to have m_c = 5 t. The volume for the
propellants is about 4.7 m^3 (1200 kg/m^3 density). This is over three times
less than for H2/O2.
For a LEO payload the required delta-v is 150 m/s. We assume that the Leros 1
from Royal Ordnance is used. This motor has a thrust of 500 N, a dry mass of
3.8 kg, uses MON3 and hydrazine propellants, and has an exhaust speed of 3040
m/s. Thus r_2 = 1.0506 and from the previous section we have m_p_2 = 0.5 t.
Assuming gamma_2 = 0.16 we have m_s_2 = 0.1 t and m_c = 9.9 t.
The vehicle lift-off mass is 791.2 t. This would require 12 HM-60's (sea level
thrust of 770 kN) for a lift-off thrust of 9240 kN (a thrust to weight ratio of
1.19 with single engine out capability at sea level). The mass for 12 engines
is 15.6 t which is a significant fraction (24%) of the SSTO dry mass. The
minimum landing thrust is 633 kN, which is 82% of the thrust of a single HM-60
(which would have to be made variable in thrust).
3.3 SSTO with extendable nozzles
A way of improving the performance of SSTO vehicles is to use engines that have
extendable nozzles. For sea-level operations the engines have the skirts lifted.
For vacuum operations, the skirts are lowered, increasing the expansion ratio
of the engines and therefore the effective exhaust speed of the engine. Let
the vacuum response be the same as the HM-7B (v_e = 4372 m/s). We reduce this
by 4.5% to take into effect atmosphere operations. This reduction value was
calculated by assuming that atmosphere operations occur within the first 2500
m/s of flight and then vacuum operations for the remaining 6750 m/s. This gave
an exhaust speed of 3738 m/s for atmosphere operations (17% greater than sea
level exhaust speed). The effective exhaust speed for the whole flight was then
calculated using the new vacuum exhaust speed, which was found to be about 4.5%
less. Thus, v_e_1 = 4175 m/s, a 2% increase over the previous value used.
The new value of r_1 = 9.1666. This gives beta_c = 17.1067 and beta_s = 9.2318.
Thus for gamma = 0.09 we have m_c/m_s = 0.1099. This reduces m_s for a constant
payload mass by 29%. The new mass numbers for m_c = 5 t to GTO (with m =
10.5 t) are
m_s = 45.5 t
m_p = 505.5 t
m_p_4 = 5.3 t (v_d_4 = 351 m/s check)
m_p_1 = 500.2 t (v_d_1 = 9247 m/s check)
Total lift-off mass is 551.5 t which implies that 9 HM-60 engines are required
for single engine out capability. This gives a thrust to weight ratio of 1.28.
Total engine mass is at least 11.7 t (more would actually be required due to the
extendable nozzles), about 26% of the dry SSTO vehicle mass. The minimum landing
thrust required is 446 kN, 58% of the maximum value of 770 kN for a single
engine.
4 CONCLUSIONS AND DISCUSSION
SSTO is possible, but low weight structures are definitely required. H2/O2
appears to be the best propellant combination. It appears to be unwise to have
the SSTO vehicle perform orbital operations. Mass savings of the vehicle by up
to 44% can be achieved with a NEO trajectory. The final insertion of the payload
into LEO is achieved with a very small second stage. For GTO a larger second
stage is required. If lower performance but more reliable engines are used,
the restraint on obtaining low weight structures is even more important
(especially as the engine mass may be from 25% to 30% of the SSTO dry mass).
A further 29% decrease in vehicle dry mass could be achieved if extendable
nozzles are used.
If the payload is placed between the propellant tanks, the payload must be
deployed before apogee is reached (about a 30 minute window). This will require
relatively quick deploy mechanisms to open the payload doors and then release
the payload.
To minimise the vehicle mass, a single bulkhead may need to be used between the
propellant tanks (as in the SII). This implies that the payload will need to be
placed at the top of the vehicle with an expendable shroud. This has the
advantage that bulky payloads can be carried (especially if H2/O2 second stage
is used). Also, the payload can be immediately deployed at the end of the
SSTO burn. For a nose first re-entry, the attach points for the payload can be
made under doors which close after payload separation.
A disadvantage is that ground operations are increased, increasing the cost of
launching the payload. Also, if the vehicle cannot make orbit, the payload may
be lost during re-entry. Greater margins on the second boost stage may thus
be required to overcome this possibility. Other potential disadvantages are the
greater stresses placed on the upper tank and the large change in centre of
gravity on payload release.
For crewed missions, a capsule can be placed on top of the SSTO. A launch
escape system can then be easily included if desired. The capsule can provide
access to space stations and satellites without having to be concerned about
propellant boil-off and atmospheric drag which limits the on-orbit stay time.
The capsule can also provide the small number of satellite servicing and cargo
return missions that are required.
APPENDIX
For a circular orbit of altitude h above the Earth's surface the orbital
velocity is
v_o = R sqrt(g/(R+h))
where
g = 9.80665 m/s (the acceleration of gravity at the Earth's surface)
R = 6,367.5 km (the radius of the Earth)
For an altitude h = 200 km, we obtain v_o = 7781 m/s. For an eliptical orbit
we have
2g r_p 2g r_a
v_a = R sqrt(------------), v_p = R sqrt(------------)
(r_a+r_p)r_a (r_a+r_p)r_p
where
v_a = velocity at apogee
v_p = velocity at perigee
r_a = R + h_a = apogee radius at apogee altitude h_a
r_p = R + h_p = perigee radius at perigee altitude h_p
For perigee of h_p = 0 and and an apogee of h_a = 200 km we have v_a = 7721 m/s.
Therefore the required delta-v to go from the eliptical to circular orbit is
delta-v = 7781-7721 = 60 m/s. We reduce this to 50 m/s so that the perigee
altitude will be non-zero, giving some extra leeway for the SSTO vehicle to
reach the landing site. The extra 10 m/s raises the apogee speed to v_a = 7721
+ 10 = 7731 m/s. Rearranging the equation for v_a we obtain
R 1
r_p = (2g(-------)^2 - ---)^-1
v_a r_a r_a
Substituting h_a = 200 km and v_a into the above we obtain h_p = 34.2 km.
To reach geo-synchronous transfer orbit with an apogee altitude of h_a =
35,762 km and a perigee altitude of h_p = 200 km the perigee velocity is
v_p = 10,114 m/s. Therefore, the required delta-v at 200 km is 10,114-7721 =
2393 m/s. We increase this to 2500 m/s to ensure there is sufficient margin to
reach GTO (assuming an equatorial launch site).
REFERENCES
[1] A. Wilson, "Interavia space directory," 1989-90.
[2] M. Pouliquen, "Space transportation systems," International Space
University Space Engineering Core Lectures, Summer 1990.
[3] W. P. Blase, "The first reusable SSTO spacecraft for the exploration of
space and expansion of humankind into the Solar System," Spaceflight,
vol. 35, pp. 90-94, Mar. 1993.