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.