Staging Condition Effects on Optimal Trajectory Hypersonic TSTO Systems

Justin A. Richeson* and Darryll J. Pines† Department of Aerospace Engineering, University of Maryland, College Park, MD 20742-3015

The effects of staging Mach number and dynamic pressure on TSTO systems with optimal trajectories are investigated. LOX/LH2 second stage rocket orbiters were designed from specified staging points (Mach = 5-12.5, dynamic pressure = 0.1-100kPa) to a 185km circular orbit with a designated payload of 455kg (1klb), 11400kg (25klb), or 20tons (44klb). Airbreathing first stages were parametrically designed by initial mass ratio and their aerodynamic and propulsion capabilities were sized by the gross system mass. All ascent trajectories were optimized using NASA’s POST. A 27-37% decrease in 2nd stage mass was achieved for optimal staging between 3-10kPa at the cost of a 1st stage 15-30% increase in maximum flight Mach number and 40-60% increase in fuel fraction. An empirical staging parameter was also found to predict 2nd stage rocket mass for a given staging flight path angle and speed of sound. These trajectory-optimal TSTO systems will aid future engineers by quantifying the effects of various staging points over a wide design space.

Nomenclature a = speed of sound Ae = reference exit area Aw = reference wing area CL = lift coefficient CD = drag coefficient CT = thrust coefficient D = drag g0 = gravitational constant h = altitude Isp = specific impulse L = lift M = Mach number m = mass q = dynamic pressure T = thrust α = angle of attack ∆V = velocity increment ∆Vlosses = rocket total velocity loss correction εp = propellant fraction Γ = initial mass ratio γ = flight path angle subscripts 0 = initial 1 = first stage 2 = second stage f = final

* Graduate Research Assistant, Student Member, AIAA, e-mail: jariche@wam.umd.edu † Professor, Associate Fellow, AIAA, djpterp@eng.umd.edu

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AIAA/CIRA 13th International Space Planes and Hypersonics Systems and Technologies AIAA 2005-3245

Copyright © 2005 by Justin Richeson and Darryll Pines. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission.

i = inert p = propellant pl = payload sl = sea level

I. Introduction

M ORE than any rocket system, the design of hypersonic airbreathing vehicles is tightly coupled to its trajectory because of the extreme conditions in which they fly. The combined propulsion, structural, and control

constraints (among others) restrict vehicles to a narrow band of operability typically around 1atm,1 referred to as the “hypersonic corridor” (Fig. 1). Efficient, optimal acceleration though this region could substantially increase the achievable payload to orbit over a non-optimal trajectory. Therefore, it is important to identify optimal trajectories that exploit airbreathing access to space designs.

In particular, two stage airbreathing launcher/rocket orbiter systems and their optimal trajectories should be investigated for access to space missions. This is motivated by the following factors:

• The vast improvement of specific impulse in a first stage airbreather • The decoupling of a second rocket propulsion system (needed for orbit insertion) • The mass and energy savings associated with multi-stage systems As an example, the recent SpaceShipOne win of the X-prize combined these aforementioned advantages into a

subsonic airbreather and a small hybrid rocket to attain a suborbital mission profile. Similarly, Orbital Science’s Pegasus launch vehicle uses a subsonic airbreather / multistage rocket system to place small payloads into orbit.2 The DARPA Responsive Access, Small Cargo, Affordable Launch (RASCAL) program was designed to use a specialized turbine engine for the supersonic first stage propulsion of a reusable aircraft and two expendable solid rockets to quickly and cost effectively launch 50-75kg payloads into orbit.3

RASCAL and other two-stage-to-orbit (TSTO) designs also employ an unusual pull-up maneuver shortly before main-engine-cut-off (MECO) of the first stage and ignition of the second stage.4,5 This maneuver attempts to minimize the energy losses during transition between the low flight path angle airbreathing climb and the high γ ascent of the rocket stage. The optimal initiation of the pull-up, MECO, and second stage ignition are all relatively unknown. Moreover, the effect of vehicle sizing on these parameters has not been thoroughly investigated in the open literature.

The goal of this paper is to quantify the sensitivities of staging points for a large design space of TSTO systems. To limit the scope of this goal, a second stage cryogenic hydrogen/oxygen rocket with a fixed specific impulse and propellant fraction were used for all TSTO concepts. Liquid hydrogen/oxygen was preferred because its energy density is much higher than that of other rocket propellants. Even though the LOX/LH2 packing density lends itself to a larger vehicle, it has been shown that the improved efficiency outweighs the increased drag penalties.6 The rockets were then designed from a given staging Mach number and dynamic pressure to a 185km (100 nm) circular orbit with a fixed final payload. The trajectory was optimized by NASA’s POST and the rocket was resized to account for velocity losses. This step was repeated until no changes were made in the rocket mass or trajectory. Next, the gross, staged mass of the rocket was used to parametrically size the 1st stage airbreather. The first stage was flown on a constant 1atm dynamic pressure trajectory to a 3.25g pull-up acceleration ending at the prescribed staging condition. The staging flight path angle, velocity and altitude from the 1st stage trajectory segment were then used as the initial conditions for the 2nd stage and the rocket and its trajectory were re-optimized. The entire TSTO system was iterated until the 1st and 2nd stage vehicles and trajectories were “closed.” From these TSTO systems, figures of merit (Table 1) were calculated, and can serve as a baseline for future access-to-space designs.

1st Stage: Propellant M2nd Stage: Initia

Am

Table 1. TSTO System Figures of Merit ass Fraction Max Initial Mass Ratio Maximum Mach Number

l Mass % ∆V Losses Optimal Staging γ

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Figure 1. Hypersonic Airbreathing Corridor

ics and Astronautics

II. First Stage Vehicle Model

A. Vehicle Sizing The first stage initial mass was parametrically determined by using the 2nd stage initial weight as the design

point. The 2nd stage initial masses were multiplied by an initial mass ratio (Γ = m0,1/m0,2) to determine the 1st stage initial mass. Initially, Γs from 1-5 were chosen to represent a wide range of RBCC or TBCC first stage propulsion systems.5,7 However, due to the non-dimensional nature of the first stage model, it was quickly discovered that all Γs performed the same by the above figures of merit. Thus, an initial mass ratio of 3 was used throughout this study. It should be noted that the 1st stage initial mass here does not constitute its gross takeoff mass because the trajectory optimization was only considered from Mach 2+ to ignore transonic performance issues. Nevertheless, the propellant fractions presented are still important in determining the 1st stage supersonic propellant needs.

B. Aerodynamics and Propulsion The first stage vehicle model used for this analysis was a scaled version of Chuang and Mortimoto’s curve-fitted

aerodynamic and propulsion models.8 The aerodynamic model assumes a typical hypersonic vehicle with lift and drag polars given algebraically:

(deg))()(0 αα MCMCC LLL += (1)

(2) 20 )()(

LCMKMCC DD +=

with zero-α lift, lift slope, and induced drag coefficients given by Eq. 3-5. Profile drag (CD0) is given in Fig. 2.

035.0)]1(10arctan[))20/(1()(0 −−= MMCL π (3)

Lα (4) 014.0)654.0exp(057.0)( +−= MMC

)]2356.0exp(1[85.1)( MMK (5) −−=

Figure 2. Profile Drag Coefficient

The propulsion model assumes a turboramjet / scramjet engine system with transition occurring at Mach 4.

Specific impulse and thrust coefficient are also given algebraically by:

(6)

≥−−+−<−−

=4 M )20)((1054802454 M )20)((104500

),(kmhM

kmhhMIsp

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≥

−+°−

+°

<+

=4 M 35)5)((

200exp)5)((15

4M 6974.14736.0

),( 2

6.0

08.0

15.1

4/1

MM

M

MM

MCT ααα

−25.1

(7)

These models were used because they give representative specific impulse, lift, drag, and thrust for a wide range of flight conditions. Furthermore, they are continuous and differentiable, which aided in the efficiency of the gradient-based trajectory optimization process.

The aerodynamic and propulsion models were scaled by wing area (Aw) and exit area (Ae) with

wLqACL = (8)

wD (9) qACD =

eT (10) AqCT =

Aw was calculated by equating lift and weight at the beginning of the trajectory simulation with the assumption that the vehicle was at a 2º angle of attack. Ae was scaled such that a thrust-to-weight of 0.7 was achieved at the simulation beginning. This resulted in a constant Aw/Ae = 53 for all hypersonic first stages.

III. Second Stage Vehicle Model

A. Payload Sizing The payload sizes were based on three different classes. The first class was a small payload equal to 455kg

(~1klb), representative of a Pegasus XL launch.2 The medium class was on the order of a Delta-IV Medium or Atlas V rocket, and set to be 11,400kg (~25klb).9,10 The largest class was the mass of the Crew Exploration Vehicle (CEV) as defined by NASA, or 20 metric tons (~45klb).11 Payload fairings were designed comparable to the aforementioned launch vehicles and the CEV was assumed to be a scaled Apollo spacecraft. All payload fairings are assumed to be comprised of a ¾ power law, ogive nose with a prescribed length (Lnose) and diameter followed by a constant diameter cylindrical section to a final length (Lfairing). The payload dimensions and weights of each payload class are summarized in Table 2, and an example medium sized rocket is shown in Fig. 3.

Payload Class Lnose Pegasus XL 1.5mDelta IV / Atlas V 7.0mCEV 4.0m

B. Vehicle Sizing The remainder of the second s

using the rocket equation and a propessentially constant for a given propproduction stages, εp is approximrockets, and Isp is on average 450 svalues were used for all 2nd stage rocthrust-to-weight of 1.2 and a fuel-toalso set for the rocket designs.

Calculation of propellant and payload, velocity increment, propelimpulse were carried out by the mequation (Eq. 11) and propellant fr

Ame

Table 2. Second Stage Payload Fairing Lfairing Diameter mpl mfairing mtotal

3.5m 1.27m 455kg 110kg 565kg 14.0m 5.0m 11,400kg 2,600kg 14,000kg 6.0m 5.0m 20,000kg N/A 20,000kg

Figure 3. Example 2nd Stage Rocket Design

tage rocket was designed ellant fraction, εp, which is ulsion type. From existing ately 0.88 for LOX/LH2 econds.12 Thus, these two ket calculations. An initial -oxidizer ratio of 6 were

inert mass for a given lant fraction and specific anipulation of the rocket

action definition (Eq. 12).

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Equations 13 and 14 give the analytical second stage propellant and inert mass calculations.

1)]/(exp[/ 0 −∆= spfp IgVmm (11)

)/( mmm ippp (12) +=ε

}1)]/(]{exp[/)1[(1 0

0

−∆−−=

sppp

spplp IgV

mεε

}1)]/({exp[ −∆ IgVm

mm

(13)

pppi (14) εε /)1( −=

The total rocket length needed for aerodynamic predictions was found by calculating the fuel and oxidizer tank lengths and adding them to the given fairing length. Constant diameter tanks with ¼-cylindrical endcaps were assumed for both tanks. To account for gravitational, thrust vectoring and drag losses, the ideal velocity increment was augmented so ∆V = ∆Videal*(1+∆VLosses), where ∆Vlosses is a total loss percentage loss calculated during the 2nd stage trajectory optimization and ∆Videal

= ∆Vorbit – ∆Vstaging.

C. Aerodynamics The Newtonian flow method was used to calculate the 2nd stage aerodynamic characteristics. This method was

chosen because it is an analytical solution that does not require lengthy coding or computational time. While other methods such as modified Newtonian, tangent-wedge, and tangent-cone may give more accurate lift and drag predictions, Newtonian flow can be regarded as a good first-order aerodynamic analysis. The ¾ power law nose was also chosen because it produces minimum profile drag for the Newtonian method.13

IV. Trajectory Optimization

A. Overview The trajectory optimization process consisted of three parts. The first being the 2nd stage rocket from a given

staging condition (with variable initial flight path angle) to orbit, the second was the 1st stage airbreather from Mach 2 to the staging condition, and the third was the new 2nd stage rocket trajectory using the fixed flight path from the 1st stage end conditions. After each 2nd stage optimal trajectory calculation, the ∆Vlosses parameter was adjusted such that the final propellant mass is zero. This update typically had little effect on the 2nd stage optimal trajectory and the 2nd stage usually closed after only several trajectory/vehicle iterations. This process anchored the final payload mass and staging point while minimizing the TSTO system mass.

NASA’s Program to Optimize Simulated Trajectories (POST) was utilized for all trajectory optimization. The program assumes a point mass system accelerating over a circular Earth and uses the accelerated projected gradient algorithm to minimize the final payload mass subject to various flight constraints and boundary conditions.14 Run times for a single POST problem were on the order of several seconds; however to close an entire TSTO system, many restarts were needed and the entire runtime was on the order of a minute.

B. Second Stage Rocket Trajectory, Free Staging Flight Path Angle Initially, for each payload 24 second stage rockets were designed from a prescribed staging point to a 185km

circular orbit. Staging Mach numbers from 5 to 12.5 in increments of 2.5 and dynamic pressures of 0.1kPa, 1kPa, 10kPa, 25kPa, 50kPa and 100kPa made up the initial 2nd stage design matrix. These points were chosen because they represent several places in the hypersonic corridor (50 & 100kPa), outside the sensible atmosphere (0.1 & 1kPa) and in between. Staging Mach numbers between 5 and 12.5 also span most hypersonic airbreathing TSTO designs. The initial staging points are plotted in Fig. 4 on energy and dynamic pressure contours. As shown, for a given Mach number the energy variations depend not only on the potential energy but also the local speed of sound in the atmosphere, allowing 1-10kPa dynamic pressures to possess the highest total staging energy. This observation will prove important when the TSTO designs are compared.

The staging altitude and velocity were calculated from the given Mach number and dynamic pressure using an ideal gas assumption and the 1976 standard atmosphere model.15 The final circular orbital velocity at the 185km altitude was found to be 7.793km/s.16 A zero degree final flight path angle was also stated to ensure orbit

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circularization. Initial staging flight path angle and 5 pitch rates defined the control parameters for the POST optimization.

Figures 5 and 6 show a representative optimal 2nd stage trajectory and its associated control variables. One should note the high initial flight path angle (~25º) that is inherent to rocket vehicle dynamics, i.e. low lift and high drag results in a desire to quickly escape the sensible atmosphere. Also, the optimal trajectory has minimal thrust vectoring losses by keeping angle of attack near zero.

Figure 4. Staging Points on Energy Contours

Figure 5. Example Optimal 2nd Stage Trajectory Figure 6. Example Optimal 2nd Stage Controls

C. First Stage Airbreathing Hypersonic Trajectory The airbreathing first stage trajectory was comprised of five main events: 1) Constant 1atm dynamic pressure climb beginning at M = 2, α = 2º, γ = 6.5º 2) Constant 3.25g acceleration pull-up maneuver 3) Hold at maximum 20º angle of attack, if necessary 4) Engine off if dynamic pressure < 0.05atm 5) Five second linear α ramp-down to stage at α = 0º and given Mach number and dynamic pressure Mach number that initiates the pull-up maneuver and dynamic pressure that initiates the angle of attack ramp

down were the two control variables for the first stage trajectory problem. POST optimized these controls to maximize final mass subject to the given staging conditions. This portion of the trajectory problem effectively

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became a two point boundary value problem. Also, when the 0.1kPa dynamic pressure staging condition was not attainable, the maximum altitude staging point was instead used, i.e. when staging flight path angle was zero. An example optimal 1st stage trajectory and its controls are shown below. The minor oscillations occurring in Fig. 8 at 100 seconds were a result of the vehicle dynamics changing during turboramjet / scramjet mode transition. Also, the sharp increase in angle of attack at ~270s was where pull-up is initiated.

Figure 7. Example Optimal 1st Stage Trajectory Figure 8. Example Optimal 1st Stage Controls

D. Second Stage Trajectory, Fixed Staging Flight Path Angle Using the separation flight path angle obtained from the first stage, the second stage rocket analysis was

repeated. This trajectory problem was identical to that outlined in Section B with the exception that the staging flight path angle was now fixed. Also, with the addition of the 1st stage’s limited flight path angle, two dynamic pressures correspond to two 2nd stage minima (∆Vlosses and initial mass) for a given staging Mach number. These additional staging points and the dynamic pressures that produced maximum γstaging increased the number of staging conditions per Mach number to nine, or a total of 36 for a given payload size.

A fixed staging flight path angle 2nd stage optimal trajectory and control angles are shown in Fig. 9-10. One dramatic difference between these figures and Fig. 5-6 is the pull-up of the rocket quickly after separation. Due to a 60% decrease in γstaging, the rocket must use a large amount of its thrust to combat gravity in order to maintain its moderate flight path angle. This rocket pull-up was common in all 2nd stage trajectories with constrained γstaging, and resulted in heavy velocity losses and associated mass penalties. A thorough quantification of these effects follows.

Figure 9. Example Optimal 2nd Stage Trajectory Figure 10. Example Optimal 2nd Stage Controls

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V. Results

A. First Stage Airbreather Results The non-dimensional model used in this study could not predict the initial mass of the 1st stage; however it did

yield insight on some of the design parameters for the hypersonic airbreather. First, the pull-up maneuver utilized throughout this study caused the hypersonic vehicle to over-speed past the staging Mach number in order to gain kinetic energy that it then traded for potential energy. (Mach 5 cases at high dynamic pressure didn’t experience this phenomenon because the moderate flight path angle at low hypersonic speeds allowed sufficient acceleration during pull-up.) Normalized maximum Mach number is shown in Fig 11 and illustrates that a 15-30% increase was needed to perform the pull-up. In reality, the maximum flight speed would be heavily constrained by the heating, propulsion and structural limits of the hypersonic vehicle and thus would limit the feasibility of a large over-sped pull-up.

Next, the propellant mass fraction needed for the supersonic/hypersonic ascent is quantified in Fig. 12. Propellant needs tend to increase linearly as dynamic pressure decreases due to higher potential and kinetic energy (because of atmosphere temperature dependency) at staging. After reaching a maximum between 1-10kPa, propellant needs decrease near linearly. This fuel fraction reduction is attributed to engine shut off at 5kPa and the lower staging velocity at this portion in the atmosphere. The fuel penalties (3-18%) appear promising for future hypersonic TSTO designs, but it should be noted that further propellant is needed for subsonic, transonic and low supersonic regimes along with any flyback requirements. Furthermore, the pull-up maneuver increases fuel fractions 40-60% over a nominal 1atm staging, and is more sensitive at higher Mach numbers due to decreasing specific impulse efficiency. Again, the feasibility of this 1st stage design penalty must be addressed when considering pull-up initiated, low dynamic pressure staging.

Figure 11. 1st Stage Mmax/Mstaging Figure 12. 1st Stage Propellant Mass Fraction

B. Small Class Payload Two-stage results for the small, Pegasus XL class payload are presented below. Figure 13 plots the hypersonic

airbreather staging flight path angle along with the optimal γ. At best, the TSTO staging flight path angle is half that of the optimal. This reduction causes the 2nd stage rocket to pull-up immediately after separation in order to maintain or increase its flight path angle so that it will reach the required 185km orbit (Fig. 10). Compared to the optimal 2nd stage trajectory (Fig. 6), the rocket pull-up increases thrust vectoring and drag losses, which can be seen quantitatively in Fig. 14. The dynamic pressure that maximizes staging flight path angle is between 10-18kPa, with dynamic pressure decreasing as Mach increases. Similarly, the dynamic pressure that minimizes rocket velocity losses decreases as Mach increases, but the optimum is 3-10kPa. This disparity is due to fewer drag losses at the higher altitude staging conditions.

The resultant initial rocket mass for various staging points is shown in Fig. 15. A 27-37% decrease in 2nd stage initial mass is obtained with optimal pull-up, i.e. staging at 3-8kPa. The dynamic pressure that minimizes rocket mass increases as Mach number increases, which is opposite of γstaging and ∆Vlosses. The difference between these trends is because atmospheric temperature is maximized around 50km, which results in a higher speed of sound, velocity and kinetic energy. As Mach number increases, the dynamic pressure associated with a 50km altitude also

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increases, thereby explaining the trend in minimizing 2nd stage mass. There are thus two key parameters in the prediction and design of a 2nd stage rocket: staging flight path angle (effectively velocity losses) and staging speed of sound (effectively ideal velocity increment). An empirical correlation between these two parameters will be presented later. To compare the payload study to a current baseline, a maximum initial mass ratio was estimated from the gross take off weight (GTOW) of the Pegasus XL and its subsonic Orbital Carrier Aircraft. The mass ratio was computed by dividing the GTOW by the gross 2nd stage initial mass. This plot shows that for the given GTOW, a hypersonic 1st stage could be one to two orders of magnitude greater than the 2nd stage rocket. Hence, hypersonic TSTO systems look technologically feasible for small payloads or missile applications. However, for cost feasibility an initial mass ratio less than 10 is desired (see Pegasus baseline on plot for comparison).17

Figure 13. Staging Flight Path Angle, Small Payload Figure 14. 2nd Stage ∆Vlosses, Small Payload

Figure 15. 2nd Stage Gross Mass, Small Payload Figure 16. 1st Stage Max Mass Ratio, Small Payload

C. Medium Class Payload The Delta IV / Atlas V medium payload results are similar to those of the small payload. Fixed and free staging

flight path angle, velocity losses, and initial rocket mass are shown in Fig. 17-19, respectively. Staging flight path angles are again approximately half the optimal resulting in increased velocity penalties. The extremes also occur at dynamic pressures between 3 and 20kPa with maximum flight path angle being greater than minimum ∆Vlosses. Velocity losses slightly increased from the small payload results, but there is an overall insensitivity to payload size, which is advantageous for future TSTO system engineers.

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Again, to compare the hypersonic TSTO systems with the current state of the art, maximum initial mass fractions were calculated from existing expendable launch vehicles. With a baseline GTOW of 300 metrics tons, initial mass ratios are between 1 and 7 (Fig. 20). There is also greater design flexibility at higher staging Mach numbers because of the lower 2nd stage mass. Mass ratios on this order are preferable in the cost sense, but technological feasibility becomes the limiting factor.

Figure 17. Staging Flight Path Angles, Small Payload Figure 18. 2nd Stage ∆Vlosses, Medium Payload

Figure 19. 2nd Stage Gross Mass, Medium Payload Figure 20. 1st Stage Max Mass Ratio, Small Payload

D. Large Class Payload Large class, Crew Exploration Vehicle size, TSTO system results are plotted in Fig. 21-24. The trends are again

similar to the other payload sizes. Velocity losses increased only 3% and staging flight path angles varied less than 1% from medium to large payloads. The resulting rocket mass increased 45% from the medium payload—proportional to the payload increase—thus showing low system sensitivity to payload mass.

Gross take off weight was set at one million pounds, or 454 metric tons, for maximum initial mass ratio calculation. One million pounds was assumed to be the maximum runway limit for a horizontal takeoff hypersonic vehicle. The results, plotted in Fig. 24, are essentially identical to the medium class payload Γ since the GTOW and payload masses scale comparably. Like the medium payload, the initial mass ratios show cost effective first stages if they can be realized. The pull-up maneuver extends the 1st stage initial mass ratio 60% over a nominal 1atm staging, thereby increasing the design envelope of a hypersonic first stage if the additional flight speed and propellant needs prove feasible.

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Figure 21. Staging Flight Path Angles, Large Payload Figure 22. 2nd Stage ∆Vlosses, Large Payload

Figure 23. 2nd Stage Gross Mass, Large Payload Figure 24. 1st Stage Max Mass Ratio, Large Payload

VI. Staging Flight Path Angle and Speed of Sound Effect As explained qualitatively above, a combination of staging flight path angle and speed of sound minimize initial

rocket mass. The staging parameter

(15) smaaa refrefstagingstaging /280 where,)(* =−γ

best captured the correlation between these three quantities. From Fig. 25-27, as this staging parameter is increased, the 2nd stage initial mass decreases with little variation in rocket mass for a given staging parameter. Thus, the flight path angle and speed of sound at staging are known, they can predict the 2nd stage initial mass and hence the 1st stage payload. Furthermore, to decrease rocket mass either the staging flight path angle or speed of sound should be increased. The hypersonic airbreather first stage penalties are also shown in Fig. 28 and 29. As a greater pull-up is performed, the maximum flight speed and propellant fraction increase until the maximum staging parameter is achieved then decrease. The penalties associated with very low dynamic pressure staging points are greater than comparable higher q staging points with no further benefit in rocket mass reduction. Therefore, the staging design space should be limited to the minimum dynamic pressure that maximizes the staging parameter (Eq. 15) and the maximum dynamic pressure (~1atm) that satisfies the propulsion, heating, and structural limitations.

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Fi

Figure 26. 2nd Stage Gross Ma

Figure 28. 1st Stage M

A top-level TSTO hypersonic airto quantify the effects of various sta

Am

gure 25. 2nd Stage Gross Mass, Small Payload

ss, Medium Payload Figure 27. 2nd Stage Gross Mass, Large Payload

max/Mstaging Figure 29. 1st Stage Propellant Mass Fraction

Decreasing q, increasing h

Decreasing q, increasing h

VII. Conclusions breather / rocket orbiter system with integrated trajectory optimization was used ging points achieved by employing a hypersonic pull-up maneuver. The design

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space included fixed payload delivery for three masses and showed minimal scalability issues for a given staging condition. A 27-37% decrease in rocket gross mass was attained when using an optimal 3.25g pull-up maneuver between 3-8kPa or around 50km. The optimal dynamic pressure was attributed to lower rocket trajectory losses (due to higher staging flight angle) and lower velocity increment (due to increased staging velocity). The first stage hypersonic vehicle must endure a 15-30% increase in maximum flight Mach number and 40-60% increase in propellant fraction to meet these low dynamic pressure staging points. The feasibility of such tradeoffs must be addressed by more accurate first stage models and assessed by the experienced TSTO designer. Fortunately, even a slight pull-up reduces 2nd stage mass 20-25% with minimal 1st stage penalties.

To limit the pull-up design space, it was shown that the staging point that maximizes staging flight path angle and speed of sound should be the minimum staging dynamic pressure. Higher altitude staging increases rocket mass and has 1st stage penalties higher than comparable low altitude staging. The maximum staging dynamic pressure would be determined by the 1st stage flight constraints and typically be around 1atm. The point at which staging occurs will ultimately be determined by numerous factors, some limits and tradeoffs have been discussed that will aid engineers in the future design of TSTO systems.

VIII. Acknowledgements This work has been sponsored by the Space Vehicle Technology Institute, under grant NCC3-989, one of the

NASA University Institutes, with joint sponsorship from the Department of Defense. Appreciation is expressed to Claudia Meyer, Mark Klem and Harry Cikanek of the NASA Glenn Research Center, and to Dr. John Schmisseur and Dr. Walter Jones of the Air Force Office of Scientific Research.

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Conference and Exhibit, Huntsville, Alabama, July 20-23, 2003, AIAA 2003-4405. 2Orbital Sciences Corporation, “Pegasus User’s Guide, Release 5.0,” URL: http://www.orbital.com/SpaceLaunch/Pegasus/

[Cited 19 April 2005]. 3Carter, P., Balepin, V., Spath, T., and Ossello, C., “MIPPC Technology Development,” 12th AIAA International Space

Planes and Hypersonic Systems and Technologies, Dec. 15-19, 2003, Norfolk, Virginia, AIAA-2003-6929. 4Boltz, F. W., “Optimal Ascent Trajectory for Efficient Air Launch into Orbit,” Journal of Spacecraft and Rockets, Vol. 41,

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7Grallert, H., and Herrmann, O., “Generic Derivation of a Promising Air-Breathing TSTO Space Transportation System - From Saenger to FESTIP,” 8th AIAA International Space Planes and Hypersonic Systems and Technologies Conference, Apr. 27-30, 1998, Norfolk, VA, AIAA-1998-1552.

8Chuang, C.-H., and Morimoto, H., “Periodic Optimal Cruise for a Hypersonic Vehicle with Constraints,” Journal of Spacecraft and Rockets, Vol. 34, No. 2, 1997, pp. 165-171.

9Boeing Launch Services, Inc., “Delta Payload Planner’s Guide Main Page,” URL: http://www.boeing.com/defense-space/space/delta/guides.htm [cited 29 April 2005].

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11NASA, “Crew Exploration Vehicle, Solicitation NNT05AA01J, Attachment J-1 – Statement of Objectives,” URL: http://prod.nais.nasa.gov/eps/eps_data/113638-SOL-001-004.doc [cited 29 April 2005].

12Wade, M., “LOX/LH2,” Encyclopedia Astronautica, URL: http://www.astronautix.com/props/loxlh2.htm [cited 29 April 2005].

13Rasmussen, M., Hypersonic Flow, Wiley-Interscience, New York, 1994, Ch. 9, pp. 288-318. 14Braurer, G. L., Cornick, D. E., Olson, D. W., Peterson, F. M., and Stevenson, R., Program to Optimize Simulated

Trajectories (POST) Vol. I and II, 1997. 15U.S. Standard Atmosphere, 1976. National Oceanic and Atmospheric Administration, NASA, United States Air Force,

Washington, DC, 1976. 16Vallado, D., Fundamentals of Astrodynamics and Applications, Second Edition, Microcosm Press, El Segundo, CA, 2001. 17Heiser, W., and Pratt, D., Hypersonic Airbreathing Propulsion, AIAA, Washington, DC, 1994, pp. 133-6.