Ian J. Dux

Glenn Research Center, Cleveland, Ohio

Joseph A. Huwaldt and R. Steve McKamey, P.E.

BD Systems, Inc., Huntsville, Alabama

John W. Dankanich

Gray Research, Inc., Cleveland, Ohio

Mars Ascent Vehicle Gross Lift-off Mass

Sensitivities for Robotic Mars Sample Return

NASA/TM—2011-216968

April 2011
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Ian J. Dux

Glenn Research Center, Cleveland, Ohio

Joseph A. Huwaldt and R. Steve McKamey, P.E.

BD Systems, Inc., Huntsville, Alabama

John W. Dankanich

Gray Research, Inc., Cleveland, Ohio

Mars Ascent Vehicle Gross Lift-off Mass

Sensitivities for Robotic Mars Sample Return

NASA/TM—2011-216968

April 2011

National Aeronautics and

Space Administration

Glenn Research Center

Cleveland, Ohio 44135
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subject to revision as analysis proceeds.
NASA/TM—2011-216968 iii 

Contents 

1.0 Introduction .......................................................................................................................................... 1

2.0 MAV Baseline Description .................................................................................................................. 2

2.1 Top Level MAV Requirements ................................................................................................... 2

2.2 MAV TSTO Ascent Trajectory Profile ....................................................................................... 3

2.3 TSTO Baseline Vehicle Design .................................................................................................. 3

2.4 MAV SSTO Ascent Trajectory Profile ....................................................................................... 6

2.5 SSTO Baseline Vehicle ............................................................................................................... 7

3.0 Trade Space Description ...................................................................................................................... 8

4.0 Analysis Tools and Methodology ....................................................................................................... 10

4.1 OTIS .......................................................................................................................................... 10

4.2 POST 3D ................................................................................................................................... 10

4.3 Analysis Methodology .............................................................................................................. 10

5.0 MAV Baseline Comparison ............................................................................................................... 11

5.1 TSTO POST and OTIS Trajectory Comparison ....................................................................... 11

5.2 SSTO POST and OTIS Trajectory Comparison ....................................................................... 17

6.0 TSTO GLOM Sensitivities ................................................................................................................. 21

6.1 GLOM Sensitivity to Target Inclination, Launch Latitude, and Launch Elevation .................. 21

6.2 Sensitivity to Launch Azimuth and Launch Elevation ............................................................. 26

6.3 Circular Orbit Altitude Sensitivity ............................................................................................ 29

6.4 Vehicle Mass and Engine Parameter Sensitivities .................................................................... 29

6.4.1 Stage Mass .................................................................................................................. 29

6.4.2 Engine Isp and Thrust ................................................................................................. 33

6.5 Verification of Combined TSTO Sensitivities .......................................................................... 36

6.6 Nominal Mission Availability for a MAV Designed for Off Nominal Launch 

Conditions ................................................................................................................................. 38

7.0 SSTO Performance Sensitivities ........................................................................................................ 40

7.1 Engine Thrust and Isp ............................................................................................................... 40

7.2 Stage Mass Sensitivities ............................................................................................................ 42

7.3 Circular Orbit Altitude Sensitivity ............................................................................................ 43

8.0 Conclusions ........................................................................................................................................ 43

9.0 System Implications ........................................................................................................................... 44

10.0 Future Work ....................................................................................................................................... 44

Appendix A .—Gross Lift-off Mass Sensitivities for Launch Elevations From 0 to 90 Targeting 

Inclinations from 0 to 90 for Launch Latitudes From 0 to 90 ...................................................... 47

References ................................................................................................................................................... 55

List of Tables 

Table 1.—TSTO MAV Baseline Masses ...................................................................................................... 4

Table 2.—TSTO MAV Baseline Thrust and Isp .......................................................................................... 4

Table 3.—Mars Oblate Gravity Model ......................................................................................................... 5

Table 4.—TSTO MAV Baseline Launch Site and Mission Assumptions .................................................... 5

Table 5.—SSTO Vehicle Element Masses ................................................................................................... 7

Table 6.—SSTO Engine Assumptions .......................................................................................................... 7

Table 7.—SSTO Launch and Mission Assumptions .................................................................................... 7

Table 8.—Range of MAV Parameters Analyzed .......................................................................................... 9

Table 9.—Trajectory Target Parameters ..................................................................................................... 12

Table 10.—Comparison of OTIS and POST Baseline TSTO Baseline Trajectories .................................. 13

Table 11.—OTIS Constraints Necessary to Match POST SSTO Baseline................................................. 18
NASA/TM—2011-216968 iv 

Table 12.—Comparison of OTIS and POST Baseline SSTO Baseline Trajectories .................................. 18

Table 13.—Verification of Predicted TSTO GLOM Using TSTO Sensitivities ........................................ 37

Table 14.—Large GLOM Verification Cases ............................................................................................. 38

Table 15.—MAV Quantitative Vehicle Sensitivities.................................................................................. 43

List of Figures 

Figure 1.—Baseline MSR architecture. ........................................................................................................ 2

Figure 2.—MAV TSTO ascent operational concept. .................................................................................... 4

Figure 3.—GLOM growth compared 2001 TSTO baseline for restricted control rates. .............................. 5

Figure 4.—MAV SSTO ascent operational concept. .................................................................................... 6

Figure 5.—Target orbit inclination in relation to launch latitude. ................................................................ 8

Figure 6.—MAV launch platform elevation and launch azimuth orientation. ............................................. 9

Figure 7.—Comparison of POST and OTIS MAV GLOM sensitivity data. .............................................. 11

Figure 8.—Coordinate system used to define launch inertial Euler control angles. ................................... 12

Figure 9.—Launch inertial Euler control angle rotation sequence. ............................................................ 13

Figure 10.—Comparison geodetic altitude and inertial velocity histories for OTIS and POST 

TSTO baseline. ................................................................................................................................... 14

Figure 11.—Comparison of inertial Euler control angle history for OTIS and POST TSTO 

baseline. .............................................................................................................................................. 15

Figure 12.—Comparison of AOA history for OTIS and POST TSTO baseline. ........................................ 15

Figure 13.—Comparison of dynamic pressure history for OTIS and POST TSTO baseline. .................... 16

Figure 14.—OTIS inertial Euler pitch history comparison of wind modeling. .......................................... 16

Figure 15.—OTIS AOA history comparison of wind modeling effects. .................................................... 17

Figure 16.—Comparison of geodetic altitude and inertial velocity histories for POST and OTIS 

SSTO baselines. ................................................................................................................................. 19

Figure 17.—Comparison of inertial Euler pitch control history for POST and OTIS SSTO 

baselines. ............................................................................................................................................ 19

Figure 18.—Comparison of inertial Euler yaw control history for POST and OTIS SSTO 

baselines. ............................................................................................................................................ 20

Figure 19.—Comparison of dynamic pressure history for POST and OTIS SSTO baselines. ................... 20

Figure 20.—GLOM growth for an on-orbit inclination change necessary to reach inclinations 

lower than the launch latitude. ........................................................................................................... 22

Figure 21.—GLOM sensitivity for all launch elevations and target orbit inclinations at a launch 

latitude of 0. ...................................................................................................................................... 22

Figure 22.—GLOM sensitivity for selected elevations and target orbit inclinations at a launch 

latitude of 0. ...................................................................................................................................... 23

Figure 23.—Slope of GLOM change per degree of inclination for a launch latitude of 0 at 

selected launch elevations. ................................................................................................................. 23

Figure 24.—GLOM sensitivity for all launch latitudes to target orbit inclinations greater than the 

launch latitude, at a launch elevation of 90. ..................................................................................... 24

Figure 25.—GLOM sensitivity for all launch latitudes to target orbit inclinations greater than the 

launch Latitude, at a launch elevation of 45. .................................................................................... 24

Figure 26.—Impact of control continuity on TSTO GLOM sensitivity of a vertical launch 

elevation to an inclination greater than the launch latitude of 45. .................................................... 25

Figure 27.—Impact of wind modeling on TSTO GLOM sensitivity of a vertical launch elevation 

to an inclination greater than the launch latitude of 45. .................................................................... 25

Figure 28.—Impact of control rate limit on TSTO GLOM sensitivity of a vertical launch 

elevation to an inclination greater than the launch latitude of 45. .................................................... 26
NASA/TM—2011-216968 v 

Figure 29.—GLOM delta for off optimal launch azimuths based on vertical launch with GLOM 

of 272.6 kg. ......................................................................................................................................... 27

Figure 30.—GLOM delta for off optimal launch azimuths based on 45 elevation launch with 

GLOM of 265.8 kg. ............................................................................................................................ 27

Figure 31.—GLOM delta for off optimal launch azimuths using varying control rate limits, based 

on a GLOM of 272.6 kg. .................................................................................................................... 28

Figure 32.—GLOM delta for off optimal launch azimuths without second stage control 

continuity, based on a GLOM of 272.6 kg. ........................................................................................ 29

Figure 33.—TSTO GLOM sensitivity to circular orbit altitude. ................................................................ 30

Figure 34.—TSTO GLOM sensitivity to second stage mass variation for a fixed first stage mass. .......... 31

Figure 35.—TSTO GLOM sensitivity to first stage mass variation for a fixed second stage mass. .......... 31

Figure 36.—Second stage dry mass sensitivity at varying values of Isp. ................................................... 32

Figure 37.—First stage mass sensitivity at varying values of Isp. .............................................................. 32

Figure 38.—TSTO GLOM sensitivity to Isp, constant for both stages. ..................................................... 33

Figure 39.—TSTO GLOM sensitivity to second sage thrust, first stage thrust held constant. ................... 34

Figure 40.—TSTO GLOM sensitivity to first stage thrust, second stage thrust held constant. .................. 34

Figure 41.—TSTO delta GLOM difference for off azimuth launches using optimal thrust, based 

on a GLOM of 272.6 kg. .................................................................................................................... 35

Figure 42.—TSTO delta GLOM difference for off azimuth launches using a representative liquid 

Isp, based on a GLOM of 272.6 kg. ................................................................................................... 36

Figure 43.—Geodetic altitude and inertial velocity of large GLOM MAV, flown on a nominal 

mission. .............................................................................................................................................. 39

Figure 44.—Inertial Euler pitch history of large GLOM MAV, flown on a nominal mission. .................. 39

Figure 45.—Inertial Euler yaw history of large GLOM MAV, flown on a nominal mission. ................... 40

Figure 46.—SSTO GLOM sensitivity to thrust with and without wind modeling. .................................... 41

Figure 47.—SSTO GLOM sensitivity to engine Isp. .................................................................................. 41

Figure 48.—SSTO GLOM sensitivity to dry mass. .................................................................................... 42

Figure 49.—SSTO GLOM sensitivity to circular orbit altitude. ................................................................ 42

Figure 50.—TSTO GLOM sensitivities for a launch latitude of 5. ........................................................... 47

Figure 51.—TSTO GLOM sensitivities for a launch latitude of 10. ......................................................... 47

Figure 52.—TSTO GLOM sensitivities for a launch latitude of 15. ......................................................... 48

Figure 53.—TSTO GLOM sensitivities for a launch latitude of 20. ......................................................... 48

Figure 54.—TSTO GLOM sensitivities for a launch latitude of 25. ......................................................... 49

Figure 55.—TSTO GLOM sensitivities for a launch latitude of 30. ......................................................... 49

Figure 56.—TSTO GLOM sensitivities for a launch latitude of 35. ......................................................... 50

Figure 57.—TSTO GLOM sensitivities for a launch latitude of 40. ......................................................... 50

Figure 58.—TSTO GLOM sensitivities for a launch latitude of 45. ......................................................... 51

Figure 59.—TSTO GLOM sensitivities for a launch latitude of 50. ......................................................... 51

Figure 60.—TSTO GLOM sensitivities for a launch latitude of 55. ......................................................... 52

Figure 61.—TSTO GLOM sensitivities for a launch latitude of 60. ......................................................... 52

Figure 62.—TSTO GLOM sensitivities for a launch latitude of 65. ......................................................... 53

Figure 63.—TSTO GLOM sensitivities for a launch latitude of 70. ......................................................... 53

Figure 64.—TSTO GLOM sensitivities for a launch latitude of 75. ......................................................... 54

NASA/TM—2011-216968 1 

Mars Ascent Vehicle Gross Lift-off Mass Sensitivities for 

Robotic Mars Sample Return 

Ian J. Dux 

National Aeronautics and Space Administration 

Glenn Research Center 

Cleveland, Ohio 44135 

Joseph A. Huwaldt and R. Steve McKamey, P.E. 

BD Systems, Inc. 

Huntsville, Alabama 35806 

John W. Dankanich 

Gray Research, Inc. 

Cleveland, Ohio 44135 

Abstract 

The Mars ascent vehicle is a critical element of the robotic Mars Sample Return (MSR) mission. The 

Mars ascent vehicle must be developed to survive a variety of conditions including the trans-Mars journey, 

descent through the Martian atmosphere and the harsh Martian surface environments while maintaining the 

ability to deliver its payload to a low Mars orbit. The primary technology challenge of developing the Mars 

ascent vehicle system is designing for all conditions while ensuring the mass limitations of the entry descent 

and landing system are not exceeded. 

The NASA In-Space Propulsion technology project has initiated the development of Mars ascent 

vehicle technologies with propulsion system performance and launch environments yet to be defined. To 

support the project’s evaluation and development of various technology options the sensitivity of the 

Mars ascent vehicle gross lift-off mass to engine performance, inert mass, target orbits, and launch 

conditions has been completed with the results presented herein. 

1.0 Introduction 

For decades NASA and the science community have been working towards a robotic Mars Sample 

Return (MSR) mission. There have been numerous studies to evaluate MSR mission architectures, 

technology needs and development plans, and top-level mission requirements (Refs. 1 to 4). The Mars 

program has divided the MSR mission into three phases, each requiring a separate launch from Earth. The 

first launch consists of a lander and rover to perform sample collection and caching. This is followed by 

the launch of the Mars orbiter, which acts as the Earth return vehicle. The final phase of the mission is the 

launch of the second lander containing the Mars ascent vehicle (MAV). A notional depiction of the MSR 

architecture is included in Figure 1 and shows the potential for the order of the last two launches to 

change as mission planning continues. The first of these missions, the sample collection and caching, is 

scheduled as a joint NASA/ESA 2018 mission. Currently, the orbiter and lander missions are tentatively 

planned for 2022 and 2024, respectively. The MSR mission is one of the most challenging robotic 

missions ever attempted due to large number of system elements and technology development risks. One 

of the largest technology development risks for the MSR mission is the MAV. 

NASA’s In-Space Propulsion Technology (ISPT) project has recently been assigned the development 

of the MAV technologies with a requirement to perform multiple terrestrial flight demonstrations prior to 

the MSR preliminary design review (PDR). The MAV and its associated landing platform element PDR 

is expected to occur in 2018. To meet this technology readiness date, the ISPT project released a MAV 
NASA/TM—2011-216968 2 

Figure 1.—Baseline MSR architecture. 

Request for Information in December of 2008, and released a solicitation for the MAV propulsion system 

development in February of 2009. These awards will begin with system studies for various MAV propulsion 

concepts followed by a down select for the propulsion system development and demonstration. 

The critical metric for the MAV is the landed mass required to complete its mission. The landed mass 

is limited due to the use of the Mars Science Laboratory (MSL) Skycrane, in the baseline entry descent 

and landing (EDL) system, to provide the final propulsive descent (Ref. 5). As a result of the landed mass 

restrictions, the objective is to minimize the Gross Lift-Off Mass (GLOM) of the MAV system. 

MAV propulsion concepts being considered include solid, liquid, hybrid systems with state-of-the-art 

propellants and numerous subsystem architectures. These various concepts all have GLOM implications 

on the MAV system. The MSR science team is also still evaluating potential landing sites and evaluating 

landing accuracy of the EDL system. The landing site latitude, surface gradient, MAV launch platform 

orientation, MAV angle of elevation at launch, and other parameters all impact the MAV GLOM. To 

understand the primary MAV GLOM sensitivities to the MAV performance characteristics and landing 

site requirements, an extensive parametric trade has been completed and the results are presented herein. 

2.0 MAV Baseline Description 

2.1 Top Level MAV Requirements 

The fundamental requirement for a successful MAV mission is the delivery of 5 kg of payload, which 

includes samples of the Martian surface as well as the sample containment system, to orbit. This 

requirement can be accomplished using a wide variety of engine and vehicle assumptions that fall into 

two major categories. First is a family of in-line two-stage vehicle designs to reach orbit known as two 

stage to orbit (TSTO) solutions. TSTO concepts use two separate propulsion systems with the first stage 

jettisoned before the second stage is used. The other major category of vehicle designs uses only a single 

stage with a restartable propulsion system and is referred to as a single stage to orbit (SSTO) solution. 

SSTO vehicle concepts do not jettison any part of the stage during ascent with considerations given to 

both restartable liquid and hybrid engines as well as timed solid rocket motor designs. 
NASA/TM—2011-216968 3 

To allow for a stable orbit at Mars, the MAV must be able to place the sample into a 500 km circular 

orbit, with dispersions no greater than 100 km (Ref. 6). The inclination of the rendezvous orbit has yet to 

be established and will ultimately depend on the largest landing latitude that the EDL system can guarantee 

for the MAV. This is due to the assumption that the target orbit inclination of the MAV will be greater than 

the launch site latitude. The vehicle must be capable of achieving its target inclination within 0.2 (Ref. 6). 

The MAV must be designed to accommodate a wide variety of launch conditions due to the inability 

of the EDL system to precisely land at a predetermined location with desired launch orientation. At the 

time of this analysis, the MAV was targeted to land at Martian latitudes within 45 of the equator, 

resulting in the assumption of a 45 baseline launch latitude. Additional analysis of the EDL system 

indicates that launch latitudes of no greater than 30 could be provided to the MAV, however this 

information could not be included in this assessment. The current GLOM results, although baselined for a 

45 latitude launch, encompass launches from any latitude less than or equal to 45. 

Uncertainty in landing location also necessitates that the MAV be capable of launching from a wide 

range of launch orientations. The results presented show the performance impact of a requirement to land 

on slopes of up to 20 from horizontal and guarantee a launch within 30 of the targeted launch elevation 

(Ref. 6). In addition to the launch elevation of the MAV, the azimuth of the launch platform on the Mars 

surface may also be uncontrolled. This could result in a launch into a nonoptimal launch azimuth 

orientation resulting in an associated reduction in performance. Currently the precision with which the 

optimal launch azimuth could be maintained during EDL is unknown. Options exist to mitigate the 

performance impact due to launch azimuth variation, including tighter controls on the final portions of 

EDL to orient the lander along the optimal launch azimuth or the use of a turntable to rotate the MAV into 

an optimal launch orientation. The elevation and azimuth assumptions made are intended guide decisions 

on the necessary lander capabilities. Eventually, these launch requirements will be traded at a system 

level against the MAV GLOM growth necessary to accommodate off-nominal launch conditions. 

2.2 MAV TSTO Ascent Trajectory Profile 

The MAV TSTO ascent profile is relatively simple and differs from most terrestrial launch vehicle 

profiles given that it does not use a continuous burn from surface to orbit. Instead two separate burns are 

used. The first burn starts at engine ignition (time = 0) and begins a 0.2 sec fixed attitude burn necessary 

to clear the launch platform. The first burn continues with an optimal pitch over maneuver. Depending on 

the controls being used, this maneuver could include optimal roll and yaw maneuvers in conjunction with 

pitch. Following the optimal control section of the burn, the aerodynamic angles (angle of attack, side slip 

and bank angle) are manipulated to put the vehicle in a zero aerodynamic angle orientation by the end of 

the first burn. After first stage burnout, the vehicle coasts to apoapsis, jettisoning the first stage and 

payload fairing before the start of the second stage burn. The current baseline assumption is that jettison 

occurs at an altitude of 200 km, but realistically it can occur any time after leaving the Martian 

atmosphere (approximately 100 km above the Martian surface) and before second stage ignition with no 

penalty to performance. Just prior to reaching apoapsis, a significantly shorter second burn, using an 

optimized control profile, is performed to raise the periapsis altitude and circularize the orbit. A 

theoretical operational concept, with baseline times and Martian altitudes, can be found in Figure 2. 

2.3 TSTO Baseline Vehicle Design 

The TSTO vehicle concept used for this analysis is a based on a vehicle previously developed by the 

NASA MAV team in 2001 (Ref. 7). The system masses, as sized for this vehicle, are shown in Table 1 with 

the baseline thrust and Isp assumptions in Table 2. These assumptions result in a total vehicle GLOM of 

267.5 kg. The MAV solid rocket motor performance assumptions are consistent with the use of a stretched 

STAR 17A solid motor first stage and a stretched STAR 13A second stage. It is assumed for all studies, 

except for those involving stage masses, that propellant mass can be adjusted while holding dry mass static. 
NASA/TM—2011-216968 4 

Figure 2.—MAV TSTO ascent operational concept. 

TABLE 1.—TSTO MAV BASELINE MASSES 

MAV element Mass, 

kg 

Description 

Stage 1 dry 27.7 Motor casing, nozzle and interstage 

Stage 1 propellant 158.6 Solid propellant stretched Star 17A derivative 

Stage 2 dry 38.4 Motor casing, avionics, payload attach structure 

Stage 2 propellant 34.7 Solid propellant Star 13A derivative 

Payload fairing 3.1 PLF jettisoned with first stage at 200 km 

Payload 5.0 Sample and Container 

TABLE 2.—TSTO MAV BASELINE 

THRUST AND ISP 

Engine parameter Value 

Stage 1 thrust (N) 21576.8 

Stage 1 Isp (s) 285.7 

Stage 1 exit area (m2) 0.032 

Stage 2 thrust (N) 6318.9 

Stage 2 Isp (s) 285.5 

Stage 2 exit area (m2) 0.0093 

The Martian atmosphere and winds were modeled using a tabular representation of a mean Mars 

Global Reference Atmospheric Model (GRAM). Mars shape and gravity were specified using an oblate 

model with the constants listed in Table 3. 

As the analysis to follow will show, mission and launch site assumptions have a large effect on the 

resulting vehicle GLOM. Therefore, it is necessary to identify the specific mission and launch site 

assumptions used in TSTO baseline such that the effects of the vehicle sensitivities presented can be 

better understood. The baseline launch site location and launch site orientation assumptions are specified 

in Table 4 along with the target orbital parameters. 
NASA/TM—2011-216968 5 

TABLE 3.—MARS OBLATE GRAVITY MODEL 

Parameter Value 

J2 1.96e-03 

J3 0.0 

J4 0.0 

Mars gravitational constant (km3/s2) 42828.3 

Mars rotation rate (rad/s) 0.71e-04 

Mars equatorial radius (km) 3393.9 

Mars polar radius (km) 3376.8 

TABLE 4.—TSTO MAV BASELINE LAUNCH SITE 

AND MISSION ASSUMPTIONS 

Trajectory assumption Value 

Latitude (degrees) 45.0 

Longitude (degrees) 0.0 

Launch elevation angle (degrees) 90.0 (Vertical) 

Launch azimuth (degrees) 88.8 (Optimal) 

Target circular orbit altitude (km) 500 

Target orbit inclination (degrees) 45 

It is important to note that the 2001 TSTO vehicle assumes use of only pitch control with-in the plane 

of the launch azimuth, which is varied at the start of the problem to target a 45 inclination. Additionally, 

there is no control rate limit imposed, which results in control rates of approximately 20 per second. 

During this study, a concern was immediately raised that control rates of this magnitude were too large 

for a reasonable flight profile. A decision was made to limit all body control rates to 5 per second, since 

previous experience has shown that body control rates larger than this may result in the vehicle exceeding 

structural limits or requiring additional vehicle structure (James McDuffie, personal communication, 

December 16, 2009). Figure 3 shows the effect on the baseline GLOM, 267.5 kg, as the body pitch rate is 

constrained to various levels. The performance deltas in Figure 3 assume only pitch control, with launch 

azimuth optimized. Since the goal is to produce the lightest possible MAV to meet mission requirements, 

the 5 kg (2 percent) growth that results from a control rate change is not insignificant. The performance 

delta for control rate restrictions placed on out-of-pitch-plane control rates at a nonoptimal launch 

azimuth are larger and are addressed in Section 6.0. 

Figure 3.—GLOM growth compared 2001 TSTO baseline for restricted control rates. 
NASA/TM—2011-216968 6 

2.4 MAV SSTO Ascent Trajectory Profile 

The SSTO MAV mission profile is similar to the TSTO trajectory in that it also uses two separate burns 

to reach orbit. The primary difference for the SSTO trajectory is that these burns are completed by the same 

stage. The first burn starts at engine ignition (time = 0) and begins the 0.2 sec vertical rise necessary to clear 

the launch platform. After vertical rise, the first burn continues with an optimal pitch over maneuver. 

Depending on the controls being used, this maneuver could include optimal roll and yaw maneuvers in 

conjunction with pitch over. Following the optimal control section of the burn, the aerodynamic angles 

(angle of attack, side slip, and bank angle) are varied to put the vehicle in a zero aerodynamic angle 

orientation by the end of the first burn. After burnout, the vehicle coasts to apoapsis, jettisoning the payload 

fairing before the start of the second stage burn. The current baseline assumption is that payload fairing 

jettison occurs at an altitude of 200 km, but can realistically occur any time after leaving the Martian 

atmosphere (approximately 100 km above the Martian surface) and before the start of the second burn with 

no effect on performance. Just prior to reaching apoapsis, a significantly shorter second burn, with an 

optimized pitch profile, is performed by the same stage to raise periapsis altitude and circularize the orbit. A 

theoretical operation concept, with baseline times and altitudes, can be found in Figure 4. 

Figure 4.—MAV SSTO ascent operational concept. 
NASA/TM—2011-216968 7 

2.5 SSTO Baseline Vehicle 

Differing from the TSTO vehicle concept, the SSTO concept was not based on an existing vehicle 

design. The SSTO baseline inert mass was assumed to be similar to the sum of the TSTO baseline inert 

stage masses with some mass savings due to the removal of systems duplicated on both TSTO stages. An 

Isp equal to the stretched Star 17A motor was assumed, with an optimized thrust level. The much lower 

thrust level allowed the SSTO vehicle to complete the MAV mission with much less propellant than 

would have been necessary at higher thrust levels. The SSTO baseline vehicle configuration, including 

the optimized engine thrust, is detailed in Table 5 and Table 6. The SSTO mission and launch site 

assumptions were identical to those used for the TSTO vehicle and are repeated in Table 7 with the 

vehicle launching from a vertical orientation. 

The SSTO baseline used only pitch steering, with control rates limited to 5 per second, while varying 

launch azimuth to target inclination. Models for the MAV aerodynamics, Mars Gravity and Mars 

atmosphere are identical to the TSTO vehicle baseline. Further discussion of the SSTO baseline trajectory 

assumptions is included in the Section 5.0.

TABLE 5.—SSTO VEHICLE ELEMENT MASSES 

MAV element Mass, 

kg 

Description 

Stage dry 61.9 Motor casing, avionics, 

payload attach structure 

Payload fairing 3.1 PLF jettisoned with first 

stage at 200 km 

Payload 5.0 Sample and container 

TABLE 6.—SSTO ENGINE ASSUMPTIONS 

Engine parameter Value 

Thrust (N) 4425.7 

Isp (s) 285.7 

Exit area (m2) 0.032 

TABLE 7.—SSTO LAUNCH AND MISSION ASSUMPTIONS 

Trajectory assumption Value 

Latitude (degrees) 45.0 

Longitude (degrees) 0.0 

Launch elevation angle (degrees) 90.0 (Vertical) 

Launch azimuth (degrees) 87.3 (Optimal) 

Target circular orbit altitude (km) 500 

Target orbit inclination (degrees) 45 
NASA/TM—2011-216968 8 

3.0 Trade Space Description 

The mission and launch assumptions of the MAV have a direct effect on the vehicle GLOM, primarily 

through the amount of propellant necessary to successfully reach orbit for each set of assumptions. Vehicle 

mass and engine performance assumptions also have an effect on MAV GLOM, through the mass of the 

components used as well as their effect on the amount of propellant needed to reach orbit. 

To better understand the sensitivities to be discussed, Figure 5 depicts the assumed relationship 

between launch latitude and launch inclination with targeted inclination always assumed to be greater 

than or equal to the launch latitude. The orientation of the launch platform on the surface of Mars is also 

important to understand and is illustrated in Figure 6. The platform orientation is defined using two 

angles, the launch elevation angle, 90 as shown, and the launch azimuth, measured clockwise from 

north. For each combination of launch latitude, targeted orbit inclination and launch elevation angle the 

optimal launch azimuth is calculated during analysis. The optimal launch azimuth corresponds to the 

minimum GLOM solution for each latitude and inclination combination. For the sensitivities presented 

here, it is more useful to express the simulated vehicle launch azimuth as the angle from the optimal 

launch azimuth, as defined in Figure 6. Further description and discussions of these values is found in 

Section 6.0, along with the sensitivity results. 

Figure 5.—Target orbit inclination in relation to launch latitude. 
NASA/TM—2011-216968 9 

Figure 6.—MAV launch platform elevation and launch azimuth orientation. 

TABLE 8.—RANGE OF MAV PARAMETERS ANALYZED 

Parameter Minimum Maximum 

Launch latitude (degrees) 0 90 

Launch elevation (degrees) 30 90 

Angle from optimal launch azimuth (degrees) 0 180 

Engine Isp (s) 255 355 

Engine thrust (N) Optimal 21576.8 

Total inert mass (kg) 30 70 

Target inclination (deg) 0 90 

Target orbit altitude (km) 400 600 

The large trade space of mission, launch and vehicle assumptions that were analyzed for MAV 

GLOM sensitivities are listed, with ranges, in Table 8. It should be noted that this analysis looked only at 

northern latitudes but it is assumed, due to symmetry, that launches from southern latitudes would remain 

the same. To break down this vast trade space, the parameters were studied in several different ways. 

First, assuming use of an optimal launch azimuth, a large matrix of MAV GLOM sensitivities were 

completed for all combinations of launch latitude, launch elevation, and targeted orbit inclination. 

Second, sensitivities for launches at a nonoptimal launch azimuth were run for all launch elevation angles 

at the baseline launch latitude of 45 targeting a 45 orbital inclination. Although only off-azimuth 

launches from 0 to 180 were analyzed, it is assumed due to symmetry that launch from 0 to –180

would produce similar results. The remaining vehicle and mission sensitivities were run using the 

baseline launch and mission assumptions, including the use of an optimal launch azimuth at a vertical 

launch elevation, as listed in Table 4. 

The previously developed TSTO MAV solid rocket concept is assumed to be the primary MAV 

baseline design for this analysis. Therefore, sensitivities to all parameters listed in Table 8 were run with 

vehicle assumptions consistent with the TSTO baseline vehicle. This included a range of vehicle 

sensitivities large enough to show how GLOM would change if using a liquid engine instead of the solid 

motor design. A subset of vehicle and mission sensitivities were also evaluated for the SSTO concept, 

such that the viability for further evaluation could be established. 
NASA/TM—2011-216968 10 

4.0 Analysis Tools and Methodology 

4.1 OTIS 

Optimal Trajectories by Implicit Simulation program (OTIS) is a general-purpose simulation and 

optimization program, which can be used to perform trajectory performance studies (otis.grc.nasa.gov) 

(Ref. 8). A user can simulate and optimize a wide variety of vehicles such as aircraft, missiles, reentry 

vehicles, ascent vehicles, satellites, and interplanetary vehicles. The vehicle models used in OTIS are 

defined by user inputs; there are no embedded, vehicle specific aerodynamic or propulsion models. OTIS 

is primarily a point mass, three-degree of freedom (3DOF) program. It makes available to the user two 

well known and proven optimizer options: SNOPT and SLSQP. The program name is derived from the 

implicit methods used to solve differential equations, which were distinctive at the time of OTIS’ origin. 

Although named after its implicit integration capabilities, OTIS is capable of generating flight paths using 

implicit, explicit or analytical integration. Trajectory analysis using OTIS can be performed with respect 

to any of the major bodies in the solar system. 

4.2 POST 3D 

Program to Optimize Simulated Trajectories (POST) 3D is a generalized point mass, discrete 

parameter targeting and optimization program (Ref. 9). POST provides the capability to target and 

optimize point mass trajectories for a powered or unpowered vehicle near an arbitrary rotating, oblate 

planet. POST has been used successfully to solve a wide variety of atmospheric ascent and reentry 

problems. The generality of the program is evidenced by its multiple phase simulation capability which 

features generalized planet and vehicle models. This flexible simulation capability is augmented by an 

efficient discrete parameter optimization capability that includes equality and inequality constraints. 

4.3 Analysis Methodology 

Vehicle sensitivities were established for the MAV through the minimization of the GLOM. In all 

cases, this results in the vehicle propellant load being varied to minimize the total vehicle mass. POST 

and OTIS used control angles, along with propellant weights, to find the optimal combination of 

parameters. In selected cases, thrust was also left open for optimization to also characterize the thrust 

level providing minimal vehicle mass. The majority of cases used static vehicle weights and engine 

parameters as described in Section 2.0. 

The sensitivities presented here were initially run in both POST and OTIS such that both the baseline 

cases and sensitivity results could be compared. To do so, Python scripts were developed to independently 

run each desired vehicle sensitivity. The functionality of the scripts necessary to run each analysis program 

was quite different due to the differing methods in which POST and OTIS operate. Despite differences in 

operation, these run scripts provided three important functions: run each optimization case while ensuring an 

optimal result, vary the input parameters necessary to accomplish each parameter sweep and record desired 

output data for post processing. 

To run each case, the scripts contained the ability to correctly read and interpret the optimization output 

from POST or OTIS. After each case was successfully optimized, the script would automatically increment 

the parameter, or parameters, of interest and rerun the program. This process was repeated until the entire 

parameter range was completed. For OTIS, no additional guess generation or guess tweaks were necessary, 

as the next case was easily converged from a previously converged case. In POST, the operation was a bit 

more complex as it was necessary to use a combination of a bi-section step algorithm and a genetic 

algorithm to automatically generate independent variable guesses for each new POST run that would allow 

successful problem completion. This allowed for less user interaction with each POST run and helped to 

minimize noise in the POST GLOM results. 
NASA/TM—2011-216968 11 

Figure 7.—Comparison of POST and OTIS MAV GLOM sensitivity data. 

POST and OTIS comparisons show matching results for the baseline cases as well as matching trends 

for the various GLOM sensitivities completed. A detailed comparison of the POST and OTIS SSTO and 

TSTO baseline cases can be found in Section 5.0. A close match between these programs is not 

unexpected, as previous studies have shown a close correspondence between POST and OTIS results 

(Ref. 10). Although great care was taken to ensure that POST found the most optimal solution, a great 

deal of noise was observed in the POST GLOM sensitivity results. An in depth comparison between the 

POST and OTIS sensitivities is not included here, but matching trends were observed for all sensitivities 

analyzed. Due to the smoother resulting OTIS trends, all GLOM sensitivity data discussed in this 

document is derived from OTIS results. An example of the noise in the POST GLOM results, compared 

to OTIS results, is found in Figure 7. 

5.0 MAV Baseline Comparison 

5.1 TSTO POST and OTIS Trajectory Comparison 

Using the payload, dry mass, thrust and Isp assumptions listed in Table 1 and Table 2 an OTIS TSTO 

model was developed at NASA’s Glenn Research Center (GRC) along with a POST TSTO model by the 

team at NASA’s Marshall Space Flight Center (MSFC). The existing TSTO baseline mission and launch 

site assumptions were also used as defined in Table 4. This includes the important assumption of a 

vertical launch orientation and the use of an optimal launch azimuth. As described above, the propellant 

loads for both the first and second stages were allowed to vary so that the minimum overall GLOM could 

be achieved. The orbital targets were defined using orbit radius, inertial velocity, inertial flight path angle 

and inclination with the values listed in Table 9. 
NASA/TM—2011-216968 12 

TABLE 9.—TRAJECTORY TARGET PARAMETERS 

Orbital target parameter Value 

Orbit radius (km) 3893.9 

Inertial velocity (km/s) 3.316 

Inertial flight path angle (degrees) 0.0 

Orbital inclination (degrees) 45.0 

Figure 8.—Coordinate system used to define launch inertial Euler control angles. 

Both programs used launch inertial Euler angles to control the vehicle orientation during the first and 

second burns. Figure 8 shows the basis for the launch inertial Euler control angles. This coordinate 

system is centered at the longitude and geodetic latitude of the launch site with a fundamental plane 

formed by the y and z-axis, parallel to local horizontal. The x-axis, Xlaunch, is perpendicular to this plane 

and points up (i.e., lies along the positive radius vector). The z-axis, Zlaunch, is the reference direction and 

points downrange along the launch site azimuth, as measured clockwise around Xlaunch, with the y-axis, 

Ylaunch, completing the right-handed system. The launch inertial Euler angles, are then calculated based on 

the coordinate system in Figure 8 using a 1-3-2 Euler angle rotation as shown in Figure 9. In this diagram, 

the first rotation is by the inertial Euler roll angle, , around the vehicle’s x-axis, Xbody, which in initially 

concurrent with Xlaunch. The second rotation of the inertial Euler yaw angle, , is then completed around 

the vehicle z-axis, Zbody. The third and final rotation is the inertial Euler pitch angle, , around the vehicle 

y-axis, Ybody. 
NASA/TM—2011-216968 13 

Figure 9.—Launch inertial Euler control angle rotation sequence. 

TABLE 10.—COMPARISON OF OTIS AND POST BASELINE TSTO 

BASELINE TRAJECTORIES 

Comparison parameter POST OTIS POST - OTIS 

Gross lift-off mass (kg) 271.75 272.63 –0.88 (0.32%) 

Launch azimuth (deg) 88.77 87.56 1.21 (1.37%) 

First stage propellant load (kg) 149.31 153.85 –4.54 (–3.04%) 

Second stage propellant load (kg) 48.24 44.67 3.58 (7.41%) 

Mission time (s) 656.67 659.09 –2.42 (–0.37%) 

Maximum dynamic pressure (Pa) 11956.65 12290.78 –334.13 (–2.79%) 

Maximum dynamic pressure (psf) 249.72 256.70 –6.98 (–2.79%) 

Both the POST and OTIS models use one linear segment to control the inertial Euler pitch angle during 

pitch over, with inertial roll and yaw angles set to zero. For this analysis, a linear control segment is defined 

as period of time where the control angle is varied at a constant (linear) rate. To reach a zero angle of attack 

(AOA) before first stage burnout, aerodynamic control angles (AOA, side slip, and bank angle) are then 

used with one linear control segment for each angle. After first stage burnout, aerodynamic control angles 

continue to be used to maintain a zero aerodynamic angle gravity turn. The second stage burn then uses one 

linear segment to control the inertial Euler pitch angle, with the inertial Euler roll and yaw angles held 

constant. For the TSTO vehicle model, the vehicle orientation is assumed to remain unchanged throughout 

the coast period up to the start of the final burn through use of the vehicle’s reaction control system (RCS). 

The OTIS and POST baseline vehicle models, using the assumptions detailed above, are shown in Table 10. 

All comparisons in Table 10 are relative to POST, meaning the OTIS result is subtracted from POST and 

then compared to the POST result to determine the percentage difference. 

The comparison results demonstrate a match of the MAV trajectory from each program with a GLOM 

difference between the POST and OTIS baselines of less than 1 kg or about 0.3 percent. Due to the control 

rate restriction imposed it can be seen that both the OTIS and POST GLOM are approximately 5 kg greater 

than the existing TSTO baseline of 267.5 kg, which is consistent with the GLOM trend found in Figure 3. 

The percentage deltas in the propellant load of each stage appear to be large, but the total propellant burned 

by each simulation is similar, as evident by the small GLOM differences. The different solutions found by 

each program cause more propellant to be burned by OTIS in the first stage and less in the second. It is 
NASA/TM—2011-216968 14 

evident that these differences in each burn also result in slightly different burn times, again with little change 

to the overall trajectory. Finally the maximum dynamic pressure difference is a direct result of the slightly 

longer OTIS burn on the first stage. A dynamic pressure difference of 6.98 psf, out of 249.7 psf, is a small 

difference compared to loads experienced by many Earth based launch vehicles. 

In conjunction with the small deltas in the parameters discussed, similar trends in other key trajectory 

parameters also demonstrate the close POST/OTIS model match. Important trajectory parameters compared 

for match purposes include all vehicle control angles, physical states and loading indicators. All parameter 

comparisons are not shown here for brevity. Figure 10 through Figure 13 show the geodetic altitude, inertial 

velocity, inertial pitch angle, angle of attack, and dynamic pressure plotted against mission elapsed time 

(MET). All plots show matching trends with only minor differences. The differences in the length of the 

first and second burn, as discussed above, can be seen more clearly in the plot of inertial velocity and 

geodetic altitude versus time, Figure 10. OTIS adds more velocity in the first burn; both programs then lose 

velocity through the coast to apoapsis and, after the second burn, end at the same inertial velocity target. The 

effects of the Mars GRAM wind model are evident in the plot of inertial pitch angle, Figure 11, between 

approximately 20 and 150 sec. The odd shape found from the control history of both programs results from 

holding zero angle of attack through the wind profile modeled. The assumption made is that the vehicle will 

always stay oriented with the velocity vector relative to the wind, which may not be the case in the real 

world. This simplifying assumption has very little impact in overall vehicle performance but does affect the 

shape of the controls and launch azimuth necessary to target the required inclination. Figure 14 and 

Figure 15 demonstrate how the control angle histories change when no wind profile is modeled. For the 

baseline case, when wind was not included, the GLOM increased by approximately 0.2 kg, demonstrating 

dependence on the wind for additional vehicle performance is insignificant. Further impacts of wind 

modeling and the assumption of control continuity will be discussed in Section 6.0. 

Figure 10.—Comparison geodetic altitude and inertial velocity histories for OTIS and POST TSTO baseline.
NASA/TM—2011-216968 15 

Figure 11.—Comparison of inertial Euler control angle history for OTIS and POST TSTO baseline. 

Figure 12.—Comparison of AOA history for OTIS and POST TSTO baseline. 
NASA/TM—2011-216968 16 

Figure 13.—Comparison of dynamic pressure history for OTIS and POST TSTO baseline. 

Figure 14.—OTIS inertial Euler pitch history comparison of wind modeling. 
NASA/TM—2011-216968 17 

Figure 15.—OTIS AOA history comparison of wind modeling effects. 

5.2 SSTO POST and OTIS Trajectory Comparison 

Similar to the TSTO models, a GRC OTIS model and MSFC POST model were completed for the 

SSTO baseline vehicle. Comparison of the POST and OTIS SSTO models were complicated by the 

optimization of thrust. As comparisons between the POST and OTIS solutions were completed, using the 

assumptions in Table 5 through Table 7, two main points became evident: POST was locked onto a suboptimal solution which did not utilize all available pitch control rate and OTIS was leveraging the 

modeled wind profile to find a slightly lower GLOM solution. To mitigate the effect of wind on the 

design solution, the wind profile was removed from all SSTO cases to prevent it from driving the design 

of the vehicle. With POST locked onto a suboptimal solution, a decision was made to compare POST and 

OTIS with OTIS constrained to use the POST generated values of optimal thrust and control rate. 

The SSTO baseline comparison also shows that allowing the vehicle orientation to vary at the start of 

the second burn results in both a smaller GLOM and smaller optimized thrust value. Similar to the TSTO 

vehicles, where it is assumed that the MAV RCS system is used to maintain a constant vehicle orientation, 

the SSTO RCS system would be used to orient the vehicle to a more optimal second stage burn orientation. 

A minimum GLOM OTIS solution was established using the baseline assumption of a 5 per second 

control rate with no lower limit on the optimized thrust value. As noted, matching the POST solution 

required additional constraints in OTIS, as listed in Table 11, to model the values used by POST. The 

parameters in Table 11 are the optimal values of the independent variables calculated by POST to 

minimize initial mass for the SSTO baseline. All three solutions for the SSTO vehicle can be found in 

Table 12, which compares the POST solution to the OTIS case that uses the restricted parameters in 

Table 11. Importantly, the last column in Table 12 is the minimum GLOM OTIS case that is considered 

the baseline solution to which all SSTO sensitivities should be compared. All comparisons in Table 12 are 

relative to POST, meaning the OTIS results is subtracted from POST and then compared to the POST 

results to determine the percentage difference. 
NASA/TM—2011-216968 18 

TABLE 11.—OTIS CONSTRAINTS NECESSARY 

TO MATCH POST SSTO BASELINE 

Additional OTIS constraints Value 

POST thrust (N) 6082.0 

POST control rate (degree/sec) 3.1 

TABLE 12.—COMPARISON OF OTIS AND POST BASELINE SSTO BASELINE TRAJECTORIES 

Comparison parameter POST OTIS (POST Match 

assumptions) 

POST - OTIS OTIS (minimum GLOM 

assumptions) 

Gross lift-off mass (kg) 288.2 288.6 –0.4 (–0.1%) 285.6 

Launch azimuth (deg) 91.8 87.2 4.6 (5.0%) 87.3 

Propellant load (kg) 218.2 218.8 –0.6 (–0.3%) 215.7 

Mission time (s) 1039.8 1062.0 –22.1 (–2.1%) 1204.2 

Maximum dynamic pressure (Pa) 3363.3 3505.6 –142.3 (4.2%) 2996.0 

Maximum dynamic pressure (psf) 70.2 73.2 –3.0 (–4.2 %) 62.6 

Thrust (N) 6082.0 6082.0 0.0 4425.7 

Max control rate (deg/s) 3.1 3.1 0.0 5.0 

Comparisons of POST to the OTIS cases using similar thrust and control rate assumptions, show that 

the OTIS GLOM matches POST within 0.1 percent or approximately 0.4 kg. However, this close match 

in GLOM does come with a slight difference to the trajectories flown by both programs. The two major 

differences show up in total mission time, 22.1 sec, and initial launch azimuth, 4.6. Differences in launch 

azimuth are primarily related to the control sets used for both solutions. Similar to the TSTO solution, the 

OTIS model uses the launch inertial Euler control set, Figure 9, for both vehicle burns. The POST model 

used the launch inertial Euler control set for the first burn, but due to convergence issues used the inertial 

aerodynamic control set for the second burn. Differing control sets necessitated the use of different launch 

azimuths to target the same inclination. The total mission time difference is closely correlated with the 

remaining large difference observed in dynamic pressure of 2.9 psf. This difference is smaller than that 

found in the TSTO comparisons, but a larger percentage due to the smaller over all SSTO maximum 

dynamic pressure. Compared to the TSTO baseline, the SSTO trajectories all fly a much slower, more 

depressed trajectory, due to the much smaller thrust used on the SSTO vehicle. When comparing the 

SSTO trajectories, the POST case flies a slightly more lofted trajectory, hence the lower dynamic pressure 

of 70.2 psf. This causes POST to reach apoapsis slightly before the OTIS trajectory resulting in a smaller 

overall mission time. 

The minimum GLOM OTIS case, by using a lower thrust and body control rates of up to 5 per 

second, is able to reduce GLOM by an additional 3 kg compared to POST. This comes with a dynamic 

pressure 7.7 psf lower than the POST case and a significantly longer total mission time. The lower thrust, 

coupled with a higher control rate, allows OTIS to gain velocity over a longer period of time resulting in 

longer first burn. This effect results in the lower dynamic pressure observed for this trajectory. The 

differences and similarities between all three trajectories are more easily observed in plots of geodetic 

altitude, inertial velocity, inertial Euler pitch angle, inertial Euler yaw angle, and dynamic pressure plotted 

against mission elapsed time (MET) found in Figure 16 through Figure 19. 

In looking at these comparison plots, key characteristics are noted. First is the difference in burn 

lengths that is evident in Figure 16, which shows inertial velocity and geodetic altitude. The Minimum 

OTIS GLOM case can be observed to burn substantially longer than the other two cases and adds more 

velocity during the first burn. However it is interesting to note, that this larger velocity is coupled with a 

less lofted trajectory, resulting in the much longer burn time. Also of note is the absence of wind effects 

in the inertial control angles, due to the removal of the wind model for the SSTO vehicle analysis. Finally, 

both the inertial pitch and yaw plots, Figure 17 and Figure 18, clearly show the discontinuous control 

angles at the beginning of the second burn in both the POST and OTIS simulations. 
NASA/TM—2011-216968 19 

Figure 16.—Comparison of geodetic altitude and inertial velocity histories for POST and OTIS SSTO 

baselines. 

Figure 17.—Comparison of inertial Euler pitch control history for POST and OTIS SSTO baselines. 
NASA/TM—2011-216968 20 

Figure 18.—Comparison of inertial Euler yaw control history for POST and OTIS SSTO baselines. 

Figure 19.—Comparison of dynamic pressure history for POST and OTIS SSTO baselines. 
NASA/TM—2011-216968 21 

The SSTO match results again demonstrate that with consistent assumptions, POST and OTIS produce 

similar trajectory results. Comparisons between these trajectories show that both programs are modeling the 

SSTO vehicle in a similar manner indicating matching simulations. This is demonstrated both in the 

performance match and through comparison of the trajectory parameter trends. In this case, OTIS was able 

to fully utilize the baseline mission constraints to find a more optimal solution. Additional discussion of the 

use of a wind model and its effects on the SSTO GLOM sensitivities is included in Section 7.0. 

6.0 TSTO GLOM Sensitivities 

6.1 GLOM Sensitivity to Target Inclination, Launch Latitude, and Launch Elevation 

Before, and to a lesser degree after, a landing site is selected there is the potential for variability in the 

location and type of terrain on which the MAV launch platform may come to rest. Although the MAV 

lander is targeted to land with 30 latitude of the equator, a broader latitude range of 0 to 90 was 

analyzed to establish complete GLOM growth trends. The launch elevation angle, as shown in Figure 6, is 

defined as the launch angle of the MAV measured from local horizontal. This results in a 90 elevation 

angle when the MAV is launched vertically as modeled for the TSTO and SSTO baseline cases. Launch 

latitudes between 0 and 90 were analyzed at launch elevations from 30 to 90. Also shown in Figure 6 is 

the orientation of the MAV launch azimuth relative to the optimal launch azimuth. For all latitude/ 

inclination/elevation sensitivities shown, the vehicle is always launched along the optimal launch azimuth, 

which corresponds to an off optimal azimuth angle of zero as defined in Figure 6. Section 6.2 will discuss 

the nonoptimal launch azimuth geometry in further detail and present GLOM sensitivities at varying off 

optimal launch azimuth and elevation combinations. 

For each latitude and elevation combination, a range of target inclinations up to 90 was also 

analyzed. From spherical geometry, only inclinations greater than or equal to the current latitude can be 

reached during ascent, as shown in Figure 5. To reach an inclination lower than the current latitude, an 

additional burn would be necessary after reaching orbit. The GLOM penalty for doing an additional burn 

is quite high as demonstrated in Figure 20, which shows the total GLOM increase from the OTIS TSTO 

baseline, 272.6 kg, plotted against on-orbit inclination change capability. The GLOM increase observed 

consists of the propellant necessary to perform the on-orbit inclination change maneuver as well as the 

additional MAV GLOM needed to lift that propellant to orbit. If the MAV were to launch from a 30

inclination and needed to end up in an equatorial (0 inclination) orbit, a 30 on-orbit inclination change 

would be necessary with an associated GLOM increase of approximately 168 kg. 

For a launch latitude of 0 (equatorial) the resulting GLOM growth for varying both launch elevation 

and target orbit inclination are shown in Figure 21. It is noted that for optimal azimuth launches at a 

launch latitude and target inclination of zero, any elevation angle less than 90 results in a GLOM less 

that the TSTO baseline of 272.6 kg. The minimum total GLOM was found at a launch elevation angle 

near 45. This can be more clearly seen in Figure 22, which shows only the 90, 45, and 30 launch 

elevation angles. A direct relationship between GLOM and inclination was hard to develop due to the 

nonlinear nature of the results. Figure 23 plots the slope of the curves shown in Figure 22 and 

demonstrates this nonlinear behavior. It can be observed that as the targeted inclination reaches 90, the 

change in GLOM per degree inclination approaches a constant value of 0.33 kg GLOM per degree in 

inclination. This translates into a maximum GLOM necessary to cover launches to inclinations up to 90

of approximately 286 kg, an increase of about 13 kg over the TSTO baseline. Further, by limiting 

launches to inclinations less than or equal to 45, the baseline GLOM can be maintained for any launch 

elevation angle. For brevity, only the equatorial latitude results are shown here. The remaining elevation 

and inclination combinations for all launch latitudes are shown in Appendix A. 
NASA/TM—2011-216968 22 

Figure 20.—GLOM growth for an on-orbit inclination change necessary to reach inclinations lower 

than the launch latitude. 

Figure 21.—GLOM sensitivity for all launch elevations and target orbit inclinations at a launch latitude of 0. 
NASA/TM—2011-216968 23 

Figure 22.—GLOM sensitivity for selected elevations and target orbit inclinations at a launch 

latitude of 0. 

Figure 23.—Slope of GLOM change per degree of inclination for a launch latitude of 0 at selected 

launch elevations. 
NASA/TM—2011-216968 24 

Interesting insight results from looking at the same GLOM sensitivities at a constant launch elevation 

angle for combinations of launch latitude and target inclination, found in Figure 24 for a 90 launch 

elevation and Figure 25 for a 45 launch elevation. Both of these figures demonstrate that for any target 

inclination, GLOM grows by about 0.23 kg per 10 of launch latitude. The data run for all other 

combinations of launch parameters, not shown here, demonstrates that GLOM growth of this magnitude 

can be expected for all launch elevations. This means that if targeting a 90 inclination orbit, the GLOM 

difference between launching from a pole, instead of the equator, is only about 2 kg. This is a significant 

finding as this indicates that launch latitude makes very little difference in the size of the MAV, as long as 

that latitude is less than or equal to the target inclination. 

Figure 24.—GLOM sensitivity for all launch latitudes to target orbit inclinations greater than 

the launch latitude, at a launch elevation of 90. 

Figure 25.—GLOM sensitivity for all launch latitudes to target orbit inclinations greater than 

the launch Latitude, at a launch elevation of 45. 
NASA/TM—2011-216968 25 

For a launch latitude of 45 and a vertical launch elevation, a number of inclination sweeps were run 

to estimate the effects of control rate, control continuity and wind modeling on the GLOM sensitivities 

presented in this section. It is expected that the trends shown here are representative of the remaining 

launch elevations and launch latitudes. As Figure 26 and Figure 27 show, control continuity and the use 

of a wind model have less that 0.25 kg effect on the GLOM trends generated. Although not shown here, 

the effects of these modeling assumptions remain similar when combined. The use of varying pitch body 

control rates for these sweeps was also analyzed, with the results found in Figure 28. GLOM is 

predictably lower with the use of higher body control rate limits and matches closely with the GLOM 

trend presented in Figure 3. 

Figure 26.—Impact of control continuity on TSTO GLOM sensitivity of a vertical 

launch elevation to an inclination greater than the launch latitude of 45. 

Figure 27.—Impact of wind modeling on TSTO GLOM sensitivity of a vertical 

launch elevation to an inclination greater than the launch latitude of 45. 
NASA/TM—2011-216968 26 

Figure 28.—Impact of control rate limit on TSTO GLOM sensitivity of a vertical launch 

elevation to an inclination greater than the launch latitude of 45. 

6.2 Sensitivity to Launch Azimuth and Launch Elevation 

The GLOM sensitivities discussed for latitude, inclination and launch elevation, all assume that the 

MAV is able to lift off and pitch over directly into the optimal launch azimuth. This provides the minimal 

GLOM for each set of launch conditions. The optimal launch azimuth varies greatly as the launch latitude 

and target inclination change. However, the entry, descent and landing system may not be able to 

guarantee that the MAV launch platform will land in an orientation that allows a direct launch into the 

optimal launch azimuth. This necessitates that GLOM sensitivities be established for launches to 

azimuths not aligned with the optimal launch azimuth. As depicted in Figure 6, the distance from the 

optimal launch azimuth for each case considered is quantified as the angle from the optimal launch 

azimuth. An angle from optimal azimuth of zero results in a vehicle launch aligned with optimal, while an 

angle 180 represents a launch in exactly the opposite direction from the optimal azimuth. 

GLOM sensitivities were established from the baseline launch assumptions, with a launch from a 

latitude of 45 and an inclination target of 45. Each nonoptimal launch azimuth case was analyzed using 

the full set of control angles, allowing for the vehicle’s pitch, yaw and roll angles to be varied. This is 

necessary since it is not possible to launch from varying launch azimuths to the same inclination target 

without the use of out of pitch plane control. Similar to the TSTO baseline, all out of pitch plane controls 

are calculated using one linear control segment during the first stage burn with a second linear segment 

used to ramp aerodynamic angles to zero. Each angle is also controlled using one linear segment during 

the second stage burn. 

Launch elevation angle is a key driver in the sensitivity of GLOM to launch azimuth variation. If the 

vehicle is assumed to always launch at a 90 launch elevation angle, as shown in Figure 6, the optimal 

azimuth can be reached with very little effect to GLOM. As launch elevation angle is decreased, the effect 

on GLOM to launch at varying azimuths increases dramatically. This assessment considers the impact to 

GLOM if launch elevation can be guaranteed within 30 of the targeted launch elevation. Therefore, 

GLOM comparisons were made for elevation angles from 60 to 90, to establish sensitivities for a 
NASA/TM—2011-216968 27 

mission designed to launch vertically. GLOM comparisons were also made for a mission designed to 

launch at a 45 elevation, for elevation angles from 30 to 75. The results for off optimal azimuth angles 

from 0 to 180 are shown for the vertical launch in Figure 29 with deltas based on the baseline GLOM of 

272.6 kg. Figure 30 shows the 45 launch elevation sensitivities, compared to a baseline GLOM of 

265.8 kg. It is assumed that GLOM sensitivities to launch azimuth are symmetric, with the GLOM growth 

for off azimuth angles from 0 to –180  being similar to the results for off azimuth angles from 0 to 

180 shown here. 

Figure 29.—GLOM delta for off optimal launch azimuths based on vertical launch with 

GLOM of 272.6 kg. 

Figure 30.—GLOM delta for off optimal launch azimuths based on 45 elevation 

launch with GLOM of 265.8 kg. 
NASA/TM—2011-216968 28 

The off optimal launch azimuth cases analyzed demonstrate that for a nonvertical launch, maintaining 

the launch azimuth within approximately 80 of optimal, keeps the total GLOM under the documented 

TSTO baseline of 272.6 kg. For a targeted 45 launch, if the launch azimuth can be guaranteed with 

approximately 70 of optimal, the TSTO baseline GLOM can be maintained. Additionally a launch 

azimuth restriction of approximately 40 from optimal would allow for GLOM to be reduced by about 

6 kg from the TSTO baseline vertical launch GLOM. If the launch azimuth cannot be guaranteed within 

these ranges, it is apparent that launching close to vertical provides the smallest GLOM growth for large 

off azimuth angles. The performance sensitivities shown are only valid for launch inclinations and 

latitudes between 0 and 45. Launches to inclinations greater than 45 will result in higher GLOM 

increases for off azimuth launches, caused by the larger GLOM necessary for an optimal azimuth launch 

to high inclinations. 

Similar to the previous set of sensitivities, additional GLOM sweeps were completed to identify the 

effects of varying control rates as well as not enforcing control continuity for the start of the second burn. 

These cases were run for only a launch elevation of 45 while targeting an orbital inclination of 45. The 

angle from optimal azimuth was varied between 0 and 90, with GLOM comparisons made back to the 

baseline TSTO GLOM of 272.6 kg. Figure 31 shows the effect on the presented GLOM sensitivities, when 

the maximum body control rate was varied. In these cases all angles were controlled and therefore limited to 

this maximum rate. These cases are driven primarily by the speed at which they can roll and yaw into the 

optimal azimuth so it is not surprising that increasing controls rates reduce the GLOM at 90 off azimuth by 

10 kg. The use of control continuity was also examined, while maintaining the baseline body control rate of 

5 per second with results shown in Figure 32. It is quickly observed that control continuity has very little 

effect the GLOM trend observed, with GLOM being reduced by less than 0.25 kg. 

Figure 31.—GLOM delta for off optimal launch azimuths using varying control rate limits, based on a 

GLOM of 272.6 kg. 
NASA/TM—2011-216968 29 

Figure 32.—GLOM delta for off optimal launch azimuths without second stage control continuity, 

based on a GLOM of 272.6 kg. 

6.3 Circular Orbit Altitude Sensitivity 

With the sensitivity to insertion orbit inclination well characterized, it was also necessary to 

determine sensitivity to the targeted circular orbit altitude. As Figure 33 shows, the delta in GLOM for 

variations in targeted altitude are small. A weight change of approximately 5.1 kg of GLOM per 50 km of 

altitude was observed, with GLOM growing as circular orbit altitude increases. This partial was much 

lower than expected and results in minimal impact to the vehicle for changes in final orbit altitude. 

6.4 Vehicle Mass and Engine Parameter Sensitivities 

6.4.1 Stage Mass 

All sensitivities presented to this point assumed vehicle mass and engine parameters consistent with 

the TSTO baseline. To analyze the effect of changes to the inert mass of both TSTO stages, a matrix of 

different first and second stage mass combinations were run. The range studied represents a total inert 

mass range of 30 to 70 kg, with the mass shifted between each stage to cover all combinations of first and 

second stage masses. After running the entire matrix of cases developed, two different plots were 

generated. The first, Figure 34, shows the GLOM growth along lines of constant first stage mass, for 

varying second stage masses. The second, 

Figure 35, show the opposite, with lines of constant second stage mass for varying first stage weights. 
NASA/TM—2011-216968 30 

Figure 33.—TSTO GLOM sensitivity to circular orbit altitude. 

From Figure 34 and Figure 35, partials were identified for GLOM growth with respect to mass 

changes in each stage. These show that for every kilogram of first stage growth, a GLOM increase of 

1.9 kg can be expected. For the same 1 kg growth on the second stage, a 4.6 kg growth in GLOM can be 

expected. A third partial falls out from the first two; in that vehicle GLOM can be decreased by 2.7 kg for 

every kilogram of mass that can be shifted from second stage to the first. Since the first stage can stay 

with the vehicle until just before second stage ignition, this could present the opportunity to reduce 

GLOM by shifting functionality, and mass, to the first stage. These partials demonstrate the well-known 

benefit of staging, showing that mass added to the first stage comes at a cheaper cost to performance than 

mass added to the second stage. 

For a constant Isp, the partials identified apply to any combination of inert masses, and do not change 

as total vehicle mass increases. As other vehicle parameters changed, the calculated mass partials also 

change. This is evident in Figure 36 and Figure 37, which show the change in dry mass partial as Isp is 

changed for both the first and second stage. Although the partial does not change drastically over the Isp 

range analyzed, it does show that increases in Isp allow mass to be added to the vehicle at a lower rate. 

However, the reverse also applies that the GLOM savings are mitigated at higher Isp values for decreases 

in stage mass. These are important partials for vehicle designers to keep in mind as investments are 

considered in stage mass reductions and Isp improvement. 
NASA/TM—2011-216968 31 

Figure 34.—TSTO GLOM sensitivity to second stage mass variation for a fixed first stage mass. 

Figure 35.—TSTO GLOM sensitivity to first stage mass variation for a fixed second stage mass. 

 
NASA/TM—2011-216968 32 

Figure 36.—Second stage dry mass sensitivity at varying values of Isp. 

Figure 37.—First stage mass sensitivity at varying values of Isp. 
NASA/TM—2011-216968 33 

Figure 38.—TSTO GLOM sensitivity to Isp, constant for both stages. 

6.4.2 Engine Isp and Thrust 

Engine parameter GLOM sensitivities are also very important to consider for the MAV design. As 

done for other sensitivities, vehicle masses and mission parameters are held constant to the baseline 

assumptions. For thrust variations, Isp is held constant to baseline values while the thrust is held constant 

for the Isp partial. It is recognized the Isp and thrust are typically linked, along with potential mass 

increases. But as with other sensitivities discussed, this is intended to demonstrate the singular effect of 

each parameter. The effect to GLOM of varying the Isp is shown in Figure 38. The assumption was made 

that the Isp of both stages is the same, leading to the Isp listed in Figure 38 being used for both the first 

and second stages. 

It is noted the resulting trend follows what would be expected due to the exponential nature of the 

rocket equation. An Isp range of 255 to 355 sec was analyzed assuming a representative solid propellant 

Isp similar to the baseline of 285 sec with a representative liquid system Isp of 310 sec. Due to the 

nonlinear nature of the Isp GLOM trend, linear relationships around each representative system Isp were 

established, and are valid for approximately 10 sec of Isp around each design point. For a solid system, 

every additional second of Isp, a GLOM reduction of approximately 1.3 kg can be expected. A liquid 

system showed similar results with each additional second of Isp resulting in a GLOM reduction of 

approximately 1 kg. 

Unlike Isp, the thrust of each stage was considered separately. For each stage the sensitivity was 

analyzed around the baseline thrust value. The GLOM sensitivity for variations in second stage thrust, 

Figure 39, shows that MAV GLOM is insensitive to second stage thrust, which is not unexpected. The 

very low vehicle gross mass of the second stage (payload, propellant, and dry mass) results in a very high 

thrust to weight ratio for the range analyzed, allowing little change in the propellant mass needed for a 

short circularization burn. The first stage thrust GLOM sensitivity, Figure 40, shows a reduction of 

GLOM is possible by reducing first stage thrust. The minimum GLOM solution was found at a thrust 

value of 8930 newtons, which is less than half the baseline first stage thrust value. Reducing thrust to this 

value results in a GLOM reduction of only 4.4 kg. 
NASA/TM—2011-216968 34 

Figure 39.—TSTO GLOM sensitivity to second sage thrust, first stage thrust held constant. 

Figure 40.—TSTO GLOM sensitivity to first stage thrust, second stage thrust held constant. 
NASA/TM—2011-216968 35 

Figure 41.—TSTO delta GLOM difference for off azimuth launches using optimal thrust, based on a 

GLOM of 272.6 kg. 

Although the effects of using an optimized thrust are small for the baseline launch assumptions used 

for Figure 40 and Figure 41 shows that the effect of thrust on GLOM begins to increase when 

incorporated in with other vehicle sensitivities. At angles far from the optimal azimuth, the GLOM 

savings from the longer burn resulting from a lower, optimal, thrust grow considerably. 

Figure 42 demonstrates that the GLOM reduction from Isp improvements is maintained for off 

azimuth launches at an almost constant reduction in GLOM. Both curves in Figure 42 were run using the 

same thrust value of 21,577 N further indicating that GLOM savings result from increases in Isp only. 

These results indicate that further study is necessary of the secondary effects on other vehicle sensitivities 

caused by engine parameter changes, as large additional GLOM benefits may be possible. 
NASA/TM—2011-216968 36 

Figure 42.—TSTO delta GLOM difference for off azimuth launches using a representative liquid Isp, based 

on a GLOM of 272.6 kg. 

6.5 Verification of Combined TSTO Sensitivities 

The TSTO sensitivities, as presented, all considered changes in only a maximum of three parameters at 

a time. Additionally sensitivities to off optimal azimuth were run only for nominal mission assumptions. 

The data presented in this paper is most useful if the multiple sensitivities can be combined to quickly 

determine GLOM predictions for numerous vehicle and mission configurations. To show the effect of doing 

this, cases were selected that combined various sensitivities. In some cases this included changing launch 

site, mission and vehicle parameters concurrently. 

To complete these comparisons, the plots of GLOM sensitivity for elevation and inclination as well as 

those of elevation and off optimal azimuth angle were used in combination with the numerous vehicle 

partials identified. For each case, a set of parameters was selected to vary from their nominal values. The 

GLOM increase, or decrease, from TSTO baseline is then estimated using the presented vehicle sensitivities. 

OTIS cases were then run using the same sets of parameters to verify the GLOM predictions. Cases were 

not chosen at random but instead use combinations of parameters that are expected to be of some interest for 

the current MAV design and are intended to show the potential effects of using the sensitivities presented 

outside the ranges analyzed. The vehicle cases verified are shown in Table 13, with the vehicle parameters, 

mission parameters, predicted GLOM and the actual GLOM from OTIS. The GLOM comparisons are 

calculated as the actual GLOM subtracted from the predicted GLOM and then compared back to the actual 

GLOM as a percentage. All parameters from the baseline TSTO case are also included in Table 13 to allow 

comparisons of the changes made for each verification case. 
TABLE 13.—VERIFICATION OF PREDICTED TSTO GLOM USING TSTO SENSITIVITIES 

NASA/TM-2011-216968 37
NASA/TM—2011-216968 38 

When nominal thrust and Isp values are used, the results demonstrate that for launches under a latitude 

of 45, off azimuth GLOM predictions using performance sensitivities match within approximately 

5 percent of the actual GLOM. When thrust and Isp variations are combined with off optimal azimuth 

angles, predictions are off by larger amounts, but still match within approximately 10 percent of the actual 

GLOM. It is clear that additional study of off azimuth results at all possible launch latitudes is necessary to 

establish more accurate predictions. GLOM savings are observed for using lower Isp and thrust values for 

all launch conditions. As already discussed, the engine sensitivities established for the baseline TSTO case 

do not directly apply when baseline mission and launch conditions are changed as shown in Figure 41 and 

Figure 42. This is due to the changes in burn times that occur with changing engine parameters, which 

cannot be easily predicted. If engine improvements are considered, additional studies of off nominal 

launches need to be analyzed in further detail. Overall these results demonstrate that the off azimuth GLOM 

sensitivities, run at a 45 latitude, provide a good preliminary estimate of off azimuth GLOM growth at 

lower latitudes. However, caution is advised for application of performance sensitivities at latitudes close to 

the equator and in cases that use large changes in thrust and Isp.

6.6 Nominal Mission Availability for a MAV Designed for 

Off Nominal Launch Conditions 

To cover off nominal launches, the MAV will be designed with a GLOM large enough to cover a wide 

variety of launch and mission conditions. The possibility exists that a large GLOM MAV could still land in 

an optimal launch configuration, making it necessary for it to provide only enough performance for the 

baseline mission. To verify that a large GLOM MAV can fly a baseline mission, propellant masses from 

two verification cases, shown in Table 14, were run using the baseline mission and launch site assumptions 

as described in Table 4. The assumption was maintained that a solid rocket system was used, such that the 

burn could not be cut off early. Three-angle control was allowed and launch at the optimal launch azimuth 

was assumed. In all cases, a control scheme could be found in OTIS that allows the vehicle to waste the 

extra performance and achieve nominal mission targets with a mass equal to the payload and second stage 

dry mass. Figure 43 through Figure 45 show the selected cases compared to the TSTO baseline in geodetic 

altitude, inertial velocity, inertial Euler pitch and inertial Euler yaw control angles. All plots show large 

differences that are a result of OTIS bleeding off extra performance to accomplish a nominal mission. This 

analysis clearly demonstrates that the MAV can be designed for the worst possible launch conditions while 

maintaining the ability to launch at more optimal launch orientations. 

TABLE 14.—LARGE GLOM VERIFICATION CASES 

Verification 

case 

Launch 

latitude, 

deg 

Angle from 

optimal 

azimuth, 

deg 

Target 

inclination, 

deg 

Launch 

elevation, 

deg 

Gross 

liftoff 

mass, 

kg 

Stage 1 

propellant, 

kg 

Stage 2 

propellant, 

kg 

Case 1 30 180 45 30 343.4 203.0 66.4 

Case 4 30 180 45 80 275.1 152.7 48.3 
NASA/TM—2011-216968 39 

Figure 43.—Geodetic altitude and inertial velocity of large GLOM MAV, flown on a nominal mission. 

Figure 44.—Inertial Euler pitch history of large GLOM MAV, flown on a nominal mission. 
NASA/TM—2011-216968 40 

Figure 45.—Inertial Euler yaw history of large GLOM MAV, flown on a nominal mission. 

7.0 SSTO Performance Sensitivities 

7.1 Engine Thrust and Isp 

Only a small subset of the TSTO sensitivities were run for the SSTO vehicle. This was done to get a 

better understanding of the validity of using a SSTO for this mission, without committing resources to a 

study of the full set of launch site sensitivities analyzed for the current baseline TSTO design. The SSTO 

baseline description noted that thrust optimization was used to establish the SSTO baseline. In addition to 

the optimal thrust value of 4425 Newtons, the SSTO GLOM corresponding to thrust values up to the 

TSTO baseline of 21576 Newtons were calculated. Results are shown for a trajectory without wind 

modeling as the curve with diamond markers in Figure 46. All points in Figure 46 were run by varying 

thrust only, with all other vehicle parameters, launch conditions and mission targets set to SSTO baseline 

values as described in Table 5, Table 6, and Table 7. Additionally, GLOM sensitivities over the same 

thrust range were completed using the wind profile modeled in the TSTO case with results in Figure 46 

plotted with square markers. 

Three important conclusions are drawn from this data. First, is that the difference in GLOM with and 

without wind modeling over the same thrust range is less than 0.5 kg. Using an optimized thrust for the 

SSTO case a larger GLOM reduction is observed when compared to the TSTO thrust sensitivities. For the 

TSTO case, shown in Figure 40, a reduction in GLOM of approximately 4.4 kg is observed when using 

an optimized thrust value. Figure 46 clearly shows that for the SSTO case, the use of an optimal thrust 

value reduces GLOM by 21.6 kg, almost five times the TSTO results. Although an overall optimal thrust 

was established, which corresponds to the minimum GLOM SSTO case, the curve is very flat near this 

optimal thrust with only 0.4 kg of GLOM growth at thrust level up to 5300 N. This allows for a broader 

array of thrust design solutions, with minimal penalty to GLOM. This has important design ramifications 

for the SSTO design. If a near optimal thrust vehicle design cannot be used for an SSTO MAV, a 

significant increase in GLOM would be necessary. 
NASA/TM—2011-216968 41 

Figure 46.—SSTO GLOM sensitivity to thrust with and without wind modeling. 

Figure 47.—SSTO GLOM sensitivity to engine Isp. 

GLOM values for variations in Isp were also calculated; again holding thrust at the optimal values 

with all other vehicle parameters set to the SSTO baseline values. Figure 47 shows GLOM sensitivities to 

Isp from 255 to 355 sec. Similar to the TSTO Isp sensitivity two average Isp values were established for 

solid and liquid systems: 285 for solid motors and 310 sec for liquid rocket systems. Around these Isp 

values, approximate linear slopes were established with 1.4 kg of GLOM reduction found for every 

second of solid motor Isp increase and 1.1 kg of GLOM reduction predicted for every second of liquid 

rocket engine Isp increase. These values are very similar to the TSTO Isp results and are important to note 

that GLOM reductions possible may allow higher Isp engines to trade very well into the MAV system. 
NASA/TM—2011-216968 42 

7.2 Stage Mass Sensitivities 

The SSTO stage mass, including payload fairing, was varied between an absolute minimum of 25 kg 

to a maximum of 70 kg. As in other sensitivities, all other parameters were held to SSTO baseline values. 

A linear trend of approximately 3.9 kg of GLOM growth per kg of additional dry stage mass was 

calculated and shown in Figure 48. 

Figure 48.—SSTO GLOM sensitivity to dry mass. 

Figure 49.—SSTO GLOM sensitivity to circular orbit altitude. 
NASA/TM—2011-216968 43 

7.3 Circular Orbit Altitude Sensitivity 

The circular orbit altitude trade was run for the SSTO vehicle design, to determine the additional 

benefit of using a SSTO design in combination with a lower altitude circular orbit. The results, found in 

Figure 49, show that the sensitivity of the SSTO design to circular orbit altitude is smaller than that of the 

TSTO design. A slope was calculated of approximately 2.3 kg of GLOM for every 50 km of additional 

orbital altitude, compared to the 5.1 kg slope for the TSTO vehicle. This difference is largely due to the 

lower thrust used in the SSTO case, allowing for adjustments in the trajectory to be made without large 

changes in the SSTO GLOM. 

8.0 Conclusions 

A large number of vehicle sensitivities were completed for both the TSTO and SSTO MAV designs. 

When possible simple numerical sensitivities, commonly referred to as vehicle partial derivatives, were 

established to directly relate GLOM growth with the design parameter of interest. These design 

relationships have been highlighted throughout this paper and are summarized below for the TSTO and 

SSTO vehicles in Table 15. 

Two areas of the MAV trade space were found to have very little effect on the resulting vehicle 

GLOM: launch latitude for inclination targets greater than that latitude (when using an optimized launch 

azimuth) and the second stage engine thrust for the TSTO orbit vehicle. While other vehicle parameters 

cannot be classified as insensitive, the results show very small GLOM growth over the ranges analyzed. 

This is the case for GLOM growth due to circular orbit altitude in both the TSTO and SSTO vehicle 

designs. The TSTO GLOM also shows very little effect over a large range of first stage thrust values. This 

allows for a wide range of thrust solutions for either stage of the TSTO MAV design. 

The greatest impact to GLOM is observed in the launch site orientation sensitivities run for the TSTO 

vehicle. If azimuth cannot be controlled within a small range around the optimal launch azimuth, large 

growth in GLOM can be expected for off azimuth cases unless a near vertical launch can be guaranteed. It 

is also obvious from the relationships presented in Table 15 that the system mass and propulsion 

performance of the MAV could also have a large effect on GLOM, especially if large changes from the 

current baseline are made. 

TABLE 15.—MAV QUANTITATIVE VEHICLE SENSITIVITIES 

 TSTO Vehicle Design Sensitivities: 

o Approximately 5.1 kg of GLOM increase per 50 km of circular orbit 

o Approximately 4.6 kg of GLOM increase per kg of second stage dry mass 

o Approximately 1.9 kg of GLOM increase per kg of first dry stage 

o Approximately 2.7 kg of GLOM decrease per kg of second stage dry mass shifted to the first stage 

o Approximately 0.23 kg of GLOM per 10 of launch latitude, for constant launch elevation angle 

and constant target inclination 

 For a 90 inclination mission, GLOM grows by 2 kg when launching from the pole 

instead of the equator 

o For a solid system: approximately 1.3 kg of GLOM reduction per second of increased Isp 

o For a liquid system: approximately 1.0 kg of GLOM reduction per second of increased Isp 

o The use of a wind model in TSTO MAV analysis has less than a 0.25 kg impact on GLOM 

 SSTO Vehicle Design Sensitivities: 

o Approximately 3.9 kg of GLOM increase per kg increase in stage dry mass 

o Approximately 2.3 kg of GLOM increase per 50 km of circular orbit 

o For a solid system: ~1.4 kg of GLOM reduction per second of increased Isp 

o For a liquid system: ~1.1 kg of GLOM reduction per second of increased Isp 

o The use of a wind model in SSTO MAV analysis has less than a 0.5 kg impact on GLOM 
NASA/TM—2011-216968 44 

9.0 System Implications 

The primary intention of the results presented was to help guide decisions on the investments 

necessary to produce a MAV capable of launching in a variety of conditions and still remain small 

enough to fit into the landed mass restrictions. As these sensitivities were completed, the authors have 

developed a set of recommendations that could allow GLOM savings and still support a variety of launch 

site locations and conditions. 

First, if the landing system can guarantee the launch azimuth within approximately 40 of the optimal 

launch azimuth, the MAV should be designed to launch at a 45 elevation and incorporate the resulting 

reduction in GLOM. A change in the baseline launch elevation to 45, from vertical, could result in 

additional benefits to the launch platform as a 45 launch angle may be easier to achieve. It should be 

noted, that if azimuth cannot be guaranteed within 40 but could be guaranteed to within approximately 

70 of the optimal launch azimuth, a 45 launch elevation could be used while maintaining the current 

TSTO baseline mass. If azimuth restrictions are not possible, a launch elevation near 90 is necessary to 

minimize GLOM growth. 

The current analysis demonstrates the impact of launching at elevations of up to 30 from the design 

point. Due to the large GLOM variations that result from changes in launch elevation, it is recommended 

that launch elevation accuracy be restricted to approximately 10 from the design point. This would allow 

additional GLOM savings and provide more flexibility in the launch azimuth constraints necessary to 

utilize a lower baseline launch elevation. 

The final recommendation is related to the physical design of the TSTO MAV. Functionality could be 

moved from the second stage to the first with a GLOM savings of 2.7 kg per kilogram moved with no 

impact to performance due to the ability to jettison the first stage just before second stage ignition. 

Reconfiguring the distribution of important systems between both stages, could allow significant GLOM 

savings without a major change to the current MAV propulsion and mission assumptions. 

10.0 Future Work 

Further work is needed in three key areas to refine the current data: MAV body control rate limits, 

TSTO nonoptimal azimuth launches at low latitudes and SSTO launch orientation sensitivities. The 

existing 2001 TSTO baseline design, utilized body control rates of 20 per second; a rate believed to be 

unsuitable for the current vehicle design. For the sensitivities presented in this paper a 5 per second body 

control rate was assumed, as it is currently well within historically used limits. However, it was shown 

that off azimuth GLOM sensitivities could be mitigated to some extent with the use of a higher body 

control rate. Therefore, a more detailed study is necessary to determine what control rates could be used 

for MAV. It would be necessary to model the MAV using a six-degree of freedom simulation, which 

would allow the interaction of a gimbaled engine with the relatively small MAV to be studied in greater 

detail. With a six-degree of freedom model, differing vehicle body rates could be imposed to determine 

when, and if, the MAV becomes uncontrollable or exceeds structural design limits. 

The verification results presented indicate that further study of nonoptimal azimuth launches at lower 

launch latitudes is required to more accurately predict GLOM trends. This would include further analysis 

using the models already completed for this study and a more extensive trade matrix of inclination and 

launch latitudes for the off azimuth angles analyzed. The current data provides an adequate initial GLOM 

estimate for launches at latitudes lower than 45, but does not incorporate all necessary effects of 

launching from those latitudes. This is especially true if a higher Isp or lower thrust MAV design is under 

consideration, as errors could grow quite high for off optimal azimuth launches due to differences in burn 

time caused by engine parameters changes. 
NASA/TM—2011-216968 45 

Finally, if the SSTO vehicle design is to be strongly considered, launch site and launch orientation 

sensitivities need to be completed similar to those shown here for the TSTO design. These could be 

completed with the previously developed models using the analysis methodology described for the TSTO 

sensitivities. It is assumed that trends will be similar to the TSTO design, but the magnitude of SSTO 

GLOM growth could far exceed the TSTO design for some cases. 

NASA/TM—2011-216968 47 

Appendix A.—Gross Lift-off Mass Sensitivities for Launch Elevations 

From 0 to 90 Targeting Inclinations from 0 to 90 for 

Launch Latitudes From 0 to 90

Figure 50.—TSTO GLOM sensitivities for a launch latitude of 5.

Figure 51.—TSTO GLOM sensitivities for a launch latitude of 10.
NASA/TM—2011-216968 48 

Figure 52.—TSTO GLOM sensitivities for a launch latitude of 15.

Figure 53.—TSTO GLOM sensitivities for a launch latitude of 20.
NASA/TM—2011-216968 49 

Figure 54.—TSTO GLOM sensitivities for a launch latitude of 25.

Figure 55.—TSTO GLOM sensitivities for a launch latitude of 30.
NASA/TM—2011-216968 50 

Figure 56.—TSTO GLOM sensitivities for a launch latitude of 35.

Figure 57.—TSTO GLOM sensitivities for a launch latitude of 40.
NASA/TM—2011-216968 51 

Figure 58.—TSTO GLOM sensitivities for a launch latitude of 45.

Figure 59.—TSTO GLOM sensitivities for a launch latitude of 50.
NASA/TM—2011-216968 52 

Figure 60.—TSTO GLOM sensitivities for a launch latitude of 55.

Figure 61.—TSTO GLOM sensitivities for a launch latitude of 60.
NASA/TM—2011-216968 53 

Figure 62.—TSTO GLOM sensitivities for a launch latitude of 65.

Figure 63.—TSTO GLOM sensitivities for a launch latitude of 70.
NASA/TM—2011-216968 54 

Figure 64.—TSTO GLOM sensitivities for a launch latitude of 75.
NASA/TM—2011-216968 55 

References 

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IEEE Aerospace Conference, March 2004, Paper #1392. 

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“Mars Sample Return: Architecture and Mission Design,” 2002 IEEE Aerospace Conference, Paper 

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2007 IEEE Aerospace Conference, Big Sky, MT, March 2007. 

6. Dankanich, J.W., “Mars Ascent Vehicle Technology Planning,” 2009 IEEE Aerospace Conference, 

Big Sky, MT, March 2009. 

7. Stephenson, D., “Mars Ascent Vehicle – Concept Development,” AIAA–2002–4318, 38th Joint 

Propulsion Conference, July 2002. 

8. Hargraves, C.R., Paris, S.W., and Vlases, W.G., “OTIS Past, Present, and Future,” AIAA 92-4530 

1992. 

9. Brauer, G.L., Cornick, D.E., and Stevenson, R., “Capabilities and Applications of the Program to 

Optimize Simulated Trajectories,” NASA CR-2770, Feb. 1977. 

10. Nelson, D., “ Qualitative and Quantitative Assessment of Optimal Trajectories by Implicit Simulation 

(OTIS) and Program to Optimize Simulated Trajectories (POST),” Masters Individual Research 

Project, School of Aerospace Engineering, Georgia Institute of Technology, Atlanta, GA, 2001. 
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 ACRONYM(S)

NASA 

11. SPONSORING/MONITORING

 REPORT NUMBER

NASA/TM-2011-216968 

12. DISTRIBUTION/AVAILABILITY STATEMENT

Unclassified-Unlimited 

Subject Categories: 91, 15, and 20 

Available electronically at http://www.sti.nasa.gov 

This publication is available from the NASA Center for AeroSpace Information, 443-757-5802

13. SUPPLEMENTARY NOTES

14. ABSTRACT

The Mars ascent vehicle is a critical element of the robotic Mars Sample Return (MSR) mission. The Mars ascent vehicle must be developed 

to survive a variety of conditions including the trans-Mars journey, descent through the Martian atmosphere and the harsh Martian surface 

environments while maintaining the ability to deliver its payload to a low Mars orbit. The primary technology challenge of developing the 

Mars ascent vehicle system is designing for all conditions while ensuring the mass limitations of the entry descent and landing system are 

not exceeded. The NASA In-Space Propulsion technology project has initiated the development of Mars ascent vehicle technologies with 

propulsion system performance and launch environments yet to be defined. To support the project’s evaluation and development of various 

technology options the sensitivity of the Mars ascent vehicle gross lift-off mass to engine performance, inert mass, target orbits, and launch 

conditions has been completed with the results presented herein.

15. SUBJECT TERMS

Ascent; Mars Sample Return (MSR) mission; Mars landing; Mars surface; Optimal Trajectories by Implicit Simulation program 

(OTIS); Mars ascent vehicle; Mars surface samples; Descent 

16. SECURITY CLASSIFICATION OF: 17. LIMITATION OF

 ABSTRACT

UU 

18. NUMBER

 OF 

 PAGES

63 

19a. NAME OF RESPONSIBLE PERSON

STI Help Desk (email:help@sti.nasa.gov) 

a. REPORT

U 

b. ABSTRACT

U 

c. THIS 

PAGE

U 

19b. TELEPHONE NUMBER (include area code)

443-757-5802 

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