Clinton B.F. Ensworth

Glenn Research Center, Cleveland, Ohio

Thrust Vector Control for Nuclear Thermal Rockets

NASA/TM—2013-218087

October 2013

AIAA–2013–4075
NASA STI Program . . . in Profi le

Since its founding, NASA has been dedicated to the 

advancement of aeronautics and space science. The 

NASA Scientifi c and Technical Information (STI) 

program plays a key part in helping NASA maintain 

this important role.

The NASA STI Program operates under the auspices 

of the Agency Chief Information Offi cer. It collects, 

organizes, provides for archiving, and disseminates 

NASA’s STI. The NASA STI program provides access 

to the NASA Aeronautics and Space Database and 

its public interface, the NASA Technical Reports 

Server, thus providing one of the largest collections 

of aeronautical and space science STI in the world. 

Results are published in both non-NASA channels 

and by NASA in the NASA STI Report Series, which 

includes the following report types:

• TECHNICAL PUBLICATION. Reports of 

completed research or a major signifi cant phase 

of research that present the results of NASA 

programs and include extensive data or theoretical 

analysis. Includes compilations of signifi cant 

scientifi c and technical data and information 

deemed to be of continuing reference value. 

NASA counterpart of peer-reviewed formal 

professional papers but has less stringent 

limitations on manuscript length and extent of 

graphic presentations.

• TECHNICAL MEMORANDUM. Scientifi c 

and technical fi ndings that are preliminary or 

of specialized interest, e.g., quick release 

reports, working papers, and bibliographies that 

contain minimal annotation. Does not contain 

extensive analysis.

• CONTRACTOR REPORT. Scientifi c and 

technical fi ndings by NASA-sponsored 

contractors and grantees.

• CONFERENCE PUBLICATION. Collected 

papers from scientifi c and technical 

conferences, symposia, seminars, or other 

meetings sponsored or cosponsored by NASA.

• SPECIAL PUBLICATION. Scientifi c, 

technical, or historical information from 

NASA programs, projects, and missions, often 

concerned with subjects having substantial 

public interest.

• TECHNICAL TRANSLATION. Englishlanguage translations of foreign scientifi c and 

technical material pertinent to NASA’s mission.

Specialized services also include creating custom 

thesauri, building customized databases, organizing 

and publishing research results.

For more information about the NASA STI 

program, see the following:

• Access the NASA STI program home page at 

http://www.sti.nasa.gov

• E-mail your question to help@sti.nasa.gov

• Fax your question to the NASA STI 

Information Desk at 443–757–5803

• Phone the NASA STI Information Desk at

 443–757–5802

• Write to:

 STI Information Desk

 NASA Center for AeroSpace Information

 7115 Standard Drive

 Hanover, MD 21076–1320
Clinton B.F. Ensworth

Glenn Research Center, Cleveland, Ohio

Thrust Vector Control for Nuclear Thermal Rockets

NASA/TM—2013-218087

October 2013

AIAA–2013–4075

National Aeronautics and

Space Administration

Glenn Research Center

Cleveland, Ohio 44135

Prepared for the

49th Joint Propulsion Conference and Exhibit

cosponsored by AIAA, ASME, SAE, and ASEE

San Jose, California, July 14–17, 2013
Available from

NASA Center for Aerospace Information

7115 Standard Drive

Hanover, MD 21076–1320

National Technical Information Service

5301 Shawnee Road

Alexandria, VA 22312

Available electronically at http://www.sti.nasa.gov

Trade names and trademarks are used in this report for identifi cation 

only. Their usage does not constitute an offi cial endorsement, 

either expressed or implied, by the National Aeronautics and 

Space Administration.

Level of Review: This material has been technically reviewed by technical management. 

This report contains preliminary fi ndings, 

subject to revision as analysis proceeds.

Acknowledgments

The author would like to thank Stanley Borowski and John Taylor, NASA Glenn Research Center, Dave McCurdy, Vantage 

Partners LLC, and Mike Houts, NASA Marshall Space Flight Center for their encouragement and interest in this work, as well 

as, Chris Moore and John Warren, NASA Headquarters for their continued support of the Nuclear Cryogenic Propulsion Stage 

(NCPS) project through NASA’s Advanced Exploration Systems (AES) program.
NASA/TM—2013-218087 1 

Thrust Vector Control for Nuclear Thermal Rockets 

Clinton B.F. Ensworth 

National Aeronautics and Space Administration 

Glenn Research Center 

Cleveland, Ohio 44135 

Abstract 

Future space missions may use Nuclear Thermal Rocket (NTR) stages for human and cargo missions 

to Mars and other destinations. The vehicles are likely to require engine thrust vector control (TVC) to 

maintain desired flight trajectories. This paper explores requirements and concepts for TVC systems for 

representative NTR missions. Requirements for TVC systems were derived using 6 degree-of-freedom 

models of NTR vehicles. Various flight scenarios were evaluated to determine vehicle attitude control 

needs and to determine the applicability of TVC. Outputs from the models yielded key characteristics 

including engine gimbal angles, gimbal rates and gimbal actuator power. Additional factors such as 

engine thrust variability and engine thrust alignment errors were examined for impacts to gimbal 

requirements. Various technologies are surveyed for TVC systems for the NTR applications. A key factor 

in technology selection is the unique radiation environment present in NTR stages. Other considerations 

including mission duration and thermal environments influence the selection of optimal TVC 

technologies. Candidate technologies are compared to see which technologies, or combinations of 

technologies best fit the requirements for selected NTR missions. Representative TVC systems are 

proposed and key properties such as mass and power requirements are defined. The outputs from this 

effort can be used to refine NTR system sizing models, providing higher fidelity definition for TVC 

systems for future studies. 

Nomenclature 

ASV Asteroid Survey Vehicle 

CG Center of Gravity 

GRC Glenn Research Center 

kN 1000 Newtons 

klbf 1000 pounds of force, thrust 

LH2 Liquid Hydrogen, propellant 

MTV Mars Transfer Vehicle 

NEA Near Earth Asteroid 

NERVA Nuclear Engine for Rocket Vehicle Application 

Nm Newton meter 

NTR Nuclear Thermal Rocket 

RCS Reaction Control System 

t metric ton (1 t = 1000 kg) 

TVC Thrust Vector Control 

TVT Thrust Vector Trim 
NASA/TM—2013-218087 2 

1.0 Introduction 

Nuclear Thermal Rockets have been considered for space missions for more than 55 years. These 

mission concepts have capitalized on the high specific impulse capability of NTR engines, up to 900 sec 

or more, resulting in increased payload or faster trip times compared to other propulsion technologies. 

Recent studies have looked at NTR technology for a variety of missions including lunar, near Earth 

asteroids (NEA) and Mars targets (Ref. 1). Most of these missions use elements that are assembled in low 

Earth orbit (LEO) to create one or more large vehicles to carry out the mission. Assembled vehicles may 

be 400 t or more with lengths of over 100 m. Multiple, smaller sized engines (15 to 25 klbf thrust, 66.7 to 

111 kN) are used on a vehicle to enable the mission to continue with the loss of an engine. The engine 

design is based on the ROVER program’s 25 klbf Pewee engine (Refs. 2 and 3). Loss of a larger engine 

on a single engine vehicle would almost certainly result in loss of the mission. The smaller engine is also 

more economical to build and test. Liquid hydrogen (LH2) is used as the propellant for these cases. 

2.0 Vehicle Attitude Control 

Control of these large vehicles during powered flight is expected to use some means of thrust vector 

control, TVC. Thrust vector control allows the alignment of the vehicle thrust with vehicle center of 

gravity (CG) to maintain straight line flight or to induce vehicle steering as desired. The objective of this 

paper is to define the requirements and conceptual design of thrust vector control systems for NTR 

applications. Several different vehicles will be examined to explore vehicle and mission influences on 

TVC design. 

A reaction control system (RCS) can also manage vehicle attitude, and is essential during times when 

engines are not thrusting. While the NTR engines are thrusting, the use of thrust vector control can avoid 

most use of RCS propellant. Otherwise, RCS propellant consumption could become excessive in some 

cases, especially off-nominal situations such as thrust asymmetry due to engine malfunction. In a multiengine vehicle, differential engine thrusting could be used to steer the vehicle, as an alternative to TVC. 

But this method would not work if one of three engines failed. Definition of the capabilities of a TVC 

system also helps define the requirements of the RCS.

Gimbaling of engines is the most common method of thrust vector control for large rockets. Typical 

configurations includes a gimbal bearing attached to the engine that allows two axis rotation of the engine 

(e.g., yaw and pitch rotation) but prevents rotation about the axis of the engine. The gimbal bearing 

carries most of the engine thrust load. Two actuators, attached to the engine and vehicle structure can be 

mounted 90 apart to provide full two-axis gimbaling. Instead of a gimbal bearing on the engine axis, 

gimbal motion can be achieved by the use of a gimbal ring that is external to the engine, as in a gyroscope 

mount. One gimbal actuator would be attached to the ring, the other attaches to the engine, 90 apart. 

An alternative method of engine steering was considered during the Nuclear Engine for Rocket 

Vehicle Application (NERVA) program (Ref. 4). This method, designated Thrust Vector Trim (TVT) 

uses one engine attach point with a fixed ball and socket joint and two moveable engine attach points that 

translate parallel to the rocket engine axis. The fixed and moveable points are located 120 around the 

engine axis. By actuating the moveable points fore and aft, the engine thrust axis can be directed within a 

cone of operation. The advantage of this configuration is the elimination of the engine gimbal bearing; 

there is only the need for a flexible connection to carry propellant into the engine. The disadvantage of 

this configuration is that the mechanisms that provide the engine movement must each continuously carry 

about one third of the engine thrust load. The engine attach points must similarly be designed to react the 

same thrust loads. This method may be attractive for relatively low thrust engines. Mechanical engine 

steering concepts are shown in Figure 1. 

Other thrust vector control methods include the use of paddles or vanes to alter the rocket engine 

exhaust to direct the net thrust vector. These methods are problematic because the thrust directing 

elements must withstand the high temperatures in the rocket exhaust. 
NASA/TM—2013-218087 3 

Figure 1.—Mechanical engine steering. 

Engine thrust vectoring can also be achieved by control of auxiliary paths of propellant exhaust 

alongside the main thrust or by fluid injection into the rocket nozzle to affect the net thrust. In general, 

these techniques are less efficient than mechanical engine steering. For the purpose of these studies, use 

of a conventional gimbal bearing and engine gimbaling is assumed. As in the NERVA concepts, it will be 

assumed that the entire engine assembly, including turbopumps, reactor, and nozzle will be gimbaled as a 

unit at the engine-vehicle interface. 

The thrust vector control requirements of any rocket are dependent on the configuration and the 

mission of the rocket. For nuclear thermal rockets currently under consideration, the operation of the 

rocket engine occurs only in space (conventional rocket engine boosters are used to reach Earth orbit). 

This eliminates the need to consider ascent through the atmosphere, which is usually the most demanding 

phase for the thrust vector control function. 

Table 1 lists events during an NTR mission that require control of vehicle attitude. The table indicates 

whether thrust vector control or a reaction control system is suitable to provide the necessary control. In 

all of the cases where RCS is not indicated, it is because these are long term events that would likely 

require excessive propellant. 

The effects listed in Table 1 are discussed below. As noted, some effects only apply to multi-engine 

vehicles. In the ideal case, all the vehicle thrust (one or more engines) is axisymmetric and parallel to the 

vehicle longitudinal axis (x-axis) and the vehicle CG is located on the longitudinal axis. In this situation, 

for straight line flight, no control is required. The following cases describe deviations from this ideal. 

Figure 2 shows the coordinate system used in this report with definition of vehicle pitch, yaw, and roll 

rotations. Nominal thrusting is in the vehicle + X direction. Also shown are notional engine locations for 

a three engine cluster with engine gimbal axis definitions. 
NASA/TM—2013-218087 4 

TABLE 1.—APPLICABILITY OF TVC OR RCS TO PROVIDE CONTROL TO THE VEHICLE 

Scenario TVC RCS 

2.1 Engine Thrust Asymmetry --- --- 

2.1.1 Start Transient Yes Yes 

2.1.2 Nominal Operation Yes Not likely 

2.1.3 Shutdown Transient Not likely Yes 

2.1.4 Cool Down Operation Possibly Yes 

2.1.5 Off-nominal with 1 of x engines out Yes No 

2.1.6 Off-nominal TVC gimbal failure Yes No 

2.2 Steering Maneuver (Pitch & Yaw) Yes Yes 

2.3 Roll Maneuver Possibly Yes 

2.4 Vehicle CG offset, nominal Yes Not likely 

2.5 Engine Mounting Misalignments Yes Not likely 

2.6 Unplanned CG shift Yes Not likely 

2.7 Damping Slosh Disturbance Not likely Yes 

2.8 Coast Phase Rendezvous and Docking No Yes 

2.9 Coast Phase Attitude Maneuvers No Yes 

Figure 2.—Vehicle coordinates and engine gimbal definitions. 

2.1 Engine Thrust Asymmetry 

2.1.1 Engine Start Transient 

The startup transient time of an NTR engine is longer than a typical chemical engine. The NTR 

engine has temperature and pressure ramp rate limits that result in a thrust buildup period of a half minute 

or more. During the start transient it is likely that the thrust levels will not rise simultaneously in all 

engines of a multi-engine vehicle. (An individual engine also undoubtedly has asymmetric thrust 

transients relative to its centerline during start-up, but the effects are likely to be negligible for this study.) 

2.1.2 Nominal Operations 

The net thrust from any rocket engine nozzle has some level of offsets and misalignments with 

respect to the engine reference centerline (Fig. 3). Some of these effects are static and can be quantified 

through testing and analysis. Other variances change during the operation of the engine due to thermal 

and loading effects and may be difficult to predict. Engine specifications typically define maximum 

allowable thrust offset and thrust misalignment. From a multi-engine vehicle perspective, thrust 

asymmetry can be due to unintended differences in net thrust among the engines. For an NTR engine, 

thrust is a function of propellant flow rate and temperature. Each of these variables has a tolerance for 

controllability, which should also be in engine specifications. 
NASA/TM—2013-218087 5 

Figure 3.—Engine thrust deviations: misalignment, thrust offset and combined deviations. 

2.1.3 Engine Shutdown Transient 

As with the start transient, the shutdown transient in a multi-engine vehicle will likely not occur 

simultaneously. The shutdown scenario is different from startup, however because as the thrust levels 

decrease, there is decreasing control authority from TVC. The shutdown procedure involves multiple 

steps including a throttling period, throttle hold, temperature retreat by use of reactor control drums, and 

LH2 pump tail off as thrust decreases from 100 percent. Residual vehicle attitude rates at shutdown may 

call for the use of RCS for attitude rate correction. 

2.1.4 Engine Cool Down Operation 

After each engine firing and reactor shutdown, there is a period of time required to cool the reactor 

using the propellant. The cool down period starts when the turbopump is off and propellant is fed by tank 

pressure, controlled by the propellant supply valve. Hydrogen flow is reduced to low values during this 

period, but some useful thrust is produced. The low thrust may not be sufficient to allow for thrust 

vectoring to control the vehicle attitude during these times. RCS may be required to control the vehicle. 

2.1.5 Off-Nominal, Engine Failure 

In a multi-engine vehicle, this case represents an extreme example of thrust asymmetry. The use of 

RCS alone to control the vehicle after loss of an engine would require a high rate of RCS propellant 

usage. If loss of an engine is assumed to be a credible event, then engine thrust vectoring most likely is 

required for this scenario. 

2.1.6 Off-Nominal, TVC Failure 

In a multi-engine vehicle we can look at the effect of a failure within the thrust vector control system. 

Various types of failure are conceivable. Typical TVC failure cases include failure at null engine position 

and failure at maximum engine rotation. Failure in the maximum rotation, or “hard over” case, is a 

consideration for keeping the physical engine rotation range as small as necessary. For the TVC failure 

cases it is desirable that the remaining engines have sufficient control authority to enable the mission to 

continue. 

Thrust

Misalignment

Engine 

Thrust

Gimbal Center

Thrust Offset Thrust Offset

Thrust

Misalignment

Engine
NASA/TM—2013-218087 6 

2.2 Steering Maneuver (Pitch and Yaw) 

During engine thrusting, TVC can be used to steer the vehicle along the desired trajectory. The 

maneuver is initiated by thrust vector action that rotates the vehicle about the pitch and yaw axes, 

followed by a thrust vector action that stops the vehicle rotation at the desired attitude, for the new vehicle 

heading. This maneuver could also be performed by RCS. 

2.3 Roll Maneuver 

Clustered engines in a multi-engine vehicle could provide a roll torque on the vehicle if engines were 

capable of being angled to do so. Vehicle rotation from main engine torque would require unique 

commanding (different yaw and pitch gimbal commands) to each engine, a feature that is otherwise not 

required. Roll capability would be lost however, if 1 of 2 or 1 of 3 engines was lost. For this study, 

vehicle roll capability is provided by RCS. 

2.4 Vehicle CG Offset 

Ideally, the vehicle CG would remain on the vehicle longitudinal axis (x axis) throughout the mission. 

The center of gravity will move along the longitudinal axis as propellants are consumed. Static CG offsets 

in y and z will occur because everything within and on the vehicle is not perfectly symmetric, especially 

as elements are added or jettisoned from the vehicle. Dynamic CG offsets will occur as the vehicle flexes 

and propellants slosh.

Unless the static misalignment is corrected by the TVC system, there will be a constant torque on the 

vehicle when engines are thrusting. It would be costly in propellant to use RCS to counteract this torque 

for all but the smallest torques. 

2.5 Engine Mounting Misalignment 

Engine mounting misalignment is a deviation from the ideal alignment. Deviations include lateral 

misalignments in y and z direction (deviations in x location, the nominal thrust direction, are less 

important). Deviations also include angular misalignments of the engine mounting locations and include 

engine gimbal actuator length deviations that cause unwanted bias rotations of an engine. 

2.6 Off-Nominal, Unplanned CG Shift 

This scenario may include an instance where a planned deployment or a planned jettison event does 

not occur properly, leaving the vehicle with a center of gravity point that is outside of the nominal CG 

box. Depending on the magnitude of the CG offset, TVC may be able to compensate for the unplanned 

event and may allow completion of the mission. 

2.7 Off-Nominal, Damping of Propellant Slosh 

Propellants within the propellant tanks may be excited by some event such as an attitude maneuver 

and may begin sloshing. Sloshing frequency is dependent on tank geometry and fill level, propellant 

density and vehicle acceleration. Sloshing can be detrimental to the vehicle if the moving propellants 

cause vehicle attitude to be affected, or if vehicle RCS or TVC control inadvertently reinforces the 

sloshing due to undesireable feedback. Damping can be incorporated in the tank design to suppress 

sloshing, though this adds extra mass. Extreme sloshing could potentially be dampened by use of RCS 

firings. Damping of propellant slosh by TVC may be possible if engine movements could be timed to 

counteract slosh effects. 
NASA/TM—2013-218087 7 

2.8 Coast Phase Rendezvous, Docking and Separation of Stages 

During the assembly of the vehicle in low Earth orbit and during various separation events, RCS will 

be needed to perform rendezvous and attitude control maneuvers. 

2.9 Nominal-During Coast, Vehicle Attitude Change 

During coast periods when engines are not firing, RCS will be needed to perform vehicle attitude 

maneuvers including pitch, yaw, and roll rotations for vehicle communications, thermal, power or other 

considerations. 

2.9.7 Combining Effects for Analysis Purposes 

Some of the effects requiring control action can be combined in analysis because they act in a similar 

manner. For example, a displacement of vehicle CG of 1 cm in the plus y direction and an error of engine 

mounting location by 1 cm in the negative y direction have the same effect on the vehicle. Both 

displacements tend to cause the vehicle to rotate about the z axis when the engine is firing. 

Thrust offset within an individual engine also acts the same as an engine mount displacement or a 

vehicle CG displacement. An additional consideration for engine thrust offset is that it directly affects 

TVC actuation loads, because the offset creates a moment about the engine mounting point that must be 

resisted by the actuator. 

For a multi-engine cluster, engine thrust offsets and engine mounting displacements must be 

combined for all engines to determine the net thrust effect on the vehicle. 

These individual offset and displacement deviations cannot be quantified until the vehicle and engine 

designs are very mature. For this study, the effects of engine mounting deviations, vehicle CG, engine 

thrust offset will be examined at the combined level. 

The net effect of these linear offsets from ideal is a moment on the vehicle that can be counteracted 

by rotation of the engines to put the net thrust through the vehicle center of gravity. The amount of engine 

rotation is based on the simple geometry of the effective thrust application point and the vehicle center of 

gravity. Similarly, net engine thrust asymmetry due to engine-to-engine variation contributes to a moment 

on the vehicle that can be counteracted by rotating the engines. 

Individual engine thrust angular alignment and engine mounting angular alignment effects can also be 

combined. The effects cause the engine thrust to be non-parallel with the vehicle centerline. For an 

individual engine, the correction is simply an engine rotation to counteract the misalignment. For multiple 

engines, a uniform angular correction can be applied to all engines that makes the net thrust as parallel as 

possible. Uniform corrections eliminate the need to determine the alignment errors for the individual 

engine axes. If biases are determined before flight for individual engine pitch and yaw axes they could be 

added to the uniform commands. This would improve thrust efficiency by making the thrust of each 

engine more parallel with the other engines. 

It is possible that engine alignment errors may combine in a manner to produce a roll torque on the 

vehicle. As noted, TVC cannot produce counteracting roll torques, unless the engines receive individual 

commands. 

All of these effects are near steady state and impact engine rotation range (gimbal range) only, not 

TVC dynamic performance. 

The vehicle attitude controller does not need to know information about any of the deviations and 

misalignment to control the vehicle. The effects produce torques on the vehicle and the controller tries to 

counteract them with thrust vector control commands. 
NASA/TM—2013-218087 8 

3.0 Study Approach 

For initial study purposes, two representative NTR vehicle concepts were considered. These vehicles 

were similar to ones described in Reference 1 and were developed by the same team at the NASA Glenn 

Research Center (GRC). A Mars Transfer Vehicle (MTV) designed for a 600 day Mars orbital mission 

(with a 60 day stay time at Mars) is shown in Figure 4. This vehicle represents one of the largest vehicles 

currently being considered using 3-25 kbf thrust engines. This combination yields a relatively low initial 

thrust to weight ratio that may have impacts on TVC design. 

The piloted Mars vehicle includes four LH2 tanks. The tank at the aft end is the core propulsion stage 

tank. The next tank is called an in-line tank. The final two tanks are called drop tanks because after the 

propellants are depleted, this tank set can be jettisoned, reducing vehicle mass. 

For this mission, the NTR engines operate for the following mission phases: 

1. Engine firings from low Earth orbit to escape on a trajectory to Mars (two perigee burns) 

2. Engine firing for Mars orbit capture 

3. Engine firing to send crew toward Earth 

The two drop tanks are jettisoned after the first perigee burn. Immediately after the first burn the 

engines will be in cool-down mode, so it may be interesting to examine this case, with a still relatively 

heavy vehicle with very low thrust. 

The other vehicle used in this study was designed for a 344 day mission to the NEA, Apophis. The 

crewed asteroid survey vehicle (ASV) is shown in Figure 5. It includes only two LH2 tanks, a core stage 

tank and a drop tank. The vehicle had 3-25 klbf engines. The engines are identical for both vehicles. As 

with the Mars vehicle, there are a total of four engine firings; two to escape Earth orbit, one for target 

capture and one for return to Earth. The vehicle at the end of this last burn will be relatively light and with 

the thrust of three engines it represents an NTR case with a high thrust to weight ratio. 

Table 2 shows key information for cases in this study including total vehicle mass and mass moment 

of inertia properties for each of the two vehicles at two different points in the two missions, as indicated. 

The mass values are from the detailed mass estimates that were produced by the GRC team for each of 

the configurations. The moments of inertia are approximate based on preliminary estimates of mass 

distributions. 

Figure 4.—Crewed vehicle for 600 day Mars obital mission. 
NASA/TM—2013-218087 9 

Figure 5.—Crewed ASV for 344-day Apophis NEA mission. 

TABLE 2.—VEHICLE PROPERTIES FOR STUDY 

Mission Vehicle case 

designation 

Phase Vehicle 

mass, 

including 

engines, 

kg 

Vehicle mass moment of inertia, not 

including engines 

No. of 

engines 

Thrust 

per 

engine, 

kN 

Ixx, 

kg-m2

Iyy, 

kg-m2

Izz, 

kg-m2

600 day Mars 

mission 

Mars 1 Start of 1st 

perigee 

burn 

423,667 7.076e6 2.072e8 2.105e8 3 111 

Mars 2 End of 1st 

perigee 

burn 

302,495 2.858e6 2.000e8 2.007e8 3 111 

344 day 

Apophis NEA 

mission 

Apophis 1 Start of 1st 

perigee 

burn 

210,600 1.576e6 7.879e7 7.879e7 3 111 

Apophis 2 End of 

trans Earth 

burn 

88,227 1.142e6 5.709e7 5.709e7 3 111 

3.1 Model Description 

A simulation model was created to explore TVC requirements for NTR missions. The model was 

created using Mathworks SimMechanics application that is an extension to Simulink. The SimMechanics 

application permits dynamic simulation of multiple connected bodies in three-dimensional space. The 

current model assumes all bodies are rigid; various techniques are possible to simulate flexible effects. 

The basic model includes one mass to represent the vehicle body and one mass for each of the three 

engines. The vehicle mass has full 6 degrees-of-freedom. Also included in the model are two-axis gimbal 

joints between the engines and vehicle masses and the actuators to move the gimbals. Interactions 

between masses is fully represented including the tail-wags-dog effect. 

Inputs to the model include vehicle and engine mass properties and geometry. Inputs for simulation 

include time histories of engine thrust and commanded vehicle attitude for three axes. The basic model is 

shown in Figure 6. 

The vehicle model has simple pitch and yaw attitude controllers based on proportional and derivative 

control of vehicle attitude. Integral control can be turned on to reduce steady state error if desired. The 

attitude controllers produce commanded yaw and pitch angles for the engine actuator controllers which 

operate on an inner control loop based on gimbal position feedback. No attempt was made to optimize 

control parameters which were manually determined to provide reasonable performance for nominal 

operations. 

 
NASA/TM—2013-218087 10 

Figure 6.—SimMechanics model for 3 engine NTR vehicle. 

Key outputs of the simulations are the resultant engine gimbal angles and rates and actuator torques. 

The gimbal actuator is an ideal actuator (i.e., no actuator dynamics or non-linear effects) and acts as a 

gimbal torque provider. In application the actuator is more likely to be a linear force provider acting with 

a torque arm, producing a gimbal torque. 

The torque required to gimbal an engine is dependent on several factors including engine inertial 

load, engine CG offset, engine thrust offset, propellant duct spring loads and gimbal friction. A gimbal 

torque limit was included in the model to represent the reality that physical hardware cannot provide 

unlimited torque. All these factors and limits are included in the model and can be varied as desired. The 

gimbal commands output by the attitude controllers were also limited, though they were set high enough 

that they rarely were in effect, since a key objective of the study was to see how large gimbal angles 

needed to be to fly various scenarios. 

 
NASA/TM—2013-218087 11 

Some simulations were performed to determine the impact of lateral or side-to-side propellant slosh 

on TVC requirements. Propellant slosh was modeled using a pendulum mass to represent the effective 

propellant mass that moves during sloshing (Ref. 5). This method is good for this simulation because the 

slosh frequency varies automatically with vehicle acceleration. For the Mars vehicle four additional 

masses were added; one for each propellant tank. 

One approach to tuning the controllers in this simulation is to examine the response to a step input 

attitude command. While not representative of a likely maneuver during a mission, it gives insight into 

the performance of the overall system. Figures 7 and 8 show responses to 0.5 and 1.0 step commands in 

pitch attitude for the Mars 1 case. Vehicle attitude shows modest overshoot and overall acceptable 

behavior. Peak engine gimbal angles are about 3 and 5. The vehicle system takes about 10 sec to get 

within 99 percent of steady state driven by the available engine thrust, gimbal rate and vehicle inertia. All 

other cases showed similar behavior for the same controller and TVC settings, except for the 1 step for 

the Apophis 2 case, which is the lightest vehicle case. The vehicle attitude control went unstable for this 

case. The initial response of the system got the vehicle rotating at a rate such that the TVC system could 

not recover. The 0.5 step simulation for Apophis 2 was acceptable. Based on all of the step response 

results, the controller and TVC parameters were assumed to be acceptable for preliminary TVC 

investigations. Note on a real vehicle it would not be unusual to change the values of controller gains as 

the vehicle properties change throughout the mission, gain scheduling, but for these studies they were 

kept constant. 

4.0 Simulation Results 

4.1 Engine Start 

Various scenarios were simulated to determine performance requirements of a TVC system. The first 

scenario is for an engine start case with engine thrust profiles as shown in Figure 9. For this scenario, 

engine 1 thrust buildup is assumed to lag thrust output of the other two engines by 10 sec. This puts a 

moment on the vehicle about the z axis (yaw axis). All engines have the same thrust when they reach 

100 percent, so thrust asymmetry ends. The engines are located equidistant about the vehicle x centerline. 

Figure 10 shows results for the two Mars vehicle cases. Results are very similar for both cases with a 

maximum engine yaw gimbal angle of 1.85. The commanded gimbal angles were the same for all three 

engines and all simulated engine gimbal angles were uniform among the engines. For comparison, a 5 sec 

lag in engine 1 thrust buildup resulted in a 1.11 maximum engine gimbal angle. 

Figure 8.—Mars 1 vehicle response to a 1.0 step 

attitude command. 

‐3

‐2

‐1

0

1

2

3

4

5

6

0 10 20 30 40

Angle, deg

Time, sec

Vehicle Pitch Attitude Cmd

Engine Pitch Gimbal Angle

Vehicle Pitch Attitude

Figure 7.—Mars 1 vehicle response to a 0.5 step 

attitude command. 

‐2

‐1

0

1

2

3

4

0 10 20 30 40

Angle, deg

Time, sec

Vehicle Pitch Attitude Cmd

Engine Pitch Gimbal Angle

Vehicle Pitch Attitude
NASA/TM—2013-218087 12 

Figure 9.—Engine start transient. 

The Apophis vehicle cases are shown in Figure 11. The case for initial burn, Apophis 1, has a 

maximum engine yaw gimbal angle of 2.36. The lighter vehicle case, Apophis 2, reaches a maximum 

gimbal angle of 2.02. Note the actual Apophis 2 case is defined at the end of a last engine burn so an 

engine start is not an expected operation. However, all of these cases and results are useful for showing 

general effect of vehicle properties on TVC requirements, which is the intent for this study. 

The relative gimbal angles for the various cases are a function of vehicle mass moment of inertia and 

also vehicle center of gravity location. The lighter Apophis vehicle reacts more to the engine start thrust 

asymmetry, resulting in higher vehicle yaw attitude and higher engine gimbal angles, compared to the 

Mars vehicle. For each vehicle, as the mission progresses the vehicle center of gravity moves as 

propellant is used. This movement may lessen or it may improve the effectivess of the vectored engine 

thrust depending on the direction of the movement. The greater the distance from the engines to CG, the 

greater the moment arm from which the engines create a moment about the vehicle CG. 

3

1

2

0

20

40

60

80

100

120

0 10 20 30 40 50 60

Engine Thrust Level,

%

Time, sec

Engines 2 & 3

Engine 1

Figure 10.—Engine start transient with engine 1 

thrust lag, Mars vehicle. 

‐2.5

‐2.0

‐1.5

‐1.0

‐0.5

0.0

0.5

1.0

0 10 20 30 40 50 60

Angle, deg

Time, sec

Mars 1

Mars 2

Engine Yaw

Gimbal Angle

Vehicle Yaw Attitude

Figure 11.—Engine start transient with engine 1 

thrust lag, Apophis vehicle. 

‐2.5

‐2.0

‐1.5

‐1.0

‐0.5

0.0

0.5

1.0

0 10 20 30 40 50 60

Angle, deg

Time, sec

Apophis 1 Apophis 2

Engine Yaw

Gimbal Angle

Vehicle Yaw Attitude

Engine Position

Looking Forward
NASA/TM—2013-218087 13 

Figure 12.—Engine start transient with engine 1 thrust 

lag, with propellant slosh, Mars 1 case. 

The effect of propellant slosh is shown in Figure 12 for the Mars 1 case. The initial gimbal transient 

with slosh is almost identical to the non-slosh scenario, with peak gimbal amplitude slightly smaller. 

There are very slight oscillations in yaw attitude and engine gimbal angle at the slosh frequency of about 

0.091 Hz (the slosh frequencies are almost the same for all four tanks because they all have the same 

diameter and all have about the same fill levels). Although no slosh damping is assumed in the model, the 

oscillations do eventually die down due to some damping in the attitude controller. This scenario 

illustrates that the slosh effects are more a factor for controller design and do not significantly impact 

TVC actuator requirements. 

Figures 13 and 14 show a start transient scenario where engine 2 has a 10 sec thrust lag. In this case 

there are thrust moments about the pitch and yaw vehicle axes, resulting in engine gimballing about both 

axes. The individual gimbal movements are less than in the previous case, though the maximum total 

gimbal angle, (pitch angle2

 + yaw angle2)

1/2 equals 1.85, is the same magnitude as before, as expected. 

Note if one engine starts early (or two engines start late) the initial moment on the vehicle will not be 

as severe, so this scenario, with a lag for one engine, represents the worst case of start lead or lag for a 

three engine cluster. Startup will be examined in more detail in a later section. 

‐2.5

‐2.0

‐1.5

‐1.0

‐0.5

0.0

0.5

1.0

0 10 20 30 40 50 60

Angle, deg

Time, sec

Mars 1

Mars 1, w/

slosh

Engine Yaw

Gimbal Angle

Vehicle Yaw Attitude

Figure 13.—Engine start transient with engine 2 thrust 

lag, Mars vehicle case 1, yaw axis. 

‐2.0

‐1.5

‐1.0

‐0.5

0.0

0.5

1.0

1.5

0 10 20 30 40 50 60

Angle, deg

Time, sec

Engine Yaw Gimbal Angle

Vehicle Yaw Attitude

Figure 14.—Engine start transient with engine 2 thrust 

lag, Mars vehicle case 1, pitch axis. 

‐2.0

‐1.5

‐1.0

‐0.5

0.0

0.5

1.0

1.5

0 10 20 30 40 50 60

Angle, deg

Time, sec

Vehicle Pitch Attitude

Engine Pitch Gimbal Angle
NASA/TM—2013-218087 14 

4.2 Engine Shutdown/Cool Down 

The total shutdown operation from 100 percent thrust may involve multiple temperature and pressure 

profiles and hold periods that are different depending on reactor operating time. The nominal 3 engine 

shutdown for this study was assumed to end with a linear thrust ramp down over a period of 3 min, 

starting at the 10 percent thrust level. As in the start-up case, it is likely that there may be variations 

among the engines that result in a net thrust asymmetry. This asymmetry will become more critical as the 

thrust levels decrease and TVC becomes less effective. Figure 15 shows the shutdown scenario with 

engine 1 lagging the other two engines by 20 sec over the final 2 min of the early cool down period. At 

the end of the 3 min ramp down all the engines continue producing 0.2 percent of nominal thrust. This 

very low thrust level represents the thrust produced from the initial cooling flow during the pulse phase 

and may continue for many minutes or until the engine is started up for another burn (as in the case of the 

1st and 2nd perigee burns). Some of the values in this scenario are based on an analysis of NERVA 

engine operations (Ref. 6). 

The Mars 2 case was used for this analysis because it represents the Mars vehicle at the end of the 1st 

perigee burn. Propellant slosh was turned on for this run. Figure 16 shows the results for the shutdown 

scenario with engine 1 lagging by 20 sec. As the shutdown continues, a small yaw attitude error begins 

growing due to the thrust imbalance. At about 180 sec into the scenario, when engine engines 2 and 3 

reach the 0.2 percent thrust level the attitude begins changing more quickly. Gimbal angle reaches a peak 

of 2 while yaw attitude remains within 0.36. It appears that TVC is barely able to maintain control of 

the vehicle for this scenario. The timing at the end of shutdown is critical; a slightly larger thrust 

asymmetry during shutdown might have prevented TVC from controlling the vehicle. In all likelihood 

RCS would be required to ensure timely attitude control during shutdown. 

Engine thrust for an off-nominal engine failure case is shown in Figure 17. Engine 1 is assumed to 

drop to zero thrust over 10 sec which puts a yaw torque on the vehicle as engines 2 and 3 continue 

operating. Figure 18 shows the response of the Mars vehicle when the engine thrust changes. Peak gimbal 

angle reaches 1.70 for the heavier vehicle and slightly less for the Mars 2 case. Vehicle attitude is well 

behaved, though a constant attitude error persists due to the constant thrust disturbance. Figure 19 shows 

the result for the same engine failure scenario for the Apophis vehicle. Peak engine gimbal angles reach 

1.92 for the Apophis 1 case and 1.70 for the lighter vehicle case. Again the vehicle attitude response is 

well behaved. 

Figure 15.—Engine thrust for 3 engine shutdown/ 

cool down transient with 20 sec lag for engine 1. 

Figure 16.—Vehicle response to 3 engine shutdown/ 

cool down transient with 20 sec lag for engine 1. 

Mars 2 case, with propellant slosh. 

 

0

2

4

6

8

10

12

0 50 100 150 200 250 300

Engine Thrust Level,

%

Time, sec

Engines 2 & 3

Engine 1

0.2% Thrust
NASA/TM—2013-218087 15 

Figure 17.—Engine thrust for off-nominal engine 1 failure 

scenario. 

Figure 18.—Off-nominal engine 1 failure, Mars vehicle 

response. 

 

Figure 19.—Off-nominal engine 1 failure, Apophis vehicle 

response. 

Figure 20.—Off-nominal engine failure, effects of 

integrator gain in attitude controller, Mars 1 case. 

The steady state attitude error in these engine failure scenarios can be reduced by increasing the 

proportional gain in the attitude controller or can be practically eliminated by adding an integrator to the 

controller. Both of these actions tend to make the system less stable, so changes are not automatically 

warranted. Figure 20 shows the effects of adding the integrator in the attitude controller for the Mars 1 

case. Maximum gimbal angle and gimbal rate are increased just slightly, oscillations are more 

pronounced, and attitude error goes to zero. Unless noted, results are for simulations without the 

integrator in the attitude controllers. 

The steady state gimbal angle is the angle that puts the net thrust through the vehicle CG. In the 

Mars 1 case with engine 1 out, the net thrust location is –1.035 m from the vehicle centerline on the y axis 

(the y coordinates of both engines 2 and 3, note the z coordinates cancel out so there is no pitch moment). 

The vehicle body CG is 42.35 m from the engine gimbal points. Taking the arctangent of (1.035/42.35) 

yields 1.40, close to simulated value of 1.44. More precise calculations would include the small effect 

due to the fact that the engine net thrust does not pass through the net engine CG when one engine is out. 

This effect is automatically included in the model. 

 

0

20

40

60

80

100

120

0 10 20 30 40 50 60

Engine Thrust Level,

%

Time, sec

Engines 2 & 3

Engine 1

‐2.5

‐2.0

‐1.5

‐1.0

‐0.5

0.0

0.5

1.0

0 10 20 30 40 50 60

Angle, deg

Time, sec

Mars 1

Mars 2

Engine Yaw

Gimbal Angle

Vehicle Yaw Attitude

‐2.5

‐2.0

‐1.5

‐1.0

‐0.5

0.0

0.5

1.0

0 10 20 30 40 50 60

Angle, deg

Time, sec

Apophis 1

Apophis 2

Engine Yaw

Gimbal Angle

Vehicle Yaw Attitude

‐2.5

‐2.0

‐1.5

‐1.0

‐0.5

0.0

0.5

1.0

0 10 20 30 40 50 60

Angle, deg

Time, sec

Mars 1, no Integrator Gain

Mars 1, w/Integrator Gain

Engine Yaw

Gimbal Angle

Vehicle Yaw Attitude
NASA/TM—2013-218087 16 

It is worth noting that getting to zero attitude in this simulation, which makes the vehicle body axis 

aligned with the inertial x axis, is not the same as flying in the inertial x direction. The vehicle flies in the 

direction of the thrust from the engines, not in the direction of vehicle body alignment. To fly in the pure 

x direction, the attitude command needs to match the actual gimbal angle, putting the thrust in the pure 

x direction. A real attitude controller would use inertial guidance information to derive the vehicle attitude 

necessary to get the thrust in alignment with the desired trajectory. The inertial guidance function is not 

included this simulation because it not important for the derivation of TVC requirements. 

4.3 Thrust Vector—CG Offset 

As in the engine out case, a CG offset in the vehicle body also results in steady state gimbal angles to 

maintain steady vehicle attitudes. For a 2.0 m offset in the y axis in the vehicle body CG, a steady state 

yaw engine gimbal angle of 2.70 results, shown in Figure 21. This is exactly the value obtained from the 

calculation that puts the net engine thrust through the vehicle body CG; arctangent (2.0/42.35) yields 

2.70. In general, CG offsets would likely be much smaller the 2.0 m throughout the mission. For the 

Mars vehicle, however it should be noted that if the two side-by-side drop tanks are not emptied 

simultaneously there will be a CG offset. 

A TVC failure is simulated in Figure 22. For this scenario it is assumed that one of the engine gimbal 

actuators, pitch on engine 2, fails to a 2.0 engine angle. The pitch actuator on the other two engines, 

engines 1 and 3, eventually settle to a 1.0 pitch gimbal actuator to counterbalance the thrust on the 

engine with the failed actuator. In general for any single bias failure of a gimbal actuator, the response of 

the other two actuators will be one half the value of the failed position (for a three engine cluster). 

As noted before, various combinations of thrust vector offsets and CG offsets can be combined to 

determine the net effect on gimbal angle requirements. 

4.4 Steering Maneuvers 

Figure 23 shows results from a commanded pitch attitude maneuver for the Mars 1 case. The 

maneuver includes attitude commanded rates of 0.1 per second. Peak engine gimbal angles are about 

1.5. Vehicle pitch attitude stays close to commanded attitude. Figure 24 shows the Apophis 1 case with 

the same commands. Peak gimbal angles are about 1.25. 

Figure 21.—CG offset of 2.0 m at time = 0. Mars 1 case, 

with integrator gain. 

Figure 22.—Off-nominal TVC failure of engine 2 pitch 

gimbal to 2, Mars 1 case, with integrator gain. 

‐4.0

‐3.5

‐3.0

‐2.5

‐2.0

‐1.5

‐1.0

‐0.5

0.0

0.5

1.0

0 10 20 30 40 50 60

Angle, deg

Time, sec

Engine Yaw

Gimbal Angle

Vehicle Yaw Attitude

‐2.0

‐1.5

‐1.0

‐0.5

0.0

0.5

1.0

1.5

2.0

2.5

3.0

0 10 20 30 40 50 60

Angle, deg

Time, sec

Engine 1 & 3 Pitch Gimbal Angles

Vehicle Pitch Attitude

Engine 2 Pitch Gimbal Failure
NASA/TM—2013-218087 17 

Figure 23.—Pitch attitude maneuver, 0.1 per second, 

Mars 1 case. 

Figure 24.—Pitch attitude maneuver, 0.1 per second, 

Apophis 1 case. 

 

Figure 25.—Pitch attitude maneuver with command 

smoothing, Mars 1 case. 

Figure 26.—Engine start transient, engine 1 with 

10 sec lag, Apophis 1 case. 

The commanded maneuver in the previous examples is not one that would be expected for a real 

mission. Transitions between various attitude rates would undoubtedly be smoothed to avoid exciting 

vehicle structural modes (Ref. 7). An example of the impact of smoothing the rate transitions is shown in 

Figure 25, for the Mars 1 case. Peak gimbal angles are between 0.7 and 1.0. 

4.5 Gimbal Range Summary 

Most of the steady state type scenarios, such as CG offset, impact gimbal range but not rate. Unless it 

is a sudden and drastic change, (such as engine out) timing is not important. The gimbal angle for trim 

conditions can be determined from straight forward geometry calculations (in general involving 

calculations of non-planar engine thrusts and offsets). The difficult part is determining the values that 

need to be considered and how they should be combined. 

For transient cases, limiting the engine gimbal range will affect the performance of the TVC system. 

Figure 26 shows the impact of limiting the gimbal range to 1.5 for an Apophis 1 case startup scenario. 

Vehicle attitude excursion almost doubles from 0.39 to 0.77. The magnitude of the attitude excursion 

for this scenario may or may not be significant. The key is to ensure that the vehicle remains controllable 

‐2.0

‐1.5

‐1.0

‐0.5

0.0

0.5

1.0

1.5

2.0

0 10 20 30 40 50 60

Angle, deg

Time, sec

Engine Pitch Gimbal Angle

Vehicle Pitch Attitude

Pitch Command

‐2.0

‐1.5

‐1.0

‐0.5

0.0

0.5

1.0

1.5

2.0

0 10 20 30 40 50 60

Angle, deg

Time, sec

Engine Pitch Gimbal Angle

Vehicle Pitch Attitude

Pitch Command

‐2.0

‐1.5

‐1.0

‐0.5

0.0

0.5

1.0

1.5

2.0

0 10 20 30 40 50 60

Angle, deg

Time, sec

Engine Pitch Gimbal Angle

Vehicle Pitch Attitude

Pitch Command

‐2.5

‐2.0

‐1.5

‐1.0

‐0.5

0.0

0.5

1.0

0 10 20 30 40 50 60

Angle, deg

Time, sec

No Gimbal Limit

1.5 deg Gimbal Limit

Engine Yaw

Gimbal Angle

Vehicle Yaw Attitude
NASA/TM—2013-218087 18 

and this will depend on a number of factors including TVC and RCS capabilities. Application of bias 

angles for CG offsets and other corrections for various deviations reduces the effective gimbal range and 

may make it non-symmetric. 

4.6 Gimbal Power Requirements 

Gimbal power requirements are dependent on the gimbal actuation torque and gimbal rotation rate. 

As noted, some of the scenarios were presented for illustrative purposes and do not represent expected 

operations. These scenarios, such as the steering maneuver, should not necessarily be used to drive TVC 

requirements. Responses for other scenarios, such as start transient and off-nominal shutdown are 

dependent on variables that are difficult to quantify at this time (engine thrust variability during start up, 

engine thrust shutdown rate for off-nominal shutdown). If we can at least bound these scenarios we have a 

basis for establishing requirements relating to power. 

Startup transient for the Apophis 1 case was examined more closely because it showed the most 

reaction to the start transient (largest gimbal angle and rate) among the vehicle cases examined. Various 

combinations of engine 1 thrust lag were examined. Results are shown in Figure 27 for start lags of 5 to 

20 sec. The results for the beginning of each run are the same, during the time that engines 2 and 3 are 

ramping up in thrust while engine 1 remains off. Once engine 1 starts ramping up the vehicle attitude and 

engine gimbal angle results start to diverge. Figure 28 shows gimbal rate versus gimbal angle for the four 

simulation runs. Peak gimbal angle was 2.37 and peak rate was 0.38 per second. 

A different startup scenario was examined to determine effects on TVC. For this scenario, engine 1 

was assumed to start at the same time as the other two engines but it has a slower rate of thrust build up. 

This situation is designated as a prolonged start, e.g., engine 1 took 5 or 10 sec longer than the nominal 

30 sec to reach 100 percent thrust. These runs, shown in Figure 29, are more benign in terms of vehicle 

attitude and gimbal angles and rates. 

If off-nominal shutdown is included as a design case for these NTR missions, it should be examined 

in more detail. The key unknown variable is the thrust decay profile for an engine that fails during a 

thrusting period. The most extreme scenario would be a sudden and complete halt of thrust for an engine. 

More plausible scenarios may include a time period over which the thrust decays. Simulation runs for 

shutdown duration for engine 1 ranging from 0 to 20 sec are shown in Figure 30. Gimbal rate versus 

gimbal angle is shown in Figure 31. The step transient (0 sec) thrust run, indicates a gimbal rate of 

1.85 per second, which is much higher than needed for the other runs with less abrupt engine shutdowns. 

Maximum gimbal angle was 2.29. 

Figure 27.—Engine start transients with various lags in 

engine 1 thrust, Apophis 1 case. 

Figure 28.—Engine start transients with various lags in 

engine 1 thrust, Apophis 1 case. 

 

‐1.0

‐0.5

0.0

0.5

1.0

‐3 ‐2 ‐10 1 2 3

Gimbal Rate, deg/sec

Yaw Gimbal Angle, deg

5 sec lag

10 sec lag

15 sec lag

20 sec lag
NASA/TM—2013-218087 19 

Figure 29.—Engine start transients with various 

prolonged engine 1 thrust profiles, Apophis 1 case. 

Figure 30.—Engine shutdown transients with various 

shutdown durations for engine 1 thrust, Apophis 1 

case. 

Figure 31.—Engine shutdown transients with various 

shutdown durations for engine 1 thrust, Apophis 1 case. 

The gimbal rate capability in these analyses is dependent on the actuator torque. The commanded 

torque is dependent on attitude and actuator controller gain settings, subject to an imposed actuator torque 

limit. For the step transient run, the peak actuator torque was 2915 Nm which was below the torque limit 

setting of 4000 Nm, so the torque limit was not a factor restricting gimbal rate. 

The gimbal torque is the other factor, along with gimbal rate, that determines gimbal actuator 

mechanical power. There are a number of sources of gimbal torque. Within the model, these torques are 

summed to produce a net torque that accelerates the engine about the gimbal axes. 

These torques include: 

 Actuator Torque—As previously described this is the driving torque, provided by an actuating 

mechanism. The actuator is commanded by the controllers to produce the desired vehicle attitude. 

 Gimbal Bearing Friction Torque—This represents the friction of the gimbal bearing. For these 

analyses, gimbal friction is assumed to act as viscous friction; the friction torque is proportional to 

gimbal rate. The gimbal friction should be the same for all of the engines and the same for each 

gimbal axis, within tolerance values. 
NASA/TM—2013-218087 20 

 Propellant Duct Spring Torque—As the engine gimbals, the LH2 propellant duct(s) between the tanks 

and the engines must flex, usually by means of a bellows section. As the duct bends it exert a moment 

on the engine because the duct acts as a spring element. The torque value is proportional to the engine 

deflection angle. Duct spring torques should be same for all engines. Depending on the configuration 

of the propellant ducts, the spring torque may be different in pitch and yaw axes. Ducts may also 

contribute to friction (not modeled in these simulations). 

 Engine Thrust Offset—If the effective thrust of the engine does not pass through the center of the 

gimbal, there will be a torque about the gimbal. The torque is equal to thrust times the thrust offset. 

Often, this torque is among the largest sources of gimbal actuator load. The thrust offset is unique for 

each engine; it is ideally near zero, and can be in any orientation. 

 Longitudinal Acceleration of Engine CG—As the engine gimbals, the center of mass of the engine 

moves off axis relative to the longitudinal acceleration of the gimbal. This results in a torque about 

the gimbal. This torque is automatically calculated in the model. 

 Lateral Acceleration of Engine Gimbal—Any lateral acceleration of the vehicle at the engine gimbal 

will result in a torque due to a reaction with the engine mass moment of inertia. This torque is also 

accounted for in the simulation model. 

 Propellant Momentum—As the propellant flows through the ducts on the engine, a change of 

direction will impart a reaction load on the engine. These effects are relatively small and are not 

included in current analyses. 

 Engine Turbopump Loads—The engine turbopump (or pumps) will impart reaction loads on the 

engine as it changes speed and will resist engine gimballing due to gyroscopic effects. These effects 

are expected to be small and are not in included in the current model. 

 Engine Rotational Inertia Load—As mentioned, engine acceleration is a resulting output of all 

torques summed about the gimbal. Peak engine acceleration for simulation runs was about 5/sec2

. 

This indicates a net peak torque applied to the engine of about 2000 Nm, for an engine inertia of 

23,000 kg-m2

 about the gimbal axis. 

Various values of engine thrust offset, gimbal bearing friction, and duct spring torques were 

examined to determine effects on gimbal actuator torque and power requirements. Figure 32 shows the 

results of parametric variations for the engine 1 step transient shutdown for the Apophis 1 vehicle, which 

Figure 32.—Gimbal actuator peak power 

versus engine thrust offset for the step 

transient off-nominal engine 1 shutdown, 

Apophis 1 case. Parametric factors: 

Gimbal Friction - F Nm/(deg/sec), Duct 

Spring Torque - D, Nm/deg, Actuator 

Torque Limit - TL, Nm. 
NASA/TM—2013-218087 21 

was the most severe case for engine gimbal rate. The curves show peak actuator power that resulted from 

a series of simulation runs with different settings for engine thrust offset, gimbal bearing friction factor 

and duct spring constant. Peak power is the maximum transient mechanical power output demand from 

one yaw gimbal actuator. 

Thrust offset is by far the largest contributor to gimbal actuator torque and power requirements. Peak 

actuator power increases as thrust offset moves from negative to positive values. For this scenario, 

negative thrust offset is aiding the movement of engine 2 that is commanded to respond to the sudden 

shutdown of engine 1. Positive thrust offset opposes engine motion. At high positive values of thrust 

offset the peak power decreases for the simulation, as a result of the actuator torque limit being reached. 

One set of runs was made with a wider actuator torque limit, 6000 Nm, resulting in a continuous curve, 

without a rollover. 

During these scenarios there are times when the actuator must act as a brake to reduce engine 

rotational velocity, indicated as negative power. The polarity of power depends on polarity of both gimbal 

torque and gimbal rate. Duct spring torques can aid the actuator when gimbal direction is returning 

towards zero gimbal angle. 

For each of the maximum peak power simulations runs in Figure 32, a time history of actuator power 

is shown in Figure 33. All the runs were for values of positive thrust offset (except a baseline case with 

nominal values and zero thrust offset). It can be seen that the general power response to the engine thrust 

step is a sharp power peak followed by a power reversal as the engine rotation is accelerated then 

decelerated. The duration of the power transient is about 15 sec. It is evident that the higher frequency 

variation in the power trace is influenced by the values of gimbal friction and duct spring constant. 

Gimbal angle and vehicle attitude are shown for these same simulation runs in Figure 34. Most of the 

outputs are similar. The two cases with the 1600 Nm per degree propellant duct spring constants, with the 

lower actuator torque limit have gimbal angles that are limited and as a result the vehicle attitude 

excursions are relatively high. 

Based on these results and assumptions of likely thrust offset and other values, it appears that 

mechanical actuation power of 140 W should be adequate for these types of missions. The largest factor 

for actuator power is engine thrust vector offset. Peak gimbal torque capability of 4000 Nm would be 

adequate. 

Figure 33.—Gimbal actuator power for step transient offnominal engine 1 shutdown, Apophis 1 case. 

Parametric factors: Gimbal Friction - F, Nm/(deg/sec), 

Duct Spring Torque - D, Nm/deg, Torque Offset - TO, 

m, Actuator Torque Limit - TL, Nm. 

Figure 34.—Engine shutdown transients with various 

torque variables for step transient off-nominal engine 1 

shutdown, Apophis 1 case. Parametric factors: Gimbal 

Friction - F, Nm/(deg/sec), Duct Spring Torque - D, 

Nm/deg, Torque Offset - TO, m, Actuator Torque Limit 

- TL, Nm. 
NASA/TM—2013-218087 22 

4.7 TVC Actuation Options 

There are several options for engine gimbal actuation for thrust vector control. For this application, 

unique mission environments and long mission durations affect the selection of technologies. In 

particular, high gamma and neutron radiation is present in the vicinity of the reactors of the NTR engines. 

Certain materials including organics and electrical components are particularly affected by radiation. 

Technologies that are more inherently immune to radiation effects are preferred. Due to long mission 

times and flight paths faraway from Earth, components exposed to deep space will see cold environments 

and may require thermal control. 

The power requirements of the actuators also influence the technology selections. Some options are 

practical only for low power applications, while other technologies such as hydraulic actuation have been 

used successfully for the highest power applications. Conventional rockets have used hydraulically 

powered actuators for many years. Typically, a pair of linear hydraulic actuators connects between the 

structure of the vehicle and the rocket engine. 

Electric actuation for TVC can be implemented in many ways. The electromechanical approach uses 

an electric motor coupled to a gearbox that actuates a screw mechanism to provide linear motion. 

Numerous configurations of motors, gearing and screw mechanisms are possible, depending on 

redundancy requirements. Other approaches for electric actuation use hydraulic components for 

converting electric rotary motion to linear motion. 

With an electromechanical actuator, it is likely that there would be a need for a motor brake to hold 

load, between transient events, particularly if the actuator uses a low friction ball screw or roller screw. 

Electric actuation also has a long heritage for space applications at relatively low power levels including 

the Apollo service module main engine gimbal actuator, the Shuttle Orbital Maneuvering System engine 

gimbals and for RL-10 engines on upper stage applications. The new Vega rocket uses electromechanical 

actuators for all 4 stages with actuator powers of 17.5 kW to 90 W mechanical output (Ref. 8). 

Based on the relatively modest power requirements indicated in these results, electromechanical 

actuation for TVC appears to be well suited for these NTR vehicles. There should also be commonality 

with other actuation needs on the NTR engine, including valve actuation and reactor control drum 

actuation. For both of these applications, electric actuation was the selected technology for the NERVA 

program. Radiation tolerant electric motors are used in the nuclear power industry. 

Controllers for electric actuators should be located as far away from radiation sources as possible. For 

vehicles that carry human crew, there would be additional shielding at the base of the vehicle. 

Table 3 shows some preliminary estimates for peak electrical power sizing, including typical losses 

and conversion efficiencies. For initial sizing estimates mechanical power for actuation is rounded up to 

200 W. It should be emphasized that during most of the flight, the TVC system would not be moving the 

engines and the electrical power requirements would be reduced to a low level for controller 

housekeeping power and the power to maintain the electric motor brake. 

TABLE 3.—ELECTRIC POWER REQUIREMENTS 

Peak 

Peak mechanical output power, W 200 

Mechanical transmission efficiency 0.64 

Motor efficiency 0.64 

Electrical cable efficiency 0.97 

Motor driver efficiency 0.85 

Single actuator, subtotal, W 592 

Electric brake power, W 30 

Single actuator electrical total power, W 622 

Single engine (two actuators) total power, W 1244 

 
NASA/TM—2013-218087 23 

For the power levels required, an electromechanical actuator is not expected to be very large or 

heavy. For reference, the Vega 3rd stage TVC electromechanical actuator, which can provide more than 

1000 W mechanical power has a mass of 17 kg. The thrust of the Vega rocket engine is over 300 kN, 

compared to the NTR engine in this study with thrust of 111 kN. The exact configuration of the actuator 

depends on how and where the actuators are mounted. Actuators that are located close to the engine 

centerline would need to provide high force over a short distance, resulting in a short, fat actuator. The 

same torque and range can be provided by an actuator that is located further from the engine centerline, 

resulting in a longer, more slender actuator, with a higher slew rate. 

It is likely that launch loads on an NTR engine and TVC actuators will exceed loads during the 

in-space mission. Some sort of engine restraint may be necessary during launch, as was assumed for some 

NERVA missions. 

5.0 Conclusion 

Vehicles for future NTR mission are likely to have steady state engine thrust imbalances and CG 

offsets that make it desirable to gimbal engine thrust, reducing the vehicle attitude control demands on 

RCS. The range of necessary engine gimbaling to trim the vehicle is dependent on the combination of 

expected thrust offsets, engine mounting misalignments and CG offsets. 

Thrust vector control can also be useful for transient scenarios such as engine start and off-nominal 

engine shutdown. These cases drive gimbal rate and gimbal power requirements. Simulation result 

showed gimbal range requirements up to 2.4 and rates up to 1.85 per second, though most cases had 

modest gimbal rates of 0.5 per second or less. Mechanical power requirements are low, based on the 

assumptions used in these simulations. Further definition of quantities such as gimbal friction and engine 

thrust offset will improve confidence in actuator power requirements. 

The use of a 6 degree-of-freedom simulation model enabled the assessment of a wide variety of flight 

scenarios for evaluation of TVC requirements. The rigid body model showed the basic controllability of 

vehicles using TVC, for various combinations of thrust levels and vehicle mass moment of inertias. Some 

investigations with propellant slosh effects indicated little impact on TVC requirements, but controller 

parameters are definitely important. A key design requirement is that the attitude controller bandwidth 

remain below slosh frequencies (on the order of 0.1 Hz) and vehicle flex mode frequencies (ideally 1 Hz 

and higher). Future studies will look further at the impacts of vehicle slosh, flexibility and the effects of 

real actuators and real attitude sensors. 

References 

1. Borowski, S.K., McCurdy, D.R., and Packard, T.W., “Modular Growth NTR Space Transportation 

System for Future NASA Human Lunar, NEA and Mars Exploration Missions,” AIAA-2012-5144, 

Sept. 2012. 

2. Finseth, J.L., “Overview of Rover Engine Tests, Final Report,” NASA CR-184270, 1991. 

3. Koeing, D.R., “Experience gained From the Space Nuclear Rocket Programs (Rover/NERVA),” 

Los Alamos National Laboratory, Report LA-10062-H, Los Alamos, NM, May 1986. 

4. Lockheed Missiles and Space Co., “The NERVA-RIFT Thrust Vector Control/Mechanical/Shielding 

Interface Review Meeting,” 1963, available from National Technical Information Service, Accession 

Number NSP-63-87. 

5. Dodge, F.T., “The New Dynamic Behavior of Liquids in Moving Containers,” Southwest Research 

Institute, San Antonio, Texas, 2000, (update of NASA SP-106 edited by Abramson, N.). 

 
NASA/TM—2013-218087 24 

6. Altseimer, J.H., Mader, G.F., Stewart, J.J., “Operating Characteristics and Requirements for the 

NERVA Flight Engine,” Journal of Spacecraft, Vol. 8, No. 7., 1971, pp. 766-773; also AIAA Paper 

70-676, July 1970. 

7. Gran, K., Rossi, M., Moyer, H.G., and Austin, F., “Control of Large Space Structures,” Grumman 

Aerospace Corporation, NASA CR-161369, 1979. 

8. Carnevale, C., Resta, P.D., “Vega Electromechanical Thrust Vector Control Development,” 

AIAA-2007-5812, July 2007. 

REPORT DOCUMENTATION PAGE Form Approved 

OMB No. 0704-0188 

The public reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the 

data needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing this 

burden, to Department of Defense, Washington Headquarters Services, Directorate for Information Operations and Reports (0704-0188), 1215 Jefferson Davis Highway, Suite 1204, Arlington, VA 22202-4302. 

Respondents should be aware that notwithstanding any other provision of law, no person shall be subject to any penalty for failing to comply with a collection of information if it does not display a currently valid OMB 

control number. 

PLEASE DO NOT RETURN YOUR FORM TO THE ABOVE ADDRESS. 

1. REPORT DATE (DD-MM-YYYY)

01-10-2013 

2. REPORT TYPE

Technical Memorandum 

3. DATES COVERED (From - To)

4. TITLE AND SUBTITLE

Thrust Vector Control for Nuclear Thermal Rockets 

5a. CONTRACT NUMBER

5b. GRANT NUMBER

5c. PROGRAM ELEMENT NUMBER

6. AUTHOR(S)

Ensworth, Clinton, B.F. 

5d. PROJECT NUMBER

5e. TASK NUMBER

5f. WORK UNIT NUMBER

WBS 279585.04.01.22 

7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES)

National Aeronautics and Space Administration 

John H. Glenn Research Center at Lewis Field 

Cleveland, Ohio 44135-3191 

8. PERFORMING ORGANIZATION

 REPORT NUMBER

E-18782 

9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES)

National Aeronautics and Space Administration 

Washington, DC 20546-0001 

10. SPONSORING/MONITOR'S

 ACRONYM(S)

NASA 

11. SPONSORING/MONITORING

 REPORT NUMBER

NASA/TM-2013-218087 

12. DISTRIBUTION/AVAILABILITY STATEMENT

Unclassified-Unlimited 

Subject Category: 18 

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

Future space missions may use Nuclear Thermal Rocket (NTR) stages for human and cargo missions to Mars and other destinations. The 

vehicles are likely to require engine thrust vector control (TVC) to maintain desired flight trajectories. This paper explores requirements and 

concepts for TVC systems for representative NTR missions. Requirements for TVC systems were derived using 6 degree-of-freedom 

models of NTR vehicles. Various flight scenarios were evaluated to determine vehicle attitude control needs and to determine the 

applicability of TVC. Outputs from the models yielded key characteristics including engine gimbal angles, gimbal rates and gimbal actuator 

power. Additional factors such as engine thrust variability and engine thrust alignment errors were examined for impacts to gimbal 

requirements. Various technologies are surveyed for TVC systems for the NTR applications. A key factor in technology selection is the 

unique radiation environment present in NTR stages. Other considerations including mission duration and thermal environments influence 

the selection of optimal TVC technologies. Candidate technologies are compared to see which technologies, or combinations of 

technologies best fit the requirements for selected NTR missions. Representative TVC systems are proposed and key properties such as 

mass and power requirements are defined. The outputs from this effort can be used to refine NTR system sizing models, providing higher 

fidelity definition for TVC systems for future studies. 

15. SUBJECT TERMS

Nuclear Thermal Rocket (NTR); Thrust Vector Control (TVC); Spacecraft; Attitude control; Simulation 

16. SECURITY CLASSIFICATION OF: 17. LIMITATION OF

 ABSTRACT

UU 

18. NUMBER

 OF 

 PAGES

32 

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 

Standard Form 298 (Rev. 8-98)

Prescribed by ANSI Std. Z39-18