AEROSPACE REPORT NO.

ATR-2008(5377)-1

Design and Analysis Guidelines for

Launch Vehicle Tether Systems

30 September 2007

Nicholas E. Martino

Structures Department

Vehicle Systems Division

Prepared for

Volpe National Transportation Systems Center

U.S. Department of Transportation

Cambridge, Massachusetts

Contract No. DTRT57-05-D-30103 

Task 12

Authorized by: Space Launch Operations

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4. TITLE AND SUBTITLE

Design and Analysis Guidelines for Launch Vehicle Tether 

Systems

5A. CONTRACT NUMBER

DTRT57-05-D-30103

5B. GRANT NUMBER

5C. PROGRAM ELEMENT NUMBER

6. AUTHOR(S)*

N. E. MARTINO

5D. PROJECT NUMBER

FA2R DL411

5E. TASK NUMBER

Task Order #12

5F. WORK UNIT NUMBER

FA2R DL411

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

U.S. Department of Transportation

Research and Innovative Technology Administration

Volpe National Transportation Systems Center

Safety Information Systems Division

Cambridge, MA 02142-1093

8. PERFORMING ORGANIZATION REPORT NUMBER

DOT-VNTSC-FAA-07-16

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U.S. Department of Transportation

Federal Aviation Administration

Office of the Assoc. Administrator for Commercial Space Transportation

Washington, DC 20591

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FAA AST-300

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*The Aerospace Corporation, El Segundo, CA 90245-4691, under contract to the Volpe National Transportation Systems Center -- Contract No. 

DTRT57-05-D-30103, Task 12

Aerospace Corporation Report No. ATR-2008(5377)-1

14. ABSTRACT

Design and analysis guidelines were developed for tether systems that could be used to restrain developmental space launch vehicles 

during demonstration tests, thus ensuring the safety of demonstration launches. Ultimately, these guidelines are intended to enable the 

Federal Aviation Administration (FAA) Office of the Associate Administrator of Commercial Space Transportation (AST) to better 

assess the acceptability of commercially developed launch vehicle tether systems. The emphasis of this report is on structural design 

and analysis. However, systems engineering considerations are also discussed, as are guidelines for design and analysis in other 

relevant technical disciplines, such as flight mechanics, structural dynamics and thermodynamics. 

The structural design criteria recommended in this report were formulated based upon applicable civil engineering and aerospace 

industry standards and requirements. These guidelines and the recommended design criteria are intended to be broadly applicable to an 

unspecified range of launch vehicle designs and tether system concepts. While it is impossible to anticipate every contingency that may 

apply to a particular launch vehicle or tether system, every effort has been made to provide FAA/AST with design criteria, insights and 

analytical methods necessary to adapt to each unique challenge. To that end, much of the focus in this report is on describing the multifaceted, interrelated processes involved in planning for a test flight, designing a tether system and verifying its adequacy.

15. SUBJECT TERMS

Commercial Space Transportation, Regulation, Reusable Launch Vehicles, Tethers

16. SECURITY CLASSIFICATION OF: 17. LIMITATION 

OF ABSTRACT

UU

18. NUMBER 

OF PAGES

59

19A. NAME OF RESPONSIBLE PERSON

A. REPORT Ruth A. Hunter

U

B. ABSTRACT

U

C. THIS PAGE

U 19B. TELEPHONE NUMBER (INCLUDE 

AREA CODE)

(617) 494-2667
AEROSPACE REPORT NO.

ATR-2008(5377)-1

Design and Analysis Guidelines for

Launch Vehicle Tether Systems

30 September 2007

Nicholas E. Martino

Structures Department

Vehicle Systems Division

Prepared for

Volpe National Transportation Systems Center

U.S. Department of Transportation

Cambridge, Massachusetts

Contract No. DTRT57-05-D-30103 

Task 12

Authorized by: Space Launch Operations

PUBLIC RELEASE IS AUTHORIZED.
ii

All trademarks, service marks, and trade names are the property of their respective owners.
iii

AEROSPACE REPORT NO.

ATR-2008(5377)-1

Design and Analysis Guidelines for

Launch Vehicle Tether Systems

Approved by:

Eric K. Hall, II, Director

Structures Department

Vehicle Systems Division

John P. Brekke, Systems Director

Civil/Commercial Launch Systems

Launch Systems Division

Ernest R. Scheyhing, Principal Director

Structural Mechanics Subdivision

Vehicle Systems Division

John P. Skratt, Principal Director

Space Launch Projects Directorate

Launch Systems Division
iv
v

Abstract

The Aerospace Corporation was tasked to provide design and analysis guidelines for tether systems 

that could be used to restrain developmental space launch vehicles during demonstration tests, thus 

ensuring the safety of demonstration launches. Ultimately, these guidelines are intended to enable the 

Federal Aviation Administration (FAA) Office of the Associate Administrator of Commercial Space 

Transportation (AST) to better assess the acceptability of commercially developed launch vehicle 

tether systems. The emphasis of this report is on structural design and analysis. However, systems 

engineering considerations are also discussed, as are guidelines for design and analysis in other 

relevant technical disciplines, such as flight mechanics, structural dynamics, and thermodynamics. 

The structural design criteria recommended in this report were formulated based upon applicable civil 

engineering and aerospace industry standards and requirements. These guidelines and the 

recommended design criteria are intended to be broadly applicable to an unspecified range of launch 

vehicle designs and tether system concepts. While it is impossible to anticipate every contingency 

that may apply to a particular launch vehicle or tether system, every effort has been made to provide 

FAA/AST with design criteria, insights, and analytical methods necessary to adapt to each unique 

challenge. To that end, much of the focus in this report is on describing the multifaceted, interrelated 

processes involved in planning for a test flight, designing a tether system, and verifying its adequacy. 
vi
vii

Foreword

This document presents the results of a study carried out by The Aerospace Corporation. This task 

was sponsored by the FAA Office of Commercial Space Transportation (FAA/AST) and was 

managed at the DOT Volpe National Transportation Systems Center. Nicholas E. Martino and Robert 

W. Seibold served as the Aerospace Principal Investigator and Program Manager, respectively. The 

purpose of this task was to recommend criteria for the design of tether systems that may be used to 

restrain launch vehicles during demonstration tests and to provide broadly applicable design and 

analysis guidelines for development of these systems.

The recommended structural design criteria for ground-based hardware closely follow the 

specifications for design of critical resources at the Eastern and Western Test Ranges (i.e., Cape 

Canaveral and Vandenberg Air Force Bases). The recommended criteria for the launch vehicle 

structures potentially affected by tether loads are based on aerospace industry standards for manned 

space flight systems. The design and analysis guidelines and considerations provided in this 

document reflect the collective expertise, experience, and judgment of the author and several of his 

colleagues at Aerospace, who graciously provided insights that were invaluable in the preparation of 

this report. 
viii
ix

Acknowledgments

The author thanks Mr. Stewart W. Jackson, Mr. Lyndon B. Bonaparte, and Ms. Michelle Murray at 

the Office of the Associate Administrator for Commercial Space Transportation, Federal Aviation 

Administration, for valuable guidance on FAA/AST needs relative to the regulation of test flights of 

developmental launch vehicles, as well as Ms. Ruth A. Hunter and Ms. Ann R. DiMare, who served 

as the Contracting Officer’s Technical Representatives (COTRs) at the Volpe National Transportation 

Systems Center. 

The preparation of this report required expertise in several technical disciplines, and therefore 

represented a significant challenge for the principal investigator, whose primary training and 

experience is in the field of structural engineering and analysis. The author gratefully acknowledges 

invaluable contributions and advice received from numerous of his Aerospace colleagues. Special 

thanks are extended to Kent Rolf Bohman, who performed the flight trajectory analysis that is 

summarized in Appendix B. The principal contributors and consultants include the following 

individuals, listed alphabetically below, with their area of support and/or expertise:

Kent Rolf Bohman, Flight Mechanics and Mission Design

Ricardo Crespo, Launch Site Operations and Structures

Han Sik Lee, Thermal Analysis

Emlyn S. McElroy, Library Research

Douglas M. Moody, Flight Mechanics

Ahmed Omar-Amrani, Guidance & Control

Robert W. Seibold, Project Management and Research

Charles E. Spiekerman, Structural Dynamics

 
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Executive Summary

Introduction and Objective

The Aerospace Corporation was tasked by the Volpe National Transportation Systems Center to 

provide technical support for use by the Federal Aviation Administration, Office of Commercial 

Space Transportation (FAA/AST), in developing guidelines for the design and analysis of Launch 

Vehicle (LV) tether systems. This report is intended to provide the technical guidance and insights 

necessary for AST to oversee the design and verification of tether systems, in accordance with wellestablished aerospace engineering practices and methods. Aerospace is pleased to submit this final 

report, in accordance with the requirements delineated in Section F.2, Deliveries or Performance, of 

Contract No. DTRT57-05-D-30103, Task 12.

Scope and Purpose

This document presents design criteria, summarizes analysis requirements, and describes verification 

methods for the development of tether restraint systems for space launch vehicles. The report also 

provides broadly applicable guidelines for planning test flights and designing tether systems. 

Implementation of the recommended criteria should result in highly reliable tether systems, thus 

mitigating concerns for property and facility damage and personnel safety during the test flights of 

developmental vehicles. 

Recommended Design Criteria 

The recommended Factors of Safety (FS) for design of tether systems are:

• For loading events that are expected in a nominal demonstration launch, the tether 

and ground systems should be designed to FS of 5.0, ultimate, and 3.0, yield.

• For the LV, the FS are dependent on whether the affected structures are tested for 

tether-induced loads. For test-qualified LV structures, the design FS are 1.4, ultimate, 

and 1.1, yield. If qualification by analysis is invoked (i.e., with no full-scale static 

testing to simulate tether loading), the FS are 2.25, ultimate, and 1.6, yield.

• The tether system must also be designed for loads that could arise in an off-nominal 

demonstration launch, wherein an unexpected LV system failure causes the vehicle to 

veer off course. Since the probability associated with any of these loading events is 

lower than for nominal conditions, lower FS may be used. For the tether and ground 

systems, the recommended design FS for “LV system failure” cases are 3.0, ultimate, 

and 2.0, yield.

Key Considerations and Guidelines

Some of the key mission and tether system design considerations and analysis guidelines are: 

• Moving the test launch to a remote coastal site or requiring an on-board flight termination 

system may be viable alternatives to performing a limited tethered flight demonstration. 

• The test LV should carry only the fuel required to complete the planned demonstration flight,

with appropriate performance margin. In the event of a mishap, this mitigates the explosive 

risk and limits the downrange potential of the LV.
xii

• The tether should be designed to engage the LV (i.e., become taut) only in the event of a 

mishap. 

• Thermal considerations could affect tether material selection or dictate that insulation is 

required over a portion of its length.

• Approximate methods of analysis to determine tether engagement loads are acceptable for 

preliminary design and for evaluation of LV failure scenarios, provided that dynamic 

amplification effects are either determined analytically or bounded.

• Although approximate methods of analysis may be employed, the structural integrity of the 

entire system – i.e., from the ground structures and attachments, to the tether and to the LV 

attachment and internal structures – must be establish via a rational analysis that demonstrates 

compliance with the recommended design factors of safety.
xiii

Contents

1. Introduction...........................................................................................................................................1

2. Background...........................................................................................................................................3

3. Structural Design Criteria .....................................................................................................................7

3.1 Rationale/Structural Reliability Considerations.........................................................................7

3.2 Summary of Relevant Structural Design Standards...................................................................7

3.3 Recommended Factors of Safety ...............................................................................................9

3.3.1 Factors of Safety for Ground Structures.......................................................................9

3.3.2 Factors of Safety for Launch Vehicle Structures........................................................10

3.4 Test and Inspection Requirements...........................................................................................11

3.4.1 Structural Qualification Testing..................................................................................11

3.4.2 Development Testing..................................................................................................11

3.4.3 Proof Testing ..............................................................................................................12

3.4.4 Fracture Control and Non-Destructive Inspection......................................................12

4. Design Drivers and Considerations....................................................................................................13

4.1 Site Selection and Survey ........................................................................................................13

4.2 Mission Design Considerations...............................................................................................13

4.2.1 Vertical Takeoff and Landing Vehicles......................................................................13

4.2.2 Propellant Loading......................................................................................................14

4.2.3 Tether Length..............................................................................................................14

4.2.4 Parachute Systems ......................................................................................................14

4.2.5 On-board Flight Termination Systems........................................................................15

4.2.6 Retractable Launch Platform ......................................................................................15

4.3 Tether Interface Design............................................................................................................15

4.3.1 Ground Interface Design.............................................................................................15

4.3.2 Vehicle Interface Design ............................................................................................15

4.4 Loads and Environments .........................................................................................................16

4.4.1 Dynamic Loads during Tether Engagement ...............................................................16

4.4.2 Ground and Aerodynamic Pressure Loads .................................................................16

4.4.3 Thermal Environments ...............................................................................................17

4.4.4 Inertial Loads and Drag on the Tether during Ascent.................................................17

4.4.5 Other Loads and Environments ..................................................................................17

4.5 Tether Stiffness........................................................................................................................17

4.6 Material Selection....................................................................................................................18

4.6.1 Conventional Metals...................................................................................................18

4.6.2 Non-metallic Materials...............................................................................................18

4.6.3 Design for Elevated Temperatures..............................................................................19

5. Analysis Requirements.......................................................................................................................21

5.1 Trajectory Analysis..................................................................................................................21

5.2 Loads and Dynamics Analysis.................................................................................................21

5.2.1 Approximate Methods for Preliminary Design...........................................................21

5.2.2 Coupled Loads Analysis.............................................................................................23

5.2.3 Loads Analysis for Unplanned Conditions.................................................................23

5.2.4 Tether Dynamic Motion Simulations..........................................................................23

5.3 Thermal Analysis.....................................................................................................................24

5.4 Strength Analysis.....................................................................................................................24
xiv

5.4.1 Design Stress Analysis...............................................................................................24

5.4.2 Launch Vehicle Stress Analysis to Assess Qualification ...........................................24

5.4.3 Safe-Life Analysis......................................................................................................25

6. Summary ............................................................................................................................................26

6.1 Design Criteria ........................................................................................................................26

6.2 Design Considerations.............................................................................................................26

6.3 Analysis Requirements............................................................................................................27

Acronyms, Abbreviations, and Symbols.....................................................................................................28

References...................................................................................................................................................30

Appendix A: Design and Analysis Guidelines for Launch Vehicle Tether Systems...............................A-1

Appendix B: Tether Design and Analysis Example— Vertical Takeoff and 

Landing Vehicle........................................................................................................................................B-1
xv

Figures

Figure 2-1. Minuteman R&D tethered launch, September 1959........................................................... 4

Figure 2-2. Minuteman IA tethered launch series, 1959 & 1960. ......................................................... 5

Figure 4-1. Effect of temperature on strength of a steel alloy............................................................. 18

Figure B-1. Candidate trajectory for test flight of VTVL launch vehicle. ........................................B-4

Figure B-2. Launch Vehicle External Attachment Fitting Conceptual Design............................... B-12

Tables

Table B-1. Launch Vehicle Design Data............................................................................................B-2

Table B-2. Material Property Comparisons.......................................................................................B-5

Table B-3. Nylon Tether Design Parameters for a Range of Assumed Lengths...............................B-9

Table B-4. 400-foot Tether Design Parameters for Various Materials ........................................... B-10

Table B-5. Launch Vehicle Trajectory Data for 10-second Ascent Case......................................... B-14

Table B-6. Launch Vehicle Trajectory Data for Failure Case 1....................................................... B-15

Table B-7. Launch Vehicle Trajectory Data for Failure Case 2....................................................... B-15

Table B-8. Launch Vehicle Trajectory Data for Failure Case 3....................................................... B-16

Table B-9. Launch Vehicle Trajectory Data for Failure Case 4....................................................... B-16

Table B-10. Launch Vehicle Trajectory Data for Failure Case 5..................................................... B-17

1

1. Introduction

Burgeoning demand for low-cost space launch vehicles designed primarily for space tourism is 

expected to lead to the development of a significant number of small launch vehicles in the 

coming years. As the number of vehicles and launches increases, so will the need for 

commercially available launch facilities. Monitoring these new facilities and ensuring the safety 

of these launches will be the responsibility of the Federal Aviation Administration (FAA). One 

measure that the FAA may take to improve confidence in the reliability and safety of new launch 

systems is to require a demonstration launch of each new vehicle under controlled conditions. 

For the demonstration launches, the safety of the communities surrounding the space launch 

facilities is of paramount concern. One way to address safety concerns is to restrain the launch 

vehicle within the test range area using a tether system. This document provides broadly 

applicable technical guidelines for the design and analysis of tether restraint systems for launch 

vehicle demonstration tests.
2
3

2. Background

The use of tether systems to restrain space launch vehicles during demonstration testing is 

uncommon, but not completely unprecedented. Larger developmental space launch vehicles, 

such as those procured for Department of Defense (DOD) satellite programs, are sometimes 

required to prove their reliability in demonstration missions to orbit using “dummy” payloads, but 

are not required to perform tethered launches. However, these vehicles are subject to stringent 

design, analysis, testing and manufacturing quality control requirements and specifications that 

are intended to promote high reliability. Moreover, these vehicles are typically launched from 

coastal sites in a manner that minimizes the risk to civilian personnel. Finally, these vehicles 

require on-board flight termination systems, so that the risk to civilian personnel and property is 

greatly mitigated.

In the early days of space exploration, limitations in both the methodology and computational 

tools made it impractical to perform rigorous analyses in all of the relevant disciplines, so 

confidence in new systems was derived largely through testing. In September 1959, a Minuteman 

research and development missile was launched at Edwards AFB, using a 2000-ft nylon tether to 

restrain the missile from leaving the test range area (see Figure 2-1). 
4

Photo courtesy Edwards Air Force Base archives, United States Air Force

Figure 2-1. Minuteman R&D tethered launch, September 1959.
5

Subsequently, in late 1959 and 1960, a series of eight Minuteman IA silo test launches, also using 

a tether system to restrain the missiles, was performed at Vandenberg Air Force Base (see Figure 

2-2).

Photo courtesy Vandenburg Air Force Base archives, United States Air Force

Figure 2-2. Minuteman IA tethered launch series, 1959 & 1960.

The use of tether systems to deploy or control satellite systems in space is quite common. 

However, the forces imposed on tethers used in these applications are relatively small, so the 

design drivers for material selection and sizing are quite different than those encountered in this 

study. Some conceptual planning has been performed on the use of tethers as part of a “space 

elevator” system. Although the feasibility of these concepts is limited by concerns about tether 

mass, strength and durability, these studies have identified some candidate materials that may be 

applicable to space launch vehicle restraint systems (see, for example, References 1 and 2). 
6
7

3. Structural Design Criteria

3.1 Rationale/Structural Reliability Considerations

The basis for all structural design criteria can be linked to structural reliability requirements. In 

classical Failure Modes and Effects Analyses (FMEA) performed on space launch systems, 

structural subsystems are somewhat optimistically assigned a reliability of 1.0, provided they 

meet a stringent and deterministic set of design, analysis, and test requirements. In reality, of 

course, there is always some chance of failure, however miniscule. The intent of a wellformulated set of structural design criteria is to ensure that the potential for structural failures is 

appropriately small, given the possible consequences of such failures. 

In design, there are three primary sources of conservatism that lead to highly reliable structures. 

One source is the requirement to use design limit loads that will reliably exceed the expected 

loads and environments to be incurred by the structure. In aerospace applications, this is 

accomplished by performing statistical analyses to define the design limit loads such that they are 

not likely to be exceeded more than once in 100 missions. 

A second source of conservatism is in the assumed strength of the material or of the structure, as 

a whole. Typically, statistically proven material properties are used in design and analysis to 

ensure, with a high degree of confidence, that the materials used to assemble the flight structure 

will have equal or better strength than that assumed. For instability failures that are not 

controlled by material strength, empirically derived buckling design “knockdown” factors are 

used to minimize the risk that the as-built structure will fail prematurely. 

A third source of conservatism is introduced when the predicted loads and the expected structural 

capability are separated by factors of safety (FS). These additional FS are imposed to achieve the 

desired structural reliability, since even the most thorough and rigorous design analysis is subject 

to uncertainties. In theory, the structural probability of failure can be calculated based upon the 

product of the probability of occurrence of loads higher than the design loads and strength less 

than the allowable values used for design, adjusted for the design FS. Therefore, when a system 

is being designed for a highly improbable loading condition, such as in fail-safe analyses, lower 

FS may be used. 

3.2 Summary of Relevant Structural Design Standards

The governing agencies and engineering societies that provide specifications and guidelines for 

the design of structural systems use different approaches to achieve similar goals. The magnitudes 

of the factors of safety vary from one application to another, depending on human safety 

considerations, practical considerations (e.g., the need to minimize structural weight or to provide 

long service life), the nature and consequences of failure in the mode under consideration (e.g., 

yield or ultimate) and the level of test verification demonstrated. Some common threads in all of 

these approaches are that higher factors of safety are imposed when human life is at risk and 

when structural weight is not an overriding concern. Consequently, the factors of safety 

employed in civil engineering practice and aerospace ground system design are considerably 

higher than those imposed for airborne structures. Similarly, manned aircraft and space systems 

are designed to higher factors of safety than unmanned systems.

In civil engineering practice, it is not uncommon to apply varying factors of safety depending on 

the type of loading involved and to impose a knockdown factor on the strength as well. For 
8

example, the working stress design approach favored for many years by the American Institute of 

Steel Construction (Reference 3) defined critical loading combinations for most buildings as 

follows: 

Design Load = 1.4*(Dead Load) + 1.7*(Live Load) 

Dead Loads include the weight of the structural elements and immobile equipment, fixtures and 

furniture. Live loads include human and vehicle traffic, operational loading and wind. In some 

cases, additional factors (e.g., for seismic design or impact loading) might be involved in the load 

combination equation. In all cases, the stresses resulting from these factored loads were 

compared with the “working stress”, which is taken as 60 percent of the expected strength 

(Reference 3). Therefore, the minimum net ultimate factor of safety on live loads, relative to the 

expected strength of the material, is:

Net Ultimate Factor of Safety (min) = 1.7/0.60 = 2.83 

References 3 though 5 are just a few of the civil engineering design manuals that could be 

deemed applicable to portions of a ground-based tether design, depending primarily upon which 

materials are selected.

References 6 and 7 provide criteria for the design of structures for aerospace ground systems at 

Air Force Space Command test ranges. The factors of safety recommended in this report are 

consistent with those specified in these documents for critical ground-based resources at the 

Eastern and Western Test Ranges (i.e., Cape Canaveral and Vandenberg Air Force Bases). 

Critical resources are subject to higher factors of safety in large part because their failure or loss 

could have long-term crippling effects on launch capability. They include, for example, launch 

platforms, static firing test engine hold-down systems and load measurement units, structures 

whose importance in terms of launch/test safety are similar to tether systems. 

The design factors of safety recommended in this report for ground systems, including the tether 

itself, are higher than typical civil engineering requirements. In part, these higher factors are 

recommended on the basis of engineering judgment. However, it is reasonable to argue that the 

inherently dynamic nature of space launches, the resulting uncertainties, and the high costs 

associated with these endeavors justify the imposition of conservative design requirements. 

Planning for a tethered launch must include an analysis of the launch vehicle structure for loads 

that may be induced through the tether. This includes not only the joint assembly that provides 

the direct interface with the tether, but also the internal structures supporting the interface. The 

factors of safety recommended for launch vehicle structures follow the specifications described in 

Reference 8, which provides structural design criteria that are broadly applicable to manned 

aerospace flight structures. 
9

3.3 Recommended Factors of Safety 

3.3.1 Factors of Safety for Ground Structures 

The factors of safety recommended for design of ground-based systems, including the tether and 

its attachments to launch facilities and/or ground equipment, are based upon range safety 

specifications for critical resources, as documented in References 6 and 7. 

3.3.1.1 Yield Factor of Safety 

The recommended minimum design factor of safety for yielding or detrimental deformations of 

ground-based structures is 3.0. The use of this factor assumes a thorough analytical approach to 

define the design limit loads and environments and to determine the internal stresses in the 

structure. 

3.3.1.2 Ultimate Factor of Safety

The recommended minimum design factor of safety for ultimate failure of ground-based 

structures is 5.0. The use of this factor assumes a thorough analytical approach to define the 

design limit loads and environments and to determine the internal stresses in the structure.

3.3.1.3 Tailoring Factors of Safety for Ground Systems

If the recommended factors of safety are considered punitive to the design of the tether, its 

ground supports or the launch vehicle, or if it can be shown that compliance with the 

recommended factors adds undue operational risks, the governing agency may consider the use of 

lower factors of safety, with the following limitations:

1. The minimum yield and ultimate factors of safety must comply with, or be equivalent to, 

the current civil engineering standards that are applicable for the design and/or materials 

in question, such as those described in References 3 through 5. 

2. The minimum yield and ultimate factors of safety must not be less than 2.0 and 3.0, 

respectively, which are the minimum values specified in References 6 and 7 for ground 

resources and facilities.

3. The structural, loads and environmental analyses for the tethered flight event must be 

either demonstrably conservative or rigorous in their approach and application. 

3.3.1.4 Factors of Safety for “LV Failure” Conditions

In the event that the loads on the tether system are incurred as a consequence of a launch system 

failure, the minimum factors of safety for yielding and failure of the tether are 2.0 and 3.0, 

respectively. For the design of other ground hardware for these conditions, the analysis need 

only consider ultimate failures, using a factor of safety of 3.0. The use of these lower FS is 

permissible, since these off-nominal loading conditions have a lower probability of occurrence 

than nominal conditions.
10

3.3.1.5 Safe-Life Requirements

For any structural element in the tether system that represents a potential single point of failure, a 

safe-life analysis is required. A minimum factor of 4.0 times the expected number of loading 

cycles during the entire service life should be used in this analysis. 

3.3.2 Factors of Safety for Launch Vehicle Structures

Although the demonstration vehicle will be unmanned, the potential consequences of a failure 

during tethered flight include loss of life. Therefore, the factors of safety used for launch vehicle 

structures for the loads induced during tethered flight must follow the requirements for manned 

space launch systems, as specified in Reference 8. Note also that the recommended factors of 

safety are consistent with those imposed for unmanned launch vehicle loading conditions, such as 

prelaunch ground winds, that expose personnel to risk. In particular, these requirements apply to 

the structures used to attach the tether system to the launch vehicle and to the airborne structures 

in the primary load paths extending from those attachments. However, these factors are 

applicable to any and all launch vehicle structural elements that might be critically loaded during 

the demonstration test flight.

3.3.2.1 Yield Factor of Safety

The minimum yield factor of safety for the design of manned launch vehicle structures is 1.10. 

However, the use of this factor of safety assumes that a full-scale structural qualification test (i.e., 

“static test”) is performed in a manner that simulates the tethered flight-loading event. If no static 

qualification test is performed to simulate the effects of a tethered flight event on the launch 

vehicle (i.e., “qualification by analysis” is invoked), the minimum factor of safety for yield is 

1.60 (Reference 8). 

3.3.2.2 Ultimate Factor of Safety

The minimum ultimate factor of safety for the design of launch vehicle structures that have been 

qualified in a full-scale static test is 1.40. If no static qualification test is performed to simulate 

the effects of a tethered flight event on the launch vehicle (i.e., “qualification by analysis” is 

invoked), the minimum ultimate factor of safety is 2.25 (Reference 8). Note that aerospace 

industry standards, such as Reference 8, permit the use of qualification by analysis only for wellunderstood failure modes in structures wherein the load paths can be accurately predicted or 

conservatively bounded. 

3.3.2.3 Factors of Safety for Unplanned Conditions

In the event that the tether is engaged with the vehicle as a consequence of a launch system 

failure, the minimum factor of safety for ultimate failure modes of flight hardware remains 

unchanged; i.e., 1.40 for test-qualified structures and 2.25 for structures qualified by analysis 

only. Yield failure modes and local instabilities (e.g., crippling) may be neglected, unless these 

failures could reasonably be expected to propagate into a catastrophic failure. 
11

3.4 Test and Inspection Requirements

3.4.1 Structural Qualification Testing

Although provisions have been made in these guidelines for using a qualification-by-analysis 

approach, full-scale testing is always the preferred technical approach for flight structures 

(References 8, 9). The probability of failure of systems designed by either method is intended to 

be the same, but testing provides an opportunity to gather potentially insightful data that can 

identify critical design flaws. Consequently, testing results in greater overall confidence in the 

structure. Moreover, use of the lower factors of safety required for a test-proven design mitigates 

the risk that the launch vehicle design would be significantly impacted by the requirement to 

perform a tethered demonstration launch. If the launch vehicle designer is appropriately 

cognizant of the tethered launch requirement during the development phase and plans accordingly 

to incorporate it into the overall static test program, the added costs of testing for tether-induced 

loads should be minimal.

3.4.2 Development Testing

3.4.2.1 Material Development Tests

If the tether or any of its critical attachments are to be made using nonstandard materials or 

noncertified manufacturing procedures, or if the usage of a conventionally available structural 

material at the predicted temperatures calls into question its properties, then material development 

tests are required. These tests should be performed on a sufficient number of test specimens to 

define “A-basis” strength values and reliable stiffness properties, as defined in Reference 10. 

3.4.2.2 Deployment Testing

The tether’s length, relatively low mass per unit length and high flexibility are contributing 

factors that might cause uncertainties in the way it responds to highly dynamic environments, 

such as pre-launch ground winds and liftoff overpressures. The design should prevent premature 

entanglement of the tether with launch support structures or other facilities. Similarly, it is 

unlikely that the tether can be designed to withstand direct plume impingement. Consequently, 

the design of the deployment system may include such complications as pre-tensioning, 

breakaway lanyards or bungee cords to keep the tether clear of hazards during pre-launch ground 

winds and liftoff. The more complex the design, the more critical it is to perform demonstration 

tests to verify system performance, preferably at the launch site. Using a motor vehicle and 

pulley system, the ascent of the launch vehicle could be simulated in a relatively simple ground 

deployment test. At a minimum, three deployment tests are recommended to verify the 

repeatability of a complex system.

3.4.2.3 Plume Heating of the Tether

Engine ignition can potentially produce extremely high temperatures and heat flux rates along the 

entire length of the vehicle, including the point of attachment of the tether. Most of the candidate 

structural materials for tether design suffer significant strength degradation at elevated 

temperatures. Consequently, the tether might have to be insulated over at least a portion of its 

length. The tether temperatures can be bounded by thermal analysis. However, thermal testing to 

determine tether response to predicted heat flux would provide data useful in addressing thermal 
12

analysis uncertainties, potentially reducing some of the conservatism that would be deemed 

necessary in a purely analytical approach.

3.4.3 Proof Testing 

The tether should be proof tested to a factor of twice the maximum predicted load, consistent with 

Reference 2 requirements for hoisting equipment and cables. Degradation of the tether strength 

due to environmental effects (primarily, elevated temperatures) must be accounted for in the 

proof test. To accomplish this objective, the tether may be preconditioned to reflect worst-case 

launch environments or the proof loads can be increased in an ambient test to account for the 

expected strength degradation during launch. 

There is one detrimental effect, relative to this application, associated with proof testing of 

stranded and/or braided cables and ropes. Pretensioning often will, at least temporarily, reduce the 

elasticity of a wound cable or rope by realigning some of the fibers axially (i.e., straightening). 

Reduced flexibility and elongation, or “stretch,” will result in higher dynamic loads for the 

critical design loading conditions. Some of the lost flexibility can be restored by “working” the 

cable or rope—i.e., flexing and twisting it back and forth—after the proof load test. 

3.4.4 Fracture Control and Non-Destructive Inspection 

A fracture control plan should be implemented to ensure that a premature failure does not occur 

due to defects or damage incurred during manufacturing or assembly. Appropriate fracture 

mechanics analysis must be performed to determine the critical flaw size for any potential single 

point of failure in the system. The attachment fittings to the launch vehicle and ground are 

primary candidates for such analyses and for rigorous Non-Destructive Inspection (NDI). The 

method of inspection (e.g., dye-penetrant, ultrasound, eddy current, radiography) should be 

appropriate for the hardware design and sufficiently detailed to discern crack-like defects of the 

size and type determined by fracture analysis to be potentially critical. 

Proof testing of the tether to a high factor of safety will ensure that no potentially critical flaws 

are present. Therefore, no stringent NDI of the tether need be required. However, the proof load 

test should be performed as close to the launch date as is practicable to minimize the risk that a 

sub-critical defect could grow dangerously large. As an added precaution, a “walk-around” 

inspection (i.e., close visual inspection) of the tether on the eve of the launch is recommended. 

That level of inspection should be sufficient to verify the integrity of the thermal protective 

coating, if any, and to ensure that no visible defect growth, damage, or corrosion of the tether or 

its attachments has been incurred since the proof test. 
13

4. Design Drivers and Considerations

It is not possible to anticipate all of the design constraints and potential solutions that may apply 

to the planning for a particular demonstration test launch. However, this section presents a broad 

range of mission and tether system design options with the intent of addressing most of the 

critical considerations affecting tether design and illustrating how mission design choices can 

impact the tether system design choices and solutions. Appendix A, “Design, Analysis and 

Verification Process Flow,” presents a series of flow charts that summarize the interrelated 

mission and tether system design processes. Appendix B, “Tether Design and Analysis Example: 

Vertical Takeoff and Landing Vehicle,” illustrates by example the proper application of 

recommended design requirements and structural analysis methods through the preliminary tether 

system design stage.

4.1 Site Selection and Survey

The primary objective of a demonstration launch of a developmental launch vehicle is to improve 

confidence in its reliability. The FAA and the launch vehicle developer should carefully consider 

how the selection of an appropriate launch site furthers this objective and impacts operational 

safety during the test flight. Performing the demonstration launch at a relatively remote and 

expansive site, such as White Sands Missile Range or Edwards Air Force Base, reduces the 

potential for loss of property and human life and may permit a longer test flight trajectory than 

would be considered prudent at a smaller facility located closer to the general population. In fact, 

the FAA might consider the option of requiring full demonstration of launch system capability, 

rather than a limited tethered flight. This could be permissible at one of the aforementioned sites, 

or might dictate that the demonstration flight take place at a launch facility in an extremely 

isolated coastal location, such as Christmas Island or the Kwajalein Atoll.

Once a site has been chosen for a tethered launch, a thorough geographical survey of the area, 

which should consider the layout of on-site facilities, surrounding civilian populations, and 

critical resources both on and off the test range, is needed. This survey supports the overall 

mission design for the test launch by identifying candidate flight azimuths and downrange 

distances that minimize safety risks.

4.2 Mission Design Considerations 

In the design of the tether system and in planning for the demonstration launch, consideration 

must be given to the potential for damage to facilities at or near the launch platform. Ideally, the 

demonstration vehicle would be launched from a remote site where relatively few structures are 

present and a sizeable target zone for the expended vehicle can be designated. However, even 

under optimum conditions, the launch pad and nearby on-site facilities and resources would be at 

risk. 

4.2.1 Vertical Takeoff and Landing Vehicles

Some of the vehicles that may be subject to tethered launch requirements might be designed to 

take off and land vertically. For these vehicles, test flights that demonstrate both liftoff and 

landing capability may be preferable to launches that demonstrate ascent only, even if the 

requirement to land limits the safe test vehicle altitude. Under these conditions, the tether should 

be designed to be long enough so that it will not engage under nominally expected conditions. 
14

Therefore, for strength, the driving condition for tether design would be one associated with the 

vehicle going off course after a major system failure (e.g., guidance, control, or propulsion). 

4.2.2 Propellant Loading 

One way to address risks during a demonstration launch is to minimize the amount of on-board 

propellants. If the launch vehicle includes multiple stages, the higher stages should be inert. The 

first-stage tanks could be partially loaded, carrying only enough propellants to satisfy the primary 

launch objectives relative to launch capability demonstration. In some cases, depending on the 

chosen design, fueling levels might be driven by the need to elevate the vehicle sufficiently to 

engage the tether system at a safe distance from the launch platform (assuming the launch pad is 

to be preserved). Using partially loaded propellant tanks may pose some concerns relative to 

mass properties, propellant sloshing and propellant tank structural stability (i.e., if they are 

pressure-stabilized). These potential problems are most likely minor in nature and solvable on a 

mission-unique basis. 

4.2.3 Tether Length

Tether length is an important design consideration. Using a relatively short tether might serve to 

simplify deployment and limit the range of travel, putting fewer resources at risk. However, a 

short tether would make preservation of the launch tower and facilities considerably more 

difficult. In most cases, the minimum tether length should be several hundred feet to allow the 

vehicle to clear the launch pad and to satisfy the primary demonstration test objective of verifying 

launch capability. 

For strength design under nominal test flight conditions, it may be advantageous to provide a 

tether of sufficient length to guarantee that all of the propellants are spent before it engages the 

vehicle. The size and weight of a tether designed for both thrust and inertial forces could make 

reliable deployment very difficult and might raise guidance and control concerns. The 

demonstration flight cited earlier of a Minuteman missile from Edwards AFB in 1959 used a 

2000-foot nylon tether, which pulled the spent vehicle into a safe impact zone. That vehicle 

reportedly had only enough fuel for approximately three seconds of powered flight, which 

suggests that the vehicle was not under thrust when the tether engaged. 

If the launch site geography supports it, an even better design solution may be to make the tether 

long enough so that it will not engage at all unless the vehicle veers off course. Obviously, this 

will greatly reduce the tether loads under nominal conditions. Moreover, the engagement of a 

tether with a launch vehicle is a highly transient loading event that introduces a significant 

amount of uncertainty in predicting the ensuing vehicle trajectory. Nominally allowing the 

vehicle to continue on a course dictated by mission design parameters and flight mechanics 

principles almost certainly improves the chances of landing within a designated impact zone. 

From a strength standpoint, the design of this sort of long tether will be driven by engagement 

loads potentially induced if the vehicle veers off course after a major system failure. 

4.2.4 Parachute Systems 

One way to reduce the potential for destruction of critical resources and/or injury to personnel is 

to require the use of a deployable parachute system during the test launch. A robustly designed 

parachute system can significantly reduce ground impact velocities and might also provide some 

measure of redundancy in the event that the tether system fails. 
15

4.2.5 On-board Flight Termination Systems

For space launches at the Eastern and Western Test Ranges, an on-board ordnance-based Flight 

Termination System (FTS) is required as a last means of protecting public safety. In the event 

that the vehicle has gone dangerously off course, destruct signals may be sent from the ground 

control station. In addition, many vehicles are equipped with an on-board destruct initiation 

capability that is triggered automatically when key interfaces fail structurally. The mission 

planners should consider whether on-board ordnance systems should be used instead of (or 

possibly, in addition to) a tether restraint system.

4.2.6 Retractable Launch Platform 

Another option is to launch the demonstration vehicle from a retractable (e.g., sled-mounted) 

launch platform. This approach allows the mission designer to consider a shorter test flight, with 

less on-board propellant and a shorter tether, thereby reducing safety risks both on and off the test 

range. However, a limiting consideration in this approach is the need to satisfy the fundamental 

test objectives, which could dictate that a longer flight is required. 

4.3 Tether Interface Design

4.3.1 Ground Interface Design 

The locations of the tether attachments to the ground and to the vehicle are critical in the design 

process. Optimizing the location for ground attachment requires detailed system engineering, 

considering the launch site layout and the desired trajectory of the vehicle. The spent vehicle can 

more easily be directed away from the pad towards a designated target area by securing the 

ground attachment at a safe distance from the launch platform. Another potentially significant 

benefit of moving the ground attachment point away from the stand relates to tether engagement 

loads. Increasing the lateral force component generated at engagement will likely reduce the 

inertial loads induced in the tether by decelerating the vehicle in a more gradual manner.

Elevating the ground attachment point, using a tower or crane, moves the tether further from the 

nozzle, potentially mitigating concern over plume impingement. Elevating the tether ground 

attachment might also result in a beneficial change in the angle of incidence between the tether 

and launch vehicle as the tether engages. With an elevated attachment point, a relatively shorter 

tether may be capable of exerting a higher lateral force vector on the spent vehicle, thus reducing 

tether loads and helping to direct the vehicle away from the launch pad and towards a safe impact 

zone. 

4.3.2 Vehicle Interface Design

To minimize potential impacts to the launch vehicle design, attaching the tether directly to the 

stage I thrust structure seems logical. The design for thrust loads in this region typically results in 

sizeable rings, frames, and/or longerons that could easily distribute the tether loads into the 

vehicle. However, an aft attachment might increase the risk that the spent launch vehicle would 

plummet to Earth on or near the launch pad. In that sense, locating the vehicle attachment point 

at a forward longitudinal station in a manner designed to turn the vehicle towards the desired 

impact zone is advantageous. Moreover, a forward attachment of the tether to the launch vehicle 

should, nominally at least, result in lower inertial loads at engagement by turning the vehicle 

gradually, rather than stopping its ascent more abruptly. Finally, attaching the tether forward of 
16

the center of gravity may provide a measure of safety in the event that the tether fails during 

engagement. In that event, the downward force exerted by the tether at a forward-mounted 

position would likely turn the vehicle Earthward and reduce its downrange potential. 

The requirement to perform a tethered flight should have minimal impact on the launch vehicle 

design. Even in the lighter forward sections of a launch vehicle, structural interfaces typically 

include sturdy ring frames that would be suitable for attaching a tether. At a minimum, an 

external mounting bracket or fitting will be required for this interface. In some cases, local 

stiffening of the ring to which the tether fitting is attached will be necessary. It is also possible 

that longerons or stiffeners will be needed (or existing elements reinforced) to distribute the loads 

axially from the point of attachment. However, these modifications could be made on a missionunique basis for the tethered demonstration flight, so the baseline design could remain unaffected. 

4.4 Loads and Environments

4.4.1 Dynamic Loads during Tether Engagement

Strength requirements are fundamentally important to the design of the tether and its attachments 

to the launch vehicle and ground. The critical design condition for strength coincides with the 

initial engagement of the tether with the launch vehicle, whether that is a planned event or one 

that results after a vehicle system failure. Even if the tether system is designed to engage only 

after all of the propellants are spent, the inertial forces induced as the tether decelerates the 

vehicle will be significant. 

The design limit loads resulting from tether engagement, whether as part of the planned flight 

profile or as a consequence of an off-nominal flight, must be determined by rigorous or 

demonstrably conservative dynamic analyses. For a tether that is designed to engage the vehicle 

in a nominal flight, standard loads analysis procedures apply (see Section 5.2 and Reference 11). 

When considering “failure cases,” the loads may be bounded using approximate methods, as 

described in Sections 5.1 and 5.2.1. For both nominal and off-nominal cases, the analyses should 

assume the worst-case engagement conditions possible (e.g., tether is “slack” prior to 

engagement, vehicle velocity is maximum) and consider the full range of potentially critical 

loading orientations plausible on both the vehicle and ground attachment structures. In addition 

to determining the design limit load on the tether itself, it is also necessary to determine the 

internal loads in all of the affected “back-up” structures supporting the vehicle and ground 

interfaces. 

4.4.2 Ground and Aerodynamic Pressure Loads

Ground winds, ignition overpressure, and aerodynamic pressures must be considered. It is 

unlikely that any of these loads are capable of overstressing the tether or its attachments. 

However, these pressures could cause potentially detrimental motion of the tether before or 

during the launch. In the worst case, the tether could become entangled, affecting its intended 

deployment, or be displaced into or closer to the nozzle exhaust, compromising its structural 

integrity. 

The magnitudes of the ground winds to be used for design might already be defined in the system 

specifications for the launch vehicle. Alternatively, they can be derived from historical data 

specific to the launch site and time of year. The ignition overpressures and aerodynamic 
17

pressures to be used for design may be determined analytically, empirically, or by using a hybrid 

approach wherein the analytical predictions are extrapolated from measured data. 

4.4.3 Thermal Environments

Ignition plume heating acting upon the tether over a portion of its length and on externally 

mounted launch vehicle attachment structures is a potentially significant design driver. The 

plume-heating rate on the tether and the mounting structure would vary depending on the launch 

pad geometry and on tether system design parameters. In general, however, the ignition plume 

heating is significant for the entire length of the vehicle, and it can rapidly elevate the temperature 

of the tether to dangerous levels. The strength of externally exposed attachment fittings might 

also be significantly degraded due to elevated temperatures. 

Presumably, many of the small vehicles being considered for tethered flights would be launched 

from simple platforms that do not include flame ducts or deluge systems. In these cases, 

elevating the launch platform can have a significant effect on both the launch overpressures and 

thermal environments. Elevating the nozzle exit plane to a minimum height of four exit 

diameters, relative to ground, should greatly reduce both the thermal and overpressure 

environments acting upon the vehicle and the tether. 

4.4.4 Inertial Loads and Drag on the Tether during Ascent

The inertial and drag forces on the tether during ascent should be small, relative to tether 

engagement loads. Therefore, these loads will not likely drive the strength design of the tether 

system. However, these forces could well have a significant effect on the flight trajectory, and 

must therefore be considered in flight mechanics simulations. It is possible that these forces 

could pose control problems. Assuming that a single tether is attached forward of the vehicle 

center of gravity, it will exert increasing asymmetric forces to the vehicle as the vehicle ascends. 

If demonstration of guidance and control is a requirement for the test launch, feasibility studies 

need to be performed early in the planning stage for the mission. Most likely, the control systems 

can counteract these effects, but in so doing may result in a test flight with control characteristics 

that are quite dissimilar to a nominal mission. In the unlikely event that the control systems 

cannot compensate, mitigation options include using a tether material with a higher strength-todensity ratio, moving the attachment point closer to the vehicle center of gravity to reduce 

moments, reducing the flight time and/or adding one or more tethers to balance the induced 

lateral forces.

4.4.5 Other Loads and Environments

All other potentially significant load sources and environments should be considered in the design 

and analysis process. Such secondary effects as random vibration, acoustics, thermal cycling and 

moisture absorption should be assessed, particularly when they act in combination with or 

aggravate the effects of the primary design drivers. 

4.5 Tether Stiffness

It is unlikely that stiffness of the tether need be limited by specification for any given system 

design. However, tether stiffness can play a significant role in the design process. For example, 

a stiffer tether will result in higher design loads as it engages more abruptly with the vehicle. Of 
18

secondary importance, the tether’s response to ground winds and ignition pressures will depend 

on its stiffness as well as mass and damping characteristics. 

4.6 Material Selection 

4.6.1 Conventional Metals 

Many of the structural materials conventionally used in aerospace and ground systems design are 

capable of providing the strength required to restrain a small launch vehicle. Simple stranded 

steel cables, for example, would seem a logical choice relative to cost and availability. However, 

limited thermal resistance might drive the design towards a different material choice, or dictate 

the use of thermal protection over some portion of the tether. Figure 4-1, from Reference 10, 

shows the effect of elevated temperatures on stainless steel. 

Fty = tensile yield strength

Ftu = tensile ultimate strength

AISI 301 (1/2-hard) stainless steel sheet

Figure 4-1. Effect of temperature on strength of a steel alloy.

The trend shown in this figure, with strength degrading at temperatures above 600°F, is similar 

for virtually any other steel alloy. Aluminum alloys, which might be considered viable candidate 

materials for the vehicle attachment bracket design, are even more vulnerable at elevated 

temperatures. Their strength falls off dramatically at temperatures above 300°F. 

4.6.2 Non-metallic Materials

Weight is a consideration in the design, particularly if the tether is very long. For weight-critical 

launch vehicle and spacecraft structural systems, the use of advanced composite materials is 

becoming increasingly common. Many of the high-strength fiber materials that comprise the 
19

lamina for advanced composites, such as Kevlar and graphite, could readily be configured for use 

as a tether. These materials offer higher strength-to-weight ratios than metals, and their structural 

properties have been well-established. Potential drawbacks include low ductility and higher 

susceptibility to damage than metals. 

Conceptual planners of space-based tether systems (References 1 and 2) have identified several 

candidate materials of much lower specific density than steel that could provide adequate strength 

for the launch vehicle tether application. Many of these materials have been developed 

commercially for marine applications and are therefore readily available, but often at high cost. 

For example, the directional polyethylene polymer, Allied Signal SpectraTM 2000, reportedly 

provides strength comparable to steel at approximately one-eighth of the density. However, 

SpectraTM appears to offer little resistance to elevated temperatures. Another polymer having 

roughly twice the density of SpectraTM 2000, ZylonTM PoBOn (PBO), reportedly offers about 

50 percent higher tensile strength than SpectraTM and maintains most of its strength at 

temperatures up to 600°F. Carbon fiber materials, such as ThornelTM T-40, offer properties 

similar to that of ZylonTM PBO. 

One note of caution should be made with respect to the use of high-strength polymeric fiber 

materials for LV tethers. In the marine applications for which many of these high-strength ropes 

are primarily designed, high modulus and low stretch are desirable properties because they 

improve responsiveness and control. At best, these characteristics will result in higher dynamic 

loads during tether engagement. At worst, some of these materials might be completely 

unsuitable for the high strain rates associated with the tether design conditions. If one of these 

materials is selected, development testing to characterize the response to elevated temperatures 

and high strain rates is strongly recommended. 

4.6.3 Design for Elevated Temperatures. 

None of the materials mentioned above appear to be entirely suitable for the extreme 

temperatures (i.e., above 1000°F) that might result from plume heating during liftoff. There are a 

significant number of heat-resistant alloys, such as Inconel, Waspalloy, Hastelloy, Haynes and 

Rene (see Reference 10 for properties) that offer good resistance to temperatures well above 

1000°F. However, all of these materials are quite expensive and may not be easily procurable. A 

more practical way to design for elevated temperatures is to insulate the tether, at least over the 

portion of its length that is most vulnerable to plume heating effects. One design approach would 

be to enclose the tether within a protective sheath, using a commercially available insulative 

material such as NextelTM. 
20
21

5. Analysis Requirements

The design of tether systems for the restraint of launch vehicles is a significant engineering 

challenge, but one that can be met using well-established methodologies and standard 

computational tools. However, the best design solutions are those that result from a well-planned 

system engineering approach that effectively integrates inputs from all of the technical 

disciplines. In many cases, an iterative approach to the problem is required. A potential design 

solution that appears optimal with respect to one set of requirements may prove unworkable when 

additional technical constraints are considered. 

5.1 Trajectory Analysis 

Trajectory analysis is a fundamental element of the overall mission design process. Preliminary 

trade studies should be performed to assess the candidate mission profiles identified in the site 

survey as having the best potential to meet performance objectives and address flight safety 

concerns. Design options that might be considered parametrically in these simulations include 

the vehicle azimuth and the amount of fuel (or thrust termination time). Potential variations of 

other key input parameters, such as thrust, ISP, drag, and wind velocity, should be considered as 

well, particularly as the design matures. The effects of tether inertial and drag forces should be 

included in these simulations.

In addition to the trade studies aimed at defining the nominally planned flight profile, flight 

mechanics analysis of failure conditions must be performed. Whether the proposed tether system 

is intended to engage the vehicle under nominal conditions or is designed to remain slack 

throughout, it must be designed to restrain the vehicle if it veers dangerously off course. It is not 

possible, of course, to evaluate all of the potential failure scenarios. At a minimum, failure 

scenarios that maximize the downrange potential of the vehicle and those that result in the highest 

loads on the tether (e.g., maximum velocity, with or without thrust) should be identified and 

simulated. 

The output from these flight simulations provides data that is critical in both the preliminary and 

final designs of the tether system. Predicted time history data for flight simulation output 

parameters such as thrust, altitude, velocity, dynamic pressure, and downrange distance provide 

the basis for the preliminary design of the system. These results, fed into preliminary loads and 

strength assessments, enable a conceptual tether system design to be formulated. In fact, flight 

simulation software should be able to accommodate the addition of a flexible tether either directly 

or by introducing a constraint equation at the appropriate flight time. In this manner, the flight 

simulation analysis can directly predict loads for preliminary design and those that may be 

suitable for final design for failure scenarios. 

5.2 Loads and Dynamics Analysis 

5.2.1 Approximate Methods for Preliminary Design 

In the preliminary design phase, it is reasonable to estimate the tether engagement load using an 

idealized dynamic analysis approach, wherein the launch vehicle is represented as a rigid body. 

A first-order approximation of the engagement event as a single degree-of-freedom (d-o-f) 

spring-mass problem can provide loads for initial sizing and material selection trades studies. The 

approach can also be used to estimate tether loads as a first-order check on predictions obtained 

directly through flight mechanics simulations or coupled loads analysis models. This analysis 
22

utilizes vehicle mass and velocity time histories from trajectory analysis trade studies and 

assumes that the tether acts as an axial spring of stiffness, K, given by the familiar equation:

K = EA/L, where E = elastic modulus

A = area

L = deployed length

(1)

One point of note here is that the effective elastic modulus (i.e., per unit area) of a stranded cable, 

bundled composite fibers, or chain links will typically be lower than the material elastic modulus. 

If the elastic modulus for a candidate tether design is not provided by vendor specification, it can 

be determined experimentally in simple pull tests. 

The analysis to support the preliminary design is iterative in nature. That is, tether stiffness 

parameters are assumed, and the corresponding tether load is determined either directly from 

flight mechanics simulations, or using a closed-form approach, such as the simple spring mass 

idealization. If the assumed tether stiffness results in a design load (including dynamic 

amplification and design factors of safety) that is incompatible with a tether having that stiffness 

(i.e., if it is either insufficient in strength or grossly over-designed), additional iterations are 

performed until a convergent solution is reached.

The building blocks for the basic equation for the simple spring mass idealization are the “forcedisplacement” equation (Reference 11) and Newton’s second law (Reference 12):

F = K δ where F = internal force in a structural element

K = stiffness of structural element

δ = displacement

(2.1)

F = m a where F = inertial force 

m = mass

α = acceleration

(2.2)

The force-displacement equation is an extension of Hooke’s Law, which defines the relationship 

between stress and strain. Combining these equations in a manner that equates the external forces 

from inertia with the internal forces developed in the structural elements results in a simple 

equation that can be used to assess the spring mass problem, as follows:

Mv av + K dt = 0 

where Mv = vehicle mass

av = vehicle deceleration

K = tether stiffness

dt = tether extensional displacement

(2.3)

In this idealized approach, which neglects tether mass and damping, the tether stops the vehicle 

when it develops a force equal to the inertial force of the vehicle, so the deceleration, av, can be 

approximated as follows:
23

av = dv/dt = vi / ( dt / 0.5 vi ) = vi

2

/2dt

 where vi =vehicle velocity when tether first engages,

(from flight mechanics simulations)

(3)

Substituting into Eq. (2.3) allows solution for the tether extensional displacement and the force in 

the tether for the idealized case. 

In reality, the engagement of the tether is a complex transient response problem that will result in 

dynamic magnification of the load predicted as outlined above. If the tether does, in fact, engage 

and stop the vehicle in a sudden manner, the amplification effects will be significant. For 

preliminary design, it is conservative to assume that a dynamic amplification factor of 2.0 will 

apply to the load predicted using the single d-o-f formulations above. 

Examples showing how Equation (3) can be used to design a tether are shown in Appendix B, 

pages B-6, B-8 and B-10. In those examples, the LV velocity at first engagement of the tether is 

determined from flight mechanics simulations. The extensional displacement of the tether is the 

product of its “stretch”, which is vendor supplied data, and the assumed length. With these 

quantities defined, the deceleration of the LV can be calculated using Equation (3), and the force 

in the tether is determined from Newton’s second law. 

These equations can also be used, in combination with data from flight mechanics analysis, to 

assess whether a proposed tether system meets the requirements recommended in this document. 

For a given tether material, cross-sectional area and length, and knowing the LV mass and its 

maximum potential velocity at engagement, the resulting force in the tether can be estimated from 

the equations provided. The tether, its ground attachments and the LV must be capable of 

withstanding the predicted force with the appropriate factors of safety, as defined in Section 3.3.

5.2.2 Coupled Loads Analysis

If the tether is designed to engage the vehicle during flight, it is recommended that final design 

loads for this event be determined using the full vehicle coupled loads analysis models and 

standard procedures, as described in Reference 13. Ideally, this analysis should be performed 

early in the overall vehicle design process, so that the results can be integrated with structural 

qualification test planning for other critical flight loading events. 

5.2.3 Loads Analysis for Unplanned Conditions

Design loads on the tether corresponding to launch vehicle failure scenarios can be determined 

using the approach described for preliminary design, modified to account for dynamic 

amplification (or bounded, as suggested above). That is, the design loads can be obtained directly 

from trajectory simulation models that include the tether or may be determined by an idealized 

transient response analysis that utilizes mass and velocity predictions from those models. 

5.2.4 Tether Dynamic Motion Simulations

Depending on the nature of the design, the tether could be vulnerable to uncontrolled dynamic 

motion under the effects of ground winds and/or liftoff overpressures. Such motion could result 
24

in entanglement of the tether with ground facilities, leading to damage (e.g., fraying) and/or 

premature deployment, or might displace a portion of the tether into the exhaust plume, 

compromising its structural integrity. Dynamic analysis simulations can be performed to predict 

the motion of tether systems, however, this analysis is inherently uncertain. Testing to determine 

key input parameters, such as frictional effects, stiffness and damping coefficients, can reduce the 

uncertainties, but the best solution is to minimize the potential for uncontrolled motion in the 

design phase. 

5.3 Thermal Analysis 

Thermal analysis is required to determine the extent to which ignition plume heating and other 

liftoff environments will elevate temperatures of the tether, its attachments to the launch vehicle, 

and any other structural elements that could be at risk. This analysis is needed to determine heat 

flux rates and the resulting temperatures on all potentially affected structural elements. Inputs to 

the thermal analysis (e.g., nozzle flow rates and temperatures) may be readily available from the 

first stage engine designer, or may be derived from engine firing test data gathered during the

development phase. 

The analysis must take into account the launch vehicle and pad configuration (e.g., elevation of 

exit plane relative to ground, ducts, deluge systems). Predictions corresponding to the maximum 

expected temperatures as well as temperatures at the time of maximum loading on the tether are 

required, unless a worst-on-worst approach can be accommodated in the design. In the absence 

of reliable empirical data or rigorous analysis to define the plume characteristics, the thermal 

analysis should make reasonable, but conservative assumptions to bound the problem. 

5.4 Strength Analysis

5.4.1 Design Stress Analysis 

Strength analyses must be performed to demonstrate that the tether, its airborne and ground 

attachments, secondary support systems, if any, and the flight vehicle meet minimum design 

factors of safety requirements. These analyses should consider the maximum expected design 

loads applied in the most critical orientation(s) and account for the effects of loading transients, 

temperature, and environmental conditions (e.g., moisture absorption in composite materials) that 

might degrade the strength. The analyses to determine internal load distributions should assume 

nominal dimensions and properties. However, the margin-of-safety calculations should be made 

assuming the minimum part dimensions permitted by the design drawings and using the 

minimum guaranteed allowable strength properties (i.e., “A-basis” as defined in Reference 10, or 

the equivalent). 

5.4.2 Launch Vehicle Stress Analysis to Assess Qualification

The design factors of safety required for flight hardware depend on whether the structure in 

question has been qualified in test. To justify the use of test-proven factors of safety, internal 

loads analysis should be performed to demonstrate that test loads envelop the design loads (see 

Reference 14). The alternative is to design for the tether induced loads using higher factors of 

safety required for qualification by analysis. These factors would apply not only to the tether 

attachment hardware, but also to supporting elements within the vehicle that are critically loaded 

by the tether. 
25

5.4.3 Safe-Life Analysis

As part of a comprehensive fracture control plan, safe-life analysis should be performed on all 

potential single points of failure in the load path for the tether system. This analysis, typically 

performed using liner-elastic fracture mechanics methodology, is needed to support definition of 

non-destructive inspection (NDI) requirements. The critical flaw size should be defined to 

guarantee sufficient operational life, with a minimum factor of 4.0 on the number of loading 

cycles. 
26

6. Summary

6.1 Design Criteria

The recommended structural design criteria mirror the requirements for manned launch vehicles 

and for critical ground resources at government space launch facilities. Some softening of these 

requirements for ground-based structures and the tether is acceptable, provided that the approach 

complies with currently applicable civil engineering standards. In designing for unplanned 

conditions that result from a launch system failure, lower factors of safety (i.e., 3.0 on ultimate) 

are recommended for the tether and ground-based systems. Recommendations for qualification 

testing of the launch vehicle, proof testing of the tether, developmental testing (as needed), and 

fracture control planning are also provided.

6.2 Design Considerations

Before proceeding with plans for a tethered launch, the governing agency should strongly 

consider whether alternative options are available that better meet the objectives of enabling a 

meaningful and safe launch and flight demonstration. These options include:

• Move the test launch to a very remote coastal site, where a full flight demonstration 

would be permissible.

• Require an on-board, ordnance-based flight termination system that, at a minimum, can 

be ground-initiated.

• Require the addition of a robust parachute system, which could be used in combination 

with a tether to enhance safety.

Once the decision is made to proceed with a tethered flight, mission and structural design choices 

are both important and interrelated. Some observations and recommendations follow.

• Recommendations:

− Carry only as much propellant as is minimally required. 

− Choose a trajectory that minimizes safety risks, based upon a survey of the site and 

region. 

− Design the tether so that it remains slack during flight (barring a mishap).

• Observations:

− Thoughtful selection of the ground and vehicle interface locations can facilitate safe 

tether deployment and reduce loads. 

− The strength required for the tether is likely to be driven by consideration of a failure 

case, wherein the vehicle has gone dangerously off course. 

− Thermal environments at liftoff may impact material selection and/or dictate that 

thermal protection be provided on portions of the tether.
27

6.3 Analysis Requirements

Effective design of tether systems requires integration of objectives, constraints and analysis in 

several technical disciplines:

• Trajectory analysis supports mission planning and preliminary design of the tether. 

• Tether loads for preliminary design and for failure cases can be determined directly from 

flight mechanics simulations or from transient response analyses that utilize output mass 

and velocity data from these simulations. 

• For nominally planned loading events affecting the launch vehicle, use of aerospace 

industry standard coupled loads analysis methodology and procedures is recommended.

• Strength analyses of both the tether system and the launch vehicle (for loads induced by 

the tether) are required. These analyses should consider in combination the effects of 

quasi-static loads and environments, such as elevated temperatures and humidity, which 

could degrade material strength. 

• The launch vehicle strength analysis should include internal loads modeling to assess 

qualification status. 

• Safe-life analysis of fracture-critical hardware is needed to define NDI requirements.
28

Acronyms, Abbreviations, and Symbols

av vehicle deceleration

AFB Air Force Base

AST Associate Administrator of Commercial Space Transportation, FAA 

CFD Computational Fluid Dynamics

CLA Coupled Loads Analysis

COTR Contracting Officer’s Technical Representative

dt tether extensional displacement

DAF Dynamic Amplification Factor

DOD Department of Defense

d-o-f degree of freedom

E Elastic Modulus

Eq equation 

ISP specific impulse

Fi Tether Inertial Force 

Ft Thrust

Ftu Ultimate Tensile Strength

FAA Federal Aviation Administration

FMEA Failure Modes and Effects Analysis

FS Factor of Safety

FTS Flight Termination System

K tether extensional stiffness

ksi kips per square inch (1 kip = 1000 pounds force)

L tether deployed length

LV launch vehicle

Mv vehicle mass

MS Margin of Safety

NDI Non-Destructive Inspection

MIL-HDBK Military Handbook

MIL-STD Military Standard

Pult ultimate load 

PF Proof Factor

psi pounds per square inch

Ult. Ultimate

v vehicle velocity

VTVL Vertical Takeoff, Vertical Landing

Wt Tether Weight

ρ Density

 
29
30

References

1. Boeing STL 2000R0001, “Hypersonic Airplane Space Tether Orbital Launch System,” Phase 

1 Final Report, 7 January 2000.

2. N. Wilson, “Space Elevators, Space Hotels, and Space Tourism,” 4 August 1998. Also 

downloadable from: 

http://www.spacefuture.com/archive/space_elevators_space_hotels_and_space_tourism.shtml

3. American Institute of Steel Construction, Manual of Steel Construction, current edition.

4. ANSI/ASCE 7-95, American Society of Civil Engineers, Minimum Design Loads for 

Buildings and Other Structures, 6 June 1996.

5. UFC 1-200-01, United Facilities Criteria, Design: General Building Requirements, 31 July 

2002.

6. EWR 127-1, Eastern and Western Range Policies and Procedures, March 1995. 

Downloadable from:

http://snebulos.mit.edu/projects/reference/NASA-Generic/EWR/EWR-127-1.html

7. AFSC Manual 91-710, Air Force Space Command, Range Safety User Requirements 

Manual, Volumes 1-7, 1 July 2004. This and many other military standards and specifications 

also available at: http://www.e-publishing.af.mil

8. ATM 84(4493-35)-10, The Aerospace Corporation, “Structural Design and Verification 

Requirements for DOD Shuttle Payloads,” SD-YV-0067, 3 April 1984.

9. MIL-STD-1540, “Test Requirements for Launch and Space Vehicles,” Revision E (Draft), 

December 2002.

10. MIL-HDBK-5G, “Metallic Materials and Elements for Aerospace Vehicle Structures,” 1 

November 1990.

11. Gallagher, R. H., Finite Element Analysis Fundamentals, Prentice-Hall Civil Engineering and

Engineering Mechanics Series, 1975.

12. Hurty, W. C. and Rubinstein, M. F., Dynamics of Structures, Prentice-Hall International 

Series in Engineering of the Physical Sciences, 1964.

13. A. M. Kabe, “Independent Structural Loads Analyses of Integrated Spacecraft/Launch 

Vehicle Systems,” Aerospace Report TOR-2003(8583)-2886, 22 August 2003. 

14. Military Handbook 340, “Application Guidelines for MIL-STD-1540,” October 1994.
31

A-1

APPENDIX A:

DESIGN AND ANALYSIS GUIDELINES FOR 

LAUNCH VEHICLE TETHER SYSTEMS
A-2

Design and Analysis Guidelines for 

Launch Vehicle Tether Systems

Design, Analysis and Verification

Process Flow

Design and Analysis Guidelines for LV Tether Systems

Mission Design: Site Selection

Launch 

Vehicle 

(LV) Design

Test Objectives 

& Requirements

(Propulsion, Control, Safety...)

Program 

Constraints:

Budget

Schedule

Site Options

Select Test

Site

Consider Test

Site Options

• Space Port

• Gov’t Launch Facility

• Isolated Coastal Site 
A-3

Design and Analysis Guidelines for LV Tether Systems

Mission Design: Trajectory

LV Design

&

Program

Constraints

Test Objectives 

& Requirements

(Propulsion, Control, Safety...)

Select

Test Launch

Trajectory

Survey

Selected 

Test Site 

& 

Region

Perform 

Trajectory 

Trade Studies

Isolated

Coastal Site?

Perform Full 

Duration Flight 

(No Tether)

Yes

No

Proceed to 

preliminary 

tether design

Design and Analysis Guidelines for LV Tether Systems

Tether Preliminary Design

LV Design

Site Considerations

Planned Trajectory

Meets

Req’ts?

Yes

Proceed to 

system 

design &

verification

No

Iterate on 

material 

& size

New Trajectory Needed?

Formulate Concept Design

• Interfaces

• Deployment

• Length

• Material, Assumed Size

Preliminary Analysis

• Flight Mechanics – Nominal and Failure Cases

• Tether Engagement Loads

• Temperatures at Liftoff & Tether Engagement

• Control Systems (Robustness Check)

• Strength Analysis of Tether
A-4

Design and Analysis Guidelines for LV Tether Systems

Tether System Design & Analysis 

Preliminary 

Tether Design

• Length

• Material

• Area

Preliminary 

Analysis Data

• Trajectory

• Loads

• Temperatures

Determine

Internal Loads

In LV 

Tether 

Designed To Engage

In Flight?

High Level

Of Uncertainty

In Material Properties

Preliminary Design 

Loads& Temps

Perform

Development Tests

and/or Refine

Analysis Models

Design Interfaces

• Attachment Locations

• Fitting Design 

Determine 

Engagement 

Loads using

CLA Models

No Yes

Yes

No

LV & Tether System 

Verification

Design and Analysis Guidelines for LV Tether Systems

LV & Tether System Verification 

Tether Loads,

Thermal 

Predictions

& LV Internal 

Loads

• Nominal Cases

• Failure Cases

Select LV 

Qualification

Approach

Perform Static Test 

or Prove Qualification

By Similarity;

Use FS = 1.4 (ult) 

For LV Strength

Use FS = 2.25 (ult) 

For LV Strength

Analysis

Qualify by 

Analysis

Qualify by Test

LV Verification

Tether System Verification

Approach

To Verify Safe 

Deployment

Bounding Analysis

Development Tests

• Deployment

• Wind Response

Proof Load 

Tether (PF = 2)

Implement 

Fracture Control

Plan and 

Perform NDI

Simple 

system

Complex 

system
B-1

APPENDIX B:

TETHER DESIGN AND ANALYSIS EXAMPLE—

VERTICAL TAKEOFF AND LANDING VEHICLE
B-2

B.1 Purpose/Scope 

In order to perform all of the system-level analysis and detailed structural analysis necessary to 

validate a tether design, a vast amount of engineering data is required. That data includes structural 

drawings for the launch system, engine heat flux rates, site layout, and launch platform configuration 

and environmental data for the launch site. It is not the intent herein to document a fully 

comprehensive tether system design and analysis since the interdisciplinary modeling and analysis, 

required for that level of effort are beyond the scope of this contract.

The focus in this example is on strength design of the tether itself, supported by a subset of the flight 

mechanics analysis that would normally be performed to support a rigorous mission design effort. 

This appendix documents a hypothetical example chosen to highlight some of the key design 

considerations and to illustrate application of the recommended structural design criteria using the 

simplified structural analysis methods described in Section 5 of the report. Any similarity between 

the launch vehicle described in this study with one in current use or planning is coincidental. 

B.2 Problem Statement

Perform preliminary strength design for a tether system to be used to restrain a Vertical Takeoff 

Vertical Landing (VTVL) launch vehicle. Some of the relevant design data for the launch vehicle is 

provided in Table B-1.

Table B-1. Launch Vehicle Design Data

Example Problem: Design a Tether System for a Demonstration Launch 

of a Single Stage Sub-orbital Launch Vehicle (LV)))

LV Flight Profile Vertical Takeoff Vertical Landing (VTVL)

Nominal Apogee 330,000 ft.

Engine Single-stage Liquid Rocket Engine

Thrust at Liftoff 15,000 lbf

Liftoff Weight 10,000 lbs

B.3 Mission Planning: Select a Launch Site

Considerations: Ultimately, the intent is to launch this vehicle from one or more commercial 

spaceports within the continental United States. Given that goal and considering budgetary 

constraints, performing the demonstration flight at one of the candidate spaceports is advantageous. 

Moreover, the VTVL capability of the vehicle affords an option to demonstrate both liftoff and 

landing capability within the bounds of the test site, provided it is relatively remote and expansive.
B-3

Site Selected: The test flight will be performed at a spaceport south of Albuquerque, New Mexico.

B.4 Mission Design: Survey Launch Site and Select Trajectory

Considerations: Mitigation of test flight safety concerns is a primary driver in selecting a candidate 

trajectory. In that regard, the layout of critical resources and facilities at the launch site and 

geographical considerations in the outlying regions must be considered. These parameters can 

identify a preferred azimuth for the launch and might suggest limits on the test flight duration. Other 

considerations include demonstration of vehicle performance, such as propulsion for liftoff and 

landing, control systems, and, to the extent possible, guidance and navigation. These performance 

objectives, which would best be met by a full-duration flight, must be weighed against safety 

concerns and, for a tethered launch, the practical limits on the length of the tether.

Supporting Analysis: Perform flight mechanics simulations to evaluate potential trajectories. For 

this study, flight trajectories corresponding to full ascent, 20 seconds of ascent under thrust and 10 

seconds of ascent under thrust were considered. Figure B-1 (next page) depicts one of the candidate

trajectories simulated in this trade study.

Candidate Trajectory Selected: For preliminary mission and tether system design, a trajectory 

limited to 10 seconds of ascent under thrust has been selected. In this essentially vertical trajectory, 

the launch vehicle reaches its apogee approximately 15 seconds after liftoff and restarts the engine 4 

seconds later to accomplish a controlled vertical landing. The altitude at apogee is 5813 feet, which is 

1113 feet over the New Mexico launch site. The controlled descent under thrust lasts 43.6 seconds, 

and the total flight time is 62.5 seconds. 

From a safety standpoint, the vertical landing capability of this LV minimizes risks for a nominal 

(i.e., successful) test flight since the vehicle approaches the ground at less than 10 feet per second. 

However, the requirement to descend slowly under thrust also carries with it a need to carry sufficient 

propellants to accomplish this task. In the event of a system failure leading to an uncontrolled flight, 

the additional propellants greatly increase the downrange potential of the vehicle and pose a 

significant challenge in terms of designing a tether system to meet basic strength requirements. 
B-4

Image source: NASA World Wind

Figure B-1. Candidate trajectory for test flight of VTVL launch vehicle.

B.5 Preliminary Tether Design: Determine Tether Length, Identify Candidate 

Materials, and Determine the Cross-sectional Area Required

Considerations: Tether length will be chosen based on the expected mission altitude and downrange 

distances. The preliminarily selected mission profile, with 10 seconds of thrust and a vertical landing 

unimpeded by the tether, dictates a long tether. Therefore, weight will be a consideration in choosing 

the tether material. Since the tether is not intended to engage the vehicle, the critical design loading 

condition for strength will be a “failure case” in which the LV has veered off course. Thermal 

conditions may affect the tether design, but the preliminary plan is to mitigate these concerns in the 

launch platform design. If necessary, thermal protection (i.e., sheathing) can be provided over the 

vulnerable section of the tether. 

Supporting Analysis: Flight mechanics simulations for the intended test flight and selected failure 

scenarios are summarized in Tables B-5 through B-10 attached at the end of this appendix. Table B-5 

shows predictions from a trajectory simulation of the nominally planned test flight, with 10 seconds 

of powered ascent. Tables B-6 through B-10 show the predicted trajectory data for five selected 

failure cases. The first three failure cases, depicted in Tables B-6 through B-8, assume that the thrust 

is terminated at 10 seconds, but that the vehicle pitches over at varying rates. The last two 

simulations represent failure cases wherein the vehicle continues under thrust after going off course. 
B-5

In the simulation summarized in Table B-9, the vehicle pitches at a constant angular rate. In the 

simulation summarized in Table B-10, the vehicle pitches at a constant acceleration.

Determine Tether Length: In the nominally planned test flight, the vehicle ascends to an altitude 

(relative to sea level) of just over 5800 feet, approximately 1100 feet above the launch platform (see 

Table B-5). The total distance traveled from the launch pad is indicated by the “slant range” column 

in Table B-5 is 0.183 nautical miles. Assuming that the ground attachment point will be relatively 

close to the launch pad, and providing a 20-percent margin on the tether length to allow for trajectory 

dispersions, the proposed length of the tether, L, based on the preliminarily selected mission profile, 

is 1335 feet or 0.219 nautical miles.

Identify Candidate Materials: Programmatic considerations such as cost and availability might 

well enter into the material selection process. From that standpoint, commercially available stranded 

steel cables might be desirable. However, weight might well be a limiting factor, particularly for a 

long tether, so nonmetallic materials having higher ratios of strength to density will also be 

considered. Finally, since the loads induced at engagement will increase proportionately with the 

stiffness of the tether, materials covering a range of elastic moduli will be considered. Some of the

potential tether materials and their relevant structural properties are summarized in Table B-2, 

following. These properties are representative values only, based upon a review of data presented in 

References B-1 through B-4 of this appendix and numerous online commercial sources. These 

properties should not be used in place of actual vendor data for a specific cable or rope under 

consideration.

Table B-2. Material Property Comparisons

Material Strength 

(ksi)

Density 

(lb/in3)

Modulus 

(ksi)

Elongation 

at failure (%)

Alloy Steel 190 0.28 29,000 7.5%

Nylon Fiber 90 0.041 565 16%

Carbon Fiber 500 0.064 38,000 1.5%

Aramid Fiber 280 0.028 15,000 3.6%

Polyethylene 300 0.022 25,000 2.7%

Trajectory Data for Preliminary Design: Since the tether length is chosen to exceed the nominal 

“slant range” for the test flight, the tether will only become taut if the vehicle goes off course. 

Therefore, the critical design loading condition for strength will correspond to an assumed worst-case 

failure condition. For this example, five failure cases were examined in trajectory simulations. Of 

those five, the one summarized in Table B-9 (i.e., continued thrust, pitching at constant rate) results in 

the highest velocity when the slant range reaches 0.219 nautical miles, the proposed length of the 

tether. Therefore, this case is the most critical. The data required for preliminary design is:
B-6

Design trajectory data, from Table B-9, at t = 12.35 seconds

Vehicle Weight = 9910 lbs

Velocity = 273 ft/sec

Thrust = 15,467 lbs

The single-d-o-f idealization described in Section 5 of this report will be used to calculate the inertial 

forces induced as the tether engages. Tether mass effects are neglected in the preliminary sizing 

analysis, so the total force in the tether will be the sum of the thrust and vehicle inertial forces, 

increased by dynamic amplification effects. For preliminary design, we will assume a dynamic 

amplification factor of 2.0. Since the critical design case results from an assumed prior LV failure, 

the ultimate FS for design is 3.0. 

Estimate Inertial Forces: Note that the properties assumed in this example are intended to illustrate 

the analysis procedure and may not be accurate for a particular cable or rope design. In practice, the 

vendor should provide strength, stretch and stiffness values for a candidate tether design. Note also 

that polymeric fiber ropes used for marine applications are typically designed to minimize stretch, as 

are high-strength steel cables used in suspension bridge design. For this application, it is preferable to 

select a rope or cable that is designed to provide a greater stretch and lower extensional stiffness. In 

theory, this can be achieved through fiber/bundle orientation without sacrificing strength, but such 

rope or cable designs may not be readily available in all materials.

The inertial forces are dependent primarily on the mass and velocity of the LV and the extensional 

stiffness of the tether. The first step is to determine the deceleration, av, of the LV using Eq. (3). As 

before, vi is the LV velocity at initial engagement and dt is the extensional displacement of the tether.

av = dv/dt = vi / ( dt / 0.5 vi ) = vi

2

/ 2dt

For many fiber ropes and stranded cables, the stretch (i.e., total extension in percent at failure) is 

largely independent of cross-sectional area. Therefore, the extensional displacement at failure for any 

candidate material can be estimated based on the length of the tether. For the preliminary design, we 

must maintain an ultimate factor of safety of 3.0. Thus, the design ultimate stretch will be limited to 

one-third of the expected stretch of the cable or rope. In order to satisfy this requirement using 

Eq. (3), which does not account for dynamic amplification, we must further reduce the permissible 

stretch by the amplification factor, conservatively estimated to be 2.0. These considerations require 

that the extensional displacement, dt, in Eq. (3) be limited to one-sixth of the stretch (i.e., expected 

stretch divided by the product of the factor of safety times the dynamic amplification factor) for 

design purposes, which results in the following relationship between deceleration and cable or rope 

stretch.

LV deceleration as a function of stretch for an 1135-ft tether:

 av = dv/dt = vi / ( dt / 0.5 vi ) = vi

2

/ 2dt

 = (273)2 ft2/sec2 / [ 2(1335 ft )(S/6)]

= 167.5 / S ft/sec2 

= (167.5 / S ft/sec2)(1g / 32.2 ft/sec2)

= 5.2 / S g’s
B-7

Note regarding cable or rope “stretch” versus material elongation: The stretch of a stranded cable 

or rope is generally greater than the elongation of the material from which it is made due to 

straightening of the fibers, braids or bundles as the tension increases. The extent to which this affects 

stiffness and elongation is a function of the design configuration (e.g., 7-strand, 12-strand, 36-strand, 

braided, double-braided, bridge strand, plaited). The effective modulus and stretch also vary with 

cross-sectional area for a given rope or cable material and design. In some cases, the softening effects 

are considerable. For example, 7-strand medium-strength steel cables may exhibit an effective 

modulus of elasticity that is one third of the Young’s modulus for the parent steel material. Braided 

nylon fiber ropes favored by mountain climbers for their elasticity will often elongate by 30 percent 

or more at failure. At the other extreme, most high-strength polyethylene (e.g., SpectraTM and 

ZylonTM PBO) ropes are intentionally designed to minimize stretch. It is not rare for the makers of

these products to boast maximum stretch values as low as 1 to 2 percent. For the purpose of this 

example, the stretch values assigned are intended to reflect general trends, but may not conform to 

vendor data for a specific rope or cable product. 

Preliminary Sizing Analysis for a Nylon Fiber Tether: Analysis for the most flexible of the 

candidate tether materials, nylon fibers, follows. This analysis utilizes the equation developed above 

for deceleration as a function of cable stretch, assuming that the deployed length of the tether is 1135 

feet. 

Stretch S = 30%

Deceleration av = 5.2 / S = 5.2/0.30 = 17.3 g’s

Inertial Force1 Fi = ma = 9910 (17.3) = 172,000 lbs

Design Ultimate Load Pult = [ Fi (DAF) + Ft ] (FSult), where

DAF = Dynamic Amplification Factor = 2.0

Ft = thrust = 15467 lbs

FSult = Ultimate Factor of Safety = 3.0

Pult = [172,000(2) + 15467](3)

Pult = 1.08 x 106 lbs = 1080 kips

Area Required A = Pult / Ftu = 1080/90 = 12.0 in2

Total Tether Weight WT = A ρL

WT = 12.0(0.041)(1335)(12)= 7,880 lbs

Apogee Weight of Tether WTp = 12.0(0.041)(1112)(12)= 6,560 lbs

Although other candidate materials provide higher strength per unit weight, none has a more 

favorable ratio of elongation to specific strength, so the areas and weights required for a rope or cable 

made from any of the other materials would be comparable or higher. It may be possible to spread 

 1 Dynamic amplification neglected here, but factored into design ultimate load
B-8

1.08 million pounds into the LV without tearing it apart by using multiple tethers. It may also be 

possible to accommodate the added weight from the tethers by offloading propellants, or by 

modifying the mission slightly. However, these results indicate that the preliminary design is far 

from optimal in terms of tether weight and the forces imposed on the launch vehicle. Therefore, other 

potential mission and tether designs will be evaluated.

B.6 Mission and Tether Design Iteration: Modify Preliminary Tether Design Concept 

to Reduce the Engagement Forces and Tether Weight

Considerations: It may be possible to develop an alternative tether design concept capable of 

restraining a LV of this size traveling at velocities exceeding 250 feet per second. For example, an 

energy-dissipating design that slows the vehicle by tearing fabric or by sequentially breaking a series 

of structural elements as a tether or tethers are deployed beyond the intended flight path could work 

by reducing the inertial forces gradually before the tether becomes taut. However, the reliability of 

such a system may be difficult to establish either empirically or analytically. 

The more direct approach to solving the design problem is to reduce the potential for excessive 

inertial forces by shortening the tether, thus engaging the wayward LV before it builds up too much 

momentum. For this example, an acceptable tether length will be determined by reviewing vehicle 

velocity data from the failure cases previously considered. Reducing the tether length will necessitate 

a shorter test flight. For this illustrative example, the permissible duration of ascent thrust will be 

extrapolated from the nominal flight trajectory cases already examined.

Supporting Analysis—Nylon Tether Length Trade Study: Using the same single d-o-f 

idealization as before, we will determine the effects of the tether length, L (in feet), on the design 

loads, which will dictate tether area requirements. For this comparison, we will assume that the tether 

material will be nylon. The applicable equations, taking into account the relevant nylon fiber rope 

properties, follow:

Acceleration ( g’s), av = 0.5vi

2

/(ag)dt where

 ag = gravitational acceleration = 32.2 ft/sec2

 

 dt = tether extensional displacement, limited to one sixth of the stretch 

 dt = L (S/6) = L (0.30/6) for a nylon tether having 30% maximum stretch 

av = 0.5 vi

2

/(32.2) L(0.30/6) = 0.3106 vi

2

/L

Inertial Force (kips), Fi = ma 

Ultimate Design Load (kips), Pult = [ Fi (DAF) + Ft ] (FSult) 

Pult = (2 Fi + Ft) (3)

Tether Area Required (in2

), A = Pult / Ftu = Pult / 90

Tether Weight (lbs), W = ρ A L = (0.041)(A)(L)(12) = 0.492 A(L)
B-9

Tether lengths from 50 feet to 800 feet will be evaluated using the trajectory data from the five failure 

cases summarized in Tables B-6 through B-10. For a given tether length, the failure case that 

produces the highest velocity is assumed to be critical, since the differences in LV mass and thrust for 

these simulations are negligible. The results, in terms of the parameters defined above, are 

summarized in Table B-3.

Table B-3. Nylon Tether Design Parameters for a Range of Assumed Lengths

L 

(ft)

vi

(fps)

av

(g’s)

WLV 

(lbs) 

Ft

(lbs)

Pult

(k-lbs)

Tether

A (in2)

Tether

W (lbs)

50 37.5 8.73 10550 15300 599 6.65 164

100 54.6 9.26 10500 15300 629 6.99 344

200 80.8 10.1 10400 15350 722 8.03 790

400 127 12.5 10240 15370 814 9.05 1780

800 218* 18.4* 10060 0* 1110 12.3 4860

1335 273 17.3 9910 15470 1080 12.0 7880

*Note: Controlled by Failure Case 3, Table B-8. All others critical for Failure Case 4, Table B-9.

Nylon Tether Length Trade Study—Conclusions: The tether design results shown in Table B-3 

are not particularly encouraging. As the tether is shortened, its stiffness increases proportionally, 

which increases inertial loads. Comparing the results for the 50-ft and 1335-ft tethers underscores 

just how much of the benefit of engaging the LV at a lower velocity is lost. The LV momentum for 

the latter case is roughly 50 times that for the former, but the acceleration is reduced only by a factor 

of 1.98. As a result, the tether design loads remain quite high. It could be a challenge to distribute 

these forces into an LV designed originally for 15,000 pounds of thrust. However, since these design 

loads correspond to a failure condition, only ultimate modes of failure that could sever the connection 

between the tether and LV need be considered. 

From a tether weight standpoint, several of the tether length options appear to be acceptable. The LV 

has a robust thrust-to-weight ratio, which could be enhanced by offloading propellants for this test 

flight. 

Material Trade Study for 400-foot Tether: For comparison purposes, other material choices will 

be considered. For this trade study, a 400-foot tether will be assumed. The critical design loads will 

be determined as before using the LV velocity, mass and thrust values shown in Table B-3 for the 

400-foot nylon tether. The applicable material properties and resulting tether design parameters are 

shown in Table B-4. 
B-10

Equation for LV deceleration, 400-ft tethers:

Acceleration ( g’s), av = 0.5vi

2

/(ag)dt 

av = 0.5vi

2

/(32.2)dt = 0.5 vi

2

/(32.2) L(0.30/6)

 = 0.5 (127)2 / [ 32.2 (400 ft)(S/6)]

 = 3.757 / S g’s

Table B-4. 400-foot Tether Design Parameters for Various Materials

Material Strength 

(ksi)

Density 

(lb/in3)

Stretch

(%)

av

(g’s)

Pult

(k-lbs)

Tether

A (in2)

Tether

W (lbs)

Alloy Steel 190 0.28 12 31.3 1970 10.4 13,900

Nylon Fiber 90 0.041 30 12.5 814 9.05 1780

Carbon Fiber 500 0.064 1.8 209 12,900 25.8 7920

Aramid Fiber 280 0.028 4.2 89.4 5540 19.8 2560

Polyethylene 300 0.022 3 125 7730 25.7 2720

Material Trade Study for 400-foot Tether—Conclusions: Based on the mechanical properties 

used in this trade study, none of the alternative materials are suitable for this application. Although 

the high-strength, high-modulus Aramid (e.g., Kevlar) and polyethylene (e.g., SpectraTM) materials 

could meet strength requirements at comparable weights to nylon, the induced loads on the LV would 

be unacceptably high. 

B.7 Preliminary Tether Design 

A 400-foot nylon fiber rope tether or, more likely, a series of tethers is selected as the most promising 

design option. Based upon the preliminary loads analysis, the total tether area required for the 90 ksi 

material is 9.05 square inches. Three 2-inch diameter tethers or a larger number of smaller ropes 

could satisfy this requirement. Product availability and LV interface loading constraints might 

influence the final design choice. The total tether weight for this design is at least 1780 pounds, 

which could be offset by reducing propellant loading for the short-duration test flight.

B.7.1 Test Flight Profile 

The test flight will be shortened so that the tether will not become fully extended under normal 

conditions. Based on the trajectory analysis shown in Table B-5 for a mission with 10 seconds of 

ascent thrust and considering the momentum of the vehicle, the ascent thrust time will be reduced to 

5.5 seconds. This will accelerate the vehicle to about 80 feet per second and elevate it 230 feet above 
B-11

the launch site. Its momentum will elevate it to an apogee roughly 330 feet above ground, so a 

reasonable margin of safety with respect to the tether length is maintained.

B.7.2 Interface Design 

The tether ground interfaces are subject to the same factor of safety requirements as the tether. 

Therefore, these structures must be designed to withstand the same ultimate loads that were predicted 

for the tether. For the 400-foot nylon tether, the ultimate load is 814,000 pounds, as shown in Table 

B-4. Assuming that three 2-inch diameter nylon fiber ropes are employed, each tether would carry 

approximately one-third of the design load, or 271,000 pounds each. The critical loading condition 

could result from the LV veering off course in any direction. Therefore, the stress analysis of the 

ground attachments must consider all possible loading orientations. Positive ultimate margins of 

safety must be shown using the minimum guaranteed material strength properties documented in a 

reliable source, such as Reference 10.

The analysis of the LV interfaces and internal structures would typically require the use of detailed 

finite element models of the LV, or at least a submodel of the regions closest to the tether attachment 

fittings. The design ultimate factor of safety for the LV attachments and internal structures depends 

upon the method of verification. If a full-scale test is performed (i.e., with worst-case tether loads 

applied), the ultimate factor of safety is 1.40. If no test is performed, the ultimate factor of safety is 

2.25. For the 400-foot nylon tether example, the ultimate LV design loads are as follows:

Case I. LV structures qualified in a full-scale static test:

(Pult)LV = (Pult)tether * [(FSult)LV /(FSult)tether] = 814,000 (1.4/3.0) = 380,000 lbs

Case II. No static test for tether loading: 

(Pult)LV = (Pult)tether * [(FSult)LV /(FSult)tether] = 814,000 (2.25/3.0) = 610,000 lbs

Since the critical case described in this example results from a LV system failure, the normal 

requirements to preclude yielding of structures are suspended. Only ultimate failure modes that have 

the potential to result in loss of tether control of the LV need be considered. As with the ground 

attachments, the analysis must consider all potentially critical orientations of the tether loads and 

demonstrate positive margins of safety using minimum guaranteed material properties.

Assuming that no test is performed and that three 2-inch diameter nylon fiber ropes are used to tether 

the LV, the design load on each LV tether attachment point would be approximately 204,000 pounds. 

Typically, the tethers would be attached to the LV using externally mounted fittings like the one 

shown in Figure B-2.
B-12

Figure B-2. Launch Vehicle External Attachment Fitting Conceptual Design

The fittings could be attached to one of the stiffening rings typically present in LV structural designs. 

Designing an appropriate interface using high-strength steel for both the fittings and fasteners is 

reasonably straightforward, and should not result in excessively large or heavy attachment structures. 

For high-strength steel having approximately 200,000 psi ultimate strength, the minimum required 

cross-sectional area per fitting is on the order of one square inch, although design for stress peaking 

effects would likely drive the fitting areas up significantly. 

The more serious design challenge would be finding a means of distributing the tether loads into the 

LV. For example, for a 6-foot diameter LV, the circumference is 226 inches. Even if the total tether 

design load of 610,000 pounds could be uniformly distributed to the LV shell structures, the resulting 

line load would be 2700 pounds per linear inch. Some stress peaking near the attachment fittings is 

unavoidable, so the design loads on the shell structures adjacent to the attachment ring will be higher. 

Typically, these shell structures are relatively thin—a thickness of 0.10 inches or less—and are made 

from aluminum alloys having ultimate tensile strengths on the order of 50,000 psi. It is quite possible 

that the LV in this design example would require some internal reinforcements, such as doublers on 

the attachment rings to distribute the tether forces circumferentially and stiffeners on the shells to 

distribute these forces longitudinally. 

B.8 Summary 

A potentially acceptable tether design concept has been identified for the flight test of a 10,000-pound 

launch vehicle from a spaceport. Since the launch vehicle is designed for vertical landing under 

thrust, the test will be designed to demonstrate that capability. As such, the tether system will not 

engage (i.e., become fully extended) under nominal conditions, but is designed to restrain the LV in 

the event that it veers off course. 

The analysis summarized in this appendix highlights the difficulty of designing a tether system that 

will reliably restrain an LV of moderate size. The necessity to design for the worst-case scenario, in 

terms of the potential flight path of the LV and the manner of its engagement with the tether system, 

results in a taxing dynamic load environment on both the tether and the LV. A few key observations 

follow.
B-13

• The preliminary design analysis methods described herein are approximate and conservative. 

For example, a more detailed analysis of the actual system as it evolves through the design 

process could be used to determine the dynamic amplification factor and, quite likely, reduce 

the design loads substantially.

• Considerably more analysis and testing would be required to develop and validate a final 

tether system design. A thermal protection system covering at least the portion of the tether 

near the LV is probably required. The attachment of the tether to the LV requires detailed 

modeling and analysis. Due to the high design loads, some internal reinforcement of the LV 

might be required.

• Many of the high-strength, low-density polymeric fiber ropes developed for marine 

applications are designed for minimum elasticity. This characteristic makes them far less 

suitable for applications involving the sudden application of load.

B.9 Supporting Analysis

Table B-5 shows predictions from a trajectory simulation of the nominally planned test flight, with 10 

seconds of powered ascent. Tables B-6 through B-10 show the predicted trajectory data for five 

selected failure cases. A key for the column headings in these tables is shown below.

Key for Column Headings, Tables B-5 through B-10

time time from ignition (seconds)

alt altitude from sea level (feet)

wt weight of LV, including propellants (pounds)

vel velocity of LV (feet/seconds)

azr LV azimuth, earth relative (degrees)

alphapt angle of attack, pitch (degrees)

eta acceleration of LV (G’s)

qdynp dynamic pressure on LV, (pounds/feet2

)

slant rng slant range – i.e., total distance from pad to LV (nautical miles)

rng downrange distance (nautical miles)

lon longitude (degrees)

lat latitude (degrees) 

machno Mach number

qalphat Q-alpha, total – i.e., dynamic pressure times total angle of attack (psf-deg)

gammar flight path angle, earth relative (degrees)

f LV thrust (pounds)
B-14

Table B-5. Launch Vehicle Trajectory Data for 10-second Ascent Case

Table B-5. Launch Vehicle Trajectory Data for 10-second Ascent Case
B-15

Table B-6. Launch Vehicle Trajectory Data for Failure Case 1

Table 

B-7. 

Launch 

Vehicle 

Traject

ory 

Data 

for 

Failure 

Case 2

Table B-6. Launch Vehicle Trajectory Data for Failure Case 1Table B-7. Launch Vehicle Trajectory Data for Failure Case 2
B-16

Table B-8. Launch Vehicle Trajectory Data for Failure Case 3

Table B-9. Launch Vehicle Trajectory Data for Failure Case 4

Table B-8. Launch Vehicle Trajectory Data for Failure Case 3Table B-9. Launch Vehicle Trajectory Data for Failure Case 4
B-17

Table B-10. Launch Vehicle Trajectory Data for Failure Case 5

Table B-10. Launch Vehicle Trajectory Data for Failure Case 5

Table B-10. Launch Vehicle Trajectory Data for Failure Case 5
B-18

Appendix B References

B-1. Flory, John F., McKenna, Henry A. and Parsey, Mike R., “Fiber Ropes for Ocean 

Engineering in the 21st Century,” ASCE Civil Engineering Oceans Conference Presentation, 

1982.

B-2. Whitehill, A. S., “A Comparison of Properties of Ropes Made from DuPont. Kevlar 29 and 

Allied-Signal SpectraTM 900 Fibers”, 1986. 

B-3. Benefield, Keith W., “SpectraTM High Performance Fibers for the Fabrication of Lightweight 

Parachute Systems,” Allied-Signal Report 89-0912-CP, 1989.

B-4. Zetlin, Lev, “Suspension Roofs,” Structural Engineering Handbook, Section 22, Edwin H. 

Gaylord, Jr. and Charles N. Gaylord, editors, McGraw-Hill, Inc, 1968.