AEROSPACE REPORT NO. ATR

- 2008(5377)

- 1



# Design and Analysis Guidelines for Launch Vehicle Tether Systems

30 September 200 7

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

### REPORT DOCUMENTATION PAGE Form Approved OMB No. 0704

- 0188 The public reporting bur den for this collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the co llection of in formation. Send comments regarding this burden estimate or any other aspect of this collection of information, including sug gestions for reducing the burden, to the Department of Defense. Executive Services and Communications Directorate (0704

- 0188). Re spondents should be aware that notwithstanding any other provision of law, no person shall be subject to any penalty for failing to com ply with a collection of information if it does not display a currently valid OMP control number. PLEASE DO NOT RETURN YO UR FORM TO THE ABOVE ORGANIZATION. 1. REPORT DATE (DD

- MM

- YYYY) 30

- 09

- 2007 2. REPORT TYPE Contractor Final Report 3. DATES COVERED (FROM

- TO) May 1, 2007

– September 30, 2007 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 T echnology Administration Volpe National Transportation Systems Center Safety Information Systems Division Cambridge, MA 02142

- 1093 8. PERFORMING ORGANIZATION REPORT NUMBER DOT

- VNTSC

- FAA

- 07

- 16

9. SPONSORING/MONITORING AGENCY NA ME(S) AND ADDRESS(ES) U.S. Department of Transportation Federal Aviation Administration Office of the Assoc. Administrator for Commercial Space Transportation Washington, DC 20591 10. SPONSOR/MONITOR'S ACRONYM(S) FAA AST

- 300

11. SPONSOR/MONITOR'S REPORT NUMBER(S)

12. DISTRIBUTION/AVAILABILITY STATEMENT PUBLIC RELEASE IS AUTHORIZED

. 13. SUPPLEMENTARY NOTES *The Aerospace Corporation, El Segundo, CA 90245

- 4691, under contract to the Volpe Natio nal 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 de velopmental 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 Commer cial Space Transportation (AST) to better assess the acceptability of commercially developed launch vehicle tether systems. The emphasis of this report is on structur al 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 en gineering and aerospace industry standards and requirements. These guidelines and the recommended design criteria are intended to be broadly applica ble to an unspecified range of launch vehicle designs and tether system concepts. While it is impossible t o 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, in sights and analytical methods necessary to adapt to each unique challenge. To that end, mu ch of the focus in this report is on describing the multi

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

15. SUBJECT TERMS Commercial Space Transportation, Reg ulation, Reusable Launch Vehicles, Tethers
16. SECURITY CLASSIFICATION OF: 17. LIMITATION OF ABSTRACT UU 18. NUMBER OF PAGES 59 19A. NAME OF RESPONSIBLE PERSON Ruth A. Hunter A. RE PORT U B. ABSTRACT U C. THIS PAGE U 19B. TELEPHONE NUMBER (INCLUDE AREA CODE) (617) 494

- 2667AEROSPACE 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 An alysis 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. S cheyhing, Principal Director Structural Mechanics Subdivision Vehicle Systems Division John P. Skratt, Principal Director Space Launch Projects Directorate Launch Systems Divisionivv 

### Abstract

The Aerospace Corporation was tasked to provide design a nd 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 Av iation 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 criteri a 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 l aunch 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 anal ytical 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 adequa cy.vivii 

### 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 Syste ms 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 crit ical 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 mann ed 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.viiiix 

### 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, Federa l Aviation Administra tion, for valuable guidance on FAA/AST needs relative to the regulation of test flights of developmental launch vehicles, as well as Ms. Ruth A. Hun t er and Ms. Ann R. DiMare , who served as the Contracting Officer’s Tech nical Represen tative s (COTR s ) at the Volpe National Transpo rtation 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 traini ng 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 perf ormed 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 Mechani cs 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 Dynamicsxxi 

## 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 Adm inistration, 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 overs ee the design and verification of tether systems, in accordance with well

established 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 vehi cles. 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 fac ility 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 laun ch, 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 laun ch 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 con siderations 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 fail ure 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 attachm ents, 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 a nd 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 El evated 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 Analys is

................................ ................................ ............................. 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

................................ ................................ ................................ ..................... 24xiv 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 Land ing Vehicle

................................ ................................ ................................ ................................ ........ B

- 1xv 

### Figures

Figure 2

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

................................ .......................... 4
Fig ure 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 Ca se 3

................................ ....................... B

- 16

Table B

- 9. Launch Vehicle Trajectory Data for Failure Case 4

................................ ....................... B

- 16

Table B

- 10. Launch Vehicle Trajectory Data for Failu re Case 5

................................ ..................... B

- 171 

### 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 y ears. 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 Administra tion (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 t he 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 guid elines for the design and analysis of tether restraint systems for launch vehicle demonstration tests.23 

### 2. Background

The use of tether systems to restrain space launch vehicles during demonstration testing is uncommon, but not completely unprecedented. La rger 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 perfor m 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 launch ed 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 expl oration, 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

rese arch 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 F orce

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 F igure 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 quit e 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 performe d 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 s pace launch vehicle restraint systems (see, for example, References 1 and 2).67 

### 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 r equirements. In reality, of course, there is always some chance of failure, however miniscule. The intent of a well

formulated set of structural design criteria is to ensure that the potential for structural failures is appropriately small, given the pos sible 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 environment s 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 conser vatism 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 fli ght 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 wi ll 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, si nce 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 stren gth 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 Des ign 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 applicat ion 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 ultima te) 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 factor s 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 s ystems.

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. For8 example, the working stress design approach favored for ma ny 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 immo bile 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 al l 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
exp ected 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 o r 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 supp orting 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 Rec ommended 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
sp ecifications 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
struc tures 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 factor s 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 thos e 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, load s 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 failu res, 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 syst em 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 Veh icle 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 teth ered 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 gro und 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 structur es 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 d esign 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 in voked), 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 well

understood failure modes in structures wherein the load paths can b e 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 f light 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 expe cted 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 prefe rred 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 critic al 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 impact ed 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 tes t 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 proce dures, 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 specime ns 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 unlikel y 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 co uld 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 temper atures 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. Consequentl y, 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 addressi ng thermal12 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 wi th 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 pre conditioned 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 pr oof 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 dat e 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 insp ection 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 des ign 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 Pro cess 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 i ts 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 rel atively 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 migh t 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 are a, 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 fli ght 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 nea r 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, contro l, 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 c ould 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 vehic le 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 prope llant 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 relativel y 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 advantag eous 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 enou gh 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 tha t 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 landin g 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 redu ce 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 mig ht 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 reduci ng 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 D esign

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 tra jectory 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 t o 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 teth er 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 of16 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 mi nimum, 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 (o r existing elements reinforced) to distribute the loads axially from the point of attachment. However, these modifications could be made on a mission

unique basis for the tethered demonstration flight, so the baseline design could remain unaffected.

4.4 Loa ds 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 in itial 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 in duced 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 demons trably 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 a pproximate 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 co nsider 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 deploymen t, 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 ca n be derived from historical data specific to the launch site and time of year. The ignition overpressures and aerodynamic17 pressures to be used for design may be determined analytically, empirically, or by using a hybrid approach wherein the analytical p redictions 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 t he 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 inert ial 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 th e 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 increas ing 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 sys tems 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

- to

density 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, pa rticularly 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. Of18 secondary importance, the tether’s response to ground winds and ignition pressures will depen d 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 restr ain 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 th ermal protection over some portion of the tether. Figure 4

- 1, from Reference 10, shows the effect of elevated temperatures on stainless steel.

F ty = tensile yield strength F tu = 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 c onsidered 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 the19 l amina 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 drawbac ks 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 adequ ate 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, Allie d 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 Spectr aTM 2000, ZylonTM PoBOn (PBO), reportedly offers about 50 percent higher tensile strength than Spectra TM 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 d esirable 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 a ssociated 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 m aterials 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 Nextel TM

.2021 

### 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 d esign 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 t hat 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
t rade 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 desig n 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 eval uate 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 identifie d 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, veloc ity, 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 simul ation 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 preliminar y 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 id ealized 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 s election 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 analysis22 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 e ither 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 simp le spring mass idealization are the “force

displacement” 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 ex ternal 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:

M

v a v + K d t = 0 where M v = vehicle mass

a v = vehicle deceleration

K = tether stiffness d

t = 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, a v , can be approximated as follows:23 a v = dv/dt = v i / ( d t / 0.5 v i ) = v i 2 /2d t

where v i = 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 predict ed 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 t o 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 det ermined 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 usin g 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 fina l 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 res ults 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 effe cts of ground winds and/or liftoff overpressures. Such motion could result24 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 plum e, 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, stiffn ess 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 hea ting 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 temperatur es 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 tempera tures 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 an y, 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 demonstrat e 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 ha rdware, 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
gua rantee 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 g overnment 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 condit ions 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, developme ntal 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 th e 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 t ermination 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 s tructural 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 t he 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 require d 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.

• Tet her 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 event s 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 a nalyses 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 a ssess qualification status.

• Safe

- life analysis of fracture

- critical hardware is needed to define NDI requirements.28 

### Acronyms, Abbreviations, and Symbols

a v vehicle deceleration AFB Air Force Base AST Associate Administrator of Commercial Space T ransportation, FAA CFD Computational Fluid Dynamics CLA Coupled Loads Analysis COTR Contracting Officer’s Tech nical Representative d t tether extensional displacement DAF Dynamic Amplification Factor DOD Department of Defense d

- o

- f degree of f reedom E Elastic Modulus Eq equation ISP specific impulse F i Tether Inertial Force F t Thrust F tu Ultimate Tensile Strength FAA Federal Aviation Administration FMEA Failure Modes and Effects Analysis FS Factor of Safety FTS Flight Terminati on System K tether extensional stiffness ksi kips per square inch (1 kip = 1000 pounds force) L tether deployed length LV launch vehicle M v vehicle mass MS Margin of Safety NDI Non

- Destructive Inspection MIL

- HDBK Military Handbook MIL

- STD Mi litary Standard P ult ultimate load PF Proof Factor psi pounds per square inch Ult. Ultimate

v vehicle velocity VTVL Vertical Takeoff, Vertical Landing W t Tether Weight
ρ Density2930 

## References

1. Boeing STL 2000R0001, “Hypersonic Airplane Spa ce 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_touris m.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 Crit eria, Design: General Building Requirements

, 31 July 2002.

6. EWR 127

- 1, Eastern and Western Range Policies and Procedures , March 1995. Downloadable from: http://snebu los.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 Syst ems,” Aerospace Report TOR

- 2003 (8583)

- 2886, 22 August 2003.

14. Military Handbook 340, “Application Guidelines for MIL

- STD

- 1540,” October 1994.31A

- 1 

### APPENDIX A: DESIGN AND ANALYSIS GUIDELINES FOR LAUNCH VEHICLE TETHER SYSTEMSA

- 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 Yes No

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 systemB

- 1 

### APPENDIX B: TETHER DESIGN AND ANALYSIS EXAMPLE

— VERTICAL TAKEOFF AND LANDING VEHICLEB

- 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 structur al 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 co ntract.

The focus in this example is on strength design of the tether itself, supported by a subset of the flight mechanics analysis that would norma lly 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 si mplified 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 f or 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 Wei ght 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 constrain ts, 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 i s 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 prefe rred 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 nav igation. 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 addition al 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. Candidat e 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 mate rial. 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 sel ected 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 tw o 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 pi tches 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 tot al 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 l ength 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 availabi lity 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 ha ving 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/in 3 ) Modulus (ksi) Elongati on 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 m iles, 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 = 15,46 7 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 shoul d 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 desig n. 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
rop e 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, a v , of the LV us ing Eq. (3). As before, v i is the LV velocity at initial engagement and d t is the extensional displacement of the tether.

a v = dv/dt = v i / ( d t / 0.5 v i ) = v i 2 / 2d t
For many fiber ropes and stranded cables, the stretch (i.e., total extension in pe rcent 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 f actor 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 red uce the permissible stretch by the amplification factor, conservatively estimated to be 2.0. These considerations require that the extensional displacement, d t , in Eq. (3) be limited to one

- sixth of the stretch (i.e., expected stretch divided by the produ ct 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:

a v = dv/dt = v i / ( d t / 0.5 v i ) = v i 2 / 2d t = (273) 2 ft 2 /sec 2 / [ 2(1335 ft )(S/6)] = 167.5 / S ft/sec 2 = (167.5 / S ft/sec 2 )(1g / 32.2 ft/sec 2 ) = 5.2 / S g’sB

- 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 so ftening 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 clim bers for their elasticity will often elongate by 30 percent or more at failure. At the other extreme, most high

- strength polyethylene (e.g., Spectra TM and Zylon TM 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.

Preli minary 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 t he deployed length of the tether is 1135 feet.

Stretch S = 30%

Deceleration a v = 5.2 / S = 5.2/0.30 = 17.3 g’s

Inertial Force 1 F i = ma = 9910 (17.3) = 172,000 lbs

Design Ultimate Load P ult = [ F i (DAF) + F t ] (FS ult ), where DAF = Dyn amic Amplification Factor = 2.0

F

t = thrust = 15467 lbs

FS ult = Ultimate Factor of Safety = 3.0

P ult = [172,000(2) + 15467](3)

P ult = 1.08 x 10 6 lbs = 1080 kips Area Required A = P ult / F tu = 1080/90 = 12.0 in 2
Total Tether Weight W T = A ρL

W

T = 12.0(0.041)(1335)(12)= 7,880 lbs Apogee Weight of Tether W Tp = 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 stren gth, 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 loadB

- 8 1.08 million pounds into the LV without tearing it apart by using multiple tethers. It may also b e 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 o n 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 t o 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 permis sible 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 t ether 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 propertie s, follow:

Acceleration ( g’s), a v = 0.5v i 2 /(a g )d t where

a g = gravitational acceleration = 32.2 ft/sec 2

d

t = tether extensional displacement, limited to one sixth of the stretch

d

t = L (S/6) = L (0.30/6) for a nylon tether having 30 % maximum stretch

a v = 0.5 v i 2 /(32.2) L(0.30/6) = 0.3106 v i 2 /L

Inertial Force (kips), F i = ma Ultimate Design Load (kips), P ult = [ F i (DAF) + F t ] (FS ult )

P ult = (2 F i + F t ) (3) Tether Area Required (in 2 ), A = P ult / F tu = P ult / 90

Tethe r 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 hi ghest 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) v i (fps) a v (g’s) W LV (lbs) F t (lbs) P ult (k

- lbs) Tether A (in 2 ) 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 t ether 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 muc h 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 hig h. 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.

Ma terial 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 t hrust 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), a v = 0.5v i 2 /(a g )d t

a v = 0.5v i 2 /(32.2)d t = 0.5 v i 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/in 3 ) Stretch (%) a v (g’s) P ult (k

- lbs) Tether A (in 2 ) 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., Spectra TM ) 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 smal ler 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 loa ding 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 sec onds 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 aboveB

- 11 the launch site. Its momentum will elev ate 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 f iber 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 interf aces 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 inte rnal 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

- f oot nylon tether example, the ultimate LV design loads are as follows:

Case I. LV structures qualified in a full

- scale static test:

(P ult ) LV = (P ult ) tether * [(FS ult ) LV /(FS ult ) tether ] = 814,000 (1.4/3.0) = 380,000 lbs

Case II. No static test for te ther loading:

(P ult ) LV = (P ult ) tether * [(FS ult ) LV /(FS ult ) 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 s uspended. 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 demon strate 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 appro ximately 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 o ne 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 atta chment 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 fitt ing 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 a ttachment 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 th is 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 a cceptable 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 t ether 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 des ign 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 prot ection 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 requi red.

• 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 Suppor ting 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 colu mn 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/feet 2 ) slant rng slant range

– i.e., total distance from pad to LV (nautical miles)
rng downrange dis tance (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 CaseTable B-5. Launch Vehicle Trajectory Data for 10-second Ascent CaseB

- 15 Table B

- 6. Launch Vehicle Trajectory Data for Failure Case 1

Table B

- 7. Launch Vehicle Traject

ory Data for Failure Case 2Table B-6. Launch Vehicle Trajectory Data for Failure Case 1Table B-7. Launch Vehicle Trajectory Data for Failure Case 2B

- 16 Table B

- 8. Launch Vehicle Trajectory Data for Failure Case 3

Table B

- 9. Launch Vehicle Trajectory Data for Failure Case 4Table B-8. Launch Vehicle Trajectory Data for Failure Case 3Table B-9. Launch Vehicle Trajectory Data for Failure Case 4B

- 17 Table B

- 10. Launch Vehicle Trajectory Data for Failure Case 5

Table B

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

- 18 Appendix B References

B

- 1. F lory, John F., McKenna, Henry A. and Parsey, Mike R., “Fiber Ropes for Ocean Engineering in the 21 st Century,” ASCE Civil Engineering Oceans Conference Presentation, 1982.

B

- 2. Whitehill, A. S., “A Comparison of Properties of Ropes Made from DuPont. Kevla r 29 a nd Allied

- Signal Spectra 

### TM 900 Fibers”, 1986.

B

- 3. Benefield, Keith W., “Spectra 

### TM 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.