U.S. Department of Transportation Federal Aviation Administration Advisory Circular Subject: Trajectory Analysis for Normal Flight Date: 08/19/2021 Initiated By: AST-1 AC No: 450.117-1
This advisory circular (AC) provides guidance and a comprehensive method for performing a normal trajectory analysis in accordance with § 450.117, Trajectory Analysis for Normal Flight, of title 14 of the Code of Federal Regulations (14 CFR). This AC assists with performing a trajectory analysis for normal flight. A normal trajectory analysis includes trajectories that characterize the nominal trajectory, as well as both variability and uncertainty per § 450.117(a), using a 6 degree of freedom trajectory model per § 450.117(b), and account for atmospheric conditions, per § 450.117(c). This AC also provides guidance for an operator that chooses to propose a means of compliance for the requirements found in § 450.117.
The Federal Aviation Administration (FAA) considers this AC a means of compliance for complying with the regulatory requirements of § 450.117. It presents one, but not the only, acceptable means of compliance with the associated regulatory requirements. The contents of this document do not have the force and effect of law and are not meant to bind the public in any way. The document is intended only to provide clarity to the public regarding existing requirements under the law or agency policies.
If you have suggestions for improving this AC, you may use the Advisory Circular Feedback form at the end of this AC.
Contents Paragraph Page 1
1 Purpose1
2 Applicability2
3 Applicable Regulations and Related Guidance Documents2
4 Definitions4
5 Acronyms5
6 Purposes of Normal Trajectory Analysis5
6.1 Background5
6.2 Scope6
6.3 Use in Flight Safety Analysis6
6.4 Use for Other Parts of Licensing7
6.5 Analysis Applies to a Single Flight7
6.6 Flight Events7
7 Trajectory Simulation8
7.1 Consideration for Vehicle Systems8
7.2 Simulation Implementation8
7.3 Developing Vehicle Parameters9
7.4 Output Interval11
8 Normal Trajectory Types11
8.1 Nominal vs. Normal11
8.2 Variability vs. Uncertainty11
8.3 Significant Influence11
8.4 Normal Trajectory Set Due to Variability12
8.5 Normal Trajectory Dispersion Due to Uncertainties13
9 Atmospheric Effects16
9.1 Data Sources16
9.2 Worst Case Analysis18
10 Satisfying Application Requirements19
10.1 Methodology Description19
10.2 Input Data for Trajectory Analysis21
10.3 Worst Atmospheric Conditions22
Contents Paragraph Page 2
10.4 Trajectory Outputs22
1 1 PURPOSE.
This advisory circular (AC) provides guidance and a comprehensive method for performing a normal trajectory analysis in accordance with § 450.117 of title 14, Code of Federal Regulations (14 CFR). A normal trajectory analysis is a required component of a flight safety analysis (FSA), per § 450.117(a). As such, the requirements of § 450.115 are applicable to the trajectory analysis developed under § 450.117.
1.1 Analysis Scope.
In accordance with § 450.115(b)(1), an FSA must demonstrate that any risk to the public satisfies the safety criteria of § 450.101, including the use of mitigations, and account for all known sources of uncertainty, using a means of compliance accepted by the FAA Administrator. In accordance with § 450.101(g), for any analysis used to demonstrate compliance with § 450.101, an operator must use accurate data and scientific principles. Also, the analysis must be statistically valid. Also, in accordance with § 450.101(g), the method must produce results consistent with or more conservative than the results available from previous mishaps, tests, or other valid benchmarks, such as higher-fidelity methods.
1.2 Description of Methods.
To satisfy the requirements of § 450.115(c), an applicant must submit a description of the flight safety analysis methodology, including identification of:
The scientific principles and statistical methods used;
All assumptions and their justifications;
The rationale for the level of fidelity;
The evidence for validation and verification required by § 450.101(g);
The extent to which the benchmark conditions are comparable to the foreseeable conditions of the intended operations; and The extent to which risk mitigations were accounted for in the analyses.
1.3 Level of Imperatives.
This AC presents one, but not the only, acceptable means of compliance with the associated regulatory requirements. The FAA will consider other means of compliance that an applicant may elect to present. Other means of regulatory compliance may be acceptable, but must be approved by the Administrator in accordance with § 450.35(b).
In addition, an operator may tailor the provisions of this AC to meet its unique needs, provided the changes are accepted as a means of compliance by the Administrator.
Throughout this document, the word “must” characterizes statements that directly follow regulatory text and therefore, reflect regulatory mandates. The word “should” describes a requirement if electing to use this means of compliance; variation from these requirements is possible, but must be justified and accepted by the FAA as an alternative means of compliance. The word “may” describes variations or alternatives allowed within the accepted means of compliance set forth in this AC. In general, these
2 alternative approaches can be used only under certain situations that do not compromise safety.
2 APPLICABILITY.
2.1 The guidance in this AC is for launch and reentry vehicle applicants and operators applying for a license under part 450. The guidance in this AC is for those seeking a launch or reentry vehicle operator license, and a licensed operator seeking to renew or modify an existing vehicle operator license.
2.2 The material in this AC is advisory in nature and does not constitute a regulation. This guidance is not legally binding in its own right and the FAA will not rely upon this guidance as a separate basis for affirmative enforcement action or other administrative penalty. Conformity with this guidance document (as distinct from existing statutes and regulations) is voluntary only, and nonconformity will not affect rights and obligations under existing statutes and regulations. It describes acceptable means, but not the only means, for demonstrating compliance with the applicable regulations. The FAA will consider other means of compliance that an applicant may elect to present.
2.3 The material in this AC does not change or create any additional regulatory requirements, nor does it authorize changes to, or deviations from, existing regulatory requirements.
3 APPLICABLE REGULATIONS AND RELATED GUIDANCE DOCUMENTS.
3.1 Related U.S.C. Statute.
51 U.S.C. Subtitle v, chapter 509.
3.2 Related FAA Commercial Space Transportation Regulations.
The following 14 CFR regulations must be accounted for when showing compliance with 14 CFR § 450.117. The full text of these regulations can be downloaded from the U.S. Government Printing Office e-CFR. A paper copy can be ordered from the Government Printing Office, Superintendent of Documents, Attn: New Orders, P.O. Box 371954, Pittsburgh, PA, 15250-7954.
Section 401.5, Definitions.
Section 450.35, Means of Compliance.
Section 450.101, Safety Criteria.
Section 450.108, Flight Abort.
Section 450.110, Physical Containment.
Section 450.111, Wind Weighting.
Section 450.113, Flight Safety Analysis Requirements-Scope.
3 Section 450.115, Flight Safety Analysis Methods.
Section 450.133, Flight Hazard Area Analysis.
Section 450.135, Debris Risk Analysis.
Section 450.137 Far-field Overpressure Blast Effects Analysis.
Section 450.139 Toxic Hazards for Flight.
Section 450.161, Control of Hazard Areas.
Section 450.169, Launch and reentry collision avoidance analysis requirements Section 450.213, Pre-flight Reporting.
3.3 Related FAA Advisory Circulars.
FAA Advisory Circulars are available through the FAA website, http://www.faa.gov.
AC 413.5-1, Pre-Application Consultation, when published.
AC 450.101-1A, High Consequence Event Protection, dated May 20, 2021.
AC 450.108-1, Flight Abort Rule Development, dated July 27, 2021.
AC 450.110-1, Physical Containment Flight Safety Analysis, when published.
AC 450.115-1A, High-Fidelity Flight Safety Analysis, dated June 22, 2021.
AC 450.115-2, Medium-Fidelity Flight Safety Analysis, when published.
AC 450.119-1, High-Fidelity Malfunction Trajectory Analysis, when published.
AC 450.123-1, Population Exposure, when published.
3.4 Other References Related to Normal Trajectory Analysis.
1. Common Risk Criteria for National Ranges (Rep. No. 321-10), White Sands, NM:
Risk Committee, Range Safety Group, Range Commanders Council, 2010.
2. Department of Defense World Geodetic System 1984, Its Definition and Relationships with Local Geodetic Systems, Third ed., Amendment 1, Tech. No.
NIMA TR8350.2, National Imagery and Mapping Agency, 2000.
3. Zipfel, P. H. Modeling and Simulation of Aerospace Vehicle Dynamics (Illustrated ed., Education). American Inst. of Aeronautics and Astronautics, 2001.
4. Vinh, N. X. Flight Mechanics of High-Performance Aircraft (Ser. 4). Cambridge:
Cambridge University Press, 1995.
5. Regan, F. J. & Anandakrishnan, S. M., Dynamics of Atmospheric Re-Entry (AIAA Education). American Institute of Aeronautics and Astronautics. 1993.
6. Tewari, A. Atmospheric and Space Flight Dynamics: Modeling and Simulation with MATLAB and Simulink. Birkhäuser, 2007.
7. Gras, T., E. Larson, E. Porterfield, “Improved Correlation of Uncertainty Within Trajectory Sets,” 10th International Association for the Advancement of Space Safety Conference, Los Angeles, California, May 2019.
8. Global Positioning System Precise Positioning Service Performance Standard (GPS PPS PS). DoD Positioning, Navigation, and Timing Executive Committee, 2007.
9. Leslie, F.W., and C.G. Justus, The NASA Marshall Space Flight Center Earth Global Reference Atmospheric Model—2010 Version, NASA/TM—2011-216467, https://ntrs.nasa.gov/citations/20110012696.
10. U. S. Standard Atmosphere, National Aeronautics and Space Administration, NASA-TM-X-74335, Washington D.C., October 1976, https://ntrs.nasa.gov/citations/19770009539.
11. Emmert, J.T., “Thermospheric mass density: A review,” Advances in Space Research, Volume 56, Issue 5, 2015, Pages 773-824, https://doi.org/10.1016/j.asr.2015.05.038.
12. Fink, R. USAF Stability and Control DATCOM. AFWAL-TR-83-3048. McDonnell Douglas Corporation, Douglas Aircraft Division, for the Flight Controls Division, Air Force Flight Dynamics Laboratory, Wright-Patterson AFB, Ohio. October 1960, revised November 1965, revised April 1978. See also http://www.pdas.com/datcomrefs.html for additional references.
13. Computational Fluid Dynamics Committee, Guide for the Verification and Validation of Computational Fluid Dynamics Simulations, AIAA G-077- 1998(2002), 1 Jan 1998, https://doi.org/10.2514/4.472855.
The industry documents referenced in this paragraph refer to the current revisions or regulatory authorities’ accepted revisions.
4 DEFINITIONS.
For this AC, the terms and definitions from § 401.7, and this list, apply:
4.1 Debris Risk Analysis.
A quantitative evaluation of the probability and severity of potentially adverse consequences from hazards due to explosive and inert items from vehicle launch or reentry.
4.2 Degrees of Freedom (DOF).
The number of independent parameters that define a configuration or state for a mechanical system.
4.3 Flight Safety Analysis (FSA).
An FSA consists of a set of quantitative analyses used to determine flight commit criteria, flight abort rules, flight hazard areas, and other mitigation measures and to demonstrate compliance with the safety criteria in § 450.101.
4.4 State Vector.
A set comprised, at minimum, of the three-component position and three-component velocity associated with a point in time along a vehicle’s trajectory. A state vector may also include vehicle mass, thrust, orientation, angular velocity, and other parameters.
5 ACRONYMS.
CFD – Computational fluid dynamics DOF – Degrees of freedom FSA – Flight Safety Analysis GPS – Global Positioning System HWIL – Hardware in the Loop IIP – Instantaneous Impact Point NASA – National Aeronautics and Space Administration WGS – World Geodetic System USAF – United States Air Force 6 PURPOSES OF NORMAL TRAJECTORY ANALYSIS.
6.1 Background.
In order to demonstrate compliance with § 450.101, an applicant must perform an FSA, unless agreed to by the Administrator based on demonstrated reliability, per § 450.113.
An FSA consists of a set of quantitative analyses used to demonstrate compliance with the safety criteria, determine flight hazard areas and other mitigation measures, and determine flight commit criteria and flight abort rules. Sections 450.117 through 450.131 specify the requirements for analyses necessary to develop quantitative input data used to inform portions of the FSA. Section 450.117 specifies the constraints and objectives of analyses sufficient to characterize the trajectory of the vehicle during normal flight. Trajectory analysis is conducted by performing numerical simulations of the flight of a vehicle, incorporating all the vehicle properties (e.g. mass distribution, shape), external environment (e.g. atmosphere, wind), and all relevant physical forces
(e.g. thrust, aerodynamics). A nominal trajectory is developed from a simulation where each input parameter is set to the expected value. Normal trajectories are developed by simulating flight where input parameters are instead sampled within the range of expected values. Thus, a trajectory analysis for normal flight is meant to analyze the variability in the intended trajectory and the uncertainties due to random sources of dispersion, such as winds and vehicle performance.
6.2 Scope.
6.2.1 For an FSA, the normal trajectory data must cover all phases of flight, as specified in § 450.113(a):
(1) For orbital launch, from liftoff through orbital insertion, and through all component impacts or landings;
(2) For suborbital launch, from liftoff through all component impacts or landings;
(3) For disposal, from the initiation of the deorbit through final impacts; and
(4) For reentry, from the initiation of the deorbit through all component impacts or landings.
6.2.2 There are two important clarifications regarding this scope:
In accordance with §§ 450.113(a)(1) and (2), a flight safety analysis is performed and documented for an orbital or suborbital launch, respectively, from liftoff. Section 401.7 defines “liftoff” to mean any motion of the launch vehicle with intention to initiate flight. Therefore, the nominal trajectory for launch vehicle systems that employ a captive carry phase, such as a piloted or unpiloted aerial vehicle or balloon, begins at first motion of the launch vehicle with the intention to initiate flight.1 For a single operation, there are normally a set of nominal trajectories, to include all parts of the vehicle. For each vehicle part, the normal trajectory analysis should continue until breakup is assured or impact occurs, as consistent with § 450.113(a).
6.3 Use in Flight Safety Analysis.
This AC provides acceptable means of compliance for the development of trajectory analyses that are required to address normal flight in accordance with § 450.117. Proper trajectory simulations are needed to support a valid FSA, which demonstrates compliance with acceptable risk thresholds and determines sufficient hazard areas.
Flight planning also normally considers potential high-risk scenarios, and applies mitigations where possible, either implicitly (e.g. launching out over the ocean) or explicitly (e.g. avoiding overflight of islands before being sufficiently downrange).
Normal trajectory simulations are necessary to perform the following general elements of a FSA:
To verify that the vehicle flight plan is achievable under the conditions at the time of launch, in accordance with § 450.117(c).
To identify the state vectors where a failure may occur, in order to initiate malfunction trajectory analysis, in accordance with § 450.119, or debris analysis, in accordance with § 450.121(c). The normal trajectory analysis is particularly
1 An FSA, including a trajectory analysis for normal flight, may not be required for the captive carry flight phase of flight, per § 450.113(b).
7 important for modeling the initial conditions for debris propagation of on-trajectory breakups and for simulation of flight in loss-of-thrust failures.
To determine the region where population data will be required (together with understanding of the malfunction flight distribution), in accordance with § 450.123.
To quantify the airspace volume and ground impact regions at risk due to planned launch vehicle ascent, reentry vehicle descent, jettison debris, and abort. These operations are required to develop land, waterborne vessel, and aircraft hazard areas in accordance with § 450.133.
To establish adequate flight abort rules, including flight safety limits, that define when an operator must initiate flight abort, in accordance with § 450.108, if flight abort is used.
6.4 Use for Other Parts of Licensing.
Normal trajectories are also used in other parts of the license application. They are used as input to:
Environmental review, per § 450.47.
Safety-critical system design, test, and documentation, per § 450.143.
Highly reliable flight safety system, per § 450.145.
Collision avoidance analysis, per § 450.169.
Pre-flight analysis, per § 450.213.
Financial responsibility requirements, per Part 440.
6.5 Analysis Applies to a Single Flight.
A normal trajectory analysis should be performed for each planned operation of a vehicle separately and needs to consider potential variation within the operation (see paragraph 8.2). A license may apply to multiple flights, but the normal trajectory analysis is specific to each flight. The application requirements include submission of the products of a representative normal trajectory analysis, and the same process should be performed for all flights. Thus, the normal trajectory envelope does not encompass all potential flights of a vehicle that could occur, but the expected range of trajectories for a single flight. The normal trajectory analysis for each flight should be used to generate the pre-flight mission information, in accordance with § 450.213(b)(2).
6.6 Flight Events.
Normal trajectory analyses should define the times of the key planned events of flight.
This includes:
Motor ignitions and cutoffs;
Guidance computer mode changes;
Navigation data transitions;
8 Configuration changes (separations, jettisons, and deployment of parachutes or aero-surfaces, etc.); and Instantaneous impact point (IIP) becoming defined (for reentry) or undefined (during ascent to orbit).
These events of flight are important to the overall FSA because they are associated with uniquely assigned failure probabilities and failure rates, debris lists, and flight safety system designs. For the nominal trajectory, times of key environmental conditions, such as maximum heating and dynamic pressure, should also be identified.
7 TRAJECTORY SIMULATION.
7.1 Consideration for Vehicle Systems.
Normal trajectory simulations typically require the system designer to integrate navigation and flight control subsystems to maintain controlled stable flight. Chemical propulsion rockets, which are long cylindrical bodies, tend to be aerodynamically unstable and develop aerodynamic structural loads that break the vehicle if the angle of attack exceeds a narrow margin. Launch and reentry systems that employ active guidance control should have some form of flight computer and sensor suite to measure linear and angular accelerations of the vehicle and compare current vehicle state with the nominal state, sense the error, and apply corrective flight controls. Flight controls include movable aerodynamic surfaces, propulsion thrust vector adjustment, or attitude control/throttle thrust system actions.
7.2 Simulation Implementation.
The software used for trajectory simulation should have acceptance within the industry or use verified methods of 6 degree of freedom (6DOF) simulation. A 6DOF simulation is a simplification of the real world. For example, it does not normally include detailed fluid dynamic calculations, but instead approximates aerodynamics and vehicle mass redistribution with a limited number of coefficients. The paragraphs below discuss the input parameters that are appropriate for a 6DOF simulation. Also, an important aspect of flight simulation is the numerical integration of the equations of motion. The algorithm for selecting the timestep should be evaluated to ensure that timesteps are sufficiently short so that vehicle behavior is accurately captured. This should be evaluated by testing the algorithm to ensure that resulting trajectories are stable with respect to small changes in the timestep approach. References 3, 4, 5, and 6 in paragraph 3.4 of this AC provide algorithms for 6DOF simulation for launch and reentry vehicles.
7.2.1 Small Vehicles.
For small, suborbital, solid rocket vehicles (e.g. less than 2,000 lbs. liftoff weight), a rigid body 6DOF simulation may be used, and a number of codes are available.
Trajectory Analysis and Optimization Software (TAOS) from Sandia National Labs, Optimal Trajectories by Implicit Simulation (OTIS4) from NASA, and Program to Optimize Simulated Trajectories II (POST2) from NASA are examples. A more
9 generalized toolset, such as Simulink with the Aerospace Blockset could also be used.
These tools are also useful for large vehicles in initial planning phases, but the influence of non-rigid behavior should be incorporated for final flight planning.
7.2.2 Medium to Large Vehicles.
For most vehicles, a more sophisticated analysis is necessary to account for the vehiclespecific complexities in guidance, materials (bending), locations (reference frames and loads), and other factors. It is possible to create these simulations in multibody dynamics tools, such as Adams from MSC Software, or within MathWorks suite of tools (SimMechanics and Simscape Multibody). Other companies have analogous products (Siemens Motion, Ansys Motion, RecurDyn, etc.). Most operators develop their own toolsets and verify them against these codes to allow for more customization.
7.3 Developing Vehicle Parameters.
For a proper 6DOF analysis, there will be a significant effort to develop vehicle parameters and model the control system. The nominal values and the expected variation in them should be considered. Time, when used as a dependent variable in these parameters, does not refer to absolute mission time, but the time relative to significant flight events (this distinction is important when developing dispersed trajectories). Alternatively, some parameters like mass properties may be dependent on the propellant use and will scale differently depending on thrust control.
7.3.1 Mass Properties.
Mass properties data includes total mass, the components of moments of inertia, and the center of gravity location. These values should reflect changes in the vehicle configuration (e.g. jettison) and depletion of consumables (e.g. propellant burn or venting). The mass properties should be developed for each vehicle configuration as a function of propellant load. For reentry vehicles, these values sometimes do not change after completion of the deorbit burn. Large control surface deflections and vehicle bending should be considered. Movement of propellant within the fuel tank should be accounted for where relevant. Propellant moves due to inertial forces and depends on vehicle orientation. Different vehicles have a variety of ways of compensating for propellant motion; these will affect the mass distribution. The mass properties will typically be developed in concert with the propulsion and any changes required in vehicle configuration. Uncertainties in propellant load and payload mass should be considered.
7.3.2 Aerodynamic Properties.
The complexity of aerodynamic parameters depends on the control system of the vehicle. For a nearly axisymmetric thrusting rocket, simple coefficients of force will suffice: a set of lift and drag or component force coefficients versus Mach, altitude, and angle of attack, and the center of pressure versus free stream condition. A vehicle with controlled lift, asymmetry, and/or under aero-surface control typically requires more complex aerodynamic coefficient data. The coefficients may need to be dependent on the flight speed, temperature, pressure, viscosity, angle of attack, lateral g-load, control surface deflection, or any number of other values. Control surfaces should be modeled.