13.6 Conditional Casualty Expectation.
The FAA has established consequence criteria, specified in requirements § 450.101(c), which state: An operator must protect against a high consequence event in uncontrolled areas for each phase of flight by:
1. Using flight abort as a hazard control strategy in accordance with the requirements of § 450.108;
2. Ensuring the consequence of any reasonably foreseeable failure mode, in any significant period of flight, is no greater than 1 × 10-3 conditional expected casualties; or
3. Establishing the launch or reentry vehicle has sufficient demonstrated reliability as agreed to by the Administrator based on conditional expected casualty criteria during that phase of flight.
13.6.1 The consequence should be measured by the casualty expectation in uncontrolled areas (defined in § 407.1) for any failure mode occurring during any significant period of flight, with an important threshold at 1 × 10-3 set in § 450.101(c)(2).
13.6.2 Since 𝐸𝐸𝐶𝐶𝑖𝑖 includes the probability of occurrence for hazardous debris generating events 𝑟𝑟𝑚𝑚𝑚𝑚𝑓𝑓𝑠𝑠𝑟𝑟𝑟𝑟, the 𝐸𝐸𝐶𝐶𝑖𝑖 𝑒𝑒𝑘𝑘 are the contributions to the total mission casualty expectation accounting for the probability that the hazardous debris generating event has occurred.
Thus, to obtain the casualty expectation 𝐶𝐶𝐸𝐸𝐶𝐶𝑖𝑖 for the hazardous debris generating event given that the event has occurred, (i.e., is conditional on the event having occurred), the probability of the event 𝑒𝑒𝑘𝑘𝑟𝑟𝑚𝑚𝑚𝑚𝑓𝑓𝑠𝑠𝑟𝑟𝑟𝑟 needs to be removed as shown below:
𝐸𝐸𝐶𝐶𝑖𝑖 𝐶𝐶𝐸𝐸𝐶𝐶𝑖𝑖 = 𝑒𝑒𝑘𝑘𝑟𝑟𝑚𝑚𝑚𝑚𝑓𝑓𝑠𝑠𝑟𝑟𝑟𝑟
13.7 Aggregate Risk.
Accumulated risk is the combined risk to all individuals that are exposed to hazards, such as that due to impacting hazardous debris. It accounts for all hazardous events that could occur for a launch or reentry mission, including all phases of the mission.
13.7.1 Collective risk represents the total risk to all individuals exposed to all the hazards that could result from a mission. It provides a measure of the risk to everyone potentially exposed. In the launch and reentry industry, risk is usually quantitatively expressed in terms of expected casualties (EC, also referred to as “casualty expectation”). EC is the expected average number of human casualties incurred per launch or reentry mission.
When the human casualties contemplated are limited to just those incurred by members of the public, EC for a mission measures the public safety risk of conducting the mission. EC is usually computed separately for each of the hazards, and these are added to obtain a conservative estimate of total collective risk.
13.7.2 In general, aggregated risk, collective and individual, must account for the three principle launch hazards: hazardous debris (which includes inert and explosive debris), far-field overpressure blast effects (which is commonly referred to as distance focusing overpressure (DFO)), and toxic release, in accordance with §§ 450.101(a)(1) and (a)(2).
The total casualty expectation is generally estimated by summing the total (accumulated) casualty expectation from each of the hazards posed by a mission.
Although this AC only addresses methods for computing the risk for hazardous debris, the total casualty expectation for the hazardous debris hazard will need to be combined with the values computed for DFO and toxic release to obtain the aggregate risk to be compared with FAA risk criteria per § 450.101(a)(1)(i).
13.7.3 The total collective risk results for a mission should include:
a. A list of the maximum individual probability of casualty for the top ten (10) population centers and all centers that exceed 10 percent of the individual risk criterion in accordance with § 450.135(c)(5)(iii),
b. A list of the probability of loss of functionality of any designated critical asset that exceeds one percent of the criterion, and
c. A list of the conditional expected casualty for each failure mode for each second of flight under representative conditions and the worst foreseeable conditions in accordance with § 450.135(c)(5)(iv), unless an operator demonstrates compliance with § 450.108(c)(6).
13.8 Analysis.
In accordance with § 450.135(a)(1), there are two options for an applicant, either to perform sufficient analyses prior to the day of the operation accounting for all foreseeable conditions within the flight commit criteria (an availability study), or to run an analysis in the countdown for the operation. Per § 450.135(c)(1), an applicant must submit a description of how the operator will account for the conditions immediately prior to enabling the flight of a launch vehicle or the reentry of a reentry vehicle, in particular:
1. Final trajectory
2. Atmospheric conditions (especially wind)
3. Exposure of people
13.8.1 Availability Study.
Thus, if an availability study is performed, which could be weeks or months ahead of the operation, the variability in the range of all input data should be accounted for. This involves running the risk analysis with a variety of these inputs that span the range of what is possible for the operation. The range of parameters should consider other flight commit criteria or hazard controls. Each combination of these variety of inputs is a potential scenario for the operation. The appropriate application of atmospheric data for an availability study is discussed in section 9.1 of this AC. Population data variability should consider seasonal, temporal, and operation-related (including any observers and visitors variations, as discussed in AC 450.123-1, Population Exposure. The trajectory 104
variability should consider the variation in mission profile due to variation in mission objectives, atmospheric conditions, and the operation timing (e.g., launch window). If some scenarios do not meet the risk requirements of § 450.101, then in accordance with § 450.165, an operator must establish and observe flight commit criteria that identify each condition necessary prior to flight to satisfy the requirements of § 450.101, and preclude initiation of the operation each condition necessary prior to initiation of the flight operation. Specifically, this includes the monitoring of the meteorological conditions necessary to be consistent with any safety analysis, as required by § 450.165(a)(2), and any hazard controls derived from any safety analysis required per § 450.165(a)(7).
13.8.2 Countdown Analysis.
Alternatively, operators may choose to perform a risk analysis during the countdown, during the hours leading up to a mission. In accordance with § 450.135(a)(2), a risk analysis during the countdown must use the best available input data, including flight commit criteria and flight abort rules. Thus, a countdown analysis is one where the uncertainties in conditions are reduced to the minimum feasible. A primary difference between a planning analysis and a countdown analysis is that a countdown analysis will use updated normal trajectory data (if different from best estimate planning data), updated population exposure data, and wind data based on the latest wind forecast or wind measurements (weather balloon, weather towers, sonars) made during the countdown. In some cases, the duration of the flight initation window may result in significant differences in predicted risks. In all cases, all risks to the public must satisfy the criteria in § 450.101 at the time of initiation of the flight operation. It is not sufficient to only assess the average risk across the flight initiation window.
14 FLIGHT HAZARD AREA DEFINITION.
In accordance with § 401.7, a flight hazard area is a region of land, sea, or air that must be surveyed, publicized, controlled, or evacuated in order to ensure compliance with the safety criteria in § 450.101. A flight safety analysis must include a flight hazard area analysis, in accordance with § 450.133(a). The concept of a hazard area can be broadened to include lower and upper altitudes, leading to the concept of a hazard volume. Hazard volumes are important for aircraft risk because hazardous debris at altitude transits to the ground over a period of time, and the dispersion, which is impacted by meteorological conditions, and the aerodynamic characteristics of hazardous debris. Flight hazard areas are publicized prior to a mission, and areas are surveyed, controlled, or evacuated, to control public risk, in accordance with § 450.161(c).
14.1 Sources of Hazards.
Consideration of hazards, and the consequences produced is part of performing a standard risk assessment. Protecting people from hazards can be approached by specifying where people can or cannot be, through measures of tolerable acceptance, mitigation, or through exclusion. Sources of hazards include planned hazardous debris events, in accordance with § 450.133(a)(1), as well as hazardous debris or other hazards that could result from all reasonably foreseeable malfunction failure modes. Planned hazards include expended and dropped stages, and jettisoned equipment (such as de-spinning devices) or ballast. Unplanned hazards include explosions leading to air blast and inert hazardous debris, burning or explosive hazardous debris, and hazardous debris that results from aerodynamic breakup or activation of a flight safety system. An operator must submit a description of the methodology to be used in the flight hazard area analysis in accordance with § 450.115(c), to satisfy § 450.133(e)(1).
14.2 Flight Hazard Areas.
Flight hazard areas are based on ensuring the risk to a protected entity (people, waterborne vessels, aircraft) meets the individual risk criteria in §§ 450.101(a)(2) or
(b)(2) in accordance with §§ 450.133(b)(2) and 450.133(c)(2); meets the collective risk criteria in §§ 450.101(a)(1) or (b)(1) in accordance with §§ 450.133(b)(3) and
450.133(c)(3); or meets the aircraft risk criteria in §§ 450.101(a)(3) or (b)(3) in accordance with § 450.133(d)(2). Implicit in such calculations is an understanding of what could be at risk. For waterborne vessels, this might include whether small fishing boats, large fishing boats, cargo vessels, oil tankers or cruise ships could potentially be in a region. The class of vessel potentially at risk affects the vulnerability of people on a vessel. Vulnerability characterization of people at risk can be defined at various levels of fidelity. An example of a conservative, low level fidelity characterization of vulnerability is one in which compact fragments that are 1 gram or larger are treated as hazardous to aircraft. Higher fidelity models consider the characteristics of impacting fragment in assessing the associated probability of a casualty.
14.3 Examples of Specific Flight Hazard Areas.
• Exclusion Zones: An exclusion zone is a hazard area or volume within which a protected entity must not be present to ensure compliance with § 450.161(a).
Exclusion zones may be stipulated because the risk to people in the open is unacceptable and can only be mitigated by excluding their presence. Exclusion in some cases may be the simplest approach to risk mitigation.
• Warning Areas: A warning area is a lower risk hazard region than an exclusion zone, in which exclusion is not enforced. Warnings are publicized to ensure awareness and to promote voluntary exclusion pursuant to § 450.161(c).
14.4 Contour Grids and their Durations.
A common step in defining a flight hazard area is to set up a gridded region within which to compute risk contours. This gridded region is typically used for people on land, on waterborne vessels, and in aircraft. Aircraft grids should be defined at the altitude of specific aircraft types to be evaluated. A gridded region may contain one or more grids. Contours are based on risk values at a set of grid vertices. These vertices are the corners of grid cells that exist within the boundaries of the grids. Each grid is typically shaped as a rectangle and specified by its outer boundaries and cell sizes. The total number of grid cells has a large effect on computer runtimes; an excessive number of cells may be undesirable.
14.4.1 There are several considerations when defining grid dimensions. The guiding principle is that they must contain, with 97 percent probability of containment, all debris resulting from normal flight events capable of causing a casualty to satisfy requirements §§ 450.133(b)(1), 450.133(c)(1), and 450.133(d)(1). The grid dimensions should contain the casualty producing IIPs, at the grid altitude level, of the normal trajectories.
They should also contain most, but not necessarily all, the casualty producing IIPs of the failure and planned event IIPs. The IIPs are used to create impact dispersions (see chapter 9 of this AC).
14.4.2 Several techniques can be applied to generate containment areas from calculated impact dispersions. Acceptable techniques include binning the impacts (empirical distribution or a 2-dimensional histogram) as discussed in paragraph 11.4 of this AC; kernel density estimators reference [18] of paragraph 3.4 of this AC; or using parameterized distributions such as a bivariate normal distribution or other distributions as discussed in paragraphs 11.2 and 11.2.1 of this AC. Scatter plots may assist in selecting the appropriate choice. Histogram-based approaches will result in discrete contours, while other approaches will yield continuous contours. Each approach has its advantages and disadvantages in terms of computational cost and accuracy. For example, two-dimensional histograms generally require many more samples to estimate the likelihood of low probability events than histograms. The analysis should include some justification as to the applicability of the specific approach adopted.
14.4.3 Not all the IIPs may be within the 97 percent containment level of the dispersions.
Alternatively, the 97% containment level may reach far beyond any the IIPs. Thus, it may be necessary to display the 97 percent containment levels to ensure that grid 107
boundaries meet the requirements. A grid cell should not be so large that it contains over 99 percent of the casualty producing impact dispersions that overlap it, and more desirably under 10 percent, to avoid issues of accuracy.
14.4.4 In the case of bivariate normal distribution for a single fragment, the “sigma” level corresponding to a confidence level CL=97 percent is 2.64 = �−2𝑆𝑆𝐾𝐾 (1 − 𝐶𝐶𝐿𝐿). If a normal flight event generates more than one fragment, then the containment should be the 97 percent confidence containment of all resulting fragments.
14.5 Development of Notices to Mariners.
Flight hazard areas applicable to waterborne vessels must be generated for regions of sea that must be surveyed, publicized, controlled, or evacuated in order to comply with the safety criteria in § 450.101 (§ 450.133(b)). Hazard areas and durations of applicability are used to develop Notices to Mariners (NOTMAR), which are provided to authorities and disseminated to waterborne vessel operators for navigation and traffic management guidance.
14.5.1 A range of waterborne vessel types that could be present in the hazard area should be used for hazard evaluation purposes. Each vessel type will be assigned to a specific grid(s) to compute risks. Casualty producing impacts to waterborne vessels result from blast and inert hazardous debris. At each grid vertex, the probability of casualty to an individual is computed by applying the waterborne vessel consequence models discussed in paragraph 12.7 of this AC. In accordance with § 450.133(e)(2)(iii), two sets of contours must be drawn that correspond to individual risk thresholds as provided in requirements §§ 450.101(a)(2) or (b)(2). The first set is the 1×10-6 individual probability of casualty contours for all selected waterborne vessel types, to represent the threshold for a member of the public. The second is the 1×10-5 individual probability of casualty contours for all selected waterborne vessel types, which represents the threshold for neighboring operations personnel. In accordance with § 450.161(a), an operator must publicize, survey, control, or evacuate the area within these contours prior to initiating flight of a launch vehicle or the reentry of a reentry vehicle to ensure compliance with § 450.101(a)(2) or (b)(2).
14.5.2 Each set of contours should be enveloped by a polygon, which does not have to touch any of the contours, as it is common practice to add a buffer zone. When there are islands of contours, separate disjoint polygons may be created. Simpler polygons are preferred to avoid placing unduly complex requirements with which waterborne vessel operators should adhere.
14.6 Development of Notices to Airmen.
In accordance with § 450.133(d), flight hazard volumes applicable to aircraft must be generated for regions of airspace that must be surveyed, publicized, controlled, or evacuated to comply with the safety criteria in § 450.101. Aircraft hazard volumes are used to develop Notices to Airmen (NOTAMs). These hazard volumes and durations of applicability are provided to the FAA. The FAA issues NOTAMs, which restrict air traffic operations, to protect the public from planned or inadvertent hazardous debris 108
from a mission. NOTAMs should not be excessively conservative or geometrically complex.
14.6.1 A range of aircraft types that could be present in the hazard area should be used for hazard evaluation purposes. Each aircraft type will be assigned to a specific grid(s) to compute risks. At each grid vertex and altitude associated with a specific aircraft type, the probability of casualty to an individual is computed by applying the aircraft consequence models discussed in paragraph 12.8 of this AC. In accordance with § 450.133(e)(2)(v), representative 1 × 10-6 and 1 × 10-7 probability of impact contours are drawn for all debris capable of causing a casualty to persons on an aircraft, regardless of location.
14.6.2 Each set of contours is enveloped by a polygon which does not have to touch any of the contours as it is common practice to add a buffer zone. When there are islands of contours, separate disjoint polygons can be created. Simpler polygons are preferred to avoid placing unduly complex requirements with which aircraft operators should adhere.
14.6.3 In addition to these contours, aircraft hazard volumes are defined by a range of altitudes that apply to the selected aircraft. This should be from ground level to the highest relevant altitude, which is typically 60,000 feet.
14.7 Development of Land Hazard Areas.
In accordance with § 450.133(c), flight hazard areas that apply to unsheltered people must be generated for any region of land that must be surveyed, publicized, controlled, or evacuated to comply with the safety criteria in § 450.101. Land Hazard Areas (LHA) are developed with a similar methodology to NOTMARs. Near shorelines, LHAs often border NOTMARs. LHAs are disseminated to the land controlling authorities to ensure surveillance, crowd control, and road traffic management.
14.7.1 LHA-based contours are designed to protect people in the open. Casualty producing events result from blast, toxic releases, and inert hazardous debris events. At each grid vertex, the probability of casualty to an unsheltered individual is computed by applying the consequence models discussed in paragraphs 12.3 and 12.11 of this AC. In accordance with § 450.133(e)(2)(iii), two set of contours are drawn that correspond to the individual risk thresholds provided in §§ 450.101(a)(2) and (b)(2). The first set is at the 1x10-6 probability level for all applicable shelter types that could house a member of the public. The second set at the 1×10-5 probability level for all applicable shelter types that could house neighboring operations personnel. An enveloping polygon is drawn about each set of contours. The polygons do not have to touch any of the contours as it is common practice to add a buffer zone. When there are islands of contours, separate disjoint polygons may be created.
15 SATISFYING APPLICANT SUBMISSION REQUIREMENTS.
A completed high-fidelity flight safety analysis must be sufficiently documented to show that related 14 CFR requirements have been met. Top-level requirements of § 450.115 must be applied to each of the flight safety analysis requirements. For each flight safety analysis requirement, the submitted material should clearly specify the scientific principles and statistical methods used to communicate that a high fidelity analysis has been performed. This will require descriptions of all methods applied, specification of analysis assumptions, justifications and underlying scientific principles, to meet the standards expected of a high-fidelity flight safety analysis in accordance with § 450.101(g). In addition, the analysis should confirm that each appropriate risk threshold specified in § 450.101 will not been exceeded given the flight commit criteria and flight abort rules employed. In accordance with § 450.115(b)(1) the results must demonstrate that any risk to the public satisfies the safety criteria of § 450.101, including the use of mitigations, accounting for all known sources of uncertainty. The application should explain how uncertainty in risk predictions were accounted for, as well as note how risk mitigations were accounted for. In accordance with § 450.115(c)(4), an applicant must provide evidence for its validation and verification (V&V) of the suitability of the submitted material as required by § 450.101(g).
15.1 Nominal and Failure Trajectories.
Advisory Circular 450.117-1, Normal and Malfunction Trajectory Analysis, discusses the usage of trajectories by placing them within the context of a flight safety analysis.
Various types of trajectories must be generated to comply with §§ 450.117(d)(2) and
450.119(c)(3) requirements. The generated trajectories should be written to data files or spreadsheets that contain:
• Time histories of the vehicle position, velocity, orientation, and associated IIPs,
• Clearly defined coordinate system for each time history parameter,
• Clearly marked units for each data parameter,
• Notation indicating whether using a right-handed or left-handed coordinate system, and
• If relevant, notation indicating whether using an Earth fixed (ECR) or Earth rotating (ECI, inertial frame) coordinate system, or any other coordinate system.
15.2 Failure and Planned Event State Vectors.
Trajectories are used to create a set of failure and planned event state vectors that account for each foreseeable cause of vehicle breakup, including breakup caused by flight safety system activation, inadvertent separation, or by impact of an intact vehicle.
The set of failure and planned event state vectors should be written to data files or spreadsheets that specify:
• Nominal state time for on-trajectory cases,
• Vehicle failure and breakup times for malfunction turn cases, 110
• Position and velocity vectors for hazardous debris modeled with 3 degrees-offreedom during ballistic fall,
• Orientation of hazardous debris body and angular velocity vector if modeled with a 5 DOF simulation for axisymmetric bodies or a 6 DOF simulation for non-axisymmetric bodies during ballistic fall,
• Clearly defined coordinate system of each state vector parameter,
• State vector failure probability, or identification of failure mode to assign failure probability to each state vector,
• Identification of breakup mode to assign hazardous debris fragment list to state vectors,
• State vector position-velocity covariance, or identification of data source, if state vector uncertainty is not accounted for in trajectories from which the state vectors are selected, and
• Clearly marked units for each data parameter.
15.3 Breakup and Jettisoned Hazardous Debris.
Paragraph 8.5 of this AC presents the creation of vehicle hazardous debris fragment lists for all foreseeable causes of vehicle breakup. Ballistic or near-ballistic hazardous debris may create a hazard at any time during flight and so it must be clearly characterized to comply with § 450.121 requirements. Such hazardous debris may be partitioned into classes that represent one or more fragments, in which case the rules used to create appropriate groups must be documented under § 450.121(d)(5). Generated hazardous debris fragment lists should be written to data files or spreadsheets that define each item by:
1. Nominal value and statistical uncertainty bounds of the ballistic coefficient,
2. Statistical uncertainty in lift coefficient,
3. Mean and statistical uncertainty in break-up induced velocity of a Maxwellian distribution, or detailed speed and direction distributions for a directed DV case,
4. Projected fragment hazard area as the direct reach of the fragment on a person or building,
5. Total weight, and constituent inert and propellant weights,
6. Identification of Mach-CD table to apply for tumbling motion and identification of Mach-CD table to apply for any stable motion,
7. For motors, engines, or propellant fragments:
a. State times corresponding to time-dependent parameter values,
b. Time history of propellant weight,
c. Identification of propellant type,
d. Indication if propellant or motor is burning at release, 111
e. For exposed solid propellant fragments: parameters used to compute change in burning propellant weight and size,
f. For contained SRMs: propellant consumption rate if burning at release,
g. For fuel venting systems: initial ratio of fuel/oxidizer and time history of fuel weight,
8. For potential inert aerothermal demise: material type and information needed to compute aerothermal ablation; for composite fragments with multiple material types, provide information to identify only those portions that may lead to aerothermal demise, and
9. Clearly marked units for each data parameter.
15.4 Probability of Failure.
Advisory Circular 450.131-1, Probability of Failure discusses how to create failure probability or rate profiles for use in computing unconditional risks. Profiles are created for each foreseeable failure mode to comply with § 450.131 requirements. The profiles can be written to a data file or spreadsheet in a tabular form that clearly indicates the time span over which to apply each failure rate or probability. Each failure probability or rate profile should be accompanied by a graph as a function of time and a plot of cumulative failure probability.
15.5 Requirements for Flight Hazard Areas.
Chapter 13 of this AC discussed the generation of land, waterborne vessel, and aircraft flight hazard areas to comply with § 450.133 requirements. Each of the associated protected zones require a 97 percent confidence of containment for all hazardous debris impacts in accordance with §§ 450.133(b)(1), 450.133(c)(1), and 450.133(d)(1). Inside hazard areas, the risk threshold levels for people cannot be exceeded for individual risk in accordance with § 450.101(b)(2)(i). Geographical coordinates of flight hazard areas should be graphically documented, and the coordinates and duration times provided.
Reference AC 450.161-1 Surveillance and Publication of Hazard Areas or Aircraft and Ship Hazard Areas for additional information.
15.6 Hazardous Debris Propagation and Impact Distributions.
Chapter 7 of this AC discussed taking each failure and planned event state vector that may cause a hazard and propagate it to the ground. Resulting hazardous debris impact distributions must be statistically valid in accordance with § 450.121(c), accounting for all foreseeable sources of impact dispersion to comply with § 450.135(b) requirements.
Under § 450.121(c)(2), sources of impact dispersions must include, at a minimum, uncertainties in atmospheric conditions; debris aerodynamic parameters, including uncertainties; pre-breakup position and velocity, including uncertainties; and hazardous debris velocities imparted at breakup, including uncertainties. If the data sources are not easily available, then the data should be written to data files or spreadsheets. Chapter 9 discussed how to define a hazardous debris cloud and impact functional distributions to comply with § 450.135(b) requirements. Since cloud distributions are typically an internal product of the risk tool, and generally not written out to file, descriptions of 112
final dispersions are not required. However, the methods of definition are required in accordance with § 450.123(c)(1).
15.7 People and Assets.
Chapter 10 of this AC discussed how to define exposure areas that hazard people and assets to comply with § 450.123 requirements. Population centers and asset sites should be written to data files and/or spreadsheets with the following considerations:
1. Mean latitude/longitude location for surface sites and stationary waterborne vessels, otherwise a time-based path for a moving object (waterborne vessel, aircraft) that covers the duration of the mission.
2. Size:
a. Floor plan area for surface site,
b. Top area and length for stationary waterborne vessel,
c. Rectangular dimensions for moving waterborne vessel, or
d. Top and front areas for aircraft.
3. Value of asset.
4. Population as a function of time of day, week, month, or year:
a. Number of unsheltered people,
b. Number of people in each shelter type, and specification of roof type, wall type, and window type,
c. For waterborne vessels: number of people on deck and separately below deck, and
d. Number of people in aircraft, and identification of aircraft type.
15.8 Consequence and Risk.
Chapters 10 and 11 of this AC discussed the details for performing a consequence analysis to comply with § 450.101(c) requirements. In addition to the risk measures specified in the requirements, in accordance with § 450.135(c)(4), the applicant must provide the computed effective casualty areas for unsheltered people for each fragment class under § 450.135(c)(3). Most of the consequences covered in chapter 11 of this AC should have computed effective casualty areas, while some cases involving propellant explosions should be dealt with the preparation of probability versus distance curves.
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