4 10 8 Max. Casualty Area / Fire Area 7 6 5 4 3 2 1 0 H/D=2 H/D=4 H/D=6 H/D=8 H/D=10 H/D=12 H/D=14 H/D=16 0 0.5 1 1.5 2 2.5 3 Heat Radiation Load, t*q , sec. (Watts/m ) 104/3 2 4/3 10 Figure 26 – Normalized Casualty Areas vs. Heat Load
12.18 Blast Wave Overpressure.
The hazard from blast waves from propellant explosions, for impacts away from buildings and not on the roof, should be represented as curves of probability of casualty versus distance from the impact propellant impact point to the building’s wall. The probabilities of casualty and impact are correlated. The impact space can be divided into cells such that the probability of impact within each cell is close to uniform. The net probability of consequence for a given population center is the sum of 𝑁𝑁𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 𝑚𝑚𝑚𝑚𝑖𝑖𝑚𝑚𝑐𝑐𝑔𝑔 𝑒𝑒𝑐𝑐𝐶𝐶𝑚𝑚𝑠𝑠𝑟𝑟𝑐𝑐𝑠𝑠𝑟𝑟𝑚𝑚𝑐𝑐𝑟𝑟 = � 𝑒𝑒𝑚𝑚 × 𝑃𝑃𝐶𝐶(𝑑𝑑𝑚𝑚) 𝑚𝑚=0
12.18.1 The sum should include all cells with 𝑃𝑃𝐶𝐶(𝑑𝑑) above 1x10-6 .
12.18.2 The blast wave strikes the side of the building and both the breakup of the walls and windows should be evaluated for injury to people inside the building. The reaction of the building should consider both the peak overpressure and impulse of the blast wave.
Walls of buildings will be subjected to different blast loading depending on the orientation of the building to the blast wave. To be conservative, shards produced by window damage should be modeled as entering the room without obstruction by drapes or other obstacles. The injury from both the wall and windows can occur together. At any given impact distance, the total probability of casualty of a person inside the building is given by 𝑃𝑃𝐶𝐶(𝑑𝑑) = 𝑃𝑃𝑤𝑤𝑚𝑚𝑓𝑓𝑓𝑓(𝑑𝑑) + 𝑃𝑃𝑤𝑤𝑚𝑚𝑚𝑚𝑑𝑑𝐶𝐶𝑤𝑤(𝑑𝑑) − 𝑃𝑃𝑤𝑤𝑚𝑚𝑓𝑓𝑓𝑓(𝑑𝑑)𝑃𝑃𝑤𝑤𝑚𝑚𝑚𝑚𝑑𝑑𝐶𝐶𝑤𝑤(𝑑𝑑)
12.18.3 Since analyzing every individual type of building is impractical, a small set of representative buildings may be evaluated instead. This requires defining classes of wall 91
!
!
j 1000 .000 - A l ~ 100 .000 Prob of Casualty( %) .....r - V' SERIOUS INJURY ;;a"'~ - ----0.1 Small Residential t-- -- _,i..- ---o.5 I/ ,, Wood Frame House -t--
1.0 / v :" t-- --5.0 ... v ,/ " . --- v --100 ... ~ I' ~ ~ t-- - v ..----200 / V / / --30.0 / _,i.,,' I 11 ./ t-- ---400 5000K ... v \ c-1~t-/ I I I I I I --500 ~v U~ I I I I I I ...
~ ~f I I I I I I I 60.0 / ... / \
I I I I I I I 70 0 / I I ,, ~ i.- ./ t-- 80.0 ~ 500K / t ~ .. .,, .- -t-- --go.a ~ ~ / J -t-- t-- --100.0 ... II' I: 1'- V .x ' ...,"" / 50K "' " ,..._ I?"' ... - 10 000
0.100 V V / V / v I/ / V V v/ / / ~ c~~ 5KL( V ""~ I I I / ,, V /,,
1.000 Incident Overpressure (psi) I 11 I I I I I I I I 10 .000 100.000 08/02/2024 AC 450.115-1B and window types. Table 6 of this AC contains a list of general building categories and their construction materials that may need to be evaluated. General wall types that should be represented are wood, metal, masonry, and concrete.
12.18.4 The degree of injury to people inside a building depends on the wall’s level of resistance to the blast wave, the size of the floor plan of the building, and the characteristics of the hazardous debris that is generated when the wall is damaged.
There are too many variables here to provide a suggestion for a conservative choice of what probability of casualty curves to apply for a building not accounted for by curves that are already on hand. Figure 24 of this AC presents an example of a series of curves that range in probability of casualty from 0.1 percent to 100 percent for a small wood structure that is common among houses. Similar curves may need to be created to describe other building types since those in Figure 27 of this AC are not necessarily the most conservative that such curves can be.
12.18.5 The red arcs that move from the lower left-hand side to the upper right-hand side correspond to specific impact yields and trace out the peak overpressure and impulse values as a function of the distance of the impact point to the wall of the structure.
Figure 27 – Probability of Casualty for a Small Wood Structure, ~2500 ft2
12.18.6 For computing probability of casualty from window breakage, the rows of Table 7 present a survey of window types that the buildings are likely to have. Annealed windows are the most sensitive to blast waves while tempered windows are the strongest. Thus, it is conservative to treat all windows as annealed if more appropriate results are not available.
Pane Size Annealed Dual ered Small Medium Lare X X X X X X X X X X X X X X X X X X X X
1) Small= 0-10 ft**2; Medium= 1 -20 ft**2; Large= >20 ft**2 1000 D Prob of Casualty (%1 ' I .....
I ...... '-~
0.01 1, .... .......
~
- 0.10 __,,, .... \ i...-- ~ ~
1.00 / ' / ~ - s.oo "'v )('" - 10.00 ../ ~
,,,V
'
- 12.00 /
,i-
/ '-..,, ,,.... v / I .s ~ 100 l / .,.,v V ...... I'---/ v .... r- .... __ ) .,, .,. .... / / / v ,....
~~~ ....... ,.. .....
I ....... ....... .......
I ~ V - -j /\ \ t,,, .......- --_ _/ \ \ ,..,,- ,,,, .... V l 500K I ' ✓ /v
"'\, .... "'v .,,...v - / ..... ' ~ rs7i ,,, r- f-..-___/' ..... r-,.. ,_ / 10 ~liBIQIHi llll.!UBY -r~ I,,".., Large Annealed Glass ,,, (Unblocked GAR= 14.5%) ,,G;~
0.1 1.0 10.0 Incident Overpressure (psi) 08/02/2024 AC 450.115-1B Table 7 – Generic Window Types
12.18.7 An example of the probability of casualty curves for a large annealed window is shown in Figure 28. As with the wall curves, these are curves that are not the most conservative, and so other curves may need to be generated for the other window types.
Figure 28 – Large Annealed Windows (~5’H x 6’W x 0.232”T), GAR = 14.5 percent 93
12.18.8 The acronym GAR stands for Glass-to-Area ratio, which is defined as area of the glass in the window to the floor area: 𝐺𝐺𝐴𝐴𝑅𝑅 = 𝐴𝐴𝑓𝑓𝑓𝑓𝑚𝑚𝑠𝑠𝑠𝑠/𝐴𝐴𝑟𝑟𝑓𝑓𝐶𝐶𝐶𝐶𝑟𝑟. The curves are shown for a 𝐺𝐺𝐴𝐴𝑅𝑅 = 14.5%. For buildings with other GAR values, the probabilities from the curves can be rescaled through the general expression:
𝐺𝐺𝐺𝐺𝐺𝐺𝑏𝑏𝑏𝑏𝑡𝑡𝑐𝑐𝑏𝑏𝑡𝑡𝑏𝑏𝑏𝑏 𝑤𝑤𝑚𝑚𝑚𝑚𝑑𝑑𝐶𝐶𝑤𝑤(𝑑𝑑).𝑃𝑃𝑤𝑤𝑚𝑚𝑚𝑚𝑑𝑑𝐶𝐶𝑤𝑤(𝑑𝑑) = 𝐺𝐺𝐺𝐺𝐺𝐺𝑏𝑏𝑐𝑐𝑏𝑏𝑐𝑐𝑔𝑔𝑡𝑡𝑐𝑐 𝑒𝑒𝑓𝑓𝑟𝑟𝑚𝑚𝑟𝑟𝑟𝑟𝑚𝑚𝑐𝑐
12.18.9 Note that the horizontal overpressure axis does not extend far enough to the right to reach large probability of casualty values. However, it is not necessary to plot out any farther since the wall probabilities have reached a value of one and the contribution from windows is no longer relevant.
12.19 People in Waterborne Vessels (Ships).
The casualty area and consequence analysis must account for the vulnerability of people to debris impact or effects, including effects of waterborne vessel upon the vulnerability of any occupants, in accordance with § 450.135(b)(4)(i). The total effective casualty area should be the sum of two sources. Further information on this topic can be found in the reference in [22] of paragraph 3.4 of this AC.
𝐶𝐶𝐴𝐴 = 𝐶𝐶𝐴𝐴𝑠𝑠ℎ𝑚𝑚𝑖𝑖 + 𝐶𝐶𝐴𝐴𝑤𝑤𝑚𝑚𝑔𝑔𝑟𝑟𝑟𝑟
12.19.1 The first contribution corresponds to the relative area on the ship deck where people are seriously injured from an explosion of a propellant that impacts the ship. The second contribution is the area around the ship for propellant explosions in water impacts that lead to casualties on the ship. Both casualties refer to the same people on the ship, but to different impact locations of the propellant.
12.19.2 The probability of consequence is given by the sum 𝑠𝑠ℎ𝑚𝑚𝑖𝑖+𝑤𝑤𝑚𝑚𝑔𝑔𝑟𝑟𝑟𝑟 𝐶𝐶𝐴𝐴𝑠𝑠ℎ𝑚𝑚𝑖𝑖 + 𝐶𝐶𝐴𝐴𝑤𝑤𝑚𝑚𝑔𝑔𝑟𝑟𝑟𝑟 =𝑒𝑒𝑐𝑐𝐶𝐶𝑚𝑚𝑠𝑠𝑟𝑟𝑐𝑐𝑠𝑠𝑟𝑟𝑚𝑚𝑐𝑐𝑟𝑟 𝑒𝑒𝑚𝑚𝑚𝑚𝑖𝑖𝑚𝑚𝑐𝑐𝑔𝑔 𝐴𝐴𝑠𝑠ℎ𝑚𝑚𝑖𝑖 which assumes that the ship sizes are much smaller than propellant impact dispersions.
For ship impacts, the effective casualty area should be evaluated separately for people on the deck and those below deck. The effective casualty area for water impacts does not require such a distinction.
12.19.3 The effective casualty area for water impacts depends on how close the propellant explodes from the ship. Table 8 of this AC provides the maximum distance 𝑒𝑒𝑐𝑐𝑚𝑚𝑠𝑠𝑠𝑠𝑚𝑚𝑓𝑓𝑔𝑔𝑔𝑔 from the ship, as a function of ship length, that the propellant can impact and cause casualty. The yield values to apply for using the table should be computed for water surface impacts, and with side-on orientation for SRM segments and CAS.
Table 8 – Water Impact Distances That Lead to Casualty Ship Length (ft) Minimum Yield (lbs-TNT) Casualty distance (ft) < 25
0.01 37.5 𝑌𝑌0.333 25-50 50-100 100-200
3.0 20 𝑌𝑌0.375 200-295 > 295 10.0 7 𝑌𝑌0.44
12.19.4 Modeling ships as a rectangle, of length L and width W, the water effective casualty 2area is given by 𝐶𝐶𝐴𝐴𝑤𝑤𝑚𝑚𝑔𝑔𝑟𝑟𝑟𝑟 = 𝜋𝜋𝑒𝑒𝑐𝑐𝑚𝑚𝑠𝑠𝑠𝑠𝑚𝑚𝑓𝑓𝑔𝑔𝑔𝑔 + 2𝑒𝑒𝑐𝑐𝑚𝑚𝑠𝑠𝑠𝑠𝑚𝑚𝑓𝑓𝑔𝑔𝑔𝑔(𝐿𝐿 + 𝑊𝑊) which cover all locations where the edge of the blast overpressure wave can just reach the ship and cause serious injury.
12.19.5 For ship impacts and people below deck, Table 9 of this AC may be used to get the effective casualty area 𝐶𝐶𝐴𝐴𝑠𝑠ℎ𝑚𝑚𝑖𝑖. The yield values to apply in the table should be computed for steel surface impacts, and with side-on orientation for SRM segments and CAS.
Table 9 – Ship Explosive Effective Casualty Areas for People Below Deck Length (ft) Yield (lbs-TNT) Sheltered Effective Casualty Area (ft2) < 100 < 0.03 0 < 100 0.03 to 0.1 10 𝐴𝐴𝑠𝑠ℎ𝑚𝑚𝑖𝑖 𝑌𝑌 < 100 > 0.1 𝐴𝐴𝑠𝑠ℎ𝑚𝑚𝑖𝑖 >= 100 < 0.05 0 >= 100 0.05 to 0.5 80 𝑌𝑌 >= 100 0.5 to 1.0 [80 𝑌𝑌, 2𝐴𝐴𝑠𝑠ℎ𝑚𝑚𝑖𝑖(𝑌𝑌 − 0.5)] >= 100 > 1.0 𝐴𝐴𝑠𝑠ℎ𝑚𝑚𝑖𝑖 95
12.19.6 For ship impacts and people on deck, the blast overpressure wave profile should be applied. This profile may be reduced to an effective casualty given by the following equation, which is a sum over ring areas by the probability of casualty within the corresponding ring.
𝑁𝑁𝑔𝑔𝑡𝑡𝑏𝑏𝑏𝑏𝑐𝑐 2 2𝐶𝐶𝐴𝐴𝑠𝑠ℎ𝑚𝑚𝑖𝑖 = 𝜋𝜋 � �𝑒𝑒𝑟𝑟𝑚𝑚𝑚𝑚𝑓𝑓(𝑑𝑑𝑚𝑚) − 𝑒𝑒𝑟𝑟𝑚𝑚𝑚𝑚𝑓𝑓(𝑑𝑑𝑚𝑚−1)� × 𝑃𝑃𝐶𝐶(𝑑𝑑𝑚𝑚) 𝑚𝑚=1
12.20 Toxic Emitters.
12.20.1 An open-air solid propellant fragment burns with hazardous combustion products, while a liquid or hypergolic tank may explode or break open and leak toxic chemicals. In the liquid case, the exposed liquids will evaporate, and in either case, the gases will form a toxic cloud plume that is directed away from the impact point by the wind. High wind speeds create narrow plumes, while weak winds produce a wider cloud. Anyone who is exposed to the toxic cloud within a threshold distance from the spill, and the cloud’s lateral span that is a function of distance, should be considered a casualty. A toxic release hazard analysis must be performed in accordance with § 450.139(c). This distance is based on the burn-time of the solid propellant fragment, evaporation rate of the liquid, time since the spill occurred, chemical type, and exposure time to the person.
The threshold distance for people in buildings is less than for people in the open. People in buildings are not exposed to the same toxic level from the plume, compared to a person standing outside, because a smaller amount will seep in over the same period.
12.20.2 The probabilities of casualty for a population center and propellant impact are correlated. The impact space should be divided into cells such that the probability of impact within each cell is close to uniform. The net probability of casualty for a given site is the sum:
𝑁𝑁𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 𝑚𝑚𝑚𝑚𝑖𝑖𝑚𝑚𝑐𝑐𝑔𝑔 (𝑃𝑃𝐶𝐶 = 1)𝑒𝑒𝑐𝑐𝐶𝐶𝑚𝑚𝑠𝑠𝑟𝑟𝑐𝑐𝑠𝑠𝑟𝑟𝑚𝑚𝑐𝑐𝑟𝑟 = � 𝑒𝑒𝑚𝑚 𝑚𝑚=0 which applied the fact that the probability of casualty (PC) is either 1 or 0. The notation "𝑃𝑃𝐶𝐶 = 1" indicates to only consider impact points whose plume reaches a population center.
12.20.3 A high-level discussion of the hazards from toxic clouds is given in Chapter 5 of reference [1] of paragraph 3.4 of this AC. The references at the end of that chapter can assist in determining the length and width of the plume. Other details that involve the nature of toxic chemicals are in AC 450.139-1, Toxic Hazards Analysis and Thresholds.
12.21 Secondary Hazardous Debris Fragments.
Secondary hazardous debris fragments are created when hazardous debris impacts the ground and then breaks into a set of smaller inert fragments. These situations must be considered when they pose a hazard to people or assets for splatter scenarios in accordance with § 450.135(b)(1). The secondary fragments may increase the hazardous 96
area beyond that of the direct impact of the intact body or fragment, resulting in impact to more people. They may also increase the risks within the overlapping areas from direct impact and secondary hazardous debris. Examples of secondary fragments that should be considered include impacting (1) intact vehicles, (2) contained propellant tanks, and (3) inert fragments.
12.22 Intact Impact Vehicle.
Impact of an intact vehicle will cause a secondary-fragments field that is generally scattered in the direction of the impact velocity vector. Without obstructions, such as trees or hills, the scatter secondary-fragments field will fan out from the impact point.
The length, width, and shape of the secondary-fragments field, and subsequent hazardous debris fragment list, depend on the impact angle, speed, and construction of the vehicle.
12.22.1 A basis for a list of secondary fragments should be evaluating similar events. There are few historical cases for launch or ballistic vehicles, which limits the sources that may be useful to other vehicles. Although not as directly applicable, there have been dozens of airplane crashes that produced secondary-hazardous debris scatter. Since creation of a proper secondary-fragments list from these cases is problematic, an acceptable alternative is to try to map out the hazardous scatter field and set probability of casualty as either 1 or 0. These selections should account for whether people are in the open or the type of building in which they reside. The probabilities of casualty for a site and intact vehicle impact are correlated. The impact space should be divided into cells such that the probability of impact within each cell is close to uniform. The net probability of consequence for a given population center is the sum, which applied the fact that PC is either 1 or 0.
𝑁𝑁𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 𝑚𝑚𝑚𝑚𝑖𝑖𝑚𝑚𝑐𝑐𝑔𝑔 (𝑃𝑃𝐶𝐶 = 1)𝑒𝑒𝑐𝑐𝐶𝐶𝑚𝑚𝑠𝑠𝑟𝑟𝑐𝑐𝑠𝑠𝑟𝑟𝑚𝑚𝑐𝑐𝑟𝑟 = � 𝑒𝑒𝑚𝑚 𝑚𝑚=0
12.23 Intact Propellant Tank Secondary Hazardous Debris.
When intact liquid or solid propellant tanks survive until impact, there should be an evaluation of the hazards due to the blast wave, from any explosion, and subsequent secondary fragments from breakup of the case or tanks. The imparted velocity of the secondary fragments should be determined by considering the impulse of the blast wave. Blast waves from propellant explosions are strong enough to eliminate any influence of the impact angle and give no preferred direction for the ejected fragments.
Some explosions may result in secondary fragments traveling several thousand feet.
12.23.1 The hazardous debris fragment lists from the secondary fragments are not the same as when vehicle breakup occurs while in flight. Properties of the fragments, such as the mean and distribution of sizes, weights, and areas should be constructed. The weights and areas are used to compute ballistic coefficients of the fragments. The mechanism of the propellant explosion for a surface impact has different physics than from the vehicle’s destruct system. At present, there are no recommended models for this purpose.
12.23.2 The risk from the secondary hazardous debris may be determined through a Monte Carlo analysis. The individual event scenario events select different characteristics of the fragments from the distributions, (i.e., speed, direction, and weight). Each event scenario should trace the trajectory of all ejected fragments. Atmospheric drag and wind can be ignored when generating these trajectories. For various distances away from the impact point, statistics should be kept of the probability of casualty.
12.23.3 The consequence for a breakup of an impacting propellant tank should be represented as a probability of casualty versus distance curve, 𝑃𝑃𝐶𝐶(𝑑𝑑). The explosion tends to overwhelm the pre-impact conditions, leading to the fragments being thrown equally in all directions as a function of distance. The probabilities of casualty and impact are correlated. The impact space should be divided into cells such that the probability of impact within each cell is close to uniform. The net probability of consequence for a given population center is the sum of 𝑁𝑁𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 𝑚𝑚𝑚𝑚𝑖𝑖𝑚𝑚𝑐𝑐𝑔𝑔 𝑒𝑒𝑐𝑐𝐶𝐶𝑚𝑚𝑠𝑠𝑟𝑟𝑐𝑐𝑠𝑠𝑟𝑟𝑚𝑚𝑐𝑐𝑟𝑟 = � 𝑒𝑒𝑚𝑚 × 𝑃𝑃𝐶𝐶(𝑑𝑑𝑚𝑚) 𝑚𝑚=0
12.23.4 The sum should include all cells with 𝑃𝑃𝐶𝐶(𝑑𝑑) above 1x10-6 .
12.24 Inert Fragment Splatter.
The impact kinetic energy of inert fragments with sufficient impact speed and weight, may have enough equivalent TNT yield to explode into a collection of shards. This situation may be handled through the same type of Monte Carlo analysis as with the propellant tank impacts. Secondary fragments from single impact inert fragment usually travel no more than a few tens of feet, compared to thousands of feet for the propellant tanks. Thus, instead of probability versus distance curves, the results of the Monte Carlo analysis can be reduced to small effective casualty areas about the impact point.
13 RISK COMPUTATION.
The objective of a launch or reentry mission risk analysis is to demonstrate that collective and individual risks are below acceptable levels as specified in § 450.101, not necessarily to quantify the precise risk levels. Such risk analyses can be conducted using a low fidelity analysis or using a higher fidelity analysis. A higher fidelity analysis will allow for greater flexibility in acceptance that the analysis results comply with the risk acceptance criteria. This results from the increased accuracy, and reduced uncertainty, of the predicted risks.
13.1 How Risk is Expressed.
Risk is defined in § 401.7 as a measure that accounts for the probability of occurrence of a hazardous event to persons or property. If there is more than one possible outcome of an event, the total risk associated with the event is determined as the logical sum over all possible outcomes of the products of the probability of each outcome and its associated consequence. The total risk for a launch or reentry mission is the logical sum of the risk over all potential hazardous events that can pose a hazard to people or 98
� property. Risk can be lowered by reducing the probability of an event occurring or by reducing the consequences of the event. For example, planning a mission that avoids flight operations over populated areas can decrease or eliminate the hazard to people (and property) and thereby reduce the risk. The process for computing the measures of risk are discussed in this section.
13.1.1 The hazardous debris risks for a mission are expressed in several forms. These are:
• The expected average number of human casualties for a mission, often referred to as the casualty expectation, EC. The EC for hazardous debris is the sum of the risk over all potential hazardous debris generating events that can pose a hazard to people or property.
• The maximum risk to an individual resulting from the launch mission, referred to as individual risk. This is the maximum risk over all individuals exposed to the launch hazardous debris hazards, and addresses the people located in all population centers and all vehicles.
• The Conditional Casualty Expectation. This is defined as the expected number of casualties that could occur from each foreseeable failure mode (hazardous event) occurring in any one-second period of flight, given that the response mode has occurred.
13.2 Risks to Population Centers and Protected Objects.
13.2.1 Casualty Expectation.
For population centers, the casualty expectation EC for a specific population center and hazardous debris resulting from a specific hazardous debris generating event is a function of the characteristics of the population center (footprint area, structural types and associated shelter categories and associated population) as discussed in AC 450.123-1, Population Exposure, the probability of impact of a fragment on a population center (see Chapter 10 of this AC), and the effective casualty areas or probabilities of casualty for each population center (see Chapter 11 of this AC). The EC for a fragment class is obtained by multiplying the EC per fragment by the number of fragments in the fragment class. The total casualty expectation for a population center hazarded by hazardous debris is the accumulation of these values over all fragment classes and all hazardous debris generating events.
13.2.2 The basic equation for casualty expectation 𝐸𝐸𝐶𝐶𝑡𝑡𝑗𝑗𝑖𝑖 for fragment class i, population center j, and the kth generating event (jettisoned hazardous debris or a given failure mode occurring at a given failure time), is given by 𝑓𝑓=𝑁𝑁𝑝𝑝𝑝𝑝𝑝𝑝𝑐𝑐 𝑟𝑟𝑚𝑚𝑚𝑚𝑓𝑓𝑠𝑠𝑟𝑟𝑟𝑟 𝑒𝑒𝑚𝑚𝑗𝑗 𝑚𝑚𝑚𝑚𝑖𝑖𝑚𝑚𝑐𝑐𝑔𝑔 𝑁𝑁𝐹𝐹𝑡𝑡 𝑐𝑐𝑚𝑚𝑠𝑠𝑠𝑠𝑚𝑚𝑓𝑓𝑔𝑔𝑔𝑔𝑁𝑁𝑃𝑃𝑗𝑗𝑐𝑐 𝐸𝐸𝐶𝐶𝑡𝑡𝑗𝑗𝑖𝑖 = 𝑒𝑒𝑘𝑘 𝑒𝑒𝑚𝑚𝑗𝑗𝑓𝑓 𝑓𝑓=1 where 𝑒𝑒𝑟𝑟𝑚𝑚𝑚𝑚𝑓𝑓𝑠𝑠𝑟𝑟𝑟𝑟 is the probability of occurrence for the hazardous debris generating event, NF is the number of fragments in the fragment class, 𝑁𝑁𝑃𝑃 is the number of people in the population center, 𝑒𝑒𝑚𝑚𝑚𝑚𝑖𝑖𝑚𝑚𝑐𝑐𝑔𝑔 is the population center impact probability, and 99
𝑒𝑒𝑐𝑐𝑚𝑚𝑠𝑠𝑠𝑠𝑚𝑚𝑓𝑓𝑔𝑔𝑔𝑔 was discussed in Chapter 11. The total casualty expectation for a given = ∑ . The total casualty expectation 𝑚𝑚𝑘𝑘 population center j is the sum 𝐸𝐸𝐶𝐶𝑃𝑃𝑝𝑝𝑝𝑝 𝑗𝑗−𝑇𝑇𝑝𝑝𝑡𝑡𝑇𝑇𝑐𝑐 𝐸𝐸𝐶𝐶𝑡𝑡𝑗𝑗𝑖𝑖 for the mission is the sum over all pop centers.
13.3 Probability of Hazardous Debris Generating Event.
The probabilities of occurrence, 𝑃𝑃𝐹𝐹𝑖𝑖 , for the hazardous debris generating events are computed using the failure rates developed as described in AC 450.131-1, Probability of Failure. They include hazardous debris jettisons (for which the probability is usually near one), applicable failures (loss of thrust, explosion, malfunction turn) resulting from discrete event failures (stage ignitions, stage shutdowns), and applicable malfunction failures occurring at specific times during the stages of flight. The probabilities for discrete event response modes are equal to the failure rate times one second, since discrete events are assumed to occur over a one second interval. Vehicle stage failure response mode probabilities are computed for short time intervals of flight, with time intervals selected such that the risk can be computed for a given time during a time interval (usually the mid-point time) that is considered representative of the risk at any time during the interval. Time intervals need to be sufficiently short such that the hazardous debris footprint for a given time interval sufficiently overlaps that of its adjacent time intervals to represent a continuous footprint. The failure probability for a given stage response mode occurring during a given time interval is computed by integrating the failure rate for the response mode over a time interval:
𝑔𝑔𝐵𝐵 𝑃𝑃𝐹𝐹 = � 𝑅𝑅(𝑆𝑆) 𝑔𝑔𝐴𝐴 where R(t) is the response mode failure rate (probability of failure per second).
13.4 Probability of Impact.
The computation of the probability of impact 𝑒𝑒𝑚𝑚𝑗𝑗 𝑚𝑚𝑚𝑚𝑖𝑖𝑚𝑚𝑐𝑐𝑔𝑔 for a given hazardous debris class i on a given population center j, is dependent on fragment type. Development of an impact probability distribution is discussed in Chapter 9. For an inert fragment impacting a population center, 𝑒𝑒𝑚𝑚𝑗𝑗 𝑚𝑚𝑚𝑚𝑖𝑖𝑚𝑚𝑐𝑐𝑔𝑔 is obtained by integrating the impact probability distribution for the fragment class over the area of the population center.
13.4.1 A population center is a populated place with a known location at launch time. This includes people in the open at a specified location, occupied buildings/structures, and vehicles. Vehicles could include road vehicles (cars, trucks, busses), trains, and waterborne vessels (aircraft are normally protected by clearing them from aircraft hazard corridors during a mission). Road vehicles can be accounted for by determining road traffic density at “population centers” placed at multiple locations along roads.
Generally, the risks to trains, waterborne vessels, and aircraft are controlled (mitigated) by defining hazard areas or corridors (such as Notices to Airmen, see Chapter 14 of this AC) and controlling their locations during a launch such that the risks are sufficiently small and considered to be acceptable.
13.4.2 Hazard areas are designed to protect these populations. However, if a train and/or a waterborne vessel will be in a hazardous area, and its location(s) during the operation are known, risks to their occupants need to be included in the risk analysis in accordance with § 450.135(b)(4)(i). They should also be included during a launch countdown risk analysis when it is known that a train or a waterborne vessel has violated its hazard area, with the projected location of the train or waterborne vessel used to compute the risk.
13.4.3 While it is unusual for an aircraft to be in a hazard corridor, and it is likely not possible to define a fixed aircraft location, it may be necessary to assess the risks to aircraft in accordance with § 450.133(d) traffic through a hazard corridor during a launch countdown. This would require a special analysis to compute the impact probability, which should involve the use of 4-dimensional hazardous debris distributions (3 dimensions in space, plus time).
13.4.4 For an explosive fragment hazarding a population center, the probability of impact needs to consider that the fragment need not physically impact the center to cause casualties. This could also be the case for a liquid propellant tank creating a fireball, or secondary hazardous debris from an exploding tank or motor. An explosive fragment can impact the ground outside the boundaries of a population center, such that overpressure loading (peak overpressure and impulse) at the population center are sufficient to cause casualties (see paragraph 13.2 of this AC). This can occur for people who are unprotected (in the open) or within a structure. Thus, for explosive hazardous debris, the area around and including a population center should to be overlaid on a grid and impact probabilities computed for each grid cell. Casualty expectation 𝐸𝐸𝐶𝐶𝑡𝑡𝑗𝑗𝑖𝑖 will then need to be computed for an explosive fragment impact in each of these cells (with the probability of impact for each cell obtained by integrating the impact probability distribution for the explosive fragment over the area of the cell), and the resulting 𝐸𝐸𝐶𝐶𝑡𝑡𝑗𝑗𝑖𝑖 values for the cells summed over all cells.
13.4.5 The concept is illustrated in Figure 29. In this figure, the area encompassing the population center is gridded to create “impact cells.” The grid extends out from the population center to include all the area within which the explosive fragment could impact and significantly contribute to the EC for the center. An explosive fragment is shown as impacting in a specific cell, with the rings denoting decreasing levels of overpressure loading with distance from the impacted cell centroid. EC for the population center is computed (using the consequence model for explosive hazardous debris, see paragraph 13.2 of this AC) for the impact occurring in the cell, using the cell 𝑚𝑚𝑚𝑚𝑖𝑖𝑚𝑚𝑐𝑐𝑔𝑔 impact probability 𝑒𝑒𝑚𝑚𝑗𝑗 . This is then repeated for all impacted cells and the results summed to obtain the total EC for the population center.
13.4.6 For a large population center, often referred to as a region, where there are various shelter levels (including people in the open) distributed over the region, a second grid should be defined that partitions the population center into grid cells (call this the population grid). The reason for this is that the overpressure loads for a given explosive fragment impact location can vary significantly over the population center. In this case, 101
impact point / \ \ \ in current impact grid cell ,,, ✓ ~(/ \ \ \ \ \ \ \ \ \ \ \ \ 1' !.\ ~..! .......
Mean Fragment Impact Point Impact Grid:
Area about population center where impacts hazard pop center Impact Distribution Equi-densit Probability Contour 08/02/2024 AC 450.115-1B the EC should be computed for an explosive fragment impact in each “impact cell” for each of the cells in the population grid, and these values summed to get the total EC for the impact cell. This is then repeated for all impact cells and the results summed to get the total EC to the population center for the explosive fragment.
Figure 29 – Calculation of the Risk to a Population Center Due to the Impact of an Explosive Fragment
13.5 Individual Risk.
Mission individual risk is the probability of any single individual becoming a casualty, evaluated over all fragment classes and hazardous debris generating events. In accordance with §§ 450.101(a)(2) and 450.101(b)(2), the risk must meet the FAA individual risk criterion. For a specific population center and shelter type, to compute the mission individual risk, divide the mission EC by the total population:
𝐸𝐸𝐶𝐶𝑃𝑃𝑝𝑝𝑝𝑝 𝑗𝑗−𝑇𝑇𝑝𝑝𝑡𝑡𝑇𝑇𝑐𝑐 =𝑃𝑃𝐶𝐶𝐺𝐺𝑗𝑗 𝑁𝑁𝑃𝑃𝐶𝐶𝑖𝑖𝑗𝑗 The largest probability over all population centers and shelter types is then compared with the threshold values in § 450.101(a)(2) and 450.101(b)(2).