10.7 Progressive Breakup and Breakup Fragment Shedding.
If vehicle breakup occurs over a span of time, rather than at an instant in time, a set of ballistic trajectories should be initiated based on the core vehicle trajectory over that time span. This situation must be considered to meet requirement § 450.121(c)(2) and applies to planned body reentry from orbit. A progressive shedding of fragments may be due to aerothermal or aerodynamic effects while inside the atmosphere. The canonical example is the Space Shuttle Columbia reentry accident. Safety Design for Space Operations, (reference [1] of paragraph 3.4 of this AC) has an expanded discussion on this topic, including mathematical details, of shedding during a reentry event. During the breakup time span, ballistic trajectories should be initiated at a rate of about 1 Hz for each fragment class. A trajectory’s initial state vectors are (interpolated) points along the nominal reentry trajectory. Each shed time should be assigned a probability of fragment release, and all probabilities sum to one for each fragment class. The probabilities may obey a distribution that is uniform, Gaussian, or a more general Beta distribution. The probabilities are applied during evaluation of risk associated with a fragment class at the given shed time. Planned reentry generally occurs over water where the focus is on risk to aircraft.
10.8 Hazardous Debris Demise.
Virtually any material, including metallic fragments, experiencing drag friction of enough severity and over a sufficient dwell-time will enter a state of ablation where the material melts. This situation should be considered for fragments descending into, or traveling through, the atmosphere at thousands of feet per second. Although the requirements do not explicitly mention hazardous debris demise, the situation must be dealt with to meet requirement § 450.121(c). The ablation activation time depends on fragment speed, air density, fragment ballistic coefficient, and type of material. The reference Safety Design for Space Operations (listed as [1] of paragraph 3.4 of this AC) has an expanded discussion, including mathematical details, of inert fragment demise during a reentry event. As the fragment loses mass, its drag coefficient will get smaller leading to an increase in drag and a slowing of motion. This changes the course of the ballistic trajectory. The ablation will end if the fragment speed reduction drops below the threshold required for demise. Although risks to people may be reduced due to slower impact speeds, different people and assets might be at risk due to the modified trajectory. Ignoring hazardous debris demise is not necessarily conservative.
11 IMPACT PROBABILITY DISTRIBUTION.
In accordance with § 450.121(c), an operator must compute statistically valid impact probability distributions, which should be computed for each predicted breakup location. For most ground or waterborne vessel risk analyses, distributions are 2-dimensional, associated with the impact points in which the statistical trajectories cross the surface. For an aircraft, one approach is to generate 3-dimensional distributions, associated with points along the statistical trajectories at a series of freefall times of the hazardous debris clouds as the aircraft passes through a cloud. Another approach is to generate 2-dimensional distributions associated with the impact points in which the statistical trajectories cross the altitude level of the aircraft at a series of short progressing time spans.
11.1 Impact Probability.
A collection of statistical hazardous debris trajectories produces a set of impact points that intersect with a given altitude level. Mean sea level is used to compute risk to people in waterborne vessels. Mean terrain altitude is used to compute ground risks, which is typically the mean sea level for coastal launches. Specific altitude levels that depend on aircraft type are used to generate aircraft risk contours. For aircraft flying along specific flight paths, a range of altitudes may be needed. The impact points are separated into time blocks to deal with the transient nature of an aircraft flying at different altitudes.
11.1.1 For risk analysis computations, impact probabilities for people and assets should consider the number of impact points that hazard a site. The dispersion pattern formed by impact points should be fit to a single functional distribution that allows a minor amount of statistical information to be lost. If a single distribution cannot be used, a collection of simple distributions should be considered, such as a kernel density estimation (KDE) procedure as described in the reference listed as [18] of paragraph 3.4 of this AC. An alternative to a distributional fit is to use histograms of impact counts over the impact space, which can deal with diverse statistical patterns.
11.1.2 The criterion for employing functional distributions is that they can account for the first few statistical moments of the impact dispersion pattern. Every functional distribution employed should account for the first moment given by the mean and the second moment given by the variance. Functional distributions should also account for the moment of skewness and the fourth moment for patterns that exhibit excessive statistics in these moments. If higher moments are relevant, then either a collection of simpler distributions or a histogram should be constructed.
11.1.3 A statistical set of hazardous debris ballistic trajectories will likely be Gaussian if the sources of uncertainty applied during the Monte Carlo simulation are Gaussian, or near-Gaussian such as log-normal. Impact points may acquire skewness for long fall times and strong wind conditions. Monte Carlo state vector uncertainty sets may exhibit too much skewness, and more often too much kurtosis. Directed velocity explosion models tend to be non-Gaussian, such as forming a ring or torus, or possess no 56
discernible pattern. Trajectories that involve residual thrust or directed lift are also likely to possess no discernible pattern.
11.2 Gaussian Distribution.
A Gaussian or “normal” distribution is usually appropriate when skewness and kurtosis are both small. Both values are 0 in an exact normal distribution. As a rule of thumb excessive skewness would be values outside the range [-1,1], and for kurtosis values outside the range [-3,3].
11.2.1 On a plane, a “bivariate” normal distribution is formed using the mean location �𝑒𝑒, 𝑦𝑦� and the associated 2-dimensional covariance matrix of the impact locations. The 2-dimensional distribution is the product of the two individual 1D distributions in which the standard deviation values �𝜎𝜎𝑚𝑚, 𝜎𝜎𝑔𝑔� are the eigenvalues of the 2-dimensional covariance matrix. The pair of 1D distributions are orthogonal along the principal axis, with direction provided by the eigenvectors of the 2-dimensional covariance matrix.
11.3 Skewed Distribution.
A Gaussian based distribution that accounts for skewness, is the Skew-Normal distribution. This is defined by a mean, covariance matrix, and an additional Shape parameter, α, that quantifies the amount of skewness.
11.3.1 Figure 1 presents a sampling of 1D skew-normal curves. The 2-dimensional skew-normal distribution cannot be reduced to the product of two 1D functions due to the nature of the shape parameters. For high skewness, the figure shows that the Gaussian distribution produces a tail in which zero probability exists.
11.3.2 Due to the nature of the shape parameter, solving for the 2-dimensional skew-normal distribution parameters involves an approach that requires the use of non-linear differential equations. A useful solution that applies to impact dispersions for the 2-dimensional distribution can be developed through a careful reading of the literature.4 Issues that should be dealt with are employment of proper coordinates, and avoidance of common runaway solutions that go to an infinite value for alpha and are usually invalid.
4 See http://azzalini.stat.unipd.it/SN/index.html.
-t-H~tt- ----,-,.c-------- ---; - alpha=O Gaussian
- alpha=2 f---------------H--cf-H- ----lll---+-~ ---------1 - alpha=5
- alpha=15
- alpha=100 -4 -3 -2 -1 0 2 3 4 08/02/2024 AC 450.115-1B Figure 1 – Comparison of Various Skew-Normal Curves
11.4 Histogram Distribution.
Impact probabilities are specified by first defining a surface grid. A histogram that specifies impact probabilities over a grid is constructed by determining the number of trajectories that pass through each cell. Cell sizes should be no larger than about one hundredth of the area of the dispersion pattern, which displays gradual differences between grid points. Otherwise, an iterative process may be needed to determine a suitably fine grid to attain the desired accuracy in computed risk. To obtain sufficient cell statistics, especially near the edges of the dispersion pattern, may require that the collection of trajectories have tens of thousands of samples. Due to long runtimes for trajectory generation, this type of approach is much less practical than the KDE in which runtime is proportional to the number of dispersions.
11.5 3-dimensional Impact Probability.
The collection of statistical hazardous debris trajectories produces sets of 3-dimensional cloud points at given free-fall times. Aircraft risk is computed by determining how much of the hazardous debris cloud the aircraft passes through between free-fall times and using the net probability inside the swept-out volume of encountering a fragment.
Typically, a single mean probability value can be used since aircraft are much smaller than the hazardous debris clouds and as such, variations in hazardous debris impact probabilities will be insignificant. The total risk is the sum over all free-fall times. If only an aircraft analysis is being performed, then the trajectories only need be computed far enough until the cloud has fallen below the aircraft and is no longer a hazard.
11.5.1 The generalization of the 2-dimensional distributions to three dimensions is straightforward. The tri-normal distribution has mean �𝑒𝑒, 𝑦𝑦, 𝑧𝑧� and standard deviation values �𝜎𝜎𝑚𝑚, 𝜎𝜎𝑔𝑔, 𝜎𝜎𝑧𝑧� that are the eigenvalues of the 3-dimensional covariance matrix. The triplet of 1D distributions are orthogonal and along the principal axis, in which directions are provided by the eigenvectors of the 3-dimensional covariance matrix. The 3-dimensional skew-normal possesses the same solution process requirements and complexities as the 2-dimensional case but can be resolved in the same manner.
11.5.2 The 3-dimensional histogram approach uses cubes rather than cells. The set of cubes span the space through which an aircraft may pass, and will likely necessitate that the collection of trajectories has millions of members for those aircraft near the edges of the cloud dispersion pattern.
12 CONSEQUENCE MODELING.
A flight safety analysis must compute the predicted consequences of each reasonably foreseeable failure mode in any significant period of flight in terms of conditional expected casualties, in accordance with § 450.135(b). The hazardous debris may be inert, explosive, or toxic that endangers people who are unsheltered, in buildings, on or below deck of waterborne vessels, or in aircraft. For some cases, sufficient information is given to fully compute the consequence. Otherwise, the discussion will outline an approach and indicate what type of effort remains. The models presented in this chapter are in current use among many of the Federal ranges. If desired, the operator may employ its own models with proper justification.
12.1 Types of Consequences.
In accordance with § 450.135(b)(2), evaluation of risks requires computing the probability of consequence 𝑒𝑒𝑐𝑐𝐶𝐶𝑚𝑚𝑠𝑠𝑟𝑟𝑐𝑐𝑠𝑠𝑟𝑟𝑚𝑚𝑐𝑐𝑟𝑟 by examining the effects of the hazardous debris hazard on population centers. Analysis using population centers is further explained in AC 450.123, Population Exposure Analysis. Some of the 𝑒𝑒𝑐𝑐𝐶𝐶𝑚𝑚𝑠𝑠𝑟𝑟𝑐𝑐𝑠𝑠𝑟𝑟𝑚𝑚𝑐𝑐𝑟𝑟 values relate directly to requirement threshold levels that should not be exceeded for a high-fidelity analysis. Others are components of the risk values, to be discussed in paragraph 12.6.1 of this AC, that then relate to all the remaining requirement threshold levels.
12.1.1 The probability of consequence depends on the probability that hazardous debris impacts at or near the population center, and the probability that the impact results in a casualty:
𝑒𝑒𝑐𝑐𝐶𝐶𝑚𝑚𝑠𝑠𝑟𝑟𝑐𝑐𝑠𝑠𝑟𝑟𝑚𝑚𝑐𝑐𝑟𝑟 = 𝑒𝑒𝑚𝑚𝑚𝑚𝑖𝑖𝑚𝑚𝑐𝑐𝑔𝑔 × 𝑒𝑒𝑐𝑐𝑚𝑚𝑠𝑠𝑠𝑠𝑚𝑚𝑓𝑓𝑔𝑔𝑔𝑔
12.1.2 There are several levels of effort that can be put forward to evaluate 𝑒𝑒𝑐𝑐𝑚𝑚𝑠𝑠𝑠𝑠𝑚𝑚𝑓𝑓𝑔𝑔𝑔𝑔, which differ by degree of conservatism.
12.1.3 The simplest and most conservative is to set 𝑒𝑒𝑐𝑐𝑚𝑚𝑠𝑠𝑠𝑠𝑚𝑚𝑓𝑓𝑔𝑔𝑔𝑔 = 1 for all hazardous debris, and thus 𝑒𝑒𝑐𝑐𝐶𝐶𝑚𝑚𝑠𝑠𝑟𝑟𝑐𝑐𝑠𝑠𝑟𝑟𝑚𝑚𝑐𝑐𝑟𝑟 = 𝑒𝑒𝑚𝑚𝑚𝑚𝑖𝑖𝑚𝑚𝑐𝑐𝑔𝑔.
12.1.4 If using 𝑒𝑒𝑐𝑐𝑚𝑚𝑠𝑠𝑠𝑠𝑚𝑚𝑓𝑓𝑔𝑔𝑔𝑔 = 1 results in meeting the risk criteria of §§ 450.101(a) to 450.101(b) then a less conservative and more complicated method to evaluate 𝑒𝑒𝑐𝑐𝑚𝑚𝑠𝑠𝑠𝑠𝑚𝑚𝑓𝑓𝑔𝑔𝑔𝑔 is not necessary.
12.1.5 Instead of setting 𝑒𝑒𝑐𝑐𝑚𝑚𝑠𝑠𝑠𝑠𝑚𝑚𝑓𝑓𝑔𝑔𝑔𝑔 = 1 for all hazardous debris, it can be set only for selected fragments that pass specific hazardous debris filters, while everything else is rejected.
Any hazardous debris on unsheltered people can be rejected if the impact kinetic energy is less than 11 ft-lbs and the mean impact kinetic energy per unit area at impact is less than 34 ft-lb/in2. For sheltered people near windows, explosive consequences only need to be considered in the region where the overpressure exceeds 0.25 psig, for the purposes of the debris risk analysis required by § 450.1355. Several additional acceptable filters are given in the reference listed as [22] of paragraph 3.4 of this AC.
Any hazardous debris on sheltered people can be rejected if the roof is struck with less than 17 ft-lbs. Explosive effects can be ignored for unsheltered people where the overpressure is less than 2 psig. For sheltered people hazarded by falling walls and roofs, the threshold is 1 psi. Finally, hazardous debris on aircraft can be rejected if its mass is less than 0.4 gram.
12.1.6 If the filters are not useful, then a probabilistic model-based evaluation of 𝑒𝑒𝑐𝑐𝑚𝑚𝑠𝑠𝑠𝑠𝑚𝑚𝑓𝑓𝑔𝑔𝑔𝑔 should be done. This would include a model for human vulnerability that considers the effects of the hazard on the human body. A valid model should account for the vulnerability of various body parts that dominate the risk. The type of consequence being performed will indicate which body parts should be considered. The degrees of injury to people and specific body parts can be separated into categories corresponding to the severity of the injury. A system that is used among many industries is the Abbreviated Injury Scale (AIS). This was originally published in 1971 to provide a taxonomy of injuries generated by road accidents, and has been refined several times since This publication is listed as reference [20] of paragraph 3.4 of this AC. There are 7 AIS levels that are defined in Table 2 of this AC. A “casualty” corresponds to AIS level 3 (or higher), which are serious injuries requiring hospitalization for recovery, or greater AIS level.
5 In accordance with § 450.137, a flight safety analysis must include a far-field overpressure blast effect analysis that demonstrates compliance with safety criteria in § 450.101. In accordance with § 450.137(b)(3), this analysis must account for the potential for broken windows due to peak incident overpressures below 0.1 psi and related casualties based on the characteristics of exposed windows and the population’s susceptibility to injury, etc.
Table 2 – AIS Severity Levels AIS Severity Level Severity Type of Injury 0 None None 1 Minor Superficial 2 Moderate Reversible injury; medical attention required 3 Serious Reversible injury; hospitalization required 4 Severe Life threatening; not fully recoverable without care 5 Critical Non-reversible injury; not fully recoverable even with medical care 6 Virtually Unsurvivable Fatal
12.1.7 Evaluating the human vulnerability model at the casualty level can then be then fed into one of two forms that lead to a proper evaluation of 𝑒𝑒𝑐𝑐𝐶𝐶𝑚𝑚𝑠𝑠𝑟𝑟𝑐𝑐𝑠𝑠𝑟𝑟𝑚𝑚𝑐𝑐𝑟𝑟. The first representation is as an “effective” casualty area. As specified in § 401.7, effective casualty area means the aggregate casualty area of each piece of debris created by a vehicle failure at a particular point on its trajectory. The effective casualty area for each piece of debris is a modeling construct in which the area within which 100 percent of the population are assumed to be a casualty, and outside of which 100 percent of the population are assumed not to be a casualty. This area need not be a single connected region, but may be comprised of several disjoint sections. The effective casualty area, CA, is a factor in the probability of 𝑐𝑐𝑆𝑆𝑐𝑐𝑐𝑐𝑆𝑆𝑆𝑆𝑆𝑆𝑦𝑦 through 𝑒𝑒𝑐𝑐𝑚𝑚𝑠𝑠𝑠𝑠𝑚𝑚𝑓𝑓𝑔𝑔𝑔𝑔 = 𝐶𝐶𝐴𝐴/𝐴𝐴𝑖𝑖𝐶𝐶𝑖𝑖 where 𝐴𝐴𝑖𝑖𝐶𝐶𝑖𝑖 is the area of the population center. The effective casualty area must account for all relevant hazardous debris characteristics and the characteristics of a representative person potentially exposed to the hazardous debris hazard in accordance with § 450.135(b)(1). For reporting purposes, the effective casualty area needs to be computed for people who may be occupying an unsheltered casualty area in accordance with § 450.135(c)(3), as well as for a representative type of building, ground vehicle, waterborne vessel, and aircraft, assuming a representative impact vector, in accordance with § 450.135(c)(4).
12.1.8 The second way in which the potential for a casualty is usually characterized is by specifying a probability of casualty versus distance profile, i.e., 𝑃𝑃𝐶𝐶(𝑑𝑑). The distance d is measured from the hazardous debris impact point, and the profiles that extend outward from that point may or may not depend on the hazardous debris’ impact direction. The profile 𝑃𝑃𝐶𝐶(𝑑𝑑) is not necessarily monotinically decreasing as d increases.
To include all non-trivial risks for distant population centers, the profiles 𝑃𝑃𝐶𝐶(𝑑𝑑) may need to go out far enough until the probability level drops below at least 1x10-6 . A ramification of this is that a given population center can be reached by hazardous debris impacts with varying impact probabilities. To properly compute risk, the impact space should be broken down into cells where the probability of impact in each cell has small impact variation, which should be less than about 1/3rd of a standard deviation of the impact distribution. The 𝑒𝑒𝑐𝑐𝐶𝐶𝑚𝑚𝑠𝑠𝑟𝑟𝑐𝑐𝑠𝑠𝑟𝑟𝑚𝑚𝑐𝑐𝑟𝑟 on a site is then expressed as a sum over all the impact cells.
𝑁𝑁𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 𝑚𝑚𝑚𝑚𝑖𝑖𝑚𝑚𝑐𝑐𝑔𝑔 𝑒𝑒𝑐𝑐𝐶𝐶𝑚𝑚𝑠𝑠𝑟𝑟𝑐𝑐𝑠𝑠𝑟𝑟𝑚𝑚𝑐𝑐𝑟𝑟 = � 𝑒𝑒𝑚𝑚 × 𝑃𝑃𝐶𝐶(𝑑𝑑𝑚𝑚) 𝑚𝑚=0
12.1.9 An effective casualty should also be computed to meet reporting requirements in §§ 450.135(c)(3) and (4), although it is generally not needed for computations that use the 𝑃𝑃𝐶𝐶(𝑑𝑑) curves. For these cases, the effective casualty is evaluated as the integral of 𝑃𝑃𝐶𝐶(d) over the area where 𝑃𝑃𝐶𝐶(d) is at least 1 percent.
12.2 Inert Hazardous Debris.
In accordance with § 450.135(b)(3), a debris risk analysis must model the casualty area, and compute the predicted consequences of each reasonably foreseeable failure mode in any significant period of flight in terms of conditional expected casualties accounting any impact or effects of hazardous debris. This section discusses the hazard cases where inert hazardous debris consequences arise, and provides guidelines for evaluating such consequence. Inert risk must be computed for people who may be occupying an unsheltered casualty area in accordance with § 450.135(c)(3), and people in buildings, people on or below deck in waterborne vessels, and people in aircraft in accordance with § 450.135(c)(4).
12.2.1 Although the discussion applies to inert consequences, in accordance with § 450.135(b)(3), the hazardous debris does not need to be inert but can also be explosive or toxic. This is because hazardous debris with small explosive or toxic risks may have higher risks by treating them as inert. In other words, the kinetic impact of the hazardous debris may pose more risk than if the fragment exploded or released toxic gases. Thus, for these cases risks should be computed both ways and the larger risks values applied against the risk thresholds.
12.3 Unsheltered People.
In accordance with § 450.135(b), the casualty consequence for inert hazardous debris impacts on unsheltered people must be represented by an effective casualty area. The hazardous debris list should include all fragments with an impact kinetic energy of at least 11 ft-lbs or a mean impact kinetic energy per unit area at impact of at least 34 ft-lb/in2. The net effective casualty area may be based on a sum over much smaller areas.
12.3.1 The full hazardous debris hazardous area may be broken down in cells, and within each cell, the effective casualty area 𝐶𝐶𝐴𝐴𝑐𝑐𝑟𝑟𝑓𝑓𝑓𝑓 is computed by 𝐶𝐶𝐴𝐴𝑐𝑐𝑟𝑟𝑓𝑓𝑓𝑓 = 𝐻𝐻𝐴𝐴𝑐𝑐𝑟𝑟𝑓𝑓𝑓𝑓 × 𝑒𝑒𝑚𝑚𝑚𝑚𝑗𝑗𝑠𝑠𝑟𝑟𝑔𝑔 where 𝐻𝐻𝐴𝐴𝑐𝑐𝑟𝑟𝑓𝑓𝑓𝑓 is the hazard area of the cell, which is the area of the cell, and 𝑒𝑒𝑚𝑚𝑚𝑚𝑗𝑗𝑠𝑠𝑟𝑟𝑔𝑔 is the probability of serious injury to a person in that cell of one or more specific body parts.
𝑁𝑁𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 12.3.2 The probability of casualty is 𝑒𝑒𝑐𝑐𝑚𝑚𝑠𝑠𝑠𝑠𝑚𝑚𝑓𝑓𝑔𝑔𝑔𝑔 = ∑𝑗𝑗=0 𝐶𝐶𝐴𝐴𝑐𝑐𝑟𝑟𝑓𝑓𝑓𝑓𝑗𝑗 /𝐴𝐴𝑐𝑐𝑟𝑟𝑓𝑓𝑓𝑓𝑗𝑗 , and the probability of impact is computed separately, which and is evaluated over the population center area 𝐴𝐴𝑖𝑖𝐶𝐶𝑖𝑖.
12.3.3 This probability 𝑒𝑒𝑚𝑚𝑚𝑚𝑗𝑗𝑠𝑠𝑟𝑟𝑔𝑔 depends on the body part(s) that are struck by hazardous debris, the type of person (male, female, adult, child), the impact velocity of the fragment, and the mass of the fragment. A partitioning of the body into parts where injury can at a minimum lead to a serious casualty, might include the head, chest, abdomen, legs, and thorax, but not arms. Hazard area cells may be associated with locations within which a particular body part is struck, and so do not need to be square shape but can assume any convenient shape.
12.3.4 The fragment shape also affects the degree of injury. To be conservative, fragments should be modeled as spheres, which tend to produce the highest probability of injury, although in some situations a plate shape may have higher risks. For a range of fragment masses, sample 𝑒𝑒𝑚𝑚𝑚𝑚𝑗𝑗𝑠𝑠𝑟𝑟𝑔𝑔 curves are shown in Figure 2 of this AC for vertical impacts to the head, in Figure 3 for horizontal impacts to the chest, in Figure 4 for horizontal impacts to the abdomen, and in Figure 5 for horizontal impacts to the legs.
These curves are for localized blunt injury impacts for a typical person in the public.
They only account for direct hits to the body and ignore any secondary injury to other body parts, such as if the person is knocked to the ground. For masses not shown in the figure, linear interpolation should be used between curves, and the bounding curves at the far left and right used instead of extrapolation. Small fragments may have a higher probability for skin penetration, while larger fragments for crushing. Larger fragments may also knock a person down causing secondary injuries when the person strikes the ground.
100 90
.80
~ ~ - 70 0 a,
- 60 -w -0 50 ~ .c 40 ra a. 30 0 .... a.. 20 10 0 0 100 90 80 -C 70 -0 cu 60 .... = w ....
0 50 ? :c 40 ro a.
0 ... 30
0.
20 ...
10 0 0
- - ··-·· ···-···- -- - -- -- - --- -- 20 40 60 80 Impact Speed (ft/s) --0.35 Ib --0.5 Ib --1 Ib
2.5 lb --5Ib --10 Ib --20 Ib --40 Ib --80 Ib --200 lb 1000I b 100
- o.35 Ib --o.5 Ib 1~ 2.5 Ib . ... .................................. ............................ - 10Ib
- 20lb ····· - 40Ib
- soIb
- 200 lb 120 . .... . ........................................ . 1000 lb ·•···•· ··- ------ ------------ -------------------------- ·--- 100 150 200 250 300 350 Impact Speed (ft/s) 08/02/2024 AC 450.115-1B Figure 2 – Probability of Casualty Curves for Non-Mission Essential, Vertical Impact to Head, Blunt Injury Figure 3 – Probability of Casualty Curves for Non-Mission Essential, Sphere Impacting Chest, Blunt Injury 64
100 -y----------- --,...s-.....--.....,...- --,___,=--- ....,........,....--..~ ----, 90 ············································ 80 -~ 70 ti ~ 60 w -0 50
2.5 lb ........... --5 1b --10 1b --20 1b --401b 20 ··············································· · ······· ············· ···· ············ ···· ······ ···············--so 1b 10 0 .J_-~ =""'~ .,.;;:~ ~ ~ ~ ~ -::_~ =-~ ~ ~ =-,_--- ~ 1000 It ~ --~ 10 100 1000 Impact Speed (ft/s) 100 ,------------- -,-"7""----- - -----,- - -,,,-...---,,,..- ------, -~ t, Q) It: w -0 >, ~ .c <Ii C.
::
CL 90 ................................... .
80 70 60 50 40 30 20
2.5 lb .......... --5 1b --101b --201b --401b 10 ........................... . ............... --200 lb 0 1000 It 10 100 1000 Im pact Speed (ft/s) 08/02/2024 AC 450.115-1B Figure 4 – Probability of Casualty Curves for Non-Mission Essential, Sphere Impacting Abdomen, Blunt Injury Figure 5 – Probability of Casualty Curves for Non-Mission Essential Sphere Impacting Leg, Blunt Injury 65
12.4 Casualty Areas.
The casualty area, from which the “effective” casualty area is based, should include where a person could be standing to experience (1) direct impact of the fragment, (2) impact of the fragment during bouncing, (3) impact if the fragment due to skipping, sliding, rolling, or ricocheting, or (4) impact of fragment pieces if the fragment splatters. The hazard area should also account for the effect of terrain where feasible.
Atmospheric drag and wind can be ignored when describing the fragment’s motion during these phases.
12.4.1 Direct Hazard Area.
The local hazard area for direct impact should account for the radius of a standing person, about one foot, and the projected hazardous area of the fragment as it reaches the person. The fragment can be assumed to be spherical. The area should also account for the angle at which the fragment is traveling just prior to impact. For a person standing in any part of the direct hazard area, the path of the fragment should be tracked close enough to identify which body parts are struck to convert to the effective casualty area. For impact on a soft surface, it should be determined if the fragment buries itself into the ground, (i.e., more than half its radius is underground), before proceeding to consider fragment bouncing.
12.4.2 Bounce Hazard Area.
The local hazard area produced by a bouncing fragment could be computed by modelling the fragment as a sphere to get a conservative area. Modeling as a football, cube, or other shape will tend to lead to smaller areas, although the dynamics may be harder to capture. The contact with the Earth’s or waterborne vessels’ surface should account for a reduction in vertical speed based on the coefficient of restitution e for that surface: 𝑣𝑣𝑟𝑟𝑟𝑟𝑠𝑠𝐶𝐶𝑠𝑠𝑚𝑚𝑑𝑑 = 𝑅𝑅 × 𝑣𝑣𝑚𝑚𝑚𝑚𝑖𝑖𝑚𝑚𝑐𝑐𝑔𝑔 . Conservative values as a function of the vertical component of the total impact speed are shown in Table 3 of this AC.