1.0E+00
1.0E+01
1.0E+02
1.0E+03
1.0E+04
1.0E+05
1.70E-01 7.10E-01 2.97E+00 1.24E+01 5.18E+01 2.16E+02 9.03E+02 3.77E+03 Impulse (psi-msec) Scaled Distance Figure 13 – Impulse vs. Scaled Distance from Blast Waves
12.11 Liquid Propellant Yield.
Yield curves have been generated for several types of liquid propellants. For other propellants, the applicant should develop a model in compliance with § 450.101(g).
These are shown in Figure 14 of this AC, where values of FTNT are shown on the vertical scale. These curves are to be applied regardless of surface type.
Note: The impact weight of the liquid tank should account for operator intentional venting of fuel that may have occurred during the failure event. Liquid propellant has two components, fuel (e.g. liquid hydrogen, kerosene, Aerozine 50, or liquid methane), and oxidizer, (e.g. liquid oxygen or nitrogen tetroxide). During venting, a propellant tank is given a crack on its side allowing the fuel to leak, that usually starts from the time of failure. By design, the venting process does not change the oxidizer weight. On impact, yield should be computed by assuming that the ratio of fuel to oxidizer, 𝑅𝑅 = 𝑤𝑤𝐶𝐶𝑚𝑚𝑚𝑚𝑑𝑑𝑚𝑚𝑧𝑧𝑟𝑟𝑟𝑟/𝑤𝑤𝑟𝑟𝑠𝑠𝑟𝑟𝑓𝑓, is such that both components mix completely to creation an explosion. The effective propellant weight that gets converted into yield is only dependent on the remaining fuel: 𝑤𝑤 = 𝑤𝑤𝑟𝑟𝑠𝑠𝑟𝑟𝑓𝑓(1 + 𝑅𝑅).
1.4
1.2 1 --L02/LH2 0 tl if 0.8 JI --L0 2/R P-1 .Ill ►
0.6 --ASO/N204
0.4
0.2 0 0 100 200 300 400 500 600 700 800 900 1000 Impa ct Speed (ft/ se<:)
08/02/2024 AC 450.115-1B Figure 14 – Yield Curves for Liquid Propellants on Hard Surfaces
12.12 Solid Propellant Yield.
Solid propellants relevant for flight safety analysis are typically represented in one of two categories: Hazard Division (HD) 1.1 detonable propellants, or HD 1.3 deflagration propellants. For other types of solid propellant, a conservative option is to apply the HD
1.1 model. The yield factors for solid propellant should account for the size and shape of the propellant, type of impact surface, total impact speed, and orientation at impact if applicable.
12.12.1 Uncontained propellant hazardous debris created during vehicle breakup should account for any loss of weight and change of shape during the ballistic fall due to burning. A determination should be made if the propellant is burning once ballistic fall commences, and if it snuffs out prior to impact. Snuff-out models depend on the propellant type and consider local air density and fragment speed. Fragments that are not initially burning may be assumed to remain non-burning during free-fall. The fragment weight and ballistic coefficient should be updated as burning occurs, and the ballistic trajectory should be based on the evolving weight and ballistic coefficient values.
12.12.2 For HD 1.1 impacts, yield factor FTNT values for various surface types can be read from Figure 15. This plot indicates that the factor will either be 0 or 1.25. These curves make no distinction of whether the propellant is in a contained motor, its impact orientation, or uncontained hazardous debris created at vehicle breakup.
120 - 100 - I- z I- 80 - ::,f;: 0 ""C 60 "'ijj - >= 40 - 20 - 0 0 125 % 1NT
- Steel irrpact surface
- Concrete -Soil
- Water 140 210 250 370
I I I I I I I 100 200 300 400 500 600 700 80( Propellant Impact Velocity , fps 08/02/2024 AC 450.115-1B Figure 15 – HD 1.1 Propellant Yield Model
12.12.3 For HD 1.3 propellant impacts, the appropriate yield model should account for the form of the solid propellant fragment. Three types of solid propellant fragments should be considered: contained motors, small uncontained chunks of hazardous debris created at vehicle breakup, or large uncontained pieces created at vehicle breakup that are shaped as a Cylindrical Annulus Sector (CAS).
12.12.4 Yield factors for intact motor segments that impact on sand in a side-on orientation may be obtained from the curves in Figure 16, where the segment sizes are measured by the lateral diameter of the motors. If the yield factor associated with the desired motors is not those presented in the figure or are not available, then the curves in Figure 16 can still be used. For other motor diameters between 41” and 146”, linearly interpolate between the nearest bounding curves. For diameters outside the range, use the closest bounding curve and do not extrapolate. For surface types other than sand or soft soil impact, adjust the impact speed by:
𝑣𝑣𝑚𝑚𝑚𝑚𝑖𝑖𝑚𝑚𝑐𝑐𝑔𝑔 𝑣𝑣 = 𝐹𝐹𝑠𝑠𝑠𝑠𝑟𝑟𝑟𝑟𝑚𝑚𝑐𝑐𝑟𝑟 where 𝐹𝐹𝑠𝑠𝑠𝑠𝑟𝑟𝑟𝑟𝑚𝑚𝑐𝑐𝑟𝑟 is 0.55 for steel, 0.78 for concrete, 1.00 for sand, and 1.61 for water.
12.12.5 Finally, for all intact motor orientations other than side-on, the conservative approach is to employ the side-on curves.
r T _,_ +- _,_ +- ..
..
► ► - ► _,_ 08/02/2024 AC 450.115-1B
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0.50 0 100 200 300 400 500 600 700 800 900 Yield Factor Impact Speed (ft/s) 41” Segment 60” Segment 92” Segment 124” Segment 146” Segment Figure 16 – Yield Curves for Motor Segment Side-On Impacts on Sand
12.12.6 Propellant chunks may be modeled as cubed shaped. To get yield factors, Figure 17 of this AC can be used where the cube size is measured by the length of any of its edges.
For other cube dimensions between 18” and 30”, linearly interpolate between the nearest bounding curves. For dimensions less than 18”, linearly interpolate using the 18” curve and zero values. Use the 30” curve for dimensions larger than 30” and do not extrapolate. For other surface types, apply the same impact speed correction as with the intact motors.
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0.18 0 200 400 600 800 1000 1200 1400 1600 1800 Yield Factor Impact Speed (ft/s) 18” Cube 24” Cube 30” Cube Figure 17 – Yield Curves for Cube Chunks Impacting on Sand 82
+ ~ ~ + + ~ + ~ + -+ + r I + + + l ~ I + -I I + - ~ + 08/02/2024 AC 450.115-1B
12.12.7 The third shape case is impacts for uncontained propellant cylindrical annulus sectors.
Apply the yield factors in Figure 18 for a CAS that subtend an angle of 120 degrees, and whose length is a half that of the origination motor. This means that the total propellant inside a motor will be modeled as six such CAS fragments. The diameters referenced in the figure’s legend are those of the originating motor. For other surfaces and diameters, apply the same rules as given for the intact motor. For smaller lengths and subtended angles, but still forming a CAS, a conservative approach is to use the curves in Figure 18. For larger lengths and angles, the conservative approach is to use the intact motor yield factor curves, although the creation of such dimensions is unlikely.
0.00
0.02
0.04
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0.12
0.14
0.16
0.18
0.20 0 100 200 Yield Factor 41” CAS 60” CAS 92” CAS 124” CAS 146” CAS 300 400 500 600 700 800 900 1000 1100 Impact Speed (ft/s) Figure 18 – Yield Curves for 120ᵒ CAS Side-On Impacts on Sand
12.12.7.1 The curves in Figure 17 and Figure 18 are given in tabular form in AC 450.137-1, Distant Focusing Overpressure Risk Analysis.
12.13 Sympathetic Yields.
Several situations should be considered when multiple motors and/or engines impact near one another during the same event. The first is when the motors or engines have different propellant compositions. For that case, the yields should be computed separately, and never as a single yield with a combined impact weight.
12.13.1 A second situation is when one motor or engine explodes on impact but at least one other motor or engine, of the same propellant composition, remains intact. If the intact motor or engine then explodes due to being struck by induced ejected hazardous debris from the exploding motor or engine, then the yield from the initially intact motor or engine should be computed separately from the others.
12.13.2 A third situation is when motors or engines of the same propellant composition explode near each other. The first motor or engine that explodes may cause a sympathetic 83
reaction of the second motor or engine, due to the shock wave, leading to its detonation at the same time. A single yield can be computed using a combined propellant weight if the shock wave pressure distance between the motors or engines is small enough. An evaluation should be done, based on distance between the motors or engines and structural properties of the second motor or engine, to determine if the blast wave overpressure on the second motor or engine exceeds its threshold for detonation. If insufficient information exists for such an evaluation, then a conservative approach is to combine the propellant weights and use this as a single yield.
12.14 Impacting Propellants for Unsheltered People.
Two types of events should be considered for impacting propellants to evaluate consequences for people that are not sheltered by a structure. First, a liquid tank on impact may explode and create a fireball. Second, on impact a solid propellant impact may create a blast overpressure wave.
12.14.1 Fireball.
When liquid tanks impact, they may create a fireball if they have sufficient fuel and impact speed. A fireball hazard should be represented as a probability of casualty versus distance curve, 𝑃𝑃𝐶𝐶(𝑑𝑑). On impact, the liquid propellant will be consumed very rapidly, usually in at most, a few seconds. This results in a fireball that grows to a maximum radius 𝑒𝑒𝑟𝑟𝑚𝑚𝑟𝑟𝑟𝑟𝑠𝑠𝑚𝑚𝑓𝑓𝑓𝑓 that is a well-defined border about an opaque region.
12.14.2 The maximum radius of the fireball depends on the type of liquid propellant. The following expressions may be used where the radii are given in feet, and W is the impact liquid propellant weight in pounds:
𝑒𝑒𝑟𝑟𝑚𝑚𝑟𝑟𝑟𝑟𝑠𝑠𝑚𝑚𝑓𝑓𝑓𝑓 = 5.02𝑊𝑊 0.316 𝐿𝐿𝐿𝐿𝐿𝐿/𝑅𝑅𝑃𝑃 − 1 𝑒𝑒𝑟𝑟𝑚𝑚𝑟𝑟𝑟𝑟𝑠𝑠𝑚𝑚𝑓𝑓𝑓𝑓 = 5.52𝑊𝑊 0.306 𝐿𝐿𝐿𝐿𝐿𝐿/𝐿𝐿𝐻𝐻 − 2 𝑒𝑒𝑟𝑟𝑚𝑚𝑟𝑟𝑟𝑟𝑠𝑠𝑚𝑚𝑓𝑓𝑓𝑓 = 4.43𝑊𝑊 0.316 𝐻𝐻𝑦𝑦𝑑𝑑𝑒𝑒𝑆𝑆𝑧𝑧𝑖𝑖𝐾𝐾𝑅𝑅
12.14.3 For all liquid types that do appear in this list, a conservative model to use is the LOX/LH-2. If a person is inside the maximum fireball radius, then the person is considered a casualty. Outside, the probability of casualty is partly due to second degree burns, and diminishes by distance based on the fireball duration and emissivity of the fireball. When a person experiences 2nd degree burns over 20 percent of their body, the person is considered to be a casualty. The probability of casualty from the fireball will need to be combined with that from the blast wave created from the explosion (discussed in the next subparagraph).
12.15 Blast Wave Overpressure.
The threat from a blast wave should be represented as a probability of casualty versus distance curve, 𝑃𝑃𝐶𝐶(𝑑𝑑). The blast wave should be treated equally in all directions, since there is no preferred direction, and can be quantified by peak overpressure and impulse as a function of distance. The probabilities of casualty and impact are correlated. The impact space can be divided into cells such that the probability of impact within each 84
101.
- 501.
- 901.
- 991.
. ... : : ,- . : : ; :
08/02/2024 AC 450.115-1B 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
12.15.1 The sum should include all cells with 𝑃𝑃𝐶𝐶(𝑑𝑑) above 1x10-6 .
12.15.2 The blast wave injury to people is dominated by the effect on four body parts: the lungs, gastrointestinal (GI) tract, larynx, and eardrum. Figure 19 presents probability of casualty curves for these body parts. The curves associated with the 50 percent casualty thresholds should be used to create the corresponding PC curves for a given impact event. A person may suffer one or more of the injuries. The following expression should be employed to obtain the total probability from all sources at a given distance “d”:
𝑃𝑃𝐶𝐶(𝑑𝑑) = 1 − �1 − 𝑒𝑒𝑟𝑟𝑚𝑚𝑟𝑟𝑑𝑑𝑟𝑟𝑠𝑠𝑚𝑚(𝑑𝑑)� �1 − 𝑒𝑒𝑓𝑓𝑚𝑚𝑟𝑟𝑔𝑔𝑚𝑚𝑚𝑚(𝑑𝑑)� �1 − 𝑒𝑒𝐺𝐺𝐺𝐺 𝑇𝑇𝑟𝑟𝑚𝑚𝑐𝑐𝑔𝑔(𝑑𝑑)� �1 − 𝑒𝑒𝑓𝑓𝑠𝑠𝑚𝑚𝑓𝑓𝑠𝑠(𝑑𝑑)�
12.15.3 For liquid tank impacts, use a probability of one inside the fireball radius and the blast wave probability outside the fireball radius.
Figure 19 – Probability of Serious Injury to a Lung 85
Severe GI Tract Injury 10~.-- -.-............. .,.,..,,.,...~ __ .,....._-_-_-_-,~.-.--~.--~--~-~-~-~.-~., ....... -. -. -. ~==~=~~=~~~ri •• •-= • • • • • • • .. • •• • I .' • •, - I • • • • :T : : : \: : ; : I : \T : : : :
:. :~ • • • • .' • • •:- .: • I • • • ,' ,: : • • • • : : : / : } ::: )/T : : : l: : l: I l k:i: : : : : ... -:-.. ,· ... ~ ,:-:-.. -~ .... ·: .. -: . · , .. ~ ·: -: ~ .... . •'• :
. . . . :- . .. • ...... : . : .. • . ,: .. . . -: . . . : . ... ... .. ·. ~ . . .. . . -:
. ,:
• ·= 10°~---~~~~-~--~~~-----~~ 100 10' 102 Impulse (psi .msec) .,...._ 102 "ij'j ..e, ~ :::, '-" '-" ~ e-,v :=, 0 10' 10°~-~-~~~-· -· ~·'--~~~~~~~-~-~~~~~ 100 10' 102 Impulse (psi.msec) 08/02/2024 AC 450.115-1B Figure 20 – Probability of Serious GI Tract Injury Figure 21 – Probability of Serious Larynx Injury 86
·c:::;
Q..
'--' ID Ear-drum Rupture 10~---.-.-.. -.-.-. . ~.-.-. . -.-.. -.-- --~--~--.-.. ~.-.. -.-.- .. -.-.-.. ~.-.-. . -.-.. -.~--. . . . . .... . ... .. . . . . . . . . . . . . . .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . - 1%
- 10%
- 50%
10..l: - 90% . . . . ... . . . ... . . . . . . . . . . . .......
• • • '• '•' • • ' '• • ' ••I • ' • ' • • • • '• • • • '
- 99% . . . .. .... ......... .. .... .. . . .. . . -~---~ ~ 101
v) ID ·.-':':':':':':':':':':':'. -':':':'.-·"!..~ :':':':':':':':'.-'.:':':':':':':':':'.
....
Q.. ....
ID > 0 ...... . . . . . - . - .. . ........... .
. . . . . . . . . . . . . . . . . . . .. . . . . ... . .. . . . . . . .. . . . .. . . . .
1 o-i- :·: ·: ·:·: ·:·: ·: ·:·: ·: ·:·:·; ·: ·:·:·: ·:·,·.-·:·:· : ·:·:·: ·: ·:·: ·:·:·: ·: ·:·:·:·:·:·:- ·: ·:·: ·:·:·:·: ·:·: . '.'.' .... '.' ..... '•.• .. .. '.'.' . ' '.'.' ...... .. .... . . ' . ... . . ... . .. . . ' . ' .. ' . ' . ' . . .. . . '.' . . . .. . ' .... '. ' ' ... . . ' .... ' . ' .'. ' . ' ' . ' .' . . . . . .. . . . . . '. ' . ' .. ' . ' .'
• • • ' • • • ' • • ' • ' • '•'••I•'•'•••••'• • • • '•' • , :, ' • '' • • • ' • . ' .' .... .. '. ' ..... ' ... .... '. ' .' . ' .. '. ' .. .. .. ... ... .
10·1 .__ __ ~ ___ _.__ __ ~~-----'------' 10-.2 1 ooi- 102 Impulse (psi .msec) 08/02/2024 AC 450.115-1B Figure 22 – Probability of Serious Eardrum Rupture
12.16 People in Structures.
Three propellant fragment impact event scenarios should be considered for evaluating the potential for injuring people in structures. The first scenario is a liquid or solid propellant tank, or solid propellant fragment that impacts the roof of a building leading to its collapse. The second scenario is a burning piece of solid propellant fragment that penetrates the roof without exploding and creates a fire on the floor below. The third scenario is a liquid or solid propellant tank, or solid propellant fragment that impacts away from a building’s roof and creates a blast overpressure wave that damages the wall and windows.
12.16.1 Roof Impact.
The hazard from a liquid or solid propellant tank, or solid propellant fragment, impacting on a roof should be represented as an effective casualty area for people on the floor below. The probability of casualty is 𝑒𝑒𝑐𝑐𝑚𝑚𝑠𝑠𝑠𝑠𝑚𝑚𝑓𝑓𝑔𝑔𝑔𝑔 = 𝐶𝐶𝐴𝐴/𝐴𝐴𝑟𝑟𝐶𝐶𝐶𝐶𝑟𝑟. The probability of impact is computed separately and evaluated over the area of the building roof 𝐴𝐴𝑟𝑟𝐶𝐶𝐶𝐶𝑟𝑟.
The effective casualty area depends on the type of roof and its size. General roof types that should be represented are wood, steel, and concrete. Table 6 of this AC presented a survey of buildings that fall into four general classes, A to D. The A Class is for lighter roofs of more temporary structures. The categories progress to the least vulnerable D Class - roofs of robust commercial structures. This simplified model does not address hazardous debris impacts on blockhouse-type structures.
d 1
0.9
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0.7 - CA-3840 .. i 0 6 --CA-8640 g 0.5 - CA-15360 "' 5 0.4 - CA-29040
0.3 - CA-54000
0.2 - CA-86640
0.1 0
0.1 1 10 100 1000 10000 Yield (lb, TNT) 08/02/2024 AC 450.115-1B
12.16.1.1 A Monte Carlo simulation may be performed to sample impact roof locations, and account made if any joists or beams are at, near, or away from the impact points. Effective casualty area related curves as a function of yield, for these general roof types for a range of roof sizes, are shown in Figure 23, Figure 24, and Figure 25. Roof areas are in units of square feet, and the vertical axis is the ratio of the effective casualty area to the modeled roof area. Wood roof curves are a conservative selection for applying to roof types other than those shown. For a roof area less than 960 ft2 the far-left curve should be used, and for areas larger than 86,640 ft2 the far-right curve.
Figure 23 – Wood Roof Effective Casualty Area Ratio as a Function of Roof Area and Yield 88
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.CA-22500
~ CA-32400 10 100 Yield {lb, TNT) ...... CA-57600 l:J==t1~ -+- CA-90000 t o ia=4 N ......
0.1 1 10 100 Yield (lb, TNT) 1000 10000 1000 08/02/2024 AC 450.115-1B Figure 24 – Steel Roof Effective Casualty Area Ratio as a Function of Roof Area and Yield Figure 25 – Reinforced Concrete Roof Effective Casualty Area Ratio as a Function of Roof Area and Yield 89
12.17 Floor Fire.
The following discussion presents the process for computing the effective casualty area for a fire resulting from a solid propellant fragment penetrating the roof and burning after impacting the floor. The probability of casualty is 𝑒𝑒𝑐𝑐𝑚𝑚𝑠𝑠𝑠𝑠𝑚𝑚𝑓𝑓𝑔𝑔𝑔𝑔 = 𝐶𝐶𝐴𝐴𝑟𝑟𝑚𝑚𝑟𝑟𝑟𝑟/𝐴𝐴𝑟𝑟𝐶𝐶𝐶𝐶𝑟𝑟, and the probability of impact is computed separately and evaluated over the building roof area 𝐴𝐴𝑟𝑟𝐶𝐶𝐶𝐶𝑟𝑟.
12.17.1 The flame from a stationary piece of burning propellant can be modeled in the shape of a cylinder whose base is the cross-section area of the solid propellant chunk, i.e. the fire area, and whose length is the flame height. The reference listed in [12] of paragraph 3.4 of this AC provides further information. The flame over the burning propellant chunk forms a cylinder whose radius is that of the fragment, 𝑒𝑒𝑟𝑟 .
12.17.2 For an HD 1.3 propellant type, the flame height in feet is computed by:
0.4̇=𝐻𝐻𝑟𝑟𝑓𝑓𝑚𝑚𝑚𝑚𝑟𝑟 0.77𝑄𝑄𝑐𝑐𝐶𝐶𝑚𝑚𝑑𝑑𝑠𝑠𝑐𝑐𝑔𝑔𝑚𝑚𝑔𝑔𝑟𝑟 − 2.04𝑒𝑒𝑟𝑟 where 𝑒𝑒𝑟𝑟 is in feet, and the 𝑄𝑄̇𝑐𝑐𝐶𝐶𝑚𝑚𝑑𝑑𝑠𝑠𝑐𝑐𝑔𝑔𝑚𝑚𝑔𝑔𝑟𝑟 is the conductive heat flow rate away from the burning chunk.
12.17.3 The expression for computing the rate is:
𝑄𝑄̇ = 𝑚𝑚 ̇ 4467𝐴𝐴𝑟𝑟 (1 − 𝑅𝑅−5.4𝑟𝑟𝑓𝑓 )𝑐𝑐𝐶𝐶𝑚𝑚𝑑𝑑𝑠𝑠𝑐𝑐𝑔𝑔𝑚𝑚𝑔𝑔𝑟𝑟 where 𝑚𝑚 ̇ is the rate at which the mass of propellant burns in lbs/s, and 𝐴𝐴𝑟𝑟 is the area of the propellant in ft2.
12.17.4 When a person experiences 2nd degree burns over 20 percent of their body, the person is considered to be a casualty. The conduction heat rate can be used to determine when a 50 percent probability of 2nd degree burn occurs. The reference for this information is [22] of paragraph 3.4 of this AC.
1𝑃𝑃50% = �1 + 𝑅𝑅𝑒𝑒𝑒𝑒 �−34.04 + 2.13 𝑆𝑆𝐾𝐾�𝑆𝑆 × 𝑞𝑞4/3��� 2 where t is time elapsed until depletion of propellant mass.
12.17.5 The quantity 𝑆𝑆 ∗ 𝑞𝑞4/3 is referred to as the “heat load.” The heat flux q is in units of W/m2 and computed by:
𝑞𝑞4/3 = 𝑆𝑆−3/8 × �5.38 × 10−0,005𝑟𝑟𝑓𝑓
12.17.6 Representative curves of floor fire effective casualty areas for 2nd degree burns as a function of heat load are given in Figure 26. The room is modeled as circular and the only room in the building. A conservative assumption was made that the people are trapped and cannot escape to another room or outside the building. The curves depend on the ratio of the flame height over diameter of the fire area, H/D.