13 angle)
The basic casualty area is illustrated in figure 2. Note that ‘d’ is the horizontal distance that the debris travels as it falls the height of a person (6 ft) and the impact angle is the angle that the velocity vector makes with the horizontal plane or surface impacted.
Adjustments to account for other effects that may increase casualty area would then be made. Among the effects to be considered are: area increases due to the impacting debris tendency to slide, skid, bounce, ricochet or splatter. Pieces of debris may slide or skid after impact adding to the casualty area as a function of horizontal velocity and the coefficient of friction of the impacted surface. Debris that remains essentially intact may bounce or ricochet along the impacted surface and also add to effective casualty area. If an inert vehicle piece or component impacts an open area, piece fragments or chunks of the impacted surface may be forcefully projected from the point of impact. For high velocity impacts o n hard surfaces such as rock or concrete, fragments and surface chunks may be thrown considerable distances. These effects are mutually exclusive so the conservative approach is to add the
14 largest increase to the basic casualty area to determine the composite casualty area for each piece of debris.
Reference "Casualty Areas from Impacting Inert Debris for People in the Open", Research Triangle Institute Report No. RTI/5180/60 -31F dated April 13, 1995, for a procedure to calculate composite casualty area as well as sample casualty area calculations for existing launch vehicles.
This report is available on AST’s Web Site. Previous analysis of various launch vehicles shows that the effective casualty area of an inert piece of debris represents an increase by a factor of from 1.7 to 7.0 over basic casualty area when the effects of slide, bounce and splatter are accounted for. Originally, basic casualty area was multiplied by 1.5 in order to account for bounce, skip and splatter. Currently used calculation me thods give effective casualty areas that range from 3.0 to 7.0 times greater that the basic casualty area. Therefore, a simple and conservative approach in the calculation of the inert portion of Ac is to apply a factor of 7.0 to the basic casualty area.
3.2.2.2 Explosive Debris . If the debris may explode on impact, equations can be used to calculate effective casualty areas based upon equivalent TNT yields. To account for explosive contributions to casualty area, the propellant or hazardous material is converted to equivalent weight of TNT. An acceptable assumption for the purposes of Ec calculation is a blast overpressure threshold of 3.5 pounds per square inch. A 3.5 psi overpressure will result in eardrum damage to 1% of exposed (unprotected) po pulation. Overpressures as low as 0.5 psi may cause glass breakage that results in casualties to building occupants.
The radius of the explosive debris casualty area is expressed as an equation of the form:
D = K x W1/3
Where: D is the distance (ft), K is a distance scaling factor (ft/lb 1/3), and W is the net equivalent weight of TNT (lb).
The factor K is derived from scaling laws (reference:
Chemical Propulsion Information Agency Publicat ion 394, Hazards of Chemical Rockets and Propellants, June 30, 1985). If D 1 is the distance from a reference explosion
15 of W1 lb of material at which a specified overpressure is found, then for any explosion of W lb of the same material, the same overpress ure will occur at a distance D such that:
D/D1 = (W/W1)1/3.
The distance scaling factor K is defined as
K = D/W1/3 (ft/lb1/3).
W is the TNT equivalent weight and D is the distance from the center of the explosion at which a specific overpressure occurs . In this methodology, the equivalent weight of a particular explosive/propellant is the weight of TNT required to produce an overpressure of equal magnitude produced by a unit weight of the explosive/propellant in question. Acceptable K factors may be obtained from DOD 6055.9 -STD, DOD Ammunition and Explosive Safety Standards, August, 1997 or from CPIA Publication 394, Hazards of Chemical Rockets and Propellants, June 30, 1985.
The explosive equivalent range for credible TNT yields varies from 5 to 50 % for LH2/LOX and 18 to 100% for solid rocket motors (reference: Hazard Analysis of Commercial Space Transportation, OCST -RD-RES01-88, May, 1988). Note that the lower bound for these yields is zero since the propellants may react or burn without producing casualties. Acceptable measures of equivalent TNT explosive yields for various propellants may be obtained from such sources as:
Farber, E.A. and J.H. Deese, A Systematic approach for the Analytical Analysis and Prediction of the Yield from Liquid Propellant Explosions, Tech. Paper 347, Engineering Progress At the University of Florida, March 3, 1966,
Kinsel, T.I., Determination of the TNT equivalency of a Typical Class 1.1 Solid Rocket Propellant (Blast Hazards), AFRPL -TR-80-24, April, 1980,
DOD 6055.9-STD, DOD Ammunition and Explosives Safety Standards, August 1997, and
16 Chemical Propulsion Information Agency Publication 394, Hazards of Chemical Rockets and Propellants, June 30, 1985.
3.2.2.3 Total A c. The contributions of explosive debris to casualty area are added to the casualty area attributed to inert debris to determine effective casualty area Ac. A conservative calculation for Ac would utilize the factor of 7.0 applied to the inert debris basic casualty area in addition to assuming the maxim um explosive casualty area for each phase of the mission.
Conservatively, the effective casualty area may be calculated as:
Aci = 7.0 x Aci(inert) + Aci(explosive).
Note: The summation of each casualty area of each contributor to inert and explosive deb ris is a conservative approach in that it is assumed that no individual debris casualty areas overlap. In actuality, individual areas may overlap, thus reducing the total effective casualty area. A piece of debris is either inert or explosive. If a frag ment could be either, the larger area should be used.
3.2.2.4 Example A c calculations . Ac may decrease as the mission progresses due to propellant consumption, stage separations and payload deliveries. Some vehicles may have large effective casualty are as during the early (low altitude) launch phase when inert and explosive debris contributions are accounted for; while explosive forces at a sufficiently high altitude of liquid fueled vehicles are not an issue other than that they cause breakup and generate debris. A reentry vehicle may not have any explosive material remaining that would impact after a breakup event and the entire Ac may be composed entirely of inert debris. Also the number of fragments of debris will depend on the failure mode and the time or phase in the mission. It may range from a handful of large pieces from a loss of thrust or aerodynamic breakup to several thousand pieces resulting from explosion. As an example, typical multistage expendable launch vehicle casualty areas range f rom 11,000 ft 2 to 20,000 ft 2 during the launch phase and from 500 ft 2 to 2000 ft2 during the late ascent phase. Likewise the number of fragments may range from a few to several thousand (Reference USDOT Office of Commercial Space Transportation, "Baseline Assessment
17 Eastern Space and Missile Center (ESMC)" September, 1988).
The following provides a simple example of an acceptable Ac calculation: A two stage to orbit vehicle breaks up into five inert pieces having basic casualty areas of 10, 30, 50, 80 and 100 ft2; and three impacting explosive pieces of 2, 16 and 54 lbs. Assuming that the TNT equivalency of the explosive pieces is 50%, the TNT equivalent weights are 1, 8 and 27 lbs respectively.
Assuming that the debris falls vertically, the basic casualty area of the inert debris is equivalent to the sum of the basic casualty areas of the inert pieces.
Therefore:
Ac(inert) = 10.+30.+50.+80.+100. = 270 ft 2.
The casualty area is calculated for each explosive piece.
Ac(explosive) = πD2
D = KW1/3 and K is 18 for a 3.5 psi overpressure level which would harm an exposed person (reference: DOD Ammunition and Explosives Safety Standards, DOD 6055.9 - STD, August, 1997). The explosive radii are:
D 1 = 18 x (1)1/3 = 18 ft D2 = 18 x (8)1/3 = 36 ft D 3 = 18 x (27) 1/3 = 54 ft, and
A c(explosive) = π x (182 +362 +542) = 3.14 x 4536.
= 14243 ft 2, and
The basic casua lty area of the inert debris is multiplied by 7.0, to conservatively account for slide, bounce and scatter and then added to the casualty area from the explosive debris. The total casualty area is:
Ac(total) = 7.0 x Ac(inert) + Ac(explosive) = 7.0 x (270) ft 2 + 14243 ft2 = 1890 ft 2 + 14243 ft2 = 16133 ft 2.
Assuming the first stage is successfully separated and the second stage fails, breaking into four inert pieces
18 with maximum cross -sectional areas having equivalent circular radii of 1, 3, 5 and 10 ft, the inert basic casualty area is:
Ac(inert) = π(1 + 1)2 + π(1 + 3)2 + π(1 + 5)2 + π(1 + 10)2 = π(4 + 16 + 36 + 121) = 556 ft 2.
Applying the 7.0 factor to conservatively account for bounce, skip and splatter, the inert casualty area is:
Ac = 7 X 556 ft 2 = 3892 ft2.
An applicant would be responsible for identification of debris characteristics and the calculation of Ac for each failure mode and time in the mission. Once again, a conservative approach to Ac calculation is to apply a factor of seven to the basic casualty area of inert debris and to add the maximum explosive co ntribution for the vehicle over each mission segment. The applicant may make further refinements to the Ac determinations as design, test and operational data allow.
3.2.3 Population Density . As noted in section 3.1, population density in the affected i mpact area is required to calculate Ec. After the launch and reentry trajectory are determined for each mission, those areas that can be affected by impacting debris for the all the failure modes and time of occurrence are identified. The population dens ities exposed in these areas are determined. Acceptable measure of population density areas used to perform the Ec analysis is no larger than a U.S. census block group for the first 100 nautical miles from a launch point and no bigger than a 1 degree latitude by 1 degree longitude grid beyond 100 nautical miles downrange. If there are different population concentrations among a number of areas, it is acceptable to assume that the entire larger area has the highest population density within that area. Thi s approach is conservative because it will overestimate the expected casualty while reducing the number of individual calculations needed. Because it is very conservative, the applicant may decide to refine the approach (e.g., divide any populated area in to smaller areas and determine the probability for each) in order to meet Ec
19 limitations if the simplified approach yields a value in excess of the Ec threshold. Sheltering of the population may also be a factor but is not considered in this advisory circ ular, as noted previously. However, any attempt by the applicant to address sheltering will be considered on a case -by-case basis.
As an example, assume that the vehicle flies for 2 seconds of dwell time over a desert area that includes .02 seconds of d well time over a city within the area.
The desert population density is 5 people per square mile and the city has 10,000 people per square mile. The conservative approach is to assume that the entire 2 seconds is flown over an area with 10,000 people per square mile. The consequence for this 2 second segment of flight is the product of the casualty area and the population density. For a vehicle casualty area of 3892 square feet, from the previous example, the expected casualty of a failure in the area w ith a population of 10,000 people per square mile is:
E ci = Pi x Aci x Dpi = Pi x (3892/(5280 x 5280)) x 10000 = 1.3961 x Pi.
A more complicated and less conservative refinement might be to proportion the flight segment according to dwell time over each area of homogeneous population density.
The result is an expected casualty of:
Eci = Pi x Aci x [(1.98/2.0) x 5 + (.02/2.0) x 10000] = Pi x (3892/(5280 x 5280)) x [.99 x 5 + .01 x 10000] = Pi x .0001396 x 104.95 = 0.01465 x Pi.
The examples presented assume the vehicle and its instantaneous impact point footprint fly a precise trajectory and ground track respectively. However, this is not likely to be the case. Veh icles typically may deviate from the planned flight path, thus the population area exposed may depend on the variance of the vehicle’s position relative to the planned trajectory.
Calculations of the probability of debris impact on populated areas are bas ed on statistical treatment of trajectory downrange and cross -range dispersions. For a
20 normal distribution these equations may take the form of:
Pi = Pi x Px x Py.
Where the equations for Px and Py are:
The x and y values are depicted in figure 3.
Figure 3.
This level of fidelity is beyond the scope of this advisory circular but is presented to illustrate the level of complexity that should be addressed during the Ec
21 determination process.
Population density data may be obtained from publishe d sources such as the U.S. Census Bureau, The United Nations FAO Yearbook, the Guinness World Data Book, the Rand McNally World Atlas and The Carbon Dioxide Information Analysis Center, Oak Ridge National Laboratory Global Population Distribution Database.
To demonstrate the sensitivity of expected casualty ( Eci = Aci x Dpi) to changes in Dpi, consider that if a vehicle with an Aci of 1000 square feet impacts an area with Dpi of
1.0 person per square mile, the expected casualty is .000036 for an impact i n that area. Likewise an area with a population density of 100 people per square mile has an Eci of .0036 and an area with a density of 5000 people per square mile has an Eci of 0.18. To put this in perspective, New York City has an Eci of .853 with 23,7 00 people per square mile, Houston, Texas has an Eci of .108 with Dp of 3,000 and Jacksonville, Florida has an Eci of .029 with Dp equal to 800.
3.3 Example Calculations of E c. As a simple example of an Ec calculation, assume a mission where a vehicle launches from a moderately populated coastal area, enters orbit, reenters and lands in a sparsely populated desert. The time to orbit is 15 minutes. During the first five minutes of flight, any debris would impact on land and for the remaining time to or bit, the debris would impact in the ocean. The reentry time from orbit to landing is 35 minutes with the final 5 minutes over sparsely populated desert (the time in orbit does not contribute to Ec). Ac for the launch segment over land is 16,133 square feet, 3,892 square feet for the over water segment and 500 square feet for the orbit and reentry segments.
The decrease is due to fuel burn, stage separation and payload release. There is a city in the first segment overflight corridor with a Dp of 600 people per square mile. Conservatively, assume that the population density for the launch segment over land is 600 people per square mile. The Dp is zero for the ocean and on orbit segments.
There is a small populated area in the desert with a density of 1 00 people per square mile and this density is assumed to apply over the entire overland mission segment. The mission probability of failure is .05 during the first five minutes, .02 for the remainder of the ascent phase, .01 in orbit (i.e., failure to ree nter)
22 and .02 during reentry. The probability of a successful mission is .85 and the probability of abort during ascent is .05 (assumed to be successful, i.e., no casualties).Therefore the total probability of all identified events totals to 1.0 indicatin g that all possibilities for the mission are accounted for:
Σ Pi = .85 + .05 + .05 + .02 + .01 + .02 = 1.0.
The expected casualty for the mission is:
E c = S Pi x Ai x Di
= (.85) x 0 + (.05) x 0 +
(.05) x 16133 x 600/(5280)(5280) +
(.02) x 3892 x 0 +
(.01) x 500 x 0 +
(.02)(30/35) x 500 x 0 +
(.02)(5/35) x 500 x 100/(5280)(5280)
= 0 + 0 + .01736 + 0 + 0 + 0 +.000005
= .01737
The mission does not meet the allowable Ec of .00003 using conservative assumptions. Adding some measure of fidelity to these assumptions demonstrates the following:
If the vehicle impact are a is only over the city for the last 2 seconds of the over land launch segment and the rest of the segment is unpopulated, the probability of failure over the city becomes (.05)(2/300). Also, the effective casualty area drops to 3892 square feet due to propellant burn -off. Likewise the overland reentry segment is only over the populated area for 10 seconds and the probability of impact becomes (.02)(10/300)(5/35).
Therefore:
Ec = (.85) x 0 + (.05) x 0
+(.05)(298/300) x 16133 x 0
23 + (.05)(2/300) x 3892 x 600/(5280)(5280)
+ (.02) x 3892 x 0
+ (.01) x 500 x 0
+ (.02)(30/35) x 500 x 0
+ (.02)(290/300)(5/35) x 500 x 0
+ (.02)(10/300)(5/35) x 500 x 100/(5280)(5280)
= 0 + 0 + 0 + .0000279 + 0 + 0 + 0 + 0 + .0000002
= .0000281
This is less than the allowable expected casualty value.
This example demonstrates how a simple refinement to a conservative Ec calculation process may produce acceptable results.
As a special example of expected casualty analysis, assume that an applicant wants to define a mission that will satisfy the requirement for an unproven reusable launch vehicle. Failure is assume d impacting in each exposed populated area along its flight. Given that failure is assumed (probability = 1.0) and that the effective casualty areas are defined by the vehicle design, the applicant must solve for allowable population densities that meet t he threshold value of expected casualty (i.e., Ec is less than 30 X 10 -6) throughout the mission.
Assume a two stage to orbit vehicle with the second stage reentering after payload insertion. The maximum casualty areas have been calculated to be 16,133 f t2 during the launch stage, 3,892 ft 2 during the second stage to orbit phase, and 500 ft 2 during the reentry phase. From the risk equation for each phase:
Eci = Pi x Aci x Dpi.
The solution for allowable population density for each phase becomes:
24 Dpi = Eci / (Pi x Aci).
With a failure probability of 1.0, the allowable population densities are:
Dp(launch) = (30. X 10 -6) / 16133ft2/(5280ft/mi) 2 = .0519 people/mi 2
Dp(2nd stage) = (30. X 10 -6) / 3892ft2/(5280ft/mi) 2 = .2149 people/mi 2 Dp(reentry) = (30. X 10 -6) / 500ft2/(5280ft/mi) 2 = 1.6727 people/mi 2
Therefore a mission using an unproven vehicle must be planned to avoid overflight of areas with population densities greater than those calculated in this example.
3.4 Summary. In the calculation of public risk ( Ec), each failure mode, its probability and its consequence must be evaluated to ensure that the 30 x 10 -6 expected casualty threshold for the total mission is not exceeded.
An applicant may elect to simplify the Ec analysis by making conservative assumptions that lead to an overestimation of Ec. These assumptions might include:
(1) Conservative or worst case assignments of probability to the failure mod es,
(2) Applying a factor of 7.0 to the basic casualty area from inert debris,
(3) Applying the maximum casualty area from explosive debris for each phase of flight over the entire phase, and
(4) Applying the population density of a segment within a flight corridor over a larger area having actual population densities equal to or less than this segment.
An applicant may apply refinements that lead to “higher fidelity” expected casualty values in order to meet expected public safety thresholds. These ana lyses will be evaluated on a case -by-case basis to validate assumptions used.
Using an acceptable methodology, such as that detailed in this Advisory Circular, an applicant would be required to demonstrate that the Ec for a proposed mission is equal to