CHAPTER X
Directional Density of Flak Fragments andBurst Patterns at High Altitudes1
Allan Palmer, M.D.
GERMAN 88 MM. HIGH EXPLOSIVE ANTIAIRCRAFT SHELL
The material in this chapter was obtained at the same timethat a survey of missile casualties was being conducted by the MedicalOperational Research Section, Professional Services Division, Office of theChief Surgeon, ETOUSA (p. 547). The survey covered all of the battle casualtiessustained by the Eighth Air Force during a 6 months' period beginning on 1June 1944. More than 99 percent of the flak fragments recovered during thesurvey were probably from German 88 mm. HEAA (high explosive antiaircraft)shells. Only two fragments observed were definitely identifiable as fragmentsfrom shells larger than 88 mm. Because of this, a discussion of Germanammunition will be limited to the 88 mm. shell.
Details of the structure of the shell are contained in USSTAFOrdnance Memorandum No. 5-6, 29 March 1944, and are shown in figure 293. Thefilled weight of the shell is about 21? pounds, the average weight of thefilling is approximately 2 pounds, and the charge-weight ratio is 8.6 percent.The body of the shell which gives rise to the majority of the fragments iscomposed of 0.72 percent carbon steel and its wall averages nine-sixteenths ofan inch in thickness. The mean burst velocity of fragments observed in trialscarried out at Millersford was 2,280 f.p.s. The velocity of the projectile atthe instant of burst at the altitude at which the shell is fired at heavy bomberaircraft is estimated to range from 1,000 to 2,000 f.p.s., being greatest whenthe angle of fire is nearest vertical and lowest the more the angle of firedeviates from the vertical.
In order to bring out certain points with respect to the flakrisk run by aircrew personnel, it is necessary to consider certain elementaryfacts relating to the manner in which the shell wall breaks up into fragments.For the sake of simplicity, certain properties of the static burst of acompletely spherical projectile breaking up over its entire surface intofragments of uniform weight and size, all traveling at the same velocity, willbe considered.
1The mathematical treatment of the data in this report was provided by the combined efforts of Prof. Sir Ronald A. Fisher, Sc. D., F.R.S., Department of Genetics, University of Cambridge, Cambridge, England, and Prof. F. Yates, Sc. D., F.R.S., Department of Statistics, Rothamsted Experimental Station, Harpenden, Herts, England.
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FIGURE 293.-Structure of German 88 mm. HEAAshell.
Considering the distribution of fragments from such a projectileafter they had traveled, say, 100 feet from the point of burst, would amount toconsidering the distribution of fragments in a sphere whose radius was 100 feet.Since the projectile broke up uniformly, the relative density of fragments-thatis, the number of fragments per unit area on the surface of the sphere-wouldbe the same all over the sphere. Since, however, the annular bands subtended onthe surface of the sphere, per unit angle at its center with respect to theequatorial plane, decrease in area as one proceeds from the "equator"to its "north or south pole," the number of fragments in each annuluswill decrease accordingly in spite of the fact that the density per unit surfacearea remains the same. This is shown in table 233 and figure 294. Column 1 ofthe table lists the annular zones with respect to the equatorial plane in 30?bands. Column 2 indicates the percent of fragments which will be found insuccessive annular zones on the surface of the sphere, if the boundary of eachof these zones subtends an angle of 30? at the center of the sphere. Column 3is merely a statement that the density per unit area on the surface of thesphere is constant.
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FIGURE 294.-Diagrammatic representation ofdirectional fragmentation density of a spherical burst.
TABLE 233.-Directionalfragmentation densities for a static spherical burst
(1) | (2) | (3) |
| Degree | ||
90 to 60 | 6.7 | 1 |
60 to 30 | 18.3 | 1 |
30 to 0 | 25.0 | 1 |
0 to -30 | 25.0 | 1 |
-30 to -60 | 18.3 | 1 |
-60 to -90 | 6.7 | 1 |
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These figures provide a basis for standardizing values forfragmentation density for shells of different types in different zones aroundthe burst. Such standardized values will be referred to in the followingparagraphs as "directional fragmentation densities."
In actual fact, the concept of a spherical burst is entirelytheoretical. Antiaircraft shells are not spherical, and their fragments aredispersed from the bursting projectiles in annular zones of varying density.This is shown in tables 234, 235, and 236 and in figure 295 which give theresults of certain
trials in which AA shells were detonated experimentally insuch a way that it was possible to measure the number of fragments in differentannular zones with respect to the equatorial plane of the shell (that is, theequatorial plane being at right angles to the axis of the shell and cuttingthrough its center).
Figure 294, constructed from the data in table 233, may beregarded as the diagrammatic representation of a spherical burst from whichthere is a uniform distribution of fragments and for which the relativedirectional fragmentation densities (D) are the same. The values of 1 forthe densities in all directions are shown by the constant length of the radii ofthe circle (representing a sphere) in zones of 30? with respect to theequatorial plane. The values under A (column 2 of table 233) are thoseareas of the annular bands expressed in percentages of the total area of thesphere, subtended
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by 30? angles at its center with respect to the equatorial plane. Theseareas are projected in figure 294.
Consider next a variation from a spherical burst. For example, a value of 5in column 3 of table 233 for a given annular zone would mean a density offragments per unit area on the surface of the sphere relatively five times asgreat as would be expected for a spherical burst. The fivefold increase in thiszone would involve relative decreases in densities in other zones. The valuesfor directional fragmentation density as used are representations of densitiesper unit solid angle. Because of the lack of complete fragmentation data for anyof the burst patterns to be discussed, a relative value as opposed to anabsolute value is desirable.
Fragmentation trials on three rounds of the German 88 mm. HEAA shell wereconducted at Millersford.2 The shells were setup vertically, nose down, 5 feet above the ground. For each detonation, two setsof three strawboard panels, 10 feet high by 40 and 60 inches wide, were placedvertically 5 feet and 10 feet from the shell and so staggered that they did notoverlap each other. For each trial, the number of strikes was counted on thepanels in such a way as to separate the strikes that occurred at 10-inchintervals above and below the equatorial plane of the center of the shell.Column 1 of table 234 indicates those zones in inches. Column 2 specifies thosezones in terms of the angle each subtended at the center of the shell. Columns 3and 4 show the number and percent of fragments observed in each zone.
TABLE 234.-Directionalfragmentation densities of German 88 mm. HEAA shell
(1) | (2) | (3) | (4) | (5) | (6) |
| Inches | |||||
50 to 60 | 5?12' | 24 | 2.0 | 3.3 | 0.6 |
40 to 50 | 6?7' | 46 | 3.8 | 4.3 | .9 |
30 to 40 | 7?7' | 80 | 6.5 | 5.3 | 1.2 |
20 to 30 | 8?8' | 33 | 2.7 | 6.5 | .4 |
10 to 20 | 8?58' | 37 | 3.1 | 7.6 | .4 |
0 to 10 | 9?28' | 495 | 40.4 | 8.3 | 4.9 |
-10 to 0 | 9?28' | 253 | 20.5 | 8.3 | 2.5 |
-20 to -10 | 8?58' | 63 | 5.1 | 7.6 | .7 |
-30 to -20 | 8?8' | 54 | 4.4 | 6.5 | .7 |
-40 to -30 | 7?7' | 61 | 4.9 | 5.3 | .9 |
-50 to -40 | 6?7' | 54 | 4.5 | 4.3 | 1.1 |
-60 to -50 | 5?12' | 21 | 2.1 | 3.3 | .6 |
90?0' | 1,221 | 100.0 | 70.6 |
NOTE.-Table, based on data obtained at Millersford trials,shows conversion of fragment distribution in 10-inch zones at 5 feet detonationdistance into relative directional densities.
2Armament Research Department Explosives Report 224/43, October 1943.
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A value for directional fragmentation density in any zone may be obtainedfrom the equation
D = n / A
in which n is the number of fragments observed in the zone, expressedas the percentage of the total number of fragments observed, and A is thearea of the annular band on the surface of a sphere subtended by an angle at itscenter, expressed as the percentage of the total surface area of a sphere.Values for A may be obtained from the equation entered as a note infigure 294.
It should be emphasized that figure 294 is a two-dimensional drawingrepresenting a three-dimensional burst pattern. Thus, the radius in figure 294that deviates 30? from the vertical would describe a relatively small conesubtending the "north polar" surface of a sphere, whereas the radiusthat makes a 30? angle with the equatorial plane would describe an annular zoneon the surface of a sphere comparable to the northern half of the Torrid Zone onthe surface of the earth.
In the Millersford trials, no observations were made about the densities offragments projected upward from the base and downward from the nose of theshell. If the burst is regarded as a spherical projection of fragments from thecenter of the projectile, the unobserved zones (shaded in fig. 295A) above andbelow the 90? zone, in which observations on fragmentation were not made,account for 29.4 percent of the surface area of the sphere. The 1,221 fragmentsnoted in table 234, while they represent 100 percent of the observed number offragments dispersed by an 88 mm. shell, were dispersed in directions whichrepresent only 70.6 percent of what would be expected for a spherical burst(column 5 of table 234). Previous experience has shown that the number offragments dispersed upward and downward in the unobserved zones in similarexperiments is negligible.
Figure 295A shows for comparison with a spherical burst (fig. 294) the burstpattern of a nose-down 88 mm. shell detonated statically. It is pointed outagain that the lengths of the lines or radii from the point of burst (D,column 6 in table 234) are measures of relative directional fragmentationdensities.
A report by the Operational Analysis Section, Mediterranean Allied Air Forces3gives the observed data pertaining to fragment distribution from a staticallydetonated, nose-up, U.S. 90 mm. HE shell. Tables 235 and 236 are similar totable 234 except that the annular zones in which fragments were counted arespecified only by the angles by which they are subtended at the center of theburst (column 1).
3Report, Operational Analysis Section, Mediterranean Allied Air Force, subject: The Physical Basis for Evasive Action to Reduce Flak Losses, May 1944.
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TABLE 235. -Directional fragmentationdensities for U.S. 90 mm. shell, static burst
(1) Zone (with respect to the equatorial plane) | (2) Number of fragments observed | (3) Percent (n) of fragments observed | (4) Corresponding values for spherical burst (percent) (A) | (5) Density |
-90? to -20? | 0 | 0 | 32.90 | 0 |
-20? to -5? | 441 | 50.9 | 12.74 | 3.95 |
-5? to 10? | 300 | 34.6 | 13.04 | 2.66 |
10? to 20? | 39 | 4.5 | 8.42 | .54 |
20? to 40? | 40 | 4.6 | 15.04 | .31 |
40? to 60? | 20 | 2.3 | 11.16 | .21 |
60? to 70? | 7 | .8 | 3.68 | .22 |
70? to 80? | 10 | 1.2 | 2.25 | .53 |
80? to 85? | 7 | .8 | .57 | 1.40 |
85? to 90? | 3 | .3 | .19 | 1.58 |
867 | 100.0 | 100.0 |
(1) Zone (with respect to the equatorial plane) | (2) Number of fragments observed | (3) Percent (n) of fragments observed | (4) Corresponding values for spherical burst (percent) (A) | (5) Density |
90? to 25?59' | 0 | 0 | 71.90 | 0 |
25?59' to 35?35' | 441 | 50.9 | 7.20 | 7.07 |
35?35' to 44?40' | 300 | 34.6 | 6.06 | 4.03 |
44?40' to 50?33' | 39 | 4.5 | 3.46 | 1.30 |
50?33' to 62?02' | 40 | 4.6 | 5.55 | .83 |
62?02' to 73?18' | 20 | 2.3 | 3.73 | .62 |
73?18' to 78?58' | 7 | .8 | 1.18 | .68 |
78?58' to 84?27' | 10 | 1.2 | .69 | 1.74 |
84?27' to 87?13' | 7 | .8 | .17 | 4.70 |
87?13' to 90?00' | 3 | .3 | .06 | 5.00 |
867 | 100.0 | 100.0 |
The divergence of the burst pattern of a shell from the burstpattern of a theoretical spherical projectile can easily be demonstrated if onefirst calculates the percent of all fragments which would be expected in thearea of each annular zone of a sphere which would be subtended by the anglesindicated in column 2 of table 234 and column 1 of tables 235 and 236. Thesepercentages are determined in the same way as those calculated for column 2 oftable 233. The values obtained are shown in column 5 of table 234 andcolumn 4 of tables 235 and 236. Since the density of strikes per unit area inthe theoretical spherical burst is unity, the divergence of the actual fragmentpattern
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of a shell for each annular zone is given by the ratio of thepercent of fragments observed in each zone to the percent of fragments expectedin that zone had the burst been that of the theoretical spherical projectile.These ratios, which are referred to as the directional fragmentation densities,are shown for the three projectiles
in columns 6, 5, and 5, of tables234, 235, and 236, respectively.
Figure 295B and C shows the burst patterns of the U.S. 90 mm.shell detonated statically and in motion. The static burst patterns of theGerman 88 mm. and the U.S. 90 mm. shells are approximately similar when one orthe other is inverted. The apparent differences in figure 295A and B are due tothe fact that the 88 mm. was nose down while the 90 mm. was nose up.
AIRCRAFT BATTLE DAMAGE DATA
Density of Flak Hits on Aircraft
If all AA shells were fired vertically, the burst patternshown in figure 295C would represent the directional fragmentation densities offlak in the atmosphere. This figure would also represent the relative importanceof the different directions from which protection would be required by aircrewpersonnel in heavy bombers. However, an enemy AA battery may fire at a formationof heavy bombers throughout approximately 12 miles (3 minutes) of the bombers'flight course and is actually unable to fire directly vertically. Therefore,fragments from bursting projectiles from one battery are likely to produce acomposite burst pattern that differs from that of shells bursting only in avertical orientation.
It was thought desirable to construct a composite burstpattern that would represent the aggregate of flak bursts that actually occurunder operational conditions. In order to do this, the frequency of flak hits onplane horizontal and vertical surfaces of a sample of aircraft was determined.All the B-17 and B-24 aircraft that were hit by flak and returned to the UnitedKingdom during July 1944 were examined. If the number of MIA aircraft due toflak damage were sufficiently great, the distribution of flak hits on them mightmaterially influence the observations made on the July sample of aircraft.Accurate data as to how many MIA aircraft were lost because of damage due toflak were not available. However, 15 percent of MIA personnel were evaders whoreturned to the United Kingdom and who were interrogated by representatives ofthe Operational Research Section, Eighth Air Force. It is estimated on the basisof information obtained from the personnel questioned that approximately 60percent of both types of MIA aircraft were lost because of damage due to flakduring July 1944. During that month, 134 B-17's and 107 B-24's were missingin action. Thus, 3,053 B-17 aircraft, of which 2,973 were examined and of whichapproximately 80 (2.6 percent) were missing in action, were possibly damaged byflak. Also, 958 B-24 aircraft, of which 894 were examined and of
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FIGURE 296.-Location of flak hits on 2,961B-17 aircraft, plane surfaces only.
which approximately 64 (6.7 percent) were missing in action,were possibly damaged by flak. It is unlikely that the small incidence of MIAflak-damaged aircraft, could they have been included in the analysis, would havegreatly changed the observations pertaining to either type of aircraft.
Only the flat portion of the main wings lateral to thenumbers 1 and 4 engines and the "unprotected" surfaces of the verticalstabilizers of both aircraft were used for these observations. Figures 296 and297 show the location of flak hits on the plane surfaces of the two types ofaircraft. The surface areas were determined by planimeter measurements of scaledrawings of the aircraft and are given in column 1 of table 237. This tableshows the data obtained from the battle damage reports for 2,961 B-17's and888 B-24's. The manner of
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FIGURE 297.-Location of flak hits on 888 B-24aircraft, plane surfaces only.
calculating the "standardized" densities of hits onplane surfaces was the same as that given for the calculation of"standardized" directional fragmentation densities, and the valuesobtained are given in column 6 of table 237.
The figures in columns 3 and 6 of table 237 show that thegreatest density of hits occurred on the bottom surfaces of B-17 aircraft. Thedensity of hits on vertical surfaces was only slightly less, whereas the densityof hits on top surfaces was approximately one-third as great as that on bottomor vertical surfaces.
Corresponding figures for B-24 aircraft (columns 3 and 6)show that vertical surfaces suffered the greatest density of flak hits. Thelatter was 54 percent
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Surface struck | (1) | (2) | (3) | (4) | (5) | (6) |
B-17 aircraft: | ||||||
| Top | 368 | 487 | 0.45 | 6.4 | 16.7 | 0.38 |
| Bottom | 368 | 1,554 | 1.43 | 20.3 | 16.7 | 1.22 |
| Sides | 156 | 598 | 5.16 | 73.3 | 66.6 | 1.10 |
| Total | 892 | 2,639 | 7.04 | 100.0 | 100.0 | |
B-24 aircraft: | ||||||
| Top | 272 | 143 | 0.59 | 5.8 | 16.7 | 0.35 |
| Bottom | 272 | 327 | 1.35 | 13.2 | 16.7 | .79 |
| Sides | 194 | 359 | 8.32 | 81.0 | 66.6 | 1.22 |
| Total | 738 | 829 | 10.26 | 100.0 | 100.0 |
1Data calculated per square foot per 1,000aircraft.
NOTE.-Figures in parentheses for one side only.
greater than the density of hits on bottom surfaces and three and a halftimes the density of hits on top surfaces. The figures in column 3 (table 237)show in general a slightly greater density of flak hits per unit surface area onB-24 than on B-17 aircraft. There was an average density of 1.00 hit per squarefoot on B-17's as compared with 1.26 per square foot on B-24's.
Directional Density of Flak in Relation to Distribution ofObserved Hits
The densities of flak hits on different plane surfaces cannot be regardeddirectly as representing the densities of fragments proceeding in space in givendirections. It stands to reason that only a small part of the total density ofhits on a plane surface are caused by fragments which struck it normally. If thedensities of flak hits on a large number of aircraft, the plane surfaces ofwhich were oriented in several different directions in space (say six), wereknown, it would be possible to calculate the directional fragmentation densitiesof flak fragments to which the aircraft were exposed. With plane surfacesoriented in three directions only, as in the present case, the data are notadequate to make an exact determination of directional fragmentation densities.In other words, a number of different sets of directional fragmentationdensities
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can be calculated, all of which will give the densities of hits on planehorizontal and vertical surfaces which were actually observed.
One such set of directional fragmentation densities, which may be regarded asthe distribution of flak in the atmosphere to which B-17 aircraft were exposed,is shown diagrammatically in figure 298A. The standardized values of r(θ)in table 238 were calculated from the equation
r(θ) = a+bcos θ+c cos2θ+d cos3θ
in which a, b, c, and d are constants that were solvedso that the equation would fit the observed densities of hits on the planehorizontal and vertical surfaces of the aircraft. They are represented in thecomposite burst pattern (fig. 298A) by the length of the radii from the point ofburst.
TABLE 238.-Directionalfragmentation densities of flak against B-17 aircraft
(1) | (2) |
| Degree | |
10 | 0.08 |
30 | .12 |
60 | .72 |
290 | 1.40 |
120 | 1.48 |
150 | .88 |
3180 | .32 |
1Vertically downward.
2Horizontally.
3Vertically upward.
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The number of flak fragments striking an object will vary directly with thesurface area it presents and inversely with the square of the distance from thepoint of a burst. The densities of hits will be further influenced by the shapeof the target and its movement in space. The figures in column 3 of table 237are absolute values and those in column 6 of the same table are standardizedvalues for the densities of hits on the plane surfaces of B-17 aircraft. Incontrast, the figures in column 2 of table 238 represent relative values fordirectional fragmentation densities of fragments dispersed in space from thepoint of a burst. These values are represented graphically in the compositeburst pattern shown in figure 298A. Relative directional fragmentation densitiesare measures of the densities of fragments dispersed in different directionstoward aircraft and in this case may be regarded as constant for the altitude atwhich the B-17's operate. These directional fragmentation densities will notvary or be influenced by any of the factors which determine variations in thedensity of hits received on different surfaces of the B-17's.
The mathematical form chosen to determine relative values fordirectional fragmentation densities of fragments which would account for theobserved distribution of hits displayed in table 237 (for B-24 aircraft)
r(θ) =a+b cos θ+c cos2θ+d cos3θ+e cos4θ+f cos5θ
has the defect that it does not immediately yield a reasonablecurve to account for the observed densities of hits. This failure is notnecessarily due to any special feature of the directional fragmentation densitydistribution for the B-24. The standardized values of r(θ)in table 239 are the "smoothed" values calculated from theequation.
Figure 298B is a diagrammatic representation of the values incolumn 2 of table 239. It shows a pattern of directional fragmentation densitieswhich will account for the observed densities of hits on B-24 aircraft. Thesmoothed parts of the curve are indicated by dotted lines.
Density of Flak Hits on Fuselages of Aircraft
It is the hits on fuselages of aircraft which principally causecasualties, and therefore it was thought worthwhile to determine the densitiesof flak hits on the fuselages of the two types of aircraft. Actually, thestandardized values for such hits should agree with those for hits on planesurfaces. Flak hits on MIA aircraft, while they might not have influenced theobserved densities and distribution on plane surfaces, might materially affectthe observed density and distribution of hits on the more vital fuselagesurfaces, could they have been included in the observations. Differences couldbe due in part to the personal error introduced by the engineer officer whomakes a record of flak damage to an aircraft and who has to distinguish betweenhits on the top and side or side and bottom of a tapering cylindrical structurewhose curved surfaces cannot readily be demarcated from each other.
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TABLE 239.- Directional fragmentationdensities of flak against B-24 aircraft
| (1) | (2) |
Degree | |
| 10 | 0.01 |
| 30 | .01 |
| 40 | .03 |
| 50 | .08 |
| 60 | .52 |
| 70 | 1.06 |
| 80 | 1.60 |
| 290 | 1.97 |
| 100 | 1. 95 |
| 110 | 1. 75 |
| 120 | 1. 32 |
| 130 | .79 |
| 140 | .33 |
| 150 | .09 |
| 3180 | .03 |
1Vertically downward.
2Horizontally.
3Vertically upward.
However, the greatest differences are more likely to be dueto "selection." In general, the greatest density of hits by flak oncertain regions of the fuselage vital for an aircraft's safe return to theUnited Kingdom could not be included in the observations. The sample of aircraftstudied for hits on the fuselage would be biased in favor of aircraft struck inregions of the fuselage not vital to the aircraft's return.
Column 6 of table 240 gives the standardized densities offlak hits on the fuselages of B-17 and B-24 aircraft. The projected surfaceareas chosen for the observations do not include the bomb bay or those portionsof the sides of the fuselage protected by the main wings. The samples of 2,973B-17 and 894 B-24 aircraft used include the 2,961 B-17's and 888 B-24'sreferred to previously. Figure 299 shows the location of flak hits on theprojected surfaces for which the relative densities were determined.
Table 240 for B-17's shows a somewhat different order ofdensities of fuselage hits when compared with hits on plane surfaces; that is,the greatest density appears to be on the sides instead of on the bottom of thefuselage. The ratio of densities for hits on top and bottom surfaces is 1:1.8 ascompared with 1:3.2 for densities of hits on plane surfaces, and the density ofhits on the sides is twice that for hits on the bottom. Table 240 for B-24'salso shows the greatest density of hits on the sides of the fuselage and achange in the ratio of densities on top and bottom surfaces from 1:2.3 to 1:0.7.The deficiencies of hits on bottoms of fuselages, as shown by decreases in theratios
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of top to bottom bits for both types of aircraft, may beregarded as hits sustained by MIA aircraft. In other words, aircraft shot downby flak probably sustained hits chiefly on the bottoms of fuselages. Could thesehits have been included in the observations, they probably would be sufficientto restore the observed ratios of top to bottom fuselage hits so that they wouldcorrespond to the ratio of top to bottom plane surface hits. The differencesobserved between the densities of hits on plane and fuselage surfaces of allaircraft will be compared later with the differences between the densities onthe plane and fuselage surfaces of casualty-bearing aircraft.
Surface struck | (1) Projected | (2) Hits | (3) Number of observed hits1 | (4) Percent (n) observed hits1 | (5) Percent (A) expected hits assuming random distribution | (6) Standardized densities (D= |
B-17 aircraft: | ||||||
| Top | 408 | 293 | 0.24 | 5.8 | 16.7 | 0.35 |
| Bottom | 408 | 537 | .44 | 10.6 | 16.7 | .63 |
| Sides | 430 | 1,106 | 3.48 | 83.6 | 66.6 | 1.26 |
| Total | 1,246 | 1,936 | 4.16 | 100.0 | 100.0 | |
B-24 aircraft: | ||||||
| Top | 270 | 170 | .70 | 10.6 | 16.7 | .63 |
| Bottom | 270 | 120 | .50 | 7.6 | 16.7 | .46 |
| Sides | 540 | 653 | 5.4 | 81.8 | 66.6 | 1.23 |
| Total | 1,080 | 943 | 6.60 | 100.0 | 100.0 |
1Data calculated per square foot per 1,000 aircraft.
NOTE.-Figures in parentheses for one side only.
Density of Flak Hits on Casualty-Bearing Aircraft
In a selected sample of casualty-bearing aircraft, one mightexpect to find an increase in the number and variations in the distribution offlak hits on all surfaces generally. The casualty-bearing portion of theaircraft, that is, the fuselage, in a sample selected for casualties might beexpected to show the greatest increases in density and variations in thedistribution of hits. The observed relationship between flak hits and casualtiesis likely to be greatly different from observations that would include MIAflak-damaged casualty-bearing aircraft. The fatality rate in MIA aircrewpersonnel is known to be
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approximately 20 percent. Such a high fatality rate wouldcorrespond to an even greater casualty rate. Thus, it is likely that most MIAaircraft due to flak damage were also casualty-bearing aircraft. If all MIAflak-damaged aircraft were to be regarded as bearing one or more flakcasualties, then there were approximately 781 B-17 flak-damagedcasualty-bearing aircraft during June, July, and August 1944. Of this number,461 aircraft returned and were examined and 320 (41 percent) were not examined(86 returned and not examined and 234 MIA). There were 465 B-24 flak-damagedcasualty-bearing aircraft during the same period. Of this number, 172 aircraftreturned and were examined and 293 (63 percent) were not examined (112 returnedand not examined and 181 MIA). Such proportions of casualty-bearing aircraft,for which observations were not available, would therefore greatly alter theflak-damage data pertaining to both types of aircraft.
Tables 241 and 242 show the densities of flak hits for planesurfaces and fuselages of all the aircraft examined in which there were flakcasualties. The aircraft concerned were examined in the same way and by the samepersonnel who examined all aircraft to which the data in tables 237, 238, 239,and 240 pertain. Figures 300 and 301 show the location of flak hits oncasualty-bearing B-17 and B-24 aircraft from which the data in tables 241and 242 were obtained.
TABLE 241.-Densities of flak hits on 461 B-17aircraft in which there were 539 battle casualties
Surface struck | (1) Area1 | (2) Hits | (3) Number of observed hits2 | (4) Percent (n) observed hits2 | (5) Percent (A) expected hits assuming random distribution | (6) Standardized densities |
Plane surfaces only: | ||||||
| Top | 368 | 236 | 1.39 | 8.6 | 16.7 | 0.51 |
| Bottom | 368 | 485 | 2.86 | 17.6 | 16.7 | 1.05 |
| Sides | 156 | 215 | 11.96 | 73.8 | 66.6 | 1.11 |
| Total | 892 | 936 | 16.21 | 100.0 | 100.0 | |
Fuselage only: | ||||||
| Top | 408 | 288 | 1.53 | 9.4 | 16.7 | .56 |
| Bottom | 408 | 218 | 1.16 | 7.1 | 16.7 | .43 |
| Sides | 430 | 675 | 13.60 | 83.5 | 66.6 | 1.25 |
| Total | 1,246 | 1,181 | 16.29 | 100.0 | 100.0 |
1Projected for "fuselage only."
2Data calculated per square foot per 1,000 aircraft.
NOTE.-Figures in parentheses for one side only.
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TABLE 242.-Densities of flak hits on 172 B-24 aircraft in which there were 193 battle casualties
Surface struck | (1) | (2) | (3) | (4) | (5) | (6) |
Plane surfaces only: | ||||||
| Top | 272 | 65 | 1.39 | 4.9 | 16.7 | 0.29 |
| Bottom | 272 | 205 | 4.38 | 15.5 | 16.7 | .93 |
| Sides | 194 | 188 | 22.52 | 79.6 | 66.6 | 1.20 |
| Total | 738 | 458 | 28.29 | 100.0 | 100.0 | |
Fuselage only: | ||||||
| Top | 270 | 107 | 2.30 | 8.0 | 16.7 | .48 |
| Bottom | 270 | 73 | 1.57 | 5.4 | 16.7 | .32 |
| Sides | 540 | 580 | 25.0 | 86.6 | 66.6 | 1.30 |
| Total | 1,080 | 760 | 28.87 | 100.0 | 100.0 |
1Projected for "fuselage only."
2Data calculated per square foot per 1,000 aircraft.
NOTE.-Figures in parentheses for one side only.
Column 3 of table 243 (compare with column 1) showssignificant increases in the number of flak hits on plane surfaces of B-17aircraft. The standardized values given in columns 3 and 1 of table 244,however, show no change in the relative density of hits on vertical surfaces.However, there is an apparent decrease in the ratio of hits on top and bottomsurfaces of casualty-bearing B-17's, from 1:3.2 to 1:2.1(36 percentdecrease).
Column 4 of table 243 (compare with column 2) shows evengreater increases in the density of flak hits on the fuselages ofcasualty-bearing B-17's. The standardized values in columns 2 and 4 of table244 show again no change in the relative density of hits on the sides of thefuselages. However, there is an apparent decrease in the ratio of top to bottomhits from 1:1.8 for the fuselages of all B-17's to 1:0.8 for the fuselagesof casualty-bearing B-17's (57 percent decrease).
Column 7 of table 243 (compare with column 5) shows greatlyincreased densities of flak hits on plane surfaces of casualty-bearing B-24aircraft. The standardized values for the B-24 in columns 5 and 7 of table 244show, as in the case of B-17 aircraft, no significant difference in therelative density of hits on vertical (sides) surfaces of casualty-bearingaircraft. However, in contrast to a reduced ratio of top to bottom hits on planesurfaces of B-17's, there appears to be an increased ratio of top to bottomhits on plane surfaces of casualty-bearing B-24's from 1:2.3 to 1:3.2 (42percent increase).
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Surface struck | (1) | (2) | (3) Plane surface3 (casualty- | (4) | (5) | (6) | (7) | (8) |
Top | 0.45 | 0.24 | 1.39 | 1.53 | 0.59 | 0.70 | 1.39 | 2.30 |
Bottom | 1.43 | .44 | 2.86 | 1.16 | 1.35 | .50 | 4.38 | 1.57 |
Sides | 5.16 | 3.48 | 11.96 | 13.60 | 8.32 | 5.4 | 22.52 | 25.0 |
| Total | 7.04 | 4.16 | 16.21 | 16.29 | 10.26 | 6.60 | 28.29 | 28.87 |
1Data are from column 3, table 237.
2Data are from column 3, table 240.
3Data are from column 3, table 241.
4Data are from column 3, table 242.
NOTE.-Figures in parentheses are for one side only.
TABLE 244.- R?sum? of standardized densities for B-17 and B-24 aircraft
[Data represent number of hits per square foot per 1,000 aircraft]
Surface struck | (1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) |
Top | 0.38 | 0.35 | 0.51 | 0.56 | 0.35 | 0.63 | 0.29 | 0.48 |
Bottom | 1.22 | .63 | 1.05 | .43 | .79 | .46 | .93 | .32 |
Sides | 1.10 | 1.26 | 1.11 | 1.25 | 1.22 | 1.23 | 1.20 | 1.30 |
1Data are from column 6, table 237.
2Data are from column 6, table 240.
3Data are from column 6, table 241.
4Data are from column 6, table 242.
Column 8 of table 243 (compare with column 6) shows greatlyincreased densities of flak hits on the fuselages of casualty-bearing B-24's.The standardized values in columns 6 and 8 of table 244 show a very slight (5 percent) decrease in the relative density of side hits and a slight apparentdecrease in the ratio of top to bottom hits on casualty-bearing B-24's from1:0.7 to 1:0.67 (8 percent decrease).
The analysis of hits on casualty-bearing B-17 aircraftlisted in table 241 shows deficiencies of flak hits on the bottom surfacesprimarily of the fuselage and secondarily of the planes. These data suggest thatMIA B-17 aircraft due to flak damage were lost primarily due to hits on thebottom surfaces of
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the fuselage and thus possibly due in part to the occurrenceof casualties produced by these hits. The "moth-eaten" appearance inthe distribution of hits on the bottom of the fuselages of casualty-bearing B-17's,shown in figure 300B in the regions carrying personnel and parts vital to theaircraft's safe return, further supports this possibility. Hits on the ballturret, a combat position relatively unimportant as far as the integrity of theaircraft is concerned, appear to be distributed normally.
The analysis of hits on casualty-bearing B-24 aircraftlisted in table 242 shows deficiencies of flak hits primarily on the topsurfaces of planes and secondarily on the sides and bottom of the fuselages.These data suggest that MIA B-24 aircraft due to flak damage were lostprimarily because of hits on the top surfaces of planes and only secondarilybecause of hits on the sides and bottom of their fuselages. Figure 301B alsoshows a somewhat moth-eaten appearance in the distribution of flak hits on thebottom of the fuselages. However, the disturbed distribution of hits observed oncasualty-bearing B-24's suggests that MIA aircraft of that type, due toflak, were more likely lost because of damage to mechanical parts rather than tothe production of casualties.
Directional Fragmentation Density of Flak That Caused Casualties
If a man were suspended in the atmosphere in which flak shells were bursting, unprotected by armor or any part of an aircraft, hewould be exposed to a distribution of flak fragments as shown in figure 298A ifhe were at the altitude at which B-17's operate or, as shown in figure 298B,if he were at the altitude at which B-24's operate. However, since a man isin a heavy bomber, he is protected in varying degrees by different parts of theaircraft, by its armament, by the proximity of other men in the aircraft, andusually by body armor either worn or placed in various positions about hisaircrew station. The observations made from an analysis of the directionalfragmentation density of flak that had caused casualties would differ from thosemade from an analysis of hits on the outer surfaces of aircraft since many ofthe fragments flying in space would first strike the exterior of the aircraft,some object within, or body armor and be stopped, thus preventing a casualtyfrom occurring. In other words, the flak fragments that caused casualties wouldappear to be most reduced in density in the directions from which the man hadthe best protection and most increased in density in the directions from whichhe had the least protection. If the unobserved hits on MIA casualty-bearingflak-damaged aircraft would materially affect the observations made oncasualty-bearing B-17's and B-24's, then the unobserved hits causingcasualties among MIA personnel would be likely to have an even greater effect onthe observations made on flak casualties sustained in the two types of aircraft.
It was possible to determine the direction traveled by theflak fragments that caused 545 casualties in B-17's and 215 casualties in B-24's.The location of flak hits on the battle damage reports for the aircraft in whichthe casualty occurred, the location of the wounds on the casualty, the directionof the wound
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track, and the wounds of entrance and exit were all takeninto account to determine in which of four "directional zones" theflak fragment which caused each wound traveled. The four directions that werearbitrarily chosen were 45? zones with respect to the equatorial plane. Allwounds that were caused by fragments traveling vertically downward or in adownward direction deviating not more than 45? from the vertical were groupedin the 0?-45? zone. Wounds caused by fragments traveling downward in thezone between the horizontal and 45? below the horizontal were grouped in the45?-90? zone. Wounds caused by fragments traveling upward in the zonebetween the horizontal and 45? above the horizontal were grouped in the 90?-135?zone. Wounds caused by fragments traveling vertically upward or in an upwarddirection deviating not more than 45? from the vertical were grouped in the135?-180? zone. Wounds that could not definitely be placed in one of thesefour zones were not included in the analysis. Tables 245 and 246 show thegrouping of wounds or "hits," by zones, sustained by the casualties inthe two types of aircraft.
The standardized densities of hits causing casualties givenin column 6 of tables 245 and 246 were obtained by correcting for the varyingprojected areas of the body (column 1 of the tables). The projected area of aman viewed at an angle of 0? is taken to be 2.3 (1+0.9 sin θ) squarefeet. This formula, though approximate, agrees with the observed projected areasufficiently well for this purpose. The way in which the projected surface areaof the body varies with the angle at which it is viewed is demonstrated infigure 302. Viewed from directly above or below, the area is approximately 2.30square feet,
TABLE 245.-Directional fragmentation densities of flak that caused 545 casualties in B-17 aircraft
Direction | (1) | (2) | (3) | (4) | (5) | (6) |
Degree: | ||||||
| 0-45 | 3.31 | 78 | 4.32 | 12.0 | 16.7 | 0.72 |
| 45-90 | 16.72 | 225 | 9.88 | 27.45 | 33.3 | .82 |
| 90-135 | 16.72 | 309 | 13.56 | 37.71 | 33.3 | 1.13 |
| 135-180 | 3.31 | 148 | 8.20 | 22.8 | 16.7 | 1.37 |
| Total | 40.06 | 760 | 35.96 | 100.0 | 100.0 |
1Data calculated per square foot per 100 casualties.
NOTE.-Figures in parentheses for one side of body surfaceonly.
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TABLE 246.-Directional fragmentationdensities of flak that caused 215 casualties in B-24 aircraft
Direction | (1) | (2) | (3) | (4) | (5) | (6) |
Degree: | ||||||
| 0-45 | 3.31 | 43 | 6.04 | 16.8 | 16.7 | 1.01 |
| 45-90 | 16.72 | 96 | 10.68 | 29.8 | 33.3 | .89 |
| 90-135 | 16.72 | 103 | 11.44 | 31.9 | 33.3 | .96 |
| 135-180 | 3.31 | 55 | 7.73 | 21.5 | 16.7 | 1.29 |
| Total | 40.06 | 297 | 35.89 | 100.0 | 100.0 |
1Data calculated per square foot per 100 casualties.
NOTE.-Figures in parentheses for one side of body surface only.
FIGURE 302.-Projected body surface areas.
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whereas, from any direction horizontally, the area isapproximately 4.37 square feet. At an angle of say 45? above or below thehorizontal, the projected area of the body is approximately 3.76 square feet.
It is seen that over two-thirds of the casualties were causedby flak fragments proceeding roughly horizontally. The standardized directionalfragmentation density of fragments causing this large proportion of casualtieshowever (column 6, tables 245 and 246) was at a minimum, particularly in thecase of B-24 casualties. Figure 302 shows that a man viewed horizontallypresents an area nearly twice as large as a man viewed vertically. Also, thefrequency with which the larger surface area is presented is greatest in thehorizontal direction and decreases as the more vertical directions areapproached. Thus, the largest proportion of casualties were caused by fragmentsproceeding, in general, in the direction in which the greatest density offragments occurred. The apparent decrease in density of fragments that causedcasualties by proceeding horizontally however is due to the factor of"protection" to personnel from horizontally dispersed fragments.
From the figures for the hits on casualties (column 2, tables245 and 246), a curve of the form
r(θ)=a+b cos θ+c cos2 θ+d cos3 θ
can be fitted to give the directional fragmentation densitiesof fragments that caused the casualties. These curves together with the curvesrepresenting the directional fragmentation densities on the aircraft (indicateddotted) are shown in figure 303 to show the relationship between hits onaircraft and hits that
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caused casualties. The standardized density values used forthe construction of the curves are shown in tables 247 and 248.
TABLE 247.-Directional fragmentation densities of flak against personnel in B-17 aircraft
Direction | Standardized Density |
| Degree | |
10 | 1.03 |
30 | .91 |
60 | .70 |
290 | .74 |
120 | 1.16 |
150 | 1.74 |
3180 | 2.01 |
1Vertically downward.
2Horizontally.
3Vertically upward.
TABLE 248.-Directional fragmentation densities of flak against personnel in B-24 aircraft
Direction | Standardized density |
| Degree | |
10 | 1.62 |
30 | 1.37 |
60 | .83 |
290 | .55 |
120 | .94 |
150 | 1.76 |
3180 | 2.19 |
1Vertically downward.
2 Horizontally.
3 Vertically upward.
Figure 303A thus indicates that, while a B-17 aircraftreceives the greatest density of hits from a direction 10?-30? above thehorizontal with comparatively small density in directions within 45? of thevertical, the casualties suffer the greatest density of hits from below, withlesser density from the sides. Figure 303B, for casualties sustained in B-24's,shows in the same way the lowest density of hits causing casualties proceedingin approximately the same direction from which the greatest density of hitsoccurred on the aircraft.
GENERAL CONCLUSIONS
With reference to the protective armor in aircraft (p. 585),the significant difference in battle casualty rates in two types of heavybombers merits special attention. There was one known battle casualty for every54 B-17's dis-
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patched to enemy territory as compared with one for every 80 B-24'sdispatched. The relationship between casualties and flak damage to the two typesof aircraft may be well expressed by the ratio of casualties to flak hitssustained on the fuselages. For every 100 hits sustained on the fuselages ofcasualty-bearing aircraft, there were 34 casualties in B-17's as comparedwith only 19 casualties in B-24's.
It has been learned unofficially that the more difficult and more heavilydefended enemy targets were attacked by B-17's and that thetargets of lesser importance were usually attacked by B-24's. If this istrue and in view of the fact that the rate of planes failing to return fromenemy territory was the same for both aircraft (approximately 1 percent), it ispossible that the B-24 is more vulnerable to attack by lower burst velocityprojectiles. The lower incidence of casualties in proportion to hits in B-24aircraft may be regarded as a measure of the relative ineffectiveness againstpersonnel of low-velocity flak and the relative effectiveness of low-velocityfragments against B-24 aircraft.
The total projected surface areas of the personnel-bearing portion of bothtypes of aircraft exposed to flak (that is, the fuselage) were approximately thesame. The B-24 fuselage presented approximately a 5 percent greater totalexposed surface than the fuselage of a B-17. However, the area of an aircraftexposed to highest velocity flak fragments is its bottom surface. The projectedbottom surface of the fuselage of a B-17 was 25 percent greater than that of aB-24 (476 square feet for a B-17 as compared with 380 square feet for a B-24).This difference may account in part for the increased vulnerability of B-17personnel to flak. The "lateral" projected surface of a B-24fuselage exposed to flak (of relatively lower velocity) was approximately 36percent greater than the corresponding surface of a B-17.
Aircraft are "lost" or reported missing in action only when theenemy has been successful in crippling a ship to such an extent that it isunable to return to its base. A ship is unable to return to its base if itsengines are "knocked out" or if certain vital mechanical parts of theship are damaged. Also vital to a ship, however, are certain of its crew membersor combinations of personnel and mechanical parts of aircraft, and an aircraftmight not return to its base if its pilot or copilot should be killed orwounded. Other crew members might not be so vital to a ship's operation, butif these men were killed or wounded it might still influence the ship's chanceof returning to its base. Followup studies have shown that the fatality rate inMIA aircrew personnel is approximately 20 percent (1 out of 5) as compared with1.2 percent for all aircrews that sustained battle casualties and only 0.017percent (approximately 1 out of 6,000) for aircrew personnel returning fromcombat missions. The known high fatality rate among MIA personnel implies thatthere is as well a higher casualty rate in MIA personnel. It is likely that mostaircraft that did not return to their bases carried casualties, if not fatalcasualties.
By regarding all MIA aircraft as casualty-bearing aircraft, it was found that1,014 (390 MIA and 624 known to be casualty bearing) B-17's probablycarried casualties and that 623 (303 MIA and 320 known to be casualty bearing)
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B-24's probably carried casualties. Thus, 2.55 percent ofB-17 as compared with 2.08 percent of B-24 aircraft sustained casualties orwere missing in action. A chi-square test of the significance of the differencein these values gives x2=16.35 (where n=1, P less than 0.01). The difference is very clearly significant.
With respect to body armor, the main conclusion reached inthe case of B-17 aircraft was that personnel were protected laterally by bodyarmor and neighboring equipment and personnel and that a given weight of armorwould provide the best protection from below in addition to, but not instead of,the protection already apparent from horizontally dispersed fragments. In thecase of the B-24, a need for protection of personnel from above, as well asfrom below, was indicated. The B-24 was subjected to the greatest density ofhits from just above the horizontal, and vulnerable parts would be bestprotected from this direction.
