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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 time that a survey of missile casualties was being conducted by the Medical Operational Research Section, Professional Services Division, Office of the Chief Surgeon, ETOUSA (p. 547). The survey covered all of the battle casualties sustained by the Eighth Air Force during a 6 months' period beginning on 1 June 1944. More than 99 percent of the flak fragments recovered during the survey were probably from German 88 mm. HEAA (high explosive antiaircraft) shells. Only two fragments observed were definitely identifiable as fragments from shells larger than 88 mm. Because of this, a discussion of German ammunition will be limited to the 88 mm. shell.
Details of the structure of the shell are contained in USSTAF Ordnance Memorandum No. 5-6, 29 March 1944, and are shown in figure 293. The filled weight of the shell is about 21˝ pounds, the average weight of the filling 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 is composed of 0.72 percent carbon steel and its wall averages nine-sixteenths of an inch in thickness. The mean burst velocity of fragments observed in trials carried out at Millersford was 2,280 f.p.s. The velocity of the projectile at the instant of burst at the altitude at which the shell is fired at heavy bomber aircraft is estimated to range from 1,000 to 2,000 f.p.s., being greatest when the angle of fire is nearest vertical and lowest the more the angle of fire deviates from the vertical.
In order to bring out certain points with respect to the flak risk run by aircrew personnel, it is necessary to consider certain elementary facts 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 a completely spherical projectile breaking up over its entire surface into fragments of uniform weight and size, all traveling at the same velocity, will be considered.
Considering the distribution of fragments from such a projectile after they had traveled, say, 100 feet from the point of burst, would amount to considering the distribution of fragments in a sphere whose radius was 100 feet. Since the projectile broke up uniformly, the relative density of fragments-that is, the number of fragments per unit area on the surface of the sphere-would be the same all over the sphere. Since, however, the annular bands subtended on the surface of the sphere, per unit angle at its center with respect to the equatorial plane, decrease in area as one proceeds from the "equator" to its "north or south pole," the number of fragments in each annulus will decrease accordingly in spite of the fact that the density per unit surface area remains the same. This is shown in table 233 and figure 294. Column 1 of the 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 in successive annular zones on the surface of the sphere, if the boundary of each of these zones subtends an angle of 30° at the center of the sphere. Column 3 is merely a statement that the density per unit area on the surface of the sphere is constant.
These figures provide a basis for standardizing values for fragmentation density for shells of different types in different zones around the burst. Such standardized values will be referred to in the following paragraphs as "directional fragmentation densities."
In actual fact, the concept of a spherical burst is entirely theoretical. Antiaircraft shells are not spherical, and their fragments are dispersed 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 the results of certain
FIGURE 295.-Directional fragmentation density. A. 88 mm. shellburst (static, nose, down; density in shaded zones not observed). B. 90 mm. shellburst (static, nose up) C. 90 mm. shellburst (moving vertically 2,000 f.p.s.).
trials in which AA shells were detonated experimentally in such a way that it was possible to measure the number of fragments in different annular zones with respect to the equatorial plane of the shell (that is, the equatorial plane being at right angles to the axis of the shell and cutting through its center).
Figure 294, constructed from the data in table 233, may be regarded as the diagrammatic representation of a spherical burst from which there is a uniform distribution of fragments and for which the relative directional fragmentation densities (D) are the same. The values of 1 for the densities in all directions are shown by the constant length of the radii of the circle (representing a sphere) in zones of 30° with respect to the equatorial plane. The values under A (column 2 of table 233) are those areas of the annular bands expressed in percentages of the total area of the sphere, subtended
by 30° angles at its center with respect to the equatorial plane. These areas are projected in figure 294.
Consider next a variation from a spherical burst. For example, a value of 5 in column 3 of table 233 for a given annular zone would mean a density of fragments per unit area on the surface of the sphere relatively five times as great as would be expected for a spherical burst. The fivefold increase in this zone would involve relative decreases in densities in other zones. The values for directional fragmentation density as used are representations of densities per unit solid angle. Because of the lack of complete fragmentation data for any of the burst patterns to be discussed, a relative value as opposed to an absolute value is desirable.
Fragmentation trials on three rounds of the German 88 mm. HEAA shell were conducted at Millersford.2 The shells were set up vertically, nose down, 5 feet above the ground. For each detonation, two sets of three strawboard panels, 10 feet high by 40 and 60 inches wide, were placed vertically 5 feet and 10 feet from the shell and so staggered that they did not overlap each other. For each trial, the number of strikes was counted on the panels in such a way as to separate the strikes that occurred at 10-inch intervals 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 those zones in terms of the angle each subtended at the center of the shell. Columns 3 and 4 show the number and percent of fragments observed in each zone.
NOTE.-Table, based on data obtained at Millersford trials, shows conversion of fragment distribution in 10-inch zones at 5 feet detonation distance into relative directional densities.
A value for directional fragmentation density in any zone may be obtained from the equation
D = n / A
in which n is the number of fragments observed in the zone, expressed as the percentage of the total number of fragments observed, and A is the area of the annular band on the surface of a sphere subtended by an angle at its center, 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 in figure 294.
It should be emphasized that figure 294 is a two-dimensional drawing representing a three-dimensional burst pattern. Thus, the radius in figure 294 that deviates 30° from the vertical would describe a relatively small cone subtending the "north polar" surface of a sphere, whereas the radius that makes a 30° angle with the equatorial plane would describe an annular zone on the surface of a sphere comparable to the northern half of the Torrid Zone on the surface of the earth.
In the Millersford trials, no observations were made about the densities of fragments projected upward from the base and downward from the nose of the shell. If the burst is regarded as a spherical projection of fragments from the center of the projectile, the unobserved zones (shaded in fig. 295A) above and below 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 fragments noted in table 234, while they represent 100 percent of the observed number of fragments dispersed by an 88 mm. shell, were dispersed in directions which represent 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 of fragments dispersed upward and downward in the unobserved zones in similar experiments is negligible.
Figure 295A shows for comparison with a spherical burst (fig. 294) the burst pattern of a nose-down 88 mm. shell detonated statically. It is pointed out again that the lengths of the lines or radii from the point of burst (D, column 6 in table 234) are measures of relative directional fragmentation densities.
A report by the Operational Analysis Section, Mediterranean Allied Air Forces3 gives the observed data pertaining to fragment distribution from a statically detonated, nose-up, U.S. 90 mm. HE shell. Tables 235 and 236 are similar to table 234 except that the annular zones in which fragments were counted are specified only by the angles by which they are subtended at the center of the burst (column 1).
The divergence of the burst pattern of a shell from the burst pattern of a theoretical spherical projectile can easily be demonstrated if one first calculates the percent of all fragments which would be expected in the area of each annular zone of a sphere which would be subtended by the angles indicated in column 2 of table 234 and column 1 of tables 235 and 236. These percentages are determined in the same way as those calculated for column 2 of table 233. The values obtained are shown in column 5 of table 234 and column 4 of tables 235 and 236. Since the density of strikes per unit area in the theoretical spherical burst is unity, the divergence of the actual fragment pattern
of a shell for each annular zone is given by the ratio of the percent of fragments observed in each zone to the percent of fragments expected in 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 tables 234, 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 the German 88 mm. and the U.S. 90 mm. shells are approximately similar when one or the other is inverted. The apparent differences in figure 295A and B are due to the 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 pattern shown in figure 295C would represent the directional fragmentation densities of flak in the atmosphere. This figure would also represent the relative importance of the different directions from which protection would be required by aircrew personnel in heavy bombers. However, an enemy AA battery may fire at a formation of 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 a composite burst pattern that differs from that of shells bursting only in a vertical orientation.
It was thought desirable to construct a composite burst pattern that would represent the aggregate of flak bursts that actually occur under operational conditions. In order to do this, the frequency of flak hits on plane 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 United Kingdom during July 1944 were examined. If the number of MIA aircraft due to flak damage were sufficiently great, the distribution of flak hits on them might materially influence the observations made on the July sample of aircraft. Accurate data as to how many MIA aircraft were lost because of damage due to flak were not available. However, 15 percent of MIA personnel were evaders who returned to the United Kingdom and who were interrogated by representatives of the Operational Research Section, Eighth Air Force. It is estimated on the basis of information obtained from the personnel questioned that approximately 60 percent of both types of MIA aircraft were lost because of damage due to flak during July 1944. During that month, 134 B-17's and 107 B-24's were missing in action. Thus, 3,053 B-17 aircraft, of which 2,973 were examined and of which approximately 80 (2.6 percent) were missing in action, were possibly damaged by flak. Also, 958 B-24 aircraft, of which 894 were examined and of
which approximately 64 (6.7 percent) were missing in action, were possibly damaged by flak. It is unlikely that the small incidence of MIA flak-damaged aircraft, could they have been included in the analysis, would have greatly changed the observations pertaining to either type of aircraft.
Only the flat portion of the main wings lateral to the numbers 1 and 4 engines and the "unprotected" surfaces of the vertical stabilizers of both aircraft were used for these observations. Figures 296 and 297 show the location of flak hits on the plane surfaces of the two types of aircraft. The surface areas were determined by planimeter measurements of scale drawings of the aircraft and are given in column 1 of table 237. This table shows the data obtained from the battle damage reports for 2,961 B-17's and 888 B-24's. The manner of
calculating the "standardized" densities of hits on plane surfaces was the same as that given for the calculation of "standardized" directional fragmentation densities, and the values obtained are given in column 6 of table 237.
The figures in columns 3 and 6 of table 237 show that the greatest density of hits occurred on the bottom surfaces of B-17 aircraft. The density of hits on vertical surfaces was only slightly less, whereas the density of hits on top surfaces was approximately one-third as great as that on bottom or vertical surfaces.
Corresponding figures for B-24 aircraft (columns 3 and 6) show that vertical surfaces suffered the greatest density of flak hits. The latter was 54 percent
1Data calculated per square foot per 1,000
greater than the density of hits on bottom surfaces and three and a half times 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 on B-24 than on B-17 aircraft. There was an average density of 1.00 hit per square foot on B-17's as compared with 1.26 per square foot on B-24's.
Directional Density of Flak in Relation to Distribution of Observed Hits
The densities of flak hits on different plane surfaces cannot be regarded directly as representing the densities of fragments proceeding in space in given directions. It stands to reason that only a small part of the total density of hits on a plane surface are caused by fragments which struck it normally. If the densities of flak hits on a large number of aircraft, the plane surfaces of which were oriented in several different directions in space (say six), were known, it would be possible to calculate the directional fragmentation densities of flak fragments to which the aircraft were exposed. With plane surfaces oriented in three directions only, as in the present case, the data are not adequate to make an exact determination of directional fragmentation densities. In other words, a number of different sets of directional fragmentation densities
can be calculated, all of which will give the densities of hits on plane horizontal and vertical surfaces which were actually observed.
One such set of directional fragmentation densities, which may be regarded as the 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+b cos θ+c cos2 θ+d cos3 θ
in which a, b, c, and d are constants that were solved so that the equation would fit the observed densities of hits on the plane horizontal and vertical surfaces of the aircraft. They are represented in the composite burst pattern (fig. 298A) by the length of the radii from the point of burst.
FIGURE 298.-Directional fragmentation density. A. Composite flak burst, constructed from the flak hits on the plane horizontal and vertical surfaces of 2,961 B-17 aircraft. B. Composite flak burst, constructed from the flak hits on the plane horizontal and vertical surfaces of 888 B-24 aircraft.
The number of flak fragments striking an object will vary directly with the surface area it presents and inversely with the square of the distance from the point of a burst. The densities of hits will be further influenced by the shape of the target and its movement in space. The figures in column 3 of table 237 are absolute values and those in column 6 of the same table are standardized values for the densities of hits on the plane surfaces of B-17 aircraft. In contrast, the figures in column 2 of table 238 represent relative values for directional fragmentation densities of fragments dispersed in space from the point of a burst. These values are represented graphically in the composite burst pattern shown in figure 298A. Relative directional fragmentation densities are measures of the densities of fragments dispersed in different directions toward aircraft and in this case may be regarded as constant for the altitude at which the B-17's operate. These directional fragmentation densities will not vary or be influenced by any of the factors which determine variations in the density of hits received on different surfaces of the B-17's.
The mathematical form chosen to determine relative values for directional fragmentation densities of fragments which would account for the observed distribution of hits displayed in table 237 (for B-24 aircraft)
r(θ) = a+b cos θ+c cos2 θ+d cos3 θ+e cos4 θ+f cos5 θ
has the defect that it does not immediately yield a reasonable curve to account for the observed densities of hits. This failure is not necessarily due to any special feature of the directional fragmentation density distribution for the B-24. The standardized values of r(θ) in table 239 are the "smoothed" values calculated from the equation.
Figure 298B is a diagrammatic representation of the values in column 2 of table 239. It shows a pattern of directional fragmentation densities which will account for the observed densities of hits on B-24 aircraft. The smoothed 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 cause casualties, and therefore it was thought worthwhile to determine the densities of flak hits on the fuselages of the two types of aircraft. Actually, the standardized values for such hits should agree with those for hits on plane surfaces. Flak hits on MIA aircraft, while they might not have influenced the observed densities and distribution on plane surfaces, might materially affect the observed density and distribution of hits on the more vital fuselage surfaces, could they have been included in the observations. Differences could be due in part to the personal error introduced by the engineer officer who makes a record of flak damage to an aircraft and who has to distinguish between hits on the top and side or side and bottom of a tapering cylindrical structure whose curved surfaces cannot readily be demarcated from each other.
However, the greatest differences are more likely to be due to "selection." In general, the greatest density of hits by flak on certain regions of the fuselage vital for an aircraft's safe return to the United Kingdom could not be included in the observations. The sample of aircraft studied for hits on the fuselage would be biased in favor of aircraft struck in regions of the fuselage not vital to the aircraft's return.
Column 6 of table 240 gives the standardized densities of flak hits on the fuselages of B-17 and B-24 aircraft. The projected surface areas chosen for the observations do not include the bomb bay or those portions of the sides of the fuselage protected by the main wings. The samples of 2,973 B-17 and 894 B-24 aircraft used include the 2,961 B-17's and 888 B-24's referred to previously. Figure 299 shows the location of flak hits on the projected surfaces for which the relative densities were determined.
Table 240 for B-17's shows a somewhat different order of densities 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 the fuselage. The ratio of densities for hits on top and bottom surfaces is 1:1.8 as compared with 1:3.2 for densities of hits on plane surfaces, and the density of hits on the sides is twice that for hits on the bottom. Table 240 for B-24's also shows the greatest density of hits on the sides of the fuselage and a change 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 the ratios
of top to bottom bits for both types of aircraft, may be regarded as hits sustained by MIA aircraft. In other words, aircraft shot down by flak probably sustained hits chiefly on the bottoms of fuselages. Could these hits have been included in the observations, they probably would be sufficient to restore the observed ratios of top to bottom fuselage hits so that they would correspond to the ratio of top to bottom plane surface hits. The differences observed between the densities of hits on plane and fuselage surfaces of all aircraft will be compared later with the differences between the densities on the plane and fuselage surfaces of casualty-bearing aircraft.
1Data calculated per square foot per
Density of Flak Hits on Casualty-Bearing Aircraft
In a selected sample of casualty-bearing aircraft, one might expect to find an increase in the number and variations in the distribution of flak hits on all surfaces generally. The casualty-bearing portion of the aircraft, that is, the fuselage, in a sample selected for casualties might be expected to show the greatest increases in density and variations in the distribution of hits. The observed relationship between flak hits and casualties is likely to be greatly different from observations that would include MIA flak-damaged casualty-bearing aircraft. The fatality rate in MIA aircrew personnel is known to be
approximately 20 percent. Such a high fatality rate would correspond to an even greater casualty rate. Thus, it is likely that most MIA aircraft due to flak damage were also casualty-bearing aircraft. If all MIA flak-damaged aircraft were to be regarded as bearing one or more flak casualties, then there were approximately 781 B-17 flak-damaged casualty-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-damaged casualty-bearing aircraft during the same period. Of this number, 172 aircraft returned and were examined and 293 (63 percent) were not examined (112 returned and not examined and 181 MIA). Such proportions of casualty-bearing aircraft, for which observations were not available, would therefore greatly alter the flak-damage data pertaining to both types of aircraft.
Tables 241 and 242 show the densities of flak hits for plane surfaces and fuselages of all the aircraft examined in which there were flak casualties. The aircraft concerned were examined in the same way and by the same personnel 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 on casualty-bearing B-17 and B-24 aircraft from which the data in tables 241 and 242 were obtained.
1Projected for "fuselage only."
1Projected for "fuselage only."
Column 3 of table 243 (compare with column 1) shows significant increases in the number of flak hits on plane surfaces of B-17 aircraft. 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 bottom surfaces of casualty-bearing B-17's, from 1:3.2 to 1:2.1(36 percent decrease).
Column 4 of table 243 (compare with column 2) shows even greater increases in the density of flak hits on the fuselages of casualty-bearing B-17's. The standardized values in columns 2 and 4 of table 244 show again no change in the relative density of hits on the sides of the fuselages. However, there is an apparent decrease in the ratio of top to bottom hits from 1:1.8 for the fuselages of all B-17's to 1:0.8 for the fuselages of casualty-bearing B-17's (57 percent decrease).
Column 7 of table 243 (compare with column 5) shows greatly increased densities of flak hits on plane surfaces of casualty-bearing B-24 aircraft. The standardized values for the B-24 in columns 5 and 7 of table 244 show, as in the case of B-17 aircraft, no significant difference in the relative density of hits on vertical (sides) surfaces of casualty-bearing aircraft. However, in contrast to a reduced ratio of top to bottom hits on plane surfaces of B-17's, there appears to be an increased ratio of top to bottom hits on plane surfaces of casualty-bearing B-24's from 1:2.3 to 1:3.2 (42 percent increase).
1Data are from column 3, table 237.
[Data represent number of hits per square foot per 1,000 aircraft]
1Data are from column 6, table 237.
Column 8 of table 243 (compare with column 6) shows greatly increased 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 apparent decrease in the ratio of top to bottom hits on casualty-bearing B-24's from 1:0.7 to 1:0.67 (8 percent decrease).
The analysis of hits on casualty-bearing B-17 aircraft listed in table 241 shows deficiencies of flak hits on the bottom surfaces primarily of the fuselage and secondarily of the planes. These data suggest that MIA B-17 aircraft due to flak damage were lost primarily due to hits on the bottom surfaces of
the fuselage and thus possibly due in part to the occurrence of casualties produced by these hits. The "moth-eaten" appearance in the 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 the aircraft's safe return, further supports this possibility. Hits on the ball turret, a combat position relatively unimportant as far as the integrity of the aircraft is concerned, appear to be distributed normally.
The analysis of hits on casualty-bearing B-24 aircraft listed in table 242 shows deficiencies of flak hits primarily on the top surfaces 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 lost primarily because of hits on the top surfaces of planes and only secondarily because of hits on the sides and bottom of their fuselages. Figure 301B also shows a somewhat moth-eaten appearance in the distribution of flak hits on the bottom of the fuselages. However, the disturbed distribution of hits observed on casualty-bearing B-24's suggests that MIA aircraft of that type, due to flak, were more likely lost because of damage to mechanical parts rather than to the 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, he would be exposed to a distribution of flak fragments as shown in figure 298A if he 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 is in a heavy bomber, he is protected in varying degrees by different parts of the aircraft, by its armament, by the proximity of other men in the aircraft, and usually by body armor either worn or placed in various positions about his aircrew station. The observations made from an analysis of the directional fragmentation density of flak that had caused casualties would differ from those made from an analysis of hits on the outer surfaces of aircraft since many of the fragments flying in space would first strike the exterior of the aircraft, some object within, or body armor and be stopped, thus preventing a casualty from occurring. In other words, the flak fragments that caused casualties would appear to be most reduced in density in the directions from which the man had the best protection and most increased in density in the directions from which he had the least protection. If the unobserved hits on MIA casualty-bearing flak-damaged aircraft would materially affect the observations made on casualty-bearing B-17's and B-24's, then the unobserved hits causing casualties among MIA personnel would be likely to have an even greater effect on the observations made on flak casualties sustained in the two types of aircraft.
It was possible to determine the direction traveled by the flak 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 which the casualty occurred, the location of the wounds on the casualty, the direction of the wound
track, and the wounds of entrance and exit were all taken into account to determine in which of four "directional zones" the flak fragment which caused each wound traveled. The four directions that were arbitrarily chosen were 45° zones with respect to the equatorial plane. All wounds that were caused by fragments traveling vertically downward or in a downward direction deviating not more than 45° from the vertical were grouped in the 0°-45° zone. Wounds caused by fragments traveling downward in the zone between the horizontal and 45° below the horizontal were grouped in the 45°-90° zone. Wounds caused by fragments traveling upward in the zone between the horizontal and 45° above the horizontal were grouped in the 90°-135° zone. Wounds caused by fragments traveling vertically upward or in an upward direction deviating not more than 45° from the vertical were grouped in the 135°-180° zone. Wounds that could not definitely be placed in one of these four zones were not included in the analysis. Tables 245 and 246 show the grouping of wounds or "hits," by zones, sustained by the casualties in the two types of aircraft.
The standardized densities of hits causing casualties given in column 6 of tables 245 and 246 were obtained by correcting for the varying projected areas of the body (column 1 of the tables). The projected area of a man viewed at an angle of 0° is taken to be 2.3 (1+0.9 sin θ) square feet. This formula, though approximate, agrees with the observed projected area sufficiently well for this purpose. The way in which the projected surface area of the body varies with the angle at which it is viewed is demonstrated in figure 302. Viewed from directly above or below, the area is approximately 2.30 square feet,
1Data calculated per square foot per 100 casualties.
1Data calculated per square foot per 100 casualties.
whereas, from any direction horizontally, the area is approximately 4.37 square feet. At an angle of say 45° above or below the horizontal, the projected area of the body is approximately 3.76 square feet.
It is seen that over two-thirds of the casualties were caused by flak fragments proceeding roughly horizontally. The standardized directional fragmentation density of fragments causing this large proportion of casualties however (column 6, tables 245 and 246) was at a minimum, particularly in the case of B-24 casualties. Figure 302 shows that a man viewed horizontally presents an area nearly twice as large as a man viewed vertically. Also, the frequency with which the larger surface area is presented is greatest in the horizontal direction and decreases as the more vertical directions are approached. Thus, the largest proportion of casualties were caused by fragments proceeding, in general, in the direction in which the greatest density of fragments occurred. The apparent decrease in density of fragments that caused casualties 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, tables 245 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 densities of fragments that caused the casualties. These curves together with the curves representing the directional fragmentation densities on the aircraft (indicated dotted) are shown in figure 303 to show the relationship between hits on aircraft and hits that
FIGURE 303.-Directional fragmentation density. A. Composite flak burst, constructed from 760 flak hits sustained by 545 casualties in B-17 aircraft. B. Composite flak burst, constructed from 297 flak hits sustained by 215 casualties in B-24 aircraft.
caused casualties. The standardized density values used for the construction of the curves are shown in tables 247 and 248.
Figure 303A thus indicates that, while a B-17 aircraft receives the greatest density of hits from a direction 10°-30° above the horizontal with comparatively small density in directions within 45° of the vertical, the casualties suffer the greatest density of hits from below, with lesser 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 proceeding in approximately the same direction from which the greatest density of hits occurred on the aircraft.
With reference to the protective armor in aircraft (p. 585), the significant difference in battle casualty rates in two types of heavy bombers merits special attention. There was one known battle casualty for every 54 B-17's dis-
patched to enemy territory as compared with one for every 80 B-24's dispatched. The relationship between casualties and flak damage to the two types of aircraft may be well expressed by the ratio of casualties to flak hits sustained on the fuselages. For every 100 hits sustained on the fuselages of casualty-bearing aircraft, there were 34 casualties in B-17's as compared with only 19 casualties in B-24's.
It has been learned unofficially that the more difficult and more heavily defended enemy targets were attacked by B-17's and that the targets of lesser importance were usually attacked by B-24's. If this is true and in view of the fact that the rate of planes failing to return from enemy territory was the same for both aircraft (approximately 1 percent), it is possible that the B-24 is more vulnerable to attack by lower burst velocity projectiles. The lower incidence of casualties in proportion to hits in B-24 aircraft may be regarded as a measure of the relative ineffectiveness against personnel of low-velocity flak and the relative effectiveness of low-velocity fragments against B-24 aircraft.
The total projected surface areas of the personnel-bearing portion of both types of aircraft exposed to flak (that is, the fuselage) were approximately the same. The B-24 fuselage presented approximately a 5 percent greater total exposed surface than the fuselage of a B-17. However, the area of an aircraft exposed to highest velocity flak fragments is its bottom surface. The projected bottom surface of the fuselage of a B-17 was 25 percent greater than that of a B-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-17 personnel to flak. The "lateral" projected surface of a B-24 fuselage exposed to flak (of relatively lower velocity) was approximately 36 percent greater than the corresponding surface of a B-17.
Aircraft are "lost" or reported missing in action only when the enemy has been successful in crippling a ship to such an extent that it is unable to return to its base. A ship is unable to return to its base if its engines are "knocked out" or if certain vital mechanical parts of the ship are damaged. Also vital to a ship, however, are certain of its crew members or combinations of personnel and mechanical parts of aircraft, and an aircraft might not return to its base if its pilot or copilot should be killed or wounded. Other crew members might not be so vital to a ship's operation, but if these men were killed or wounded it might still influence the ship's chance of returning to its base. Followup studies have shown that the fatality rate in MIA aircrew personnel is approximately 20 percent (1 out of 5) as compared with 1.2 percent for all aircrews that sustained battle casualties and only 0.017 percent (approximately 1 out of 6,000) for aircrew personnel returning from combat missions. The known high fatality rate among MIA personnel implies that there is as well a higher casualty rate in MIA personnel. It is likely that most aircraft that did not return to their bases carried casualties, if not fatal casualties.
By regarding all MIA aircraft as casualty-bearing aircraft, it was found that 1,014 (390 MIA and 624 known to be casualty bearing) B-17's probably carried casualties and that 623 (303 MIA and 320 known to be casualty bearing)
B-24's probably carried casualties. Thus, 2.55 percent of B-17 as compared with 2.08 percent of B-24 aircraft sustained casualties or were missing in action. A chi-square test of the significance of the difference in 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 in the case of B-17 aircraft was that personnel were protected laterally by body armor and neighboring equipment and personnel and that a given weight of armor would provide the best protection from below in addition to, but not instead of, the protection already apparent from horizontally dispersed fragments. In the case of the B-24, a need for protection of personnel from above, as well as from below, was indicated. The B-24 was subjected to the greatest density of hits from just above the horizontal, and vulnerable parts would be best protected from this direction.