An adequate supply of fuel is obviously critical to operational capability at an airbase. If the bulk fuel storage were difficult to replace quickly, as it is on many overseas bases and as it might be on even ZI bases after a massive enemy attack, destruction of fuel stocks would effectively hamstring SAC operations. A rational enemy, planning an attack on SAC might then consider as a potential primary goal the destruction of fuel stocks. But, with atomic weapons, even an attack aimed primarily at some other element of a SAC base complex might completely destroy fuel stocks. In this event, fuel destruction would occur as a bonus to an attack aimed against, say, runways. It would impose on the enemy no added requirement for either bombs or vehicles.
1. Fuel as a Secondary Target
The first consideration in protecting base fuel stocks is to deny the enemy the situation in which fuel is a free target. This may be accomplished by two measures, which are most effectively used together. They consist in removing bulk fuel from the vicinity of the aiming point and hardening the storage tanks against blast. Aboveground fuel storage tanks located close to the runways would have very high probability of destruction because an overpressure of 8 PSI is sufficient to destroy them, and the circle within which overpressures of 8 PSI or greater are experienced is very large. For example, suppose the fuel were stored in conventional tanks on the surface, at one-half nautical mile from the point where the runways crossed. If the enemy were to aim one 500 KT bomb at the runway intersection with a 4000-foot CEP, he would have a .90 probability of destroying the fuel - or an expectation of destroying 90 percent of the fuel.[1] The situation is not radically improved if the fuel is located one nautical mile from the aiming point. The probability of destruction is then about .75. When the fuel is located as much as two nautical miles from the aiming point, some improvement is noted in the probability of survival, but only if the kind of attack is held constant. Figure 1 shows the effect of yield and CEP on the probability of destruction of fuel stored on the surface, two nautical miles from the aiming point. In Figure 1, each point represents a particular combination of CEP and yield. To each combination there also corresponds some degree of destruction for a target of specified hardness. The curves in Figure 1 connect CEP-yield combinations which result in equal target destruction. They are, in other words, contours of equal destruction. All such contours have the characteristic of rising to the right, at least over some part of the range. This merely signifies the need to offset higher CEP with greater yield to keep a constant level of destruction. It is evident from the figure that while this distance from the aiming point gives moderate protection against a 500 KT weapon delivered with 4000-foot CEP (the probability of destruction is between .10 and .50), it is totally inadequate for an attack with the same CEP and a 4 MT bomb (the probability of destruction is greater than .9). As a means of preventing bonus damage to fuel stocks, even greater distances could be interposed between fuel tanks and aiming point, or the fuel tanks themselves might be hardened. Either measure will serve so long as the enemy is aiming at some other element. However, the enemy can, of course, reduce the distance form the aiming point to zero by aiming at the fuel so that distance from, say, runway intersection cannot be relied upon as the sole means of protection. This situation will be analyzed below, but the possibility of it justifies examinations of the effects of hardening even when fuel is not the primary target.
Before going on to hardening of the fuel tanks, consider a measure akin to removal from the aiming point, namely, the device of splitting the fuel storage into widely separated units. If this measure is taken with no change in the hardness of the target or the distance from the aiming point, the expected or average destruction is not affected. However, the variability of the results of a number of similar attacks on a split storage configuration will be reduced relative to a configuration with the fuel all in one location. The analogy with the proverbial advice against putting all one's eggs into one basket is clear. If there is too high a probability of dropping the baskets, increasing the number of baskets may serve merely to insure against the lucky chance of arriving at market with a satisfactory number of the eggs intact.[2] The average number of eggs arriving unbroken, over many trips, is unaffected and still too low. However, if the probability of dropping a basket has been made very low, then increasing the number of baskets provides useful insurance against the unlucky event that one basket is dropped. The saw might be rewritten this way: "If you aren't accident-prone don't put all your eggs into one basket - if you are accident-prone, become less so."
In the case of fuel storage this may be interpreted to mean that splitting the storage sites offers obvious insurance benefits only when the expected proportion surviving has been increased to a satisfactory level. The preceding discussion of splitting as a defense measure is relevant only when the fuel is not the primary target. As we shall see, when fuel is the primary target, splitting increases the average proportion surviving a given attack.
We have seen that very large distances are required to protect fuel storage, if sole reliance is placed on removal from the aiming point. The reason for this is, of course, that unprotected fuel tanks aboveground are destroyed by low overpressures, of the order of 8 PSI. Clearly, a substitute for removal from the aiming point is hardening of the structure. The method most often considered for fuel tanks is to place the tanks underground. Empty underground tanks will resist overpressures up to 100 PSI if buried somewhat deeper than the usual 3 feet or so below the surface, but without going deep enough to increase costs appreciably. Full tanks can be made resistant to all but the crater and the violent earth movements in its immediate vicinity by burying them at a distance about 3 to 4 times their diameter from the surface.
Figure 2 shows the vulnerability of underground storage on this assumption. Figure 2 is similar to Figure 1. However, the iso destruction contours have shifted sharply rightward in Figure 2, as a result of the greater target resistance. This, of course, is another way of saying that for any CEP- yield combination, the expected damage has fallen. It should be noticed that the yield scale of Figure 2 has had to be compressed relative to that of Figure1.
It may be noticed that the contours of equal destruction double back. This is true of Figure 1 but is more evident in Figure 2. This leads to the paradox of greater destruction with higher CEP, for a fixed yield. The paradox is resolved when we remember that we are dealing with a situation where the aiming point is offset from the element whose vulnerability we are measuring. Lower CEP increases the enemy's chances of success against his primary target, but, unless the lethal radius is large enough simultaneously to cover primary and incidental targets (say, runway and fuel, respectively), it may decrease his chances of bonus damage. For this reason the doubling back is emphasized as the distance from the bonus target to the aiming point is increased, or as the bonus target is made harder. The point of substantive interest here is that if the enemy voluntarily increases his CEP to improve his chances against the fuel, he may be sacrificing his chances against the primary target. If the primary target were, in fact, the runway, where CEP is of critical importance, the sacrifice might be serious. In that event, the fuel would no longer be purely a bonus target.
We will continue to discuss the vulnerability on the assumption of a 4000-foot CEP. The effects of variation in CEP can, of course, be read from the figures. If the enemy has a 4000-foot CEP, Figure 2 shows that putting the fuel underground two miles from the aiming point increases very markedly the yield required for a given average destruction of fuel. Whereas 2 MT sufficed to destroy 90 percent of fuel stored aboveground, 5 MT yields only 10 percent destruction of belowground fuel. Indeed, a 50 MT bomb yields only slightly more than 50 percent destruction of fuel so stored.
However, if the primary target were very hard, the enemy might be forced to use a greater number of bombs. Figure 3 shows the effects on fuel stored underground of 4 bombs aimed at a point two nautical miles away. Again it is assumed that destruction occurs at 100 PSI. Even with 4 bombs, the yield requirements for substantial destruction of fuel are high. For 50 per cent destruction, for example, 4 bombs in the neighborhood of 15 MT are needed.
A direct way to an even greater reduction in the vulnerability of bulk fuel stocks would be to keep the fuel in full underground storage tanks. Since bases do not usually stock fuel to the full amount of their storage capacity, this would mean concentrating all fuel in full tanks while other tanks were left completely empty to the extent possible. This could be arranged by cross pumping. Such a measure would be directed mainly toward the preservation of the fuel rather than the storage capacity, although it would, in many instances, increase the survival of both. Because underground tanks, when full, will resist all but cratering or violent earth shock, the lethal radius of any particular bomb is tremendously reduced. When, in addition, the tank is located two nautical miles from the aiming point, it becomes all but invulnerable as a bonus target. Very close to 100 percent would survive an attack with a 100 MT bomb and a CEP of 4000 feet.
2. Fuel as a Primary Target
Although the enemy could not expect to destroy fuel, protected as we have indicated, without taking special pains to do so, if it were a profitable primary target, he might choose to focus his attack on it. Obviously, distance from an independently chosen aiming point is not a factor in this situation. The important considerations are the hardness of the target and the number of widely separated units into which it is split. It is assumed in what follows that the enemy can either locate the fuel tanks directly as aiming points or that he is sufficiently acquainted with the base configuration to bomb them using offset aiming. In fact, underground fuel tanks being harder to locate than a runway, for example, the bombing accuracy would be degraded, perhaps to an important extent. Since this has not been taken into account, the estimates below overstate the vulnerability of underground fuel when it is a primary target.Let us examine first the vulnerability of partially empty tanks in a single cluster. Figures 4 and 5 show the results of attacks aimed primarily at the fuel. They are analogous to Figure 1-3. Figure 4 deals with the empty underground tanks, which fails at 100 PSI, while Figure 5 relates to the full underground tanks which resist all but the crater or violent earth shocks.
The doubling back of the iso-destruction contours which was present in Figures 1-3 are, of course, missing from Figure 4 and 5, because the target now coincides with the aiming point. The effect of the sharp increase in target hardness which distinguishes the two figures is not to shift the curves to the right as in Figures 1-3 but to make them less steep. This, too, follows from the coincidence of aiming point and target. When the aiming point is far from the target, a small lethal radius cannot give high expectation of destruction, whatever the CEP. When the bomb is aimed directly at the target, reduction in lethal radius can be offset by reduction in CEP, and so the curves come close to passing through the origin.
Specific comparison of the vulnerability of full and empty underground tanks reveals a startling difference. A 4000- foot CEP and a 10 MT bomb give expected damage of 90 percent against empty underground tanks, and only 10 percent against full underground tanks.
Instead of increasing his accuracy or yield, the enemy may choose to multiply the number of bombs aimed at the target. The dashed curve of Figure 6 shows, for a 4000-foot CEP and a 10 MT bomb, the number of independently aimed bombs required to achieve a given probability of destroying full underground tanks. Ignoring, for the moment, the other curves in Figure 6, we observe that .5 probability of destruction requires 5 bombs and greater probabilities require large increases in the number of bombs. For example, 15 bombs would be required to achieve a probability of .9.
But this still leaves the defense the option of splitting the target. This is in fact quite inexpensive in the case of underground fuel, since technical and cost considerations indicate, in any case, a low upper limit to the size of tanks and tank farms therefore have large numbers of tanks. If we assume that the fuel is stored in clusters of full underground tanks, separated from one another by from one to two nautical miles, the results given on page 9 above show that they are actually independent targets. This means that the number of enemy bombs required at the bomb release line to do a specified amount of damage to the fuel stocks is multiplied by the number of clusters among which the fuel is distributed.
Destruction of base capacity to mount sorties by attacks aimed at the fuel can be made a goal of formidable difficulty. There would be no point, however, in making this element indefinitely hard to destroy, since the enemy would then ignore the fuel in favor of some more vulnerable, and equally essential, element. Let us take the vulnerability of the runways on a conventional base configuration as the criterion, and specify that, to serve as a fully effective operational or staging base, a base should possess an uninterrupted length of runway of at least 6000 feet. The dotted curve of Figure 6 shows the number of 10 MT bombs delivered with a 4000-foot CEP which would be required to "destroy" the runways in our sense.[3] It can be seen from the relative positions of the dashed and dotted curves in Figure 6 that the runways are somewhat harder to destroy than underground fuel in a single cluster. But, form our previous discussions we have seen that multiplying the number of clusters by splitting the tank farms multiplies the number of bombs needed for a given probability of destruction. This effect is shown by the solid curve of Figure 6 which shows the results for underground fuel in four clusters of tanks. This presents a target which is substantially harder to destroy than the runways of a conventional base. The runways also could be made harder targets, of course, for example by adding emergency runways parallel to the original ones. It is obvious, however, that at moderate cost the bulk fuel stocks may always be made the hardest fixed and critical element on a base.
[1] Estimates of destruction are based on a circular Gaussian distribution. Lethal effects are expressed in terms of "cookie cutters" obtained by extrapolation of curves presented in: Capabilities of Atomic Weapons, AFOAT 305.2, Department of the Army, the Navy, and the Air Force, Revised Ed., 1 October 1952 (SECRET), Figure 15, p. 29. The lethal radii so obtained, and the CEP and distance from aiming point assumed have been used to enter tables of Offset Circle Probabilities to estimate probability of destruction. These tables are presented in: Offset Circle Probabilities, The Numerical Analysis Department, The RAND Corporation, R-234, 14 March, 1952 (Unclassified).
[2] If the number of eggs
arriving at market unbroken is a binomial variable,
the mean is (N/n)np = Np and the variance is (N/n)
where N is the number of eggs, n is the
number of baskets and (1 - p) is probability of dropping of
basket.
[3] This curve is the result of a random bomb drop experiment assuming a circular Gaussian distribution and "cookie cutter" lethal effects. The lethal radius assumed was equal to the creater radius + 1/2 the lip.
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