Anti-ship missiles should be militarily worthless.
The energy of the bolts would be kinetic, the sum of the velocity of the bolt plus the velocity of the missile. If the muzzle velocity of the bolt is 1 000 ft/sec, it might be travelling at 800 ft/s at contact with the missile. If the missile is travelling at 1 000 ft/s (speed of sound is 1 100 ft/s) the total velocity is 800 + 1 000 = 1 800 ft/s. Kinetic energy is one half mass times velocity squared, for 100 lb-ft of energy, 1 800 X 1 800 = 3 240 000. Times 1/2 = 1 600 000, mass is weight divided by 32 ft/ s/s (acceleration of gravity), 1 600 000 / 32 = 50 000 for 100 lb-ft weight = 1/ 500 lb. 3 cubic inches (cu.in) = 1 lb of steel ( steel weighs 560-600 lb/cubic foot, 1 cubic foot = 1 728 cu.in.) 1/500 of 3 cu.in = 1/160 cu.in, if the bolt takes up half the volume of a box containing the bolt the box would be 1/ 80 cu.in If the bolt is 8:1 length to width = 1/8 inch wide and 1 inch long, or a little less.
At 100 lb-ft of energy, the bolt would, if stopped in 1/8 inch or 0.01 ft would generate an average force of 10 000 lb for 0.000 01 sec, the relative velocity goes from 1 800 ft/s to 0 for an average of 900 ft/s over
0.01 ft. If it stops in 0.1 ft, it would generate 1 000 lb of force for 0.000 1 sec. Test bolts would have to be fired at missile bodies to determine whether that is adequate to degrade the missile and cause failure.
When it strikes the missile, g, that energy would rupture the nose cone and the debris would strike the radar antenna if not penetrating further. The energy is the equivalent of a 100 lb block being dropped from 1 foot onto a nail. The Russians have a missile referred to some by some as the Sizzler, it approaches at 3 000 ft/s. The energy would be proportional to 3 800 X 3 800 = 14 400 000, over 4 times as much energy > 400 lb ft.
Damage to the forward end of any vehicle flying above the speed of sound, such as the Sizzler, creates large aerodynamic forces, at sub-sonic speeds there is disturbed flow but the forces are significantly less.
The question is how much energy is needed to seriously disrupt if not destroy the missile. The bolts could strike the nose cone or winglets as well as gauging out material along the length of the missile body.
A missile might have a protective plate of armored steel, maybe 1/2 inch thick. For a missile 6 inches in diameter the armored plate would weigh about 5 lb, for a missile 8 inches in diameter, it would weigh about
8 lb. The plate would be in back of the radar antenna. The nose cone might be shattered and the antenna destroyed but the armor would protect the electronics and allow the missile to continue to fly inertially guided unless the damage to the nose cone, body and winglets are so severe as to destabilize the missile.
If an approaching missile travels at 1 000 ft/s and can turn at even 9 gs it would have a turning radius of
3 500 ft. If the diameter of the shotgun blast is designed to be 80 ft at the point of contact, the missile would have to turn 40 feet to avoid intercept, at 3 500 radius, that would require over 500 feet of forward movement or about 1/2 second of flight time. 1/2 second for the shot gun would be 400-500 ft of flight so the intercept would occur within 500 feet of the ship. The missile has to be destabilized relatively quickly to be effective.
80 ft diameter = 5 000 sq ft area. If the missile is 6 inches in diameter it has 1/5 sq ft of area. Allowing 2 bolts per area to allow for uneven dispersion of bolts = 10 bolts/ sq ft., or a total of 50 000 bolts. At 1/500 lb per bolt, the bolts would way 100 lb in this example.
The shotgun would be a smooth tube with a propellant charge at the back and the cluster of bolts, c. They would be mounted in clusters of perhaps 9-12, e. They would be mounted every 50 ft of the length of the ship, d. To ensure a high probability of intercept, perhaps 3 would fire simultaneously, d. By spacing them every 50 ft, the firing is down the length of the missile and there is no need to consider deflection. The 3 firing also cover a wider range of motion of the missile.
If the tube of the shotgun is 6 inches diameter, the radius would be 3 inches, which would allow 24 rows of bolts at 1/8 inch each. The middle row would be at about 12, which would have 6 X 12 around the rows or
72 for the average number of bolts in circumference (bolts are 1 at center then 6 in first row, then 12 in next, etc.). 72 X 24 rows = 1 700, or some more. For 50 000 there would be 30 stacks of 1 700, if they are 1 inch long that would be 30 inches. In front of the bolts the tube could be 5 feet long plus 2.5 feet, 30 inches, for the bolts and maybe 0.5 feet, 6 inches for the propellant charge, or a total of 8 feet. To accelerate to 1 000 ft/s in 5 feet of barrel, the equation is velocity squared equals 2 times length times acceleration, assuming constant acceleration. So 1 000 X 1 000 / 2 X 5 = 100 000 ft/s or, /32 = 3 000 g. For 100 lb of bolts, 100 X 3 000 g = 300 000 lbs of force / 3 X 3 X pi, area of tube, = 11 000 psi. For a 6 inch wide tube 6 X 11 000 = 66 000 lb per inch across the tube wall. That can be 1 inch total wall, 1/2 inch wall thickness. 6 inch X pi = diameter, 1.5 feet. Steel weighs 560-600 lb / cubic foot, for 1/2 inch, 1/24 foot = 24 lb per foot of length, X 1.5 circumference = 36 lb / foot, X 8 foot length = 300 lb. Allowing thicker wall near end, end cap, 100 lb of bolts and propellant, total = 500 lb. Having separate tubes for each firing guarantees reliability and rapid firing over a gun which is sequentially loaded but adds substantial weight. If there are 12 tubes in each cluster that would be 12 X 500 or 6 000 lb, maybe 10 000 lb, 5 tons, with all mountings. For 12 on each side and another 2 at the stern, that would be 26 X 5 tons or 130 tons total weight. US destroyers weigh at least 8 000 tons dry and empty, the weight is added above the waterline and would have to be compensated by ballasting, the weight should not be excessive. Fired 3 at a time, and allowing for some random distribution of missile attacks, at least 8 clusters should be firing, at 12 tubes divided by 3 = 32 missiles defended on each side of the ship.
The bolts could all be embedded in a solid block of plastic so they would be fired down the tube as one unit. After leaving the tube the plastic could ignite, that energy causing separation and dispersal of the bolts. The entire tube could have a cap of plastic over its end to seal and weather proof the tube. The volume of the tube could be filled with inert nitrogen instead of air to aid storage and prevent oxidation. With firing the nitrogen will pressurize and blow off the plastic end cap. The tubes can be reloaded at a factory after use for re-use.
After the 3 fire, the central one could fire again to increase missile damage. That would reduce missiles defended to 24 per side.
Above the ship could be stationed an electrically driven tethered helicopter, f. It would be perhaps 500 ft above the ship. It would have a body roughly resembling a flying saucer on the underside of which would be lens-photo chip assemblies which would continuously monitor the ocean for unusual movement signalling a missile approach. Underneath, it would have camera-laser assemblies. The laser would illuminate any object suspected of being a missile, simultaneously measuring its velocity through Doppler. The camera would allow identification of the object, with, or without, human intervention. If the tethered helicopter and cable weigh
2 000 lb and the disc loading is 5 lb/sq ft, the rotors would have to be 23 ft diameter and it would need 350 hp, 270 kilowatts of power plus generator inefficiencies. The cable would have the communication line plus power cord and would be used to winch the copter down when not deployed. The copter could have contra-rotating rotors and with electric power would have a low thermal signature and could be fairly stealthy. The speeds of naval ships are, however, the least efficient speed for helicopters, at faster speeds the forward motion produces additional lift through the rotor blades, at naval speeds the rotors are producing all lift through downforce and also have to overcome the additional drag of forward flight.
Getting a good dispersion pattern for the bolts is extremely difficult.
The navy has shown concern over an attack by a swarm of small boats. At close range, the bolts would shred a small boat and can fire quickly to defend against repeated boats. The tethered copter could also use lasers to aim mortar shells to attack boats, see post New Army.
This is another idea ignored by both DARPA and the US Navy.
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