Ballistic missile

A ballistic missile works by burning propellant and ejecting the hot gases through a nozzle, typically at a velocity of around 2500 meters per second (m/sec). The thrust from the exhaust causes the missile to accelerate. A given thrust will cause progressively higher accelerations as the missile lightens due to the consumption of its propellant. All of the propellant is consumed in the first few minutes of flight, following which the missile coasts above the atmosphere at a speed of several kilometers per second to its target. In an idealized case, the burnout velocity would be equal to the exhaust velocity times the natural logarithm of the ratio of gross missile weight to the payload. In real life, the missile will need additional impulse to reach a given velocity. Account must be taken of: the structural weight of the missile (typically discarded in several stages during boost phase); air resistance during boost; and gravity during boost. Still, the idealized relationship is useful: it provides an optimistic upper bound on what can be achieved when parameters are varied. At short ranges, the range of the missile will go as the square of its burnout velocity. Due to the curvature of the earth, at longer ranges the range will increase more rapidly. Table 2 shows the burnout velocity needed to reach various ranges, together with the payload fractions associated with missiles that attain any given velocity.


For example, a 6000-km range missile would need a 6200 m/sec burnout velocity and could achieve this while devoting 2-5% of its gross weight to payload; a 10,000-km range missile would need 7200 m/sec and could devote 1.3-3.5% of its weight to payload, about two-thirds as much. Thus, the table can be used to scale payload fractions as the missile range is varied. The scaling indicated in Table 2 is probably a bit optimistic from the missile designer's perspective. The original missile design is optimized to produce the best possible distribution of propellant and structural weight among the stages. Adding a new upper stage (adapted from a different missile) or offloading payload will not necessarily yield an optimal mix. Thus, the payload penalty for increasing the range could be greater than the table indicates.

The concept of payload merits discussion because definitions can vary widely. Consider the weight remaining when the missile reaches burnout velocity. It includes the empty weight of the burned-out final stage. If this is deducted, what remains is the throw-weight or payload (shown in Table 2 as a fraction of gross weight). This includes the MIRV bus (if any), the decoys (if any), the guidance system, and one or more re-entry vehicles (RVs). Typically, a single RV will account for two-thirds or more of the payload; but because of the need for a bus, multiple RVs will add up to only about half the payload. The RV consists of a nuclear warhead, a fuze, and a heat shield. The heat shield may account for about one-third of this weight. Thus, less than half the payload will commonly be available for the weight of a nuclear warhead.

Table 2. Burnout Velocity and Payload Fraction vs. Missile Range

Range (km) Burnout Velocity (m/sec) Payload Gross Weight 300 1700 .150 - .200 600 2400 .080 - .120 1000 3000 .070 - .110 1500 3600 .055 - .095 2000 4100 .040 - .080 3000 4800 .030 - .065 4000 5400 .025 - .060 6000 6200 .020 - .050 8000 6800 .016 - .042 10,000 7200 .013 - .035 12,000 7400 .011 - .030

The first US nuclear warheads weighed 4100-4500 kg. The likely weight of a first warhead produced by a proliferating country has been variously estimated at 450-1000 kg. The lower estimate was for the first effort of an advanced, industrialized country and the higher estimate for a third world country. The United States and the Soviet Union each needed six to eight years to reduce their warhead weights to 1000 kg. Existing North Korean ballistic missiles could carry a 500 kg nuclear warhead. ICBM-range derivatives of these missiles could carry only 200-300 kg. Thus, even assuming that North Korea's first generation nuclear warhead is at the low end of the estimated range (450 kg), an ICBM derivative of the existing missiles could not lift the warhead.

A guidance system is needed to hit a predictable target. This functions only during the boost phase, correcting the flight path to adjust for various deviations. After burnout, the missile is unguided and any further deviations from course, such as those caused by winds during the re-entry phase, are not corrected by the guidance system. The ballistic missiles now in use by North Korea, Iraq, and Iran achieve CEPs (Circular Error, Probable, the radius of a circle within which one-half of the warheads can be expected to fall) of several kilometers. This corresponds to velocity errors on the order of 0.1%, which in turn could lead to CEPs as great as 40 kilometers at ICBM range. With such accuracy, a missile aimed at Los Angeles would run a significant risk of missing the entire metropolitan area. This would seem to preclude any very near-term threat. However, on the extended timetables suggested above (2010 for North Korea, 2015 for Iran and Iraq), guidance should not be a problem. There will be time to develop a new system. If adapted to an ICBM, strapdown systems coming into use in civil aviation could yield CEPs of a few kilometers at full range. Global Positioning System updates (even on the clear channel) could reduce guidance system errors to a level that is small compared to the re-entry error discussed below. Thus, while North Korea, Iraq, and Iran are not remotely prepared for ICBM guidance now, they should not be expected to have difficulty hitting large cities at ICBM range after 2010.

A final problem is re-entry. As the RV re-enters the atmosphere at a velocity of more than 7000 m/sec, it encounters tremendous drag and slows down, eventually striking the ground at somewhere between 200-3000 m/sec. While slowing down, the RV generates tremendous heat that must be removed or else the RV will burn up. The ICBMs that could be developed by North Korea, Iraq, or Iran would use a blunt, high-drag heat sink-essentially a dome of copper armor. As the RV decelerates, the heat sink warms up and transfers most of the heat to the air rushing past. Most of the deceleration occurs at high altitude where the air is thin. By the time the RV reaches the denser lower atmosphere, it is no longer traveling at tremendous speed. The heat-sink approach was used on all of the early US and Soviet ICBMs. It has three drawbacks: it is heavy; its low final velocity gives the wind a longer time to alter the RV's course, degrading its accuracy; and its low final velocity makes it vulnerable to terminal interceptors. One consequence of relying on heat sinks is that no matter how good the guidance system is, the ICBM will be limited to a CEP of at least 500 meters at full range. Shorter range missiles often use pointed, low-drag heat sinks, but this approach is not available at ICBM re-entry velocities: the RV would burn up.



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