U.S. Hypersonic Strategies Part 4

Let’s put another nail in the coffin for kinetic-kill vehicles. An EKV (exoatmospheric kill vehicle) has a  chance only if the adversary warhead climbs above the atmosphere for some portion of flight, and Avangard may never do so. If a hypersonic warhead descends enough to maneuver in flight, that contest is over.

There is a little bit of high school level math. If this turns you off, Part 5 will return to a qualitative presentation.

At lower altitudes, a winged interceptor missile, like the hypersonic adversary, can convert some forward motion into maneuvering energy. The DARPA RFPs will naturally include enhancements to winged interceptors. The logic: To intercept a hypersonic warhead requires a hypersonic interceptor missile. This means bigger, faster boosters, and a missile shape with more aerodynamics  than the vestigial fins found on today’s interceptors. Something like the Boeing Waverider on top of a Sprint booster.

There is  a major fly in the ointment. Suppose that after some years, both sides have squeezed all they can out of air frame  propulsion, and guidance. Missile development, like everything that depends on physics, is subject to the law of diminishing returns. Novelties can only delay the inevitable. It then becomes an even match,  except for one thing. The warhead knows its evasion plan. The interceptor has to observe, and estimate.

The interceptor, combined with ground-based tracking, estimates (I did not say knows) the position of the warhead. To figure it out, the interceptor thinks that:

  • Position is anticipated by velocity, which is  combination of speed and direction. So we need the velocity of the warhead.
  • Velocity is anticipated by acceleration.(The accelerator pedal in a car, and turning the steering wheel both produce acceleration.)
  • Acceleration is anticipated by jerk, which corresponds with how your foot is jiggling the accelerator pedal and twisting the steering wheel.

Jerk”, corresponding to the warhead’s next move, is known only to the warhead. What goes on in the warhead’s little brain cannot be eavesdropped. All other things equal, the warhead has the advantage.

A typical mutual closing velocity is 10,000 meters/second, split between the warhead and the interceptor. Suppose a hypersonic warhead makes this maneuver:

  • Change of course  100 milliseconds before impact, when separation is 1000 meters.
  • Converts 1% of its forward velocity, 5000 meters/second, into lateral  velocity, 50 meters/second, over 75 milliseconds.
  • A change of 50 meters/second in 75 milliseconds is an average acceleration of 66g’s. For comparison, a Sprint missile accelerated at 100g’s, impossible for humans, but comfortable for a compact, hard warhead.

Without a course change by the interceptor, it misses by about 5 meters. To correct course requires an accurate prediction. It has a camera on the front,  and a computer to interpret the images. The computer runs a program, an algorithm, to figure out the new anticipated intercept point  from a mess of data.

Now here’s a WAG of the prediction problem, where for clarity I have made certain simplifications about “filters”:

  • Position, velocity, acceleration, and jerk are coupled together.  For this problem, we need them all to get one.
  • To get all four variables requires a minimum of 4 observations. Remember your simultaneous equations from high school: 4 equations for 4 unknowns. Call each of these an observation set.
  • To get decent accuracy, we need at least 3 sets, probably more. A total of > 12 observations.
  • When a sensitive sensor, CCD or CMOS, images a point of light, it blooms, with expanding bright halos that fuzz the position of that point. Allow 10 milliseconds for the bloom to fade before another observation can be taken. Total time to observe: >120 milliseconds.
  • Time to run the program to come up with the new position and compute how the interceptor should respond by actuation of thrusters and control surfaces: 80ms.
  • Total time: 200 milliseconds.

Now the interceptor alters course,  by adjustments that require more time, to signal actuators, such as control surfaces and thrusters, which require more milliseconds. A thruster needs 2 ms just to start, and more to stabilize.

In that 200+ ms, the warhead and interceptor, moving at  closing velocity of 10,000 meters/second, have moved a further 2000 meters, 6000 feet. In the blink of an eye. And the warhead may change its mind again while all this is going on.

The above describes a scenario where the interceptor almost works, but not reliably enough to save a city. How much money do you lay on the interceptor? It has to hit to win. The warhead only has to miss.

To the above, we can add a corollary of Murphy’s Law:  Everything works a little worse than designed.

Next: Is there a game-changer?

 

 

 

 

 

 

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