North Korea lacks capacity to hit U.S. with accuracy: U.S. general; Napkin Calculation

EDIT: This discussion neglected ITAR regulations, which control the export of GPS systems for military use. Read down.

Reuters: North Korea lacks capacity to hit U.S. with accuracy: U.S. general.

The precise wording is: “What the experts tell me is that the North Koreans have yet to demonstrate the capacity to do the guidance and control that would be required,” said Selva, the second highest-ranking U.S. military official.

There is a general tendency with public statements to reassure with the phrase “has not demonstrated.” To my mind, the difference is the same as between an assailant with a gun in his pocket, and pointed straight at you. It should not be taken as much of a reassurance.

The problem of guiding an ICBM was solved in the early 1960’s. The ASC-15, built by AC Sparkplug, might be impossible for North Korea to duplicate. But things have  gotten a little easier.

I decided to do another nefarious napkin calculation. This one involves a product of VectorNav, a Dallas company who make inertial navigation systems the size of postage stamps. If you happen to want one for your hobby missile, the VN-200 GPS/INS will run you about $4000. It weighs about an ounce, and has all these nifty features:

  • Built in inertial navigation system.
  • Accuracy augmented by 50 channel GPS.
  • On-board computer with sophisticated de-noising algorithms.
  • Maximum g-load of 16 gees, which should be enough if it’s cushioned.
  • Heading accuracy of 0.3 degrees = 0.005 radians.
  • Pitch accuracy of 0.1 degrees.
  • Development system so you can customize it.

In the original post, I neglected that the VN-200 is compliant with ITAR (Intenational Traffic in Arms) regulations, which means that it has an altitude limit of 60,000 feet  and of speed, about 700 miles per hour, that make it unusable in a ballistic missile (see the spec sheet for conflicting figures that are probably more up-to-date). But GPS technology has become “disseminated”, which means that most or all parts that make up the VN-200 are available separately, if not as compactly. Generalized forms of the GPS software code base are also widely available. Quoting Wikipedia,

 These limits only apply to units or components exported from the USA. A growing trade in various components exists, including GPS units from other countries. These are expressly sold as ITAR-free.

So while it is not assured that you can buy a postage stamp sized VN-200 equivalent, neither is this discussion invalidated.

An inertial navigation system is not the same as an inertial guidance system. But mathematically, they are very closely related, by this saying, which every systems engineer knows: “The best estimator contains a model of the system.”

Here comes the napkin. The chord of a circle is a straight line connecting two points on the perimeter of a circle. The center of the circle is Pyongyang. The perimeter of the circle crosses a U.S. target about 4000 miles distant. Assuming a 0.3 degree cumulative error in heading on burnout, the length of the chord is 20 miles. With the target at either end of this chord, the accuracy of the missile, excepting the reentry vehicle, is plus or minus  20 miles. For various reasons involving the averaging of errors, the performance may be much better than that.

The above contains the assumption that the missile can be controlled; that the  vernier rockets, tiny rockets used to adjust the orientation of the missile, can actually apply the corrections called for by the navigation system. The experts cited by General Selva have available to them the telemetry, the reports sent by the missile to Pyongyang, to analyze.  So these messages would include all the commands generated inside the missile to  adjust the vernier rockets.

Since the experts did not see this tight orchestration, they concluded that the more modest goal of this test was to keep the missile pointed in approximately the right direction. Why did the North Koreans not try for more?

We would like to think that they can’t. But the more informed answer is not as reassuring.  There are dollars-and-cents reasons. The more tightly controlled the missile is, the greater the chance that it will careen wildly out of control and be a total loss. This is a universal problem with control systems, the BIBO stability problem. (I’m not providing a link; you wouldn’t enjoy the read.) The better the job you try to do, the greater the chance the machine/missile/gadget will blow up/burn up/shake apart completely.

So there are really two possibilities for the missile itself, excepting the reentry vehicle, which is a separate and equally important problem. The missile either:

  • lacks the finesse to act on what an off-the-shelf navigation system would tell it to do.
  • has all the necessary systems, with screw-tightening planned for future tests.

Reentry technology is classified, and not amenable to the napkin. But some observations can be made.

The range and capacity of current North Korea missiles requires close to the minimum energy trajectory. You can imagine this as how you would throw a baseball for max distance. In this shallow path, the reentry vehicle tends to “fly” and “skip” a little, which adds to the accuracy problem.  But recent North Korea tests have been almost straight up and straight down. This is brutal to the thermal protection, but potentially easier to guide. It offers North Korea an alternative  development path. Japan is already within range of this threat.

If you’ve read this far, with news of future tests by North Korea, you may be able to embark on your own extrapolation of the threat.

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