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Missile Defense

Technology has always found its greatest consumer in a nation's war and defense efforts. Since the last attempts at a "Star Wars" defense system, has technology changed considerably enough to make the latest Missile Defense initiatives more successful? Can such an application of science be successful? Is a militarized space inevitable, necessary or impossible?

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rshow55 - 04:38pm Sep 25, 2002 EST (# 4533 of 4536)
Can we do a better job of finding truth? YES. Click "rshow55" for some things Lchic and I have done and worked for on this thread.

To play "dogfight" with model airplanes in the way I have in mind, you'd need some space and moderate equipment.

A small field - maybe a baseball or soccar field.

At least two radio controlled model airplanes.

At least 3 "chirper senders" for microwaves- sending pulses out in the air, at specific frequencies, with pulses timed to .1 nanosecond accuracy with respect to gps or some such reference. Say these "chirpers" -"chirp" every millisecond. 5-10 chirper senders, each with its own frequency, would be better.

One reciever, with bands tuned to each chirper frequency, capable of timing incoming signals to .1 nanosecond.

Antenna arrangements so that the "chirper" signals did not go from chirpers to the reciever directly, but only by reflection from a flying object.

Plus a small computer - - maybe two. Computers made before 1990 would make the competition slightly more interesting, but not by very much.

Nothing fancy or expensive.

Call the field an x-y plane, of altitude z=0 and say there are n chirpers, at points

C1 at (x1, y1, 0)
C2 at (x2, y2, 0)
C3 at (x3, y3, 0)
and so on to
Cn at (xn, yn, 0)

The reciever is at point R
R at (xr, yr, zr)
and only gets signals from the chirpers that are reflected from flying objects (z > 0 ).

Say that flying object (the metal motor of the radio controlled airplane) has position P.

Distances along the two sides of the triangle from Ci to P to R are known by timing. For .1 nanosecond resolution - these distances are known to within about 3 cm.

Positions of Ci and R are known - the x, y , z positions of point P are unknown. If triangles corresponding to 3 Ci's are available, with known distances, you can solve for x, y, z positions of point P. With more triangles, there are several ways to solve the relation - enough for crosschecking.

With this information, how far are we from achieving optimal dogfighting behavior, where the ability of the following model plane to track the target is limited only by the dynamic limitations of the model airplane propulsion and aerodynamic control - not by control logic?

Not very far. http://www.wisc.edu/rshowalt/pap2

rshow55 - 05:02pm Sep 25, 2002 EST (# 4534 of 4536)
Can we do a better job of finding truth? YES. Click "rshow55" for some things Lchic and I have done and worked for on this thread.

So, for one model airplane, you could track x-y-z position, with respect to the reciever (or any other fixed point) - and plot that position, to ~3 cm uncertainty, every millisecond.

Plotting position against time, for 20 past points, using diffterms, you could have a very good running polynomial approximation of the motion - (and polynomial approximation of its differential equation, with boundary conditions).

A 10th degree polynomial approximation would leave enough points for noise subtraction (of "noise" in the sense of signal that didn't fit a 10th degree polynomial fit).

Integrating the differential equation "predicts that future" according to the de - a de that is continuously updated (say, every millisecond).

You could do the same for 2 airplanes, or 3 - though sorting out which triangles correspond to which points would require some logic. Getting running x,y,z positions, polynomial approximations of equations of motion, and easily integrable polynomial approximations of the de's of the motion of each airplane.

Getting these de's into handy frames of reference (for example, the frame of the individual model airplanes) isn't fancy.

Now, suppose there is a "lead" model airplane that is "flown" -- either by hand, or by machine - without information about how flight path changes going to to logic controlling the "follower" model airplane.

How well can the "follower" follow?

Can the "follower" follow a moving, jagging target?

That depends on how good the information processing is, and how good the maneuverability of the follower is, compared to the target.

Here's a game that competing teams of engineering undergraduates could play, and compete in.

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