Monday, August 25th, 2014

A couple years ago Gregory Cochran mentioned The Wizard War, R. V. Jones’ account of his time leading scientific intelligence for Britain during the war, because it had some interesting examples of thick and thin problems — but mostly because it’s so damn much fun.

I bought a copy, under the original British title, Most Secret War — “most secret” is the British equivalent of “top secret” — and recently read and enjoyed it.

The classically thin problem that Cochran cites involves the German two-beam navigation system (Knickebein). From page 97 of my copy:

It may help here if I explain what a Lorenz beam is, for this is what we expected to find. If one arranges a number of aerial units (‘dipoles’, which look like the simplest type of television aerial) side by side, as in a fence and about the same distance apart as they are long, and feeds the radio energy to them in a suitable manner they will generate the beam which emerges broadside to the fence; and, paradoxically perhaps, the longer the ‘fence’ the sharper the beam. But without a fence of prohibitive length, the beam would not be nearly sharp enough to define a target one mile wide at two hundred miles range. The clever trick in the Lorenz system was to transmit two fairly blunt beams, pointing in slightly different directions but overlapping one another in a relatively narrow region which now in effect becomes the ‘beam’ along which the aircraft are intended to fly.

Knickebein Principle of the Lorenz Beam Diagram

The two overlapping beams are most simply generated by two aerial systems pointing in slightly different directions and mounted together on a single turntable. The actual radio transmitter is switched from one of these aerials to the other and back again in a repetitive sequence, so that one aerial transmits for a short time followed by a longer interval, giving a ‘dot’ to anyone who listens to it on a suitable radio receiver, while the other transmits for a long time followed by a short interval, giving a ‘dash’. Anyone so placed as to receive the two aerials at the same strength would hear the one transmit a dot immediately followed by the other transmitting a dash, so that he would think that he was listening to a single aerial transmitting continuously. As he moved sideways into the zone in which one beam, say the ‘dot’ beam, was stronger than the other, he would being to hear the dots coming up above the continuous note, and vice versa with the dashes. By listening for the predominance of dots or dashes he would know the direction in which he would have to steer to bring himself back into the narrow ‘equi-signal’ zone. This zone can be as narrow as one hundredth or even one thousandth of the width of the ‘dot’ or ‘dash’ beam alone.  The aerials are therefore set on the turntable in such a direction that the equi-signal zone passes over the target.  To warn the pilot that he is approaching the target, a similar beam system would be set up from one site well to the side of the director beam, and this second system would transmit a marker beam to cross the director a few kilometres before the target.

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