Thursday, May 24, 2012

Ignorance? Negligence? Sloth?

As I said in my previous post about my experiences with CASARA, I was stymied by the refusal of several members, including the Director to accept rational arguments about electronic search methods. It wasn't util one of them sent me a copy of a paper with the rather imposing title Improvement in Position Accuracy for ELT and Visual Searches or Accuracy of ELT Searches for short by Anne Barr, Mike Casey and Langley Muir that I began to learn why.

In that paper, along with a discussion of received signal strength were these two diagrams that are supposed to describe how the signal strength received by a search aircraft varies as it flies by the ELT.

We are to believe that the signal strength will follow this semicircular path:

There is no other way to put it. This statement is completely ridiculous, as anyone who knows even a little about radio transmission should be aware. But let's take this one step at a time.

Radiation Pattern

A radiation pattern is simply the directional dependence of the strength of radio waves from an antenna. Figure 1 above is an azimuthal plot in that it gives the strength in various directions in the horizontal plane. They describe it as circular since it depicts radiation at the same strength in all horizontal directions or in all azimuths. 

Aircraft move in three dimensions, so we need a three dimensional radiation pattern. Since they expect a semicircular reception pattern I'm assuming they are talking about an isotropic radiator. That is one that radiates the same strength in all elevations as well as all azimuths. They are free to contact me with a correction if my assumption is incorrect and I will update this article accordingly.

What ever our radiation pattern is, we need to know the azimuth and elevation from the ELT to the search aircraft at each point along the flight path. Some simple trigonometry provides and we get the graph below with the azimuth in red and the elevation in green. The exact shapes of these curves will vary somewhat depending on the altitude of the aircraft and the distance at closest approach, but this is the general shape.

By plugging the azimuth and elevation into the formula for the radiation pattern we can find out how strong the signal is in the direction of the aircraft at each point along the flight path. Since we are using an isotropic radiator that is always going to be 0 dBi, meaning the strength is not stronger than, nor weaker than at any other point.

Inverse Square Law

Not a semicircle at all. But we aren't finished yet. One of the fundamental properties of radio waves (or light waves) is that the strength gets less as the receiver is moved further away from the transmitter. In fact it decreases in proportion to the inverse of the square of the distance, the so called inverse square law.

So we need to know the distance from the ELT to the aircraft at each point along the flight path. We actually need the slant range which takes into account not just the horizontal distance, but the altitude as well. Again simple trigonometry provides the answer.

Received Signal Strength

We can now calculate the expected received signal strength for each point along the flight path. We do need to know the transmitter power, transmitter and receiver gains, aircraft altitude and distance at closest approach. I've chosen 1 miliwatt, or 0 dBm for transmitter power, we've already decided the transmitter antenna is isotropic, so let's have an isotropic receiver antenna too. I've plotted four curves, on each the aircraft is 1000 ft above the ELT, and the points of closest approach are 0.5, 1, 2 and 3 nautical miles.

So where is our semicircle? Well, unfortunately they just made it up out of whole cloth and bovine scatology. I know they are intelligent enough to work out the simple mathematics between them if they had to. Were they ignorant of the inverse square law and its importance? If so what else are they ignorant of? Did they simply neglect to put any thought into what they were working on? Then how else might they have been negligent? Were they just too lazy to put in the effort required? Then what else did they just not bother to do? I don't know the answers, perhaps they will tell me. But it is clear that once they put what ever effort they did into devising their technique, they weren't prepared to listen to the facts about it. This would be hilarious if it were not for the fact that techniques derived from this level of ignorance, negligence, sloth or what ever their problem is, have been used on search and rescue missions. Instead it is sad and potentially deadly.

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