Saturday, March 31, 2012

SAR Proficiency Knocked Into a Cocked Hat

Recently I was explaining the Aural Null search techniques to a 'lay' person. Someone with no particular knowledge of radio, navigation or Search and Rescue. When I was describing how the geometry for Procedure B works this lay person quite correctly identified the procedure as finding the circumcircle of a triangle:

We discussed that regardless of where the three points were located, so long as they formed a triangle the bisecting lines will all meet exactly at the centre of the circumcircle, the circumcentre, of the particular triangle they form. If you have a difficult time believing this there is a very good animated site at Math Open Reference that will allow you to move the three points around and watch what happens.

We then looked at a diagram from IMPROVEMENT IN POSITION ACCURACY For ELT and VISUAL SEARCHES by Barr, Casey and Muir (which I've quoted from before), shown here with the original caption:
Details of the flight path (in black) very near the target. The distance between the actual position (A-ELT) and the reported position obtained using the Cardinal Pass method (REP-ELT) is 0.12 nm. The graphical solution is also shown with the most probable location (graph-ELT) being within the “cocked hat”. Note that without a GPS, getting accurate fixes on the waypoints would be impossible as would the necessary graphing while in the cockpit of a small aircraft. The blue squares are 1 km x 1 km.
The question as to what a "cocked hat" was came up. For those without salt water for blood, in the context of navigation a "cocked hat" is the triangle that forms when three lines of position are plotted on a chart. It comes from the shape of the hat worn by naval officers at the time the phrase was coined. A line of position is a partial result of a navigation fix. One example is a bearing to a known location. The captain of a ship may take a compass bearing on a known lighthouse. From that the captain knows the ship is located somewhere along a line drawn from the lighthouse along the reciprocal of the bearing. The distance from the lighthouse may be estimated, but not with acceptable accuracy, so the captain only knows the ship is positioned somewhere along the line. Two or more lines of position are needed to 'fix' the position in a single location. The size of the "cocked hat" gives an indication of the errors accumulated in the bearings and drawing the lines on the chart.

However, finding the circumcentre of a triangle the only possible cause of a "cocked hat" is in drawing the lines. No matter what errors were made in determining the three points or plotting them on the chart, as long as they form a triangle all bisectors must intersect at one point, the circumcentre. If you examine the chart closely you will notice that the line between points ELT2 and ELT3 is not exactly horizontal. The perpendicular bisector of that line should not be exactly vertical, as it is. If this line was draw accurately the "cocked hat" would be much smaller than it is, if not eliminated. If these lines were drawn while airborne in the cockpit of a small aircraft this level of error may be acceptable. This diagram was produced months after the flight using a computer. Did the authors not understand that the perpendicular bisectors were not lines of position and therefore should all intersect at a single point if drawn properly? Or, did they not care that their geometry is sloppy? I'm not exactly sure what the authors thought this "cocked hat" means; but, as my conversation partner observed, it certainly clearly indicates the amount of care an attention they think is appropriate when producing a paper meant to describe a procedure that could have a life or death impact on someone.

For those who are interested, the lines of position for an Aural Null would be circles, each centred on one of the points (in this case ELT1, ELT2 and ELT3) and each with a radius of the distance the ELT could be received by the search aircraft. Unfortunately these points were collected with the receiver tuned to 123.25 MHz (the beacon was on 123.1 MHz) so there is no way to even estimate what the reception distance might be. These points were, in fact, re-purposed from a flight on which the crew used the Cardinal Pass (which is where the MaxLat and MaxLong points come from). Even though they claim this is a "standard Aural Null B procedure", off tuning is not described as part of the technique in the CASARA Training manual. With this kind of sloppy workmanship put forward as the standard it is not surprising that the Aural Null procedures have acquired a poor reputation, and proficiency has been knocked into a cocked hat. A turn of phrase that has nothing to do with navigation.

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