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The Four Corners of the Map
A statistical study on the phenomenon of how searches occur at the corner of a topographic map

| Introduction | Methodology | Results | Discussion | Acknowledgements |

Introduction
One of the rules of search management is: Searches always occur at the corner of a topographic map.  Does in fact some mad sadistic search god or goddess (please note little g) love to make the lives of incident staff more miserable (we already know lost people only become lost after searchers have settled into nice warm beds).  With that thought in mind, and far too much free time while preparing for NASAR's RESPONSE 97 the following study was undertaken.  It is hypothesized that the area found in the center of a United States Geological Survey 7.5 minute topographical map is in fact rather small.  Therefore, it should not be too surprising that additional topographical maps may be required in order to make a field map of 8.5 x 11 inches.

Methodology
A 7.5 minute USGS topographical map of Portland Oregon was purchased from REI.  Using the UTM grid system already found on the borders, the map was grided into square kilometer squares. More recent editions of USGS 7.5 minute maps now include the UTM grid already overlaid with thin black lines.  However, on this particular map it was required to draw on the lines manually.  A small dot was then made in the center of each kilometer square.  Only those squares that consisted of an entire square kilometer were included.  A small hole was made in the center of an 8.5 x 11" sheet of paper.  This size paper was chosen since it represents the most common size of maps copied and issued to field resources.  The small hole on the 8.5x11" paper was aligned with the each dot made on the grided USGS topographical map landscape orientation.  A data entry was then made if the 8.5x11" paper fit completely on the grided map (One map), would have required a second map to fill the 8.5x11" space (two maps), or located in the corner of the grided map would have required four maps to make a field map (four maps).  This procedure was repeated for each dot made on the grided map.

Results:
Basic Pattern:  Using the standard sheet of paper (8.5x11") the following pattern became apparent.  Those searches that had a center point in the red areas (corners) would require four topographical maps.  Searches centered in the yellow areas (middle sides) would require two maps.  And those searches centered (Initial Planning Point) in the green areas would only require one map.  The illustration (right) is not to scale.

The largest search radius that can fit on a standard sheet of paper is 4.25 inches (half of the shortest dimension).  On a 7.5 minute (1:24,000) map 4.25 inches represents 1.6 miles

Probability of maps required for standard sheet of paper.
# of Maps % of Area
One Map 25%
Two Maps 40%
Four Maps 35%

The above table gives the probability that mission staff will have to assemble multiple maps if making a copy onto a standard sheet of paper (8.5x11").  However, it does not give the probability that the entire search area (typically the statistical max zone) will fit onto one topographical map.  Alzheimer's subjects with a max zone of 1.5 miles is the only subject category that corresponds with a sheet of paper.  The second column, gives the probability of multiple maps for a three mile search radius (hunters, lost children, mental retardation), the third column gives the probability of multiple maps for a four mile search radius (lost hikers), while the last column shows that all searches with a radius of 5 miles or greater (despondents, psychotics) will require the four maps.
# of Maps 3 mile radius (% of Area) 4 mile radius (% of Area 5 mile radius(% of Area)
One Map 0% 0% 0%
Two Maps 29% 8% 0%
Four Maps 71% 92% 100%

 

Discussion
In order to make a field map copied onto a standard sheet of copier paper (8.5x11") a 75 percent possibility exists that maps must be taped together.  It is almost just as likely that it will require taping four maps as two maps together in this scenario.  It is also important to note that only searches for Alzheimer's subjects will contain the entire search area (max zone = 1.5 miles) on a sheet of letter sized paper.  All other subject search types will require taping together at least two maps.  Most of these other searches will require taping four maps together.

Using 15 minute maps will also result in the same percentage of taping maps together.  The percentage of single, two, or four maps is based upon a ratio of scale.  While the 15 minute map contains 4 times more information, the letter sized copied map also contains 4 times more information.

The above information was determined using a map of Portland, Oregon. Topographical maps south of Portland while still 7.5 minutes will have more miles represented on the East-West line.  This will result in slightly greater chances of having the search fit on one map.  However, it should still be clear that a search that requires only one map is a rare search.  After all, there are four corners and only one middle to the map!

Acknowledgements:
It was a fine brand of Portland's Micro-brew that helped foster the idea for this study. 

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