The ivory-tower science of mathematics and the life-and-death operations of desert search and rescue seem worlds apart. But a University of Arizona mathematician has combined the two. The result is a better chance of rescue for people who become lost in the Sonoran desert around Tucson, Ariz.
Equipped with a sophisticated hand-held calculator that he has specially programmed, Prof. John W. Bownds has helped guide half a dozen search and rescue efforts in Pima County over the last six months. A longtime volunteer member of search and rescue teams, the mathematician has adapted statistical techniques developed by the US Navy and Coast Guard for search and rescue at sea to the peculiarities of desert terrain. These are beginning to bring a new degree of efficiency and effectiveness to desert rescue techniques.
''Although I've known about these methods for years, it is only recently that the political climate has made the necessary resources available to do this,'' the scientist says.
Pima County Deputy Sheriff Charles McHugh, who coordinates search and rescue efforts in the Tucson area, terms this ''a great search management tool. Before, we were making seat-of-the-pants judgments about whether we really had searched an area enough.''
One little-reported aspect of the rapid growth in the Tucson area is the increasing number of people who become lost or stranded in the unforgiving desert that surrounds the city. People can find themselves in such a situation just 15 minutes by automobile from downtown Tucson. As a result, the Pima County Sheriff's Office receives a call a day reporting desert disappearances. Not all are legitimate, but those that are genuine evoke a massive response. There can be more than 100 people involved in the search. Helicopters from a nearby Air Force base, cars, horses, search dogs, and volunteers comb the cactus-studded plains hoping to find the lost person before the heat and lack of water take their toll.
What Dr. Bownds and two fellow University of Arizona mathematicians have done , mostly in their spare time, is to help make these searches more orderly. Starting with the helicopters, which are the key element in the search, a series of trial rescues was run. ''Missing persons'' were spotted in various circumstances - out in the open, under light cover, at various times of the day, and in different weather conditions. The number of times that overflying helicopters spotted or missed these people was tabulated.
''We found some interesting and unexpected things,'' Bownds recounts. For instance, it is harder for helicopter observers to spot a person lying in the shade on a bright, sunny day than it is with a moderate overcast. This is because the shadows appear more impenetrable on a bright day. So, on bright days , they now fly helicopters in the early mornings and late afternoons whenever possible because the probability of detection is substantially higher. Also, the researchers discovered that the copters have a blind spot right beneath them because the observers are looking to each side. As a result, the Air Force crews now fly their second search patterns over an area at right angles to the first to maximize their coverage.
The real object of this mathematical exercise, however, is to provide the search director with a more precise measure of the probability that a lost person might still be in a given search area. This makes it less likely that the searchers might move to another area prematurely or waste precious time searching an area already thoroughly covered. After each search pattern is run, Bownds punches the pertinent information into his calculator and gives the search director the probability that the person might have been missed. The search director uses that information to decide whether another overflight is needed or whether it is time to extend the search into other areas.
''Next, we hope to determine how effective police dogs are as searchers,'' the mathematician says. These dogs are often used even though they are not tracking dogs but are trained to react to the unusual. ''We have no idea how good they are at this job,'' Bownds says.
He would also like to start building up statistics on the actions of people lost in various areas. Once enough records are compiled, it may be possible to determine patterns that would help rescuers in the future. Bownds already knows, for instance, that children are almost always found within three miles of where they were lost, because they wander aimlessly. Perhaps adult actions fall in similar, but less obvious, patterns.
Bownds has already crammed all the mathematics into his hand-held calculator that he can. To add more sophisticated elements to the program, a portable microcomputer adapted to run off a car battery will be necessary.
''You know, I think we can write the book on desert rescue,'' he says. It is a book that might ultimately save a great many lives.