The 
Ekelund 
Range:

A story of JO Innovation, Determination, and Communication 
By JOC Michael Foutch, USN

Never mind the speed advantage these new nuclear submarines would have over the current diesels. Anti-submarine warfare was fast becoming the primary mission of the Submarine Force, too, and the new passive sonar arrays would give submariners the ability to measure bearings to targets more accurately at greater range. Yes, the summer of 1956 was a great time to be serving in the Submarine Tactics Department at the Navy Submarine School in New London, Connecticut.

Then - LT John Ekelund was six months into his assignment teaching future submarine officers to use state-of-the-art sonar and electronics to gain accurate bearings for target motion analysis. There were plenty of junior officers (JOs) like him on the faculty – with tours on two different submarines and additional time on the Pacific Fleet submarine staff, he knew a little about undersea warfare operations. The son of a submarine officer, the young man grew up traveling from one part of the world to another, from Guam, to Puerto Rico, Florida, Washington, D.C., and plenty of places in between. He had followed his older brother to the Naval Academy and found a home in the submarine community.

As a student in school, he had liked mathematics courses and thrived on engineering. Fooling around with problems and puzzles in that environment was something he found fun – certainly not daunting or mysterious. One might even call him a tinkerer.

During his first few months at sub school, LT Ekelund had beefed up his knowledge on fire control systems and was making himself quite an expert in data analysis. That’s when he began to appreciate a key problem. Despite the new advances in technology, the submarine still relied on slow and arcane plotting methods to determine target range passively, and these required making shaky assumptions about target speed. Even as capabilities were radically improving, this problem continued to bug operators at sea. Maybe they could detect a target five times better than before, but even with faster speeds and better weapons, how could they determine range to the target passively, accurately, and quickly? 

To fire a weapon at a submerged submarine effectively, one needs to know target bearing, range, course, and speed. These are a lot of variables. No matter how advanced the applicable mathematics, none of it showed a way to solve a single algebraic equation with several unknown variables. Thus, the lieutenant was effectively presented with an insoluble mathematical conundrum. 
Only he didn’t see it that way. What was needed was some new way of looking at the range problem. According to Ekelund, figuring out how to make it work “just fell out.” By making a few assumptions he discovered a way to calculate the range. Because of the artificiality of those assumptions, it was also necessary to determine how badly they affected the accuracy of the range estimate itself.

Ekelund convinced a co-worker at the school to spend countless lunch hours in an attack-training simulator to run hundreds of scenarios with different targets, ranges, speeds, and geometry. The loss of those lunch hours was well worth the resulting proof that his mathematical algorithm actually worked. It delivered an effective technique for finding target range based on the bearing rate before and after own-ship maneuvers. 

While he didn’t think his procedure was easier or quicker but just made more use of the available information, Ekelund was excited about the prospect of getting word of his discovery to the fleet. In one stroke, the problem of putting the new long-range weapons on target seemed to be solved, and that was important news. 

The young officer wrote a detailed letter explaining his new formula, and observing proper protocol, placed “Officer in Charge, Submarine School” on the “From” line. That, he figured, would get this up the chain and out to the fleet more quickly. Once everyone saw how great an idea this was – he surely believed – we could start using our new technology in a better way. Day after day, he checked on the progress of the letter, eager to see the effect on the fleet. Day after day, the letter sat. The Officer-in-Charge had other matters on his mind, administering an entire submarine school, for one. There was little time to spend analyzing mathematical trickery that a fresh, callow officer claimed would benefit the entire force.

So LT Ekelund finally let his impatience get the best of him. He reclaimed the letter, retyped it to put his own name in the “From” line, and re-addressed his ideas to the Submarine Force Commander. That surely would get someone’s attention. Indeed, the letter made its way slowly to the top echelon, which published the new formulas in its quarterly bulletin. Just a few months later, after submarines in the fleet started working with the new procedure successfully, Ekelund’s innovation became part of the official curriculum of the Basic Officers and Prospective Commanding Officers courses.

The Ekelund Range helped revolutionize modern undersea warfare and is now a household phrase in the submarine community. An established method still used by tacticians and in automated fire-control algorithms, it has long been part of the course of study in target motion analysis at the Submarine School.

Now living comfortably down the way from the Naval Postgraduate School in Monterey, California, where his son-in-law is an associate professor, retired RADM Ekelund spends his days playing golf and serving occasionally as second reader for a student’s graduate thesis. In the years after his Submarine School experience, he wrote several subsequent articles on range determination and other navigation problems. Nonetheless, he never forgot the lessons he learned from his most famous discovery – not only from developing the Ekelund Range, but also in getting the word to the people who needed it most.

“As I worked my way up to being an XO, then a CO, I always urged people to communicate about problems and philosophies,” RADM Ekelund said. “There are whole bunches of people who under- stand the problems out there. Only you might know the answer.

“There was a tremendous value to that quarterly bulletin,” the admiral added, referring to the first publication that printed his formula. “It was an avenue for information to flow into the Sub-marine Force, thus exposing a problem, seeking a solution, and letting a greater community of minds throw in their two-cents worth.”

While the Ekelund Range is used every day on submarines around the globe, there is one place the inventor resists the temptation to use it. “I do play golf,” he said, laughing. “But I don’t use the range formula to measure the distance to the hole.”

JOC Foutch is a Military Editor of UNDERSEA WARFARE Magazine.