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World War II Operations Research

In the fall of 1939, England was again fighting Germany, the same enemy as in World War I. However, advances in the tools of war during the twenty years of peace set the scene far distant from August 1914. Advances in aviation made antiaircraft defense a high priority. The short distance from mainland Europe to England presented a minimal challenge by that time for a military aircraft.

Similarly, a scarcity of appropriate antisubmarine weapons, resources, and tactics provided further new formidable tasks in hunting an improved enemy submarine, always a complex target operating in an opaque environment. U-boats of 1939 were faster underwater, could operate at greater depths, and maneuver more skillfully. They were quieter, with longer endurance and tougher hulls.

The severity of the U-boat problem led Vannevar Bush; President Roosevelt’s adviser and chief contact on all matters of military technology including the atomic bomb, to observe in his memoir Pieces of the Action, “The United States came very close-too close to being defeated in each war by the submarine. “After the war, Winston Churchill wrote, “The only thing that ever really frightened me during the war was the U-boat peril”.2 Statistics on U-boat sinkings support the post-war reflections of Bush and Churchill.

U-Boat Sinkings
September 1939-April 1943 (44 months) 193
May-June-July 1943 1OO

Credit for this remarkable shift in the antisubmarine war against the U-boats stems from a number of activities, efforts, and approaches, by many individuals. Success was not instantaneous. The progress beginning in May 1943 was hard-earned. The introduction and evolution of operations research, the application of mathematics, and the scientific method to military operations, was some of many contributions leading to the defeat of the U-boat.

World War I was fought with weapons available at its start. World War II, sometimes referred to as the physicists’ and engineers’ war, witnessed a continuing stream of new weapons, frequently complex, and raising difficult operational questions on occasion beyond the purview of the military.

England’s late 1930s introduction of radar in conjunction with ¬∑air defense epitomizes WWII high technology. New, untried, extremely complicated, costly, and needed, it was highly effective when properly used. The military user required assistance from the scientists who conceived it and the engineers who manufactured it.

Operations research was not prescribed. It evolved, as participation by civilian physicists, engineers, mathematicians, astronomers, physiologists applied their scientific methods to equipment performance with the field military operators on land, air, and shipboard. Optimizing system performance and solving problems based on careful analysis of data collected from direct experience in real-time operations in a wartime environment followed scientific methods, bringing the term slide rule strategy into use. Operations research improvements by factors of 3 or 10 were common. This level of contribution was out of proportion to the amount of effort spent. By 1942, acceptance of the methodology brought formal operations research groups to all three of Britain’s military services.

Operations research techniques used by civilian scientists contributed to first defeat for Hitler, with the UK winning the Battle of Britain (air warfare) in the summer of 1940. Increased mastery in sinking U-boats starting in May 1943 is attributed likewise in part to operations research. Because of this and other successful WWII applications of the method, today every branch of the military has its own operations research group involving both military and civilian personnel. Military operations research provided the logistic planning for Operation Desert Storm. The United States National Security Agency has its own Center for Operations Research.

Early Operations Research

During the 1800s, two inventors, one a mathematician and the other an engineer, contributed significantly to the formulation, expansion, and acceptance of operations research as a tool in the 20th century.

The mathematician and inventor Charles Babbage (1792-1871) contributed to the early formulation of this new field. His book Economy of Machines and Manufactures (1832) is said to have initiated the field of study known as operational research. It is notable that during this same period, Babbage developed plans for an analytical engine, the forerunner of the digital computer. His participation in establishing the modem English postal system and developing the first reliable actuarial tables reflects his analytical skills and early operational analysis.

In the United States, Frederick W. Taylor (1856-1915), an inventor and engineer knows as the father of scientific management, provided additional quantitative methods addressing man-machine problems. Taylor applied scientific principles to mechanisms to make them more efficient, conducting scientific measurement of work and productivity in the work place with the workers and the machines. Taylor’s work helped to make Henry Ford’s precision automobile production line conveyor belt operation possible. Babbage and Taylor are representative of early contributors to operations research.

World War I Efforts

During World War I, F. W. Lanchester, a pioneer in the English motor car industry, made fundamental contributions by mathematically describing the outcome of military actions related to numerical and firepower superiority and concentration of forces. He also foresaw the importance of aeronautical efficiency in future great battles. His equations appear in current literature.

In 1915, Lord Tiverton completed a detailed study of strategic bombing anticipating the 1000 plane bombing raids of WW II. A. V. Hill of the experimental section of the Munitions Invention Department of the British Army studied antiaircraft gunnery and developed tactics and procedures to enhance the effectiveness of antiaircraft fire.

Thomas A. Edison, as a member of the Naval Consulting Board during WW I considering the antisubmarine problem, concluded that sinking German submarines was only one means of saving merchant ships. He directed his efforts to a study of the statistics of enemy submarine activities to evolve strategic plans for optimal merchant ship movements across the Atlantic Ocean. The impact of his findings is not clear. A 1953 paper in Operations Research commented ., Nor did Edison’s work seem to have had lasting effect on the U.S. Navy, judging by the need to rediscover his statistical procedures at the start of World War II.”

Lewis Richardson, a British ambulance driver in World War I who believed mathematical equations could quantify patterns of war, gathered data in his off-duty time. After the War, he compiled his statistical data and developed mathematical equations to predict wartime behavior. In World War II, the British armed forces found extensive use for his equations.

During the twenty years between the wars, while all the tools of war and communications moved forward there was no significant progress in operations research, tactics, and countermeasures to combat improved weaponry.

World War II

Great Britain

The development of defense against enemy aircraft had an increasing national priority as early as 1935. Large numbers of capable and creative civilian scientific and technical talent began to be drawn together to address the development of new air defense-oriented military equipment. The aim was to use scientific and technical knowledge to strengthen the current methods of defense against hostile aircraft. As the war began, the extreme national danger and risk to life and property by the weapons of the new war and the significant initial success of the enemy brought additional personnel to the problems.

By September 1939 at the onset of war, a large part of the anti-aircraft defense system, later known as (early warning) radar, was manned and operating along all of the east and southeast coasts of England. Some of the country’s best academic researchers achieved this considerable development. Their scientific methodology involved techniques for analyzing system performance by measurement, collection of data, statistics, analysis, and optimization of the man-machine interface relationships.

Battle of Britain July to September 1940

The first major battle fought entirely in the air was the consequence of Germany’s mid-July initiative to prepare for an invasion of England by air bombardment. German Luftwaffe outnumbered the British Fighter Command. The British front-line defense fighter planes numbered about 600. The Germans, with 1300 bombers and dive-bombers and 900 single-engined and 300 twin-engined fighters were formidable.

British fighter interceptors of Spitfires (unsurpassed in any other air force) and more squadrons of Hurricane fighters, plus a well-planned and executed tactic, helped to make the smaller number of fighters effectively larger. Countering the German flights consisting of up to 1500 planes per day intent on bombing fighter airfields was a most crucial undertaking for a fighter force of 600 planes, with the fate of the country dependent upon its outcome.

Preparation for fighter interception began in late 1936; experiments were conducted for two years at the R.A.F. Fighter Command station at Biggio Hill to address problems in fighter direction and controlled by civilian research engineer B.G. Dickins. During the two years before the availability of operational radar, the experiments used simulated radar data and input from the Observer Corp personnel. This planned effort provided a basis for the successful use of the fighters in the summer of 1940.

The radar chain was operational by 1939. In a report by the first radar station at Bawdsey, the term operational research originated. With a limited number of fighter planes, the tactic held the planes on the ground until the right moment. Then control directed the plane to a location within visual sighting of the enemy aircraft. Radar range capability at the time was 120 miles out to sea with 50-mile detection of low-flying aircraft. These experiments integrated the radar into the early warning systems, the Observer Corps, and the fighter direction and control.

With increased British plane production, radar, operations research methods, and extremely brave fighter pilots, the German plane losses by mid-September 1940 totaled 1700 and the British 900. With limited German plane production and his attention now focusing on Russia, Hitler put aside his plans to invade England.

P.M S. Blackette

Blackett served in the Royal Navy at sea during World War I, seeing action in the Falkland Islands in 1914 and at the battle of Jutland in 1916. Following the war, he studied physics with Nobel Laureate Lord Ernest Rutherford. He came to be widely known for his research related to the Wilson cloud chamber. Later in 1948, unrelated to his war work, Blackett received the Nobel Prize for his work in nuclear physics and cosmic rays.

Starting in mid-January 1935, Blackett served on the Committee for the Scientific Survey of Air Defence During the five years of the committee’s existence, the development and implementation of radar stands out. Commenting on the U-boat crisis in 1941-42 and Blackette’s contributions, a paper’ reported “Prof. P.M.S. Blackette, whose name will go down in the history of operational research as outstanding, came into the picture to see what could be done.”

OR and Antiaircraft Gunnery

By August 1940, antiaircraft batteries around London included new gun-laying radar sets just out of the laboratory. Blackette, the appointed science advisor to the headquarters of the Anti-Aircraft Command at Stanmore, addressed the radar implementation problem. Blackette’s Young scientists included physiologists, an astronomer, and a mathematician, as well as physicists. Problems addressed related to operational use of radar, guns, and predictors at the gun sites and headquarters. The overall problem was the blitz bombing of London and other British cities. At this time, Penguin Books published the first book dealing with the development of operations research.

Blackette’s team (referred to as Blackette’s Circus) perfected a number of operational recommendations. The Circus worked with the Service operational staffs and against very short deadlines. Results included: best use of limited radar resources in gun deployment around London, improved data plotting techniques, design of simple plotting machines, and special schools for training personnel in data handling.

Blackette pointed out a notable change in antiaircraft gunnery effectiveness and its relationship to operational research. “At the start of the blitz, when control methods were poor, the ’rounds per bird,’ as we called this number was about 20,000. As methods and instruments improved this gradually fell to some 4,000 the following summer.”‘

By May 1941, German bomber losses over Britain were more than seven percent. Improvements in the use of antiaircraft gunnery and the introduction of airborne radar contributed to the increased losses. The overlay of operational research was a strong contributor. In addition, increased attention to the Balkans and Russia by Germany also led to a diminishing of the overall bombing of Britain.

U-Boat Problem (Britain)

Upon entering the war with Germany in 1939, England’s 1936 naval treaty with the Third Reich did not allow merchant ships to be armed. From the beginning of the war, the U-boat success rate in sinking naval and merchant ships was high. To counter the U-boats the Royal Navy hunted them with planes, ships, and submarines. The Navy provided merchant convoys with escorts on some sea routes.

Hunting submarines required submarine detection. In 1935, British expectations of submarine detection performance were flawed. It was believed in some quarters that the enemy submarine was no longer a menace to national security. The Asdic surface ship performance, in reality, was an average range of the order of 1300 yards with the last 200 yards blind. Nighttime exercises with submarines were rare prewar. In retrospect, even if the performance was as anticipated, there were only limited numbers of vessels equipped with the detection equipment, as a further problem, the number of skilled operators was insufficient. Further, in 1939 the Royal Navy supply of mines for ASW was minimal.

Mahanian thinking with the capital ship at its focus still prevailed. Decreased naval budgets and the expense and long lead-time for capital ships did not allow for small ship construction for ASW, and convoy escort ships were not available in numbers as the war began.

As late as November 1938, a retired German Vice-Admiral noted in an article, “Nothing substantial has as yet been done in England (and equally in France) for the protection of oceanic convoys.”

Blackette and the Anti-U-boat Campaign

In March 1941, Blackette moved from the Anti-Aircraft Command to the Coastal Command to advise on problems arising from the air war against U-boats. The Coastal command’s purview included antisubmarine operations, convoy protection, and attacks on enemy shipping primarily an offensive role. Blackette established his new operations research team as part of the Command’s senior staff.

In the next several months, Blackette’s research revealed the small number of U-boat sinkings by aircraft dropping depth charges. Pursuing this, the OR team carefully studied in detail air attack reports and provided new insight regarding the estimate of the actual depth of the enemy submarine at the instant of an attack. This study brought to light the unsuitability of the standard setting of 100 feet for depth charge detonation.

A depth charge dropped by aircraft near the alerted U-boat’s submergence point with a lethal radius of 20 feet and a 100-foot explosion depth frequently led to a successful escape by the U-boat. Enemy submarines operating near or close to the surface escaped damage from the deep explosion depth of the charge. Operations research team analysis suggested a detonation of the order of 25 feet. U-boat sinking rate immediately improved. Related problems included aiming, depth charge size, and spacing between depth charges dropped from the aircraft. Collectively the findings and operational measures from these inquiries brought further improvement.

First usage of OR often brings outstanding results. As systems are refined improvement is sometimes less spectacular. By late spring 1943, mastery of the U-boat problem was at hand due to the coming together of a variety of efforts. OR’s role was not in creating the weapons but in providing guidance and influence in their judicious use and successfully assessing the enemy’s tactics.

Operations Research Countering the U-boat 1941-1943

Recommending an optimum depth for air dropped depth charges

Securing additional Liberator night bombers for convoy cover Painting bombers sky color to reduce U-boat sighting Expediting the night use of Leigh Lights on ASW aircraft Discerning the use of radar listening devices by U-boats Promoting the use of large convoys (1944 186-ship convoy) Implementing High Frequency Direction Finding (HF/DF)

U-Boat Problem (United States)

The U-boat crisis was one of the many defense areas Bush faced when President Roosevelt appointed him chairman of the newly created National Defense Research Committee (NDRC) on 15 June 1940, the day after Paris fell to the Germans. Within a year, Bush recruited six thousand of the country’s leading physicists, chemists, engineers, and doctors. By the end of the war, they numbered thirty thousand. From within this vast number of scientists, the personnel of operations research talent emerged.

The United States U-boat problem was twofold in December 1941. One was how to efficiently hunt and find U-boats. The other how to defend merchant ships from U-boats. The merchant ship problem needed escorts, better depth charges, and air cover. Navy convoy escort vessels were in short supply and no central ASW group or unit existed.

As late as early 1942, some U.S. Navy personnel were initially not enthusiasts for convoying merchant ships. A quotation in Morison “when the U-boats hit our coast in January 1942, we were caught with our pants down through lack of anti-submarine vessels” is concise and apt. In February, Britain gave United States 24 trawlers and 10 corvettes. These additional escorts allowed small East Coast convoys during the day and putting into the harbor at night. Soviet Admiral Gorshkov observed in 1976 that the “American Navy came into the War (II) totally unprepared to protect merchant vessels from submarine strikes.

U.S. Antisubmarine Warfare Operations Group (ASWORG)

The U.S. Navy was aware of British success with ASW due in part to their civilian scientists’ OR efforts. After the first few months of the war, it became apparent that the navy needed detailed ASW data analysis for tactical decisions. The requisite analytical skills including statistics and probability were not in the purview of the military. In March 1942 the Navy requested Bush’s NDRC to provide civilian scientific support in the U-boat campaign to the Boston ASW unit. The NDRC appointed MIT acoustic research physicist Philip M. Morse then at the Harvard Underwater Sound Laboratory to form the group.

Morse directed the U.S. Navy Operations Research Group from 1942 to 1946 starting in Boston, Massachusetts with a team of seven at the beginning of May 1942 it grew to seventy-three as the war ended. The members were primarily chosen for their general scientific training and included physicists, mathematicians, chemists, biologists, geologists, actuaries (from the six largest US insurance companies), and a champion chess player.

Beginning efforts analyzed the results of U.S. attacks on U-boats by ships and planes and examined the tactics of finding U-boats. U-boat search studies quickly provided fresh guidance to the Navy. The studies revealed potential search rates in square miles per hour of 75 for radar-equipped destroyer, 1000 for meter radar-equipped aircraft, and 3000 for an aircraft with microwave radar.

A previously established Navy Mine Warfare Operations Group from the Navy Ordnance Laboratory concerned with degaussing all U.S. naval vessels to counter German use of magnetic mines became part of ASWORG. Efforts of this team were especially significant in mining-related to Truk, invasion of the Marianas, the battle of the Philippine Sea, and mining Japan’s Inland Sea using bombers and fatally damaging Japanese shipping in 1944.

OR effort in the Pacific brought to light that Japanese antiaircraft fire was relatively ineffective at 9,000 to 10,000 feet. Tactics were changed, and U.S. aircraft losses were significantly reduced.

In October 1942, ASWORG, at the request of NDRC, arranged to assist the US Army Air Force. Early efforts quickly produced an Army Air Force manual on operational use of radar in sea search_ study and report on bombsights and photographic coverage of antisubmarine operations.

A review of ASWORG’s record reveals a response time from the inception of an action to implementation in the order of one or two months. The Bay of Biscay anti-U-boat offensive, the destruction of the German blockade-runners in the South Atlantic, and the initiation of large convoys in the Atlantic are representative of quick and successful responses.

May 1943: The Turning Point in the Battle of the Atlantic

The meeting of the allied leaders in Casablanca during early 1943 ended with a fresh and firm resolve to counter the U-boats more aggressively. After this, momentum in the ASW battle in the Atlantic increased steadily with a significant increase in U-boat sinkings beginning in May. By the end of the month, Grand Admiral Doenitz removed his U-boats from the North Atlantic to positions west of the Azores and into the Mediterranean.

May 1943 The Turning Point

January -April 41 U-boats sunk
May 41 U-boats sunk

Why after years of engagement did the tide turn against the U-boats? Men and materials are essential to success in modern wars. Significantly, the rapidly growing availability of allied weapons, aircraft, and naval ships signaled the end of the period of getting ready to fight.

A further crucial change was the 20 May emergence of Admiral Ernest J. King’s TENTH Fleet as the consolidated and centralized command of all Atlantic ASW with the broadest possible support to defeat the U-boat challenge.

Earlier in May, King’s specifications for the new fleet included a civilian scientist research statistical analysis component headed by Vannevar Bush. ASWORG became part of the TENTH Fleet in August and moved from Boston to Washington, DC. The OR group evolved into a center for the entire U.S. ASW effort. An IBM state-of-the-art data processing system provided help in analyzing and tracking the expanding U-boat data. A large percentage of the OR team were eventually widely scattered at various Navy and Army commands in both the Atlantic and Pacific.

Scientists’ recommendations on tactics and even strategy were included in the decision processes. As Admiral King pointed out later “… Operations research, bringing scientists in to analyze the technical import of the fluctuations between measure and counter-measure, made it possible to speed up our reaction rate in several critical cases.”


The impact of the civilian operations research scientists, engineers, and others with scientific orientation is abundantly clear upon examination of WWII weapons and weapon systems from the aspects of research, development, production, introduction, and implementation by the military. OR civilian scientists assisted the military in fighting the war both in the continental U.S. and in situ.


  • In June 1940, President Roosevelt appointed Bush chairman of the National Defense Research Council with the charge to the Council to implement all science and technology necessary to successfully defend the United States.
  • In 1946, he received the highest award the United States can make to a civilian, the Medal for Merit for bis application of scientific methods concerning the anti-U-boa1 campaign during the war. P.M. Morse, the American physicist, also received the Medal for Merit for his work with the Anti-Submarine Warfare Research Group in the Atlantic. (Seep. 10.)


1.Vannewar Bush Pieces of the Action, William Morrow and Company, Inc. New York, NY, 1970, p. 70.
2. Winston S. Churchill, The Second World War, Vol. II. p.598.
3. Journal of Operations Research Vol. 1, 1953, p. 83.
4. Charles Goodeve, “Operational Research” Nature No. 4089, March 13, 1948, p. 377.
5. P.M.S. Blackette, “Operational Research Recollections of Problems Studies, 1940-45; Brassey’s Annual, The Armed Forces Yearbook 1953, p. 91-92.
6. S.E. Morison “The Battle of the Atlantic: September 1939-May 1943,” Little, Brown and Company, Boston, 1988, p. 254.
7. S.G. Gorshkov, “The Sea Power of the State,” MIT 1976/79, p. 266.

[Author’s acknowledgment: primary references Joseph F. McCloskey’s Operations Research Journal papers Vol. 35 1,3,6 1987.]

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