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A Model of the U-boat Campaign in the Bay of Biscay (UCBB)

This is a "baseline" ABM of the Allied campaign to interdict Nazi U-boats as they sortied from the five ports in occupied France to the North Atlantic. It can be adapted to answer any of a large number of questions regarding search theory, especially the many-on-many search for a population of evasive targets. This creates, in NETLOGO, a computational approach to a problem that had been evaluated using mathematical search theory and game theory.

Historical Background

The Battle of the Bay of Biscay began in late 1940 and lasted until early 1944. Activity did not begin in earnest until late 1941, and data only becomes available in January 1942. By the spring of 1944 the British had nearly complete dominance of the approaches to the French coast. Submarine deployments after that point were limited to small numbers and transits nearly stopped completely after D-Day (June 1944).

This model was built around the high-tempo operations of 1942 and 1943. It was a battle between the German submarine force and the Royal Air Force. For the most part these were German Type VIIC submarines and British Short Sunderland (S.25) four-engine ASW aircraft. The British were based in Plymouth and the Germans were evenly spread among the five U-boat bases. U-boats in port were protected by thick concrete "pens" that are so indestructible that they remain in these five ports to this day. The only way to counter a U-Boat was to sink it at sea.

The German mission was to move the U-boats to the North Atlantic where they would attack convoys. The UK mission was to sink as many transiting U-boats as possible, and to delay the others. British operations research co-founder Arthur Waddington referred to the British goal as the creation of an "unclimable fence". The fence would be so wide that a U-boat could not traverse it completely submerged. This years-long operation was seen by both sides as critical to victory. Winston Churchill famously said, "The only thing that ever really frightened me during the war was the U-Boat peril."

ASW The Birth of Operations Research

The field of operations research began with the U-boat problem in World War II. In both the US and Britain multidisciplinary teams gathered to analyze and optimize antisubmarine operations. There were no computers -- this was a painstaking mathematical exercise. Scientists, statisticians, and mathematicians together determined the best search patterns, the best tactics, the best flight schedules, and the best use of new technology.

The shift to simulation in answering ASW questions was slow, mostly because of the mathematical legacy and the prestige of the WWII practitioners. Much later, during the Cold War, the scientists working this issue gave grudging acceptance to computational approaches. In reality, there are so many interacting irregular components of the ASW process that a pure mathematical solution can only be achieved through crippling simplification.

The Technological Race

Numerous advances would change the balance of power during the campaign. The British quickly developed enhancements for night time operations: the Leigh Light and various radars. The Germans developed a sequence of radar detecting equipment that allowed the submarine to dive before it was detected. The Germans tried out radar decoys and anti-aircraft guns to limited effect. These detection and counter-detection technologies can be adjusted by adjusting the vision sliders and the S25 cone angle.

For these reasons, it was decided not to distinguish daytime from nighttime in the base model. History shows that the S.25 could be just as deadly at night.

The most important submarine technology advance was the snorkel, developed by the Dutch before the war. A snorkel (or "snort" in this model from the German name) allows a submarine to remain submerged with only a "breathing tube" breaking the surface. Thus, the submarine can recharge batteries and remain nearly undetectable. German submarines were not equipped with snorkels, however, until mid-1944.

Operational Choices

The Germans made some radical adjustments to the percent of time their submarines would operate submerged. A fully submerged submarine (as opposed to a snorkeling submarine) is essentially undetectable from the air in 1943. But, their underwater endurance was limited and they were far from able to move across the barrier without surfacing to recharge batteries. The Germans had periods where they adopted a "maximum submergence" policy, and periods when they tried to sprint across on the surface. You can try both methods out.

Model Parameters

The grid of patches in this model is approximately one nautical mile per patch. The background map is a conical projection (not a Mercator), so the scale is relatively constant throughout. Each time step is one minute. A day is 1440 time steps.

Speed seems to work best by dividing real-world speed (in kts) by 100. Thus, a 10-kt U-boat should move across the ocean at the right pace if you set the speed as 0.10.

During the period of interest, there were about 50 U-boat transits per month or 0.00116 per minute. There were also over 4000 aircraft patrol hours per month. The aircraft departure rate per minute (0.01) in the model was tuned to deliver somewhat over 4000 patrol hours per 30-day period.

U-boats depart from points near the mouth of bays and estuaries outside of the five ports. Aircraft all depart from southwestern Plymouth. U-Boats move at direction 290. Aircraft have variable patrol patterns (this can be examined experimentally), but when their fuel status reaches 25% they depart for home and stop their patrol status.

Model Output

The two key measures of output are "Gone", the number of escaped U-boats (those that arrive in the North Atlantic) and the average transit time. These are both measured for one month of minute-turns. Also counted: "escapes", the number of times a submerged U-boat passes under the cone of an S25; "encounters", the number of turns that an S25 passes over a surfaced U-Boat in its cone, and "opportunities", the number of turns an S25 passes over any U-Boat (submerged or surfaced) in its cone.

Potential Experiments

This is really just the stub of a model. Much has been written in the OR literature about search patterns and tactics. Numerous historians have suggested "what if" scenarios that are worthy of experimental examination.

Probably the most fertile area for experimentation is the logic for the S25 agents as they deploy to the Bay of Biscay. In the current version, they just randomly search in the box between cell 190 and cell 375 -- ostensibly a 285 nm wall astride the U-boat transit routes.

In the current version there are no submarine kills. There are potential interactions (aircraft and U-boat are within range, and U-boat is in the cone of acquisition of the aircraft), but and "encounter" does not get counted unless the U-boat is surfaced. If the U-boat is dived, the "opportunity" is scored as an "escape". In the current construction, opportunities and encounters are counted per minute. Escapes are counted only once when the range and conditions are right. This enables the application of a key element of search theory, "glimpses", to the aircraft search, but helps to understand the operational impact of a submarine escaping under the ASW air fleet.

Experiments should probably begin by making the attack more robust. In the real world, after detection the aircraft has to classify, localize, and attack. Classify means determining if the detection was real or a false alarm. Localize means determining the position with sufficient certainty to conduct a successful attack. And, of course, attack means significant aircraft maneuver outside of the search pattern.

The literature suggests that, once an aircraft has conducted an actual attack, the aircraft returns to base. This is the behavior in this model, but it is worth examining if this is the right procedure. The Sunderland is a four-engine airplane and it has the ability to carry several bombs. What would be the impact on the campaign if the airplane continued on its mission (provided there is enough fuel)?

The model is an excellent opprtunity to explore a wide range of proposals about the best search patterns to use.

Most models, even when they don't seem to hold up to historical accuracy, can be valuable in sensitivity analysis. For this model, the sensitivity of improving detection and counter-detection ranges would be an excellent research thread. Some improvements are likely to make a big difference while others are not.

The model illuminates several variables that can't be assessed in the real world. It also provides system-wide behavioral information that would be known by commanders. As a result, it can help address the hypothesis that one thing measures another. Does the contact and attack rate, for example, affect the total number of U-boats that get through and the transit time?

Additionally, experiments can be built around weapons technology. Most of these aircraft were carrying bombs. But, an antisubmarine homing torpedo (MK 24 "Fido") sank its first U-boat in May 1943. What would be the impact of introducing such a weapon earlier or faster?

The Germans attempted using decoys and anti-aircraft artillery in the early stages of this fight. Did they give up too soon? How effective do decoys or AAA have to be in order to make their use viable?

Extending the Model

This model shows how a map can be imported and used as a substrate for analysis. There are several other areas of the world where the interaction of topography and military maneuver forces can be the basis for computational analysis. The Mediterranean, the Barents, and the western Pacific are good examples.

The overall structure of this model can also be extended to the "main event", the Battle of the Atlantic. There are many unanswered questions about action-reaction strategies in convoy attack and defense that can be evaluated using the basic structure of this model.

NETLOGO Considerations

One challenge was the structure of the Netlogo command "in-cone". The "in-cone" formulation is particularly useful for this particular problem. Unfortunately, the statement appears only to be structured to return an agentset, asin "let target-list (uboats) in-cone 5 120". Such a statement returns an agentlist, target-list. This limits the code structure available to move on from there. You can see how that was solved in the "search" procedure.

ASW in Context: Other ABMs of Military History

The most prominent predecessor to this model was developed by a team at the Air Force Institue of Technology, Lance Champagne, R. Greg Carl, and Raymond Hill (of nearby Wright State University). During the period 2003 to 2009 this team produced a number of scientific articles based on their agent-based model of this problem. The AFIT model was written in Java, and is not available publicly.

Few other naval campaign scenarios have been subjected to an ABM treatment. This historical example occupies a unique, data-driven "sweet spot". It is not a singular engagement like, for example, Midway or Trafalgar. This is a campaign that takes place over two years, and extensive data sets have been preserved from both sides of the conflict. It is a rare example in which a model and an underlying theory can be tested in real-world data.

Credits and References

Churchill, Winston S. The Second World War Vol. II., Their Finest Hour. Boston: Houghton Mifflin, 1949

McCue, Brian. U-Boats in the Bay of Biscay, An Essay in Operations Analysis. Newport, RI: Alidade Press, 2008

Washburn, Alan R. Search and Detection. Arlington, VA: Operations Research Society of America, 1981

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Authorship

(C) 2020 This model was created by Dr. Ken Comer as the basis for a series of historical studies, evaluating measures of effectiveness, sensitivity analysis, tradeoffs and parametric experiments.

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