Churchill worked out a budget allocating available shipping to Britain’s vital needs—it reminded him, he said, of the chancellor of the exchequer’s exercise of allocating government funds to the various departments—and the outlook was, he told an aide, “terrifying.” The country needed 35 million tons of imports a year; if imports fell under 31 million tons, cuts in food supplies would be unavoidable. For the first few months of 1941 imports were running at an annual rate of 28 million tons. Each day Churchill received a report on the latest shipping statistics. He would write in his memoirs of this period in early March 1941, “How willingly would I have exchanged a full-scale attempt at invasion for this shapeless, measureless peril, expressed in charts, curves, and statistics!”5
Rationing of food was tightened. A plan for communal canteens, much like that proposed in Zuckerman’s left-wing scientific manifesto, was implemented to help stretch supplies; though Churchill, characteristically, instructed his minister of food, “I hope the term ‘Communal Feedings Centres’ is not going to be adopted. It is an odious expression, suggestive of Communism and the workhouse. I suggest you call them ‘British Restaurants.’ Everybody associates the word ‘restaurant’ with a good meal, and they may as well have the name if they cannot get anything else.”6
The prime ministerial attention to the U-boat problem was as usual a mixed blessing. There were signs, however, that even Churchill was beginning to weary of Lindemann’s enthusiasm for clever gadgets and wonder weapons. In April his pet scientist sent the prime minister his latest brainstorm for yet another fantastic invention, this one to detect submerged submarines: an airplane or destroyer would drop a large number of tiny magnets fitted with electric lights or self-igniting gas that would glow when they stuck to a metallic object. Churchill impatiently wrote back, “This seems to be rather far-fetched. If the aeroplanes or destroyers were as close to the submarine as necessary it would surely be better to throw explosives by bomb or depth-charge.”7 With an entire war to run, Churchill was finding he had bigger problems to worry about than the Prof’s clever toys.
BLACKETT HAD LONG SINCE concluded that the way scientists could really improve things was not by trying to invent new tools anyway but by figuring out how to better use the tools already in hand. He set down his philosophy in a presentation on operational research he gave to an Admiralty panel later that year. Reprinted subsequently many times, “Scientists at the Operational Level” would become a sort of Magna Carta of operational research, and the crux of it was a plea to get scientists out of the laboratory and into operational units where they could do more good:
“New weapons for old” is apt to become a very popular cry. The success of some new devices has led to a new form of escapism which runs somewhat thus—“Our present equipment doesn’t work very well; training is bad, supply is poor, spare parts non-existent. Let’s have an entirely new gadget!” Then comes the vision of the new gadget, springing like Aphrodite from the M.A.P. [Ministry of Aircraft Production].… In general, one might conclude that relatively too much scientific effort has been expended hitherto in the production of new devices and too little in the proper use of what we have got. Thus there is a strong case for moving many of the best scientists from the technical establishments to the operational Commands, at any rate for a time.8
Blackett emphasized the need for scientists in this role to steer clear of “technical midwifery” so they could focus on current operational questions.
Williams jumped right into the most basic such question of all: why were the aircraft of Coastal Command sinking so few submarines? Even with the change from the 100-pound antisubmarine bomb to the 450-pound depth charge, results had scarcely improved. As of May 1941, Williams found, aircraft had sighted U-boats 200 times, carried out attacks in 130 of those cases, and definitely sunk a total of 2 U-boats—a 1 percent success rate. In most of the attacks, the U-boat had spotted the aircraft first and had time to dive by the time the aircraft arrived in position to drop its depth charges. Coastal Command’s Tactical Instruction No. 12, issued January 27, 1941, was based on a straightforward calculation: it took the average time a U-boat had been out of sight at the instant of attack—about 50 seconds—multiplied that by the U-boat’s dive rate of 2 feet per second, and concluded that dropping a series of depth charges set to explode at a depth of 100 to 150 feet would be most likely to catch the submerged boat. Because the U-boat could also have traveled as much as 1,000 feet forward during the same time, the orders also advised dropping a “stick” of four charges spaced horizontally at about 250-foot intervals, to try to blanket as much of the possible target area as possible.9
Williams had little difficulty putting his finger on the trouble once he started sifting through the data. Shooting for an average guaranteed the worst of both possible worlds. In cases where the target was at the same depth as the depth charge setting, its odds of still being on the same straight-line course last seen on the surface were almost nil: the boat would have had time to veer to the left or right, and the possible area in which it might be lurking was so vast as to be impossible to saturate with charges. Williams calculated that the average error in aim point was at least 300 feet, well beyond the 25-foot lethal radius of a 450-pound depth charge. On the other hand, the boats that had been late to react to the aircraft’s approach, and were thus still close to the surface and not far from the position where they submerged, were being attacked in the right place but with depth charges set to go off far too deep to do any damage. The 250-foot stick spacing was likewise thrown away on U-boats which had been out of sight for a quarter of a minute or less, which were sure to be within a radius of 150 feet of their last observed position. In other words, targets that were at the right depth were almost certainly in the wrong place; targets that were in the right place were definitely at the wrong depth. Williams summarized this conclusion at the very top of the first page of his report:
In as many as about 40% of all attacks the U-Boat was either visible at the instant of attack or had been out of sight for less than 1/4′. It is estimated from such statistics, and the rate at which the uncertainty in the position of a U-boat grows with time of submersion, that the U-boat which is partly visible or just submerged is about ten times more important a target, potentially, than the U-boat which has been out of sight for more than about 1/4′. The very small percentage of U-boats seriously damaged or sunk in past attacks is probably largely the result of too much attention having been given to the long submerged U-boat.10
There was also a satisfying calculation Williams was able to produce which showed that the actual successes attained to date agreed almost perfectly with what would be expected from following Instruction No. 12—which gave additional confidence to his conclusion that the only thing wrong with what Coastal Command was doing was its tactical procedures; there were no equipment malfunctions or other problems to blame for the poor performance.
Williams calculated that changing the depth charge setting to 25 feet and substantially narrowing the stick spacing would increase the percentage of U-boats sunk by an astonishing factor of ten—from the current 1 or 2 percent to 10 to 20 percent.11 His typewritten report, Coastal Command ORS No. 142, was “a paper which can certainly be taken as one of the classics of Operational Research Literature,” wrote C. H. Waddington, who would later join the group. It was formally submitted on September 11, 1941, and its results were incorporated almost verbatim into a new Coastal Command Tactical Instruction No. 18 issued on December 15:
Since it is now the intention to concentrate Coastal Command effort on attacking submarines which have not had time to submerge or have not been submerged for more than 15 seconds the weapon must be made to explode so that its lethal effect will reach the pressure hull of a U/Boat which is on or not more than 30 feet below the surface.
The instructions noted that new pistols that provided a 25-foot setting were being produced for both the Mk VII 420-lb. depth charge and the Mk VIII 250-lb. version. A full sti
ck of depth charges was to be dropped in the initial attack; larger aircraft, such as Sunderlands and Catalinas that could carry 8, were to drop them at 45-foot intervals; Hudsons, which could carry only 4, were permitted to stretch that spacing to 60 feet. In either case, though, that was a mere fraction of the 250-foot spacing specified in the earlier instructions.12
In one sense, Blackett said, Williams’s discovery was little more than “an example of the old military precept to concentrate offensive effort on the good targets and ignore the poor targets.” But it had taken the “critical but sympathetic analysis” of an outsider to spot the flaw in existing operational orders.13 It also neatly affirmed Blackett’s dictum about the relative worth of new gadgets vis-à-vis the better use of existing weapons, since Williams also was able to show that a standard depth charge with a 25-foot depth setting was almost as effective as—and much less complex than—the proximity-fused depth charge detonator he himself had been working to develop the previous year when he was at the Royal Aircraft Establishment.
BLACKETT WAS MEANWHILE producing his own piece of operational prestidigitation. In April 1941, a month after starting work at Coastal Command, he paid a visit to the operations room of Western Approaches Command in Liverpool, where a large wall map displayed the current estimated positions of all U-boats in the Atlantic. Blackett knew the number of hours being flown by Coastal Command aircraft and the areas they were patrolling. “I calculated in a few lines of arithmetic on the back of an envelope the number of U-boats which should have been sighted by the aircraft,” given the actual number of U-boats operating in the area as shown on the wall of the Western Approaches Command. The theoretical number Blackett obtained from his quick calculation was four times the actual number of sightings that Coastal Command air patrols were reporting. “This discrepancy,” Blackett continued, “could be explained either by assuming the U-boats cruised submerged or by assuming that they cruised on the surface and in about four cases out of five saw the aircraft and dived before being seen by the aircraft. Since U-boat prisoners asserted that U-boats seldom submerged except when aircraft were sighted, the second explanation was probably correct.” All of the obvious solutions were recommended: equipping the aircrews with better binoculars, avoiding flying into the sun, improving training. Then, discussing the problem one day, an RAF wing commander asked Blackett, “What color are Coastal aircraft?”
They were in fact mainly black, as they were mostly night bombers diverted from Bomber Command. Night bombers were painted black to reflect as little light as possible from searchlights. But by day, under most conditions of cloud and sun, an aircraft is seen as a dark object against a light sky. Tests were quickly ordered and it was verified that repainting the aircraft white reduced by a fifth the average maximum distance at which the planes could be seen. The undersurfaces of the wings were the part of the aircraft that stood out in particular contrast to the sky, and a scheme of using glossy reflective white paint for these surfaces was adopted. Williams calculated that the change to white camouflage would increase the number of U-boat sightings, and sinkings, by 30 percent. The plan was implemented within a few months. Air patrols during the winter had been yielding one U-boat sighting per every 700 hours of flying. By summer 1941, with the camouflage change and other improvements, the yield had doubled to one sighting per 350 hours.14
It would take longer for the benefit of Williams’s finding about depth settings to be realized; the depth charges, it turned out, tended to entrain a cavity of air as they struck the surface of the water, which prevented the pistol from immediately sensing the water pressure and it proved difficult to get them to go off at a depth as shallow as 25 feet. Once the problem was solved the results were what Williams’s calculation predicted: by 1943, the chance of killing a submarine in an air attack with depth charges had increased from 1 to 2 percent to almost exactly 10 percent.15
THE ARCHETYPAL DEMONSTRATION of operational research was provided in a postwar textbook by Philip Morse, an American physicist who would follow Blackett’s pioneering lead upon America’s entry into the war. Morse told the story of one operational research scientist who, on his first day at a field command, noticed that there was a long line of soldiers waiting to wash their mess kits after each meal. There were four tubs available; two were for washing and two for rinsing. Observing that it took each soldier three times as long to wash his kit as to rinse it, he suggested changing the setup so that three tubs were allocated for washing and one for rinsing. The change was made. The line did not merely shrink: it vanished altogether.
It was, said Morse, a “trivial” but perfect illustration. The solution in retrospect seemed almost absurdly simple. It did not involve any new equipment. And the consequences of the change were what mathematicians call nonlinear—a small perturbation produced disproportionately large results. That was a common feature of processes in which a flow hits a bottleneck. Delays and obstructions feed on themselves: the longer a line gets, the longer it tends to get. Conversely, eliminating even a small obstruction can cause a backup to disappear altogether.16
Blackett made some similar observations in lectures in which he looked back on the birth of operational research in the war and the lessons learned:
Quite a number of these results were really quite simple, and appear even more so when talked about now. There is now a kind of deceptive simplicity about the results of these investigations which tends to make previous tactics seem rather stupid and ill-advised. Actually, it wasn’t like that.
Nine times out of ten, he said, the conventional way of doing things turned out to be best. And although it often looked superficially as a matter of “the bright scientist suddenly intervening and telling the experts what to do,” it was much more a matter of scientists asking the right question—and only after having thoroughly “soaked themselves” in the problems of the operational command by attending staff meetings, looking at intelligence reports, hearing orders given, and seeing how things worked.
He added a crucial observation about sociology: the only way to get “very busy and harassed officers” to pay attention to operational research findings was “to concentrate on results which appeared certain … the scientists had to get results so definite that they didn’t need a mass of statistics to prove them correct to the Service people.” Statistics certainly was a frequent tool of the analysis that pointed out to the researchers what changes were likely to produce results, but the results themselves had to be so dramatic as to speak for themselves. That meant, too, that a scientist “put into this kind of administrative environment” had to behave “in quite a different way from in his own laboratory,” Blackett said: “His job is to improve matters if he can, and, if he cannot, to say nothing.”17
Operational scientists had to have a basic grasp of mathematics and probability theory, but beyond that Blackett thought the best candidates “knew nothing about the subject beforehand” and thus would be “prepared to ask questions that more ‘instructed’ people might not think of asking.”18 In his original version of “Scientists at the Operational Level,” Blackett described in detail the talents required and the participatory role that the operational research staff needed to play to be effective:
A considerable fraction of the Staff of an O.R.S. should be of the very highest standing in science, and many of them should be drawn from those who have had experience in the Service Technical Establishments. Others should be chosen for analytic ability, e.g. gifted mathematicians, lawyers, chess players. An O.R.S. which contents itself with the routine preparation of statistical reports and narratives will be of very limited value. The atmosphere required is that of a first class pure scientific research institution, and the calibre of the personnel should match this. All members of an O.R.S. should spend part of their time at operational stations.19
The physical chemist E. C. Baughan, who joined Coastal Command ORS later that year after returning from Princeton (where he had been a visiting professor when the war broke out)
catalogued the first members of Blackett’s staff there, and if there were no lawyers or chess players, they were indeed an eclectic bunch: “Three physicists (and one physical chemist), three communications experts (one Australian), four mathematicians, two astronomers (both Canadian), and about eight physiologists and biologists, including an expert on the sex life of the oyster.” He added: “It was not clear which background was the best.” A subsequent list would have included a classical archaeologist, several economists and statisticians, and one botanist. John C. Kendrew, who would win the Nobel Prize in chemistry in 1962, was an early member of the group; C. H. Waddington joined the following year and served as its head from 1944 to mid-1945. Other famous members of the Coastal Command group would include the mathematician J. H. C. Whitehead and the geneticist Cecil Gordon.
Leonard Bayliss thought that the large number of physiologists and biologists in the operational research sections was not a coincidence. It was true that most physicists had already been siphoned up for radar work (and some would later be drawn into the Manhattan Project), which partly explained the predominance of scientists from other fields in the operational research sections. But Bayliss thought “biologists were more accustomed to making the best of very imperfect and inadequate data, and drawing some sort of conclusions from them; physicists would be more likely to throw in their hands until the apparatus was improved and adequate data was provided.” Baughan recalled one of the mathematicians in the group sarcastically proposing a definition of operational research as “an Experimental Science where a number is equal to its square root.” It certainly required a tolerance for uncertainty and approximation. But Baughan noted that many of the most dramatic results the scientists produced were based on calculations that employed extremely rough estimates of the underlying data.20
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