Operations Research @ Bomber Command
Posted: Tue Dec 05, 2006 10:38 pm
Below are parts 1 and 2 of some recollections of Freeman Dyson from his time as an Operations Research Analyst for Bomber Command. It kind of rambles but provides some insight to applying analytical techniques to evaluate combat performance.
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Part I: A Failure of Intelligence
Prominent physicist Freeman Dyson recalls the time he spent developing analytical methods to help the British Royal Air Force bomb German targets during World War II.
By Freeman Dyson
Air War: A British Lancaster bomber is silhouetted against flares and explosions during the attack on Hamburg, Germany, on the night of January 30, 1943. (Credit: Imperial War Museum) Our editor in chief thinks you won't read this article online because long-form stories function better in print. Is he wrong? Tell us what you think.
I began work in the Operational Research Section (ORS) of the British Royal Air Force's Bomber Command on July 25, 1943. I was 19 years old, fresh from an abbreviated two years as a student at the University of Cambridge. The headquarters of Bomber Command was a substantial set of red brick buildings, hidden in the middle of a forest on top of a hill in the English county of Buckinghamshire. The main buildings had been built before the War. The ORS was added in 1941 and was housed in a collection of trailers at the back. Trees were growing right up to our windows, so we had little daylight even in summer. The Germans must have known where we were, but their planes never came to disturb us.
I was billeted in the home of the Parsons family in the village of Hughenden. Mrs. Parsons was a motherly soul and took good care of me. Once a week, she put her round tin bathtub out on her kitchen floor and filled it with hot water for my weekly splash. Each morning I bicycled the five miles up the hill to Bomber Command, and each evening I came coasting down. Sometimes, as I was struggling up the hill, an air force limousine would zoom by, and I would have a quick glimpse of our commander in chief, Sir Arthur Harris, sitting in the back, on his way to give the orders that sent thousands of boys my age to their deaths. Every day, depending on the weather and the readiness of the bombers, he would decide whether to send their crews out that night or let them rest. Every day, he chose the targets for the night.
"Bomber" Harris's entire career had been devoted to the proposition that strategic bombing could defeat Germany without the use of land armies. The mammoth force of heavy bombers that he commanded had been planned by the British government in 1936 as our primary instrument for defeating Hitler without repeating the horrors of the trench warfare of World War I. Bomber Command, by itself, was absorbing about one-quarter of the entire British war effort.
The members of Bomber Command's ORS were civilians, employed by the Ministry of Aircraft Production and not by the air force. The idea was that we would provide senior officers with independent scientific and technical advice. The experimental physicist Patrick Blackett had invented the ORS system in order to give advice to the navy. One of the crucial problems for the navy was to verify scientifically the destruction of U-boats. Every ship or airplane that dropped a depth charge somewhere near a U-boat was apt to claim a kill. An independent group of scientists was needed to evaluate the evidence impartially and find out which tactics were effective.
Bomber Command had a similar problem in evaluating the effectiveness of bombing. Aircrew frequently reported the destruction of targets when photographs showed they had missed by several miles. The navy ORS was extremely effective and made great contributions to winning the war against the U-boats in the Atlantic. But Blackett had two enormous advantages. First, he was a world-renowned scientist (who would later win a Nobel Prize), with a safe job in the academic world, so he could threaten to resign if his advice was not followed. Second, he had been a navy officer in World War I and was respected by the admirals he advised. Basil Dickins, the chief of our ORS at Bomber Command, had neither of these advantages. He was a civil servant with no independent standing. He could not threaten to resign, and Sir Arthur Harris had no respect for him. His career depended on telling Sir Arthur things that Sir Arthur wanted to hear. So that is what he did. He gave Sir Arthur information rather than advice. He never raised serious questions about Sir Arthur's tactics and strategy.
Our ORS was divided into sections and subsections. The sections were ORS1, concerned with bombing effectiveness; ORS2, concerned with bomber losses; ORS3, concerned with history. My boss, Reuben Smeed, was chief of ORS2. The subsections of ORS2 were ORS2a, collecting crew reports and investigating causes of losses; ORS2b, studying the effectiveness of electronic countermeasures; ORS2c, studying damage to returning bombers; ORS2d, doing statistical analysis and other jobs requiring some mathematical skill. I was put into ORS2d.
Two other new boys arrived at the same time I did. One was John Carthy, who was in ORS1; the other was Mike O'Loughlin, who shared an office with me in ORS2d. John had been a leading actor in the Cambridge University student theater. Mike had been briefly in the army but was discharged when he was found to be epileptic. John and Mike and I became lifelong friends. John was cheerful, Mike was bitter, and I was somewhere in between. In later life, John was a biologist at the University of London, and Mike taught engineering at the Cambridge Polytechnic. After retiring from the Polytechnic, Mike became an Anglican minister in the parish of Linton, near Cambridge.
The ORS consisted of about 30 people, a mixed bunch of civil servants, academic experts, and students. Working with us were an equal number of WAAFs, girls of the Women's Auxiliary Air Force, who wore blue uniforms and were subject to military discipline. The WAAFs were photographic interpreters, calculators, technicians, drivers, and secretaries. They did most of the real work of the ORS. They also supplied us with tea and sympathy. They made a depressing situation bearable. Their leader was Sergeant Asplen, a tall and strikingly beautiful girl whose authority was never questioned. The sergeant kept herself free of romantic entanglements. But two of her charges, a vivacious redhead named Dorothy and a more thoughtful brunette called Betty, became attached to my friends John and Mike. Love affairs were not officially discouraged. We celebrated two weddings before the War was over, with Dorothy and Betty discarding their dumpy blue uniforms for an afternoon and appearing resplendent in white silk. The marriages endured, and each afterwards produced four children.
My first day of work was the day after one of our most successful operations, a full-force night attack on Hamburg. For the first time, the bombers had used the decoy system, which we called WINDOW and the Americans called CHAFF. WINDOW consisted of packets of paper strips coated with aluminum paint. One crew member in each bomber was responsible for throwing packets of WINDOW down a chute, at a rate of one packet per minute, while flying over Germany. The paper strips floated slowly down through the stream of bombers, each strip a resonant antenna tuned to the frequency of the German radars. The purpose was to confuse the radars so that they could not track individual bombers in the clutter of echoes from the WINDOW.
That day, the people at the ORS were joyful. I never saw them as joyful again until the day that the war in Europe ended. WINDOW had worked. The bomber losses the night before were only 12 out of 791, or 1.5 percent, far fewer than would have been expected for a major operation in July, when the skies in northern Europe are never really dark. Losses were usually about 5 percent and were mostly due to German night fighters, guided to the bombers by radars on the ground. WINDOW had cut the expected losses by two-thirds. Each bomber carried a crew of seven, so WINDOW that night had saved the lives of about 180 of our boys.
The first job that Reuben Smeed gave me to do when I arrived was to draw pictures of the cloud of WINDOW trailing through the stream of bombers as the night progressed, taking into account the local winds at various altitudes as measured and reported by the bombers. My pictures would be shown to the aircrew to impress on them how important it was for them to stay within the stream after bombing the target, rather than flying home independently.
Smeed explained to me that the same principles applied to bombers flying at night over Germany and to ships crossing the Atlantic. Ships had to travel in convoys, because the risk of being torpedoed by a U-boat was much greater for a ship traveling alone. For the same reason, bombers had to travel in streams: the risk of being tracked by radar and shot down by an enemy fighter was much greater for a bomber flying alone. But the crews tried to keep out of the bomber stream, because they were more afraid of collisions than of fighters. Every time they flew in the stream, they would see bombers coming close and almost colliding with them, but they almost never saw fighters. The German night fighter force was tiny compared with Bomber Command. But the German pilots were highly skilled, and they hardly ever got shot down. They carried a firing system called Schräge Musik, or "crooked music," which allowed them to fly underneath a bomber and fire guns upward at a 60-degree angle. The fighter could see the bomber clearly silhouetted against the night sky, while the bomber could not see the fighter. This system efficiently destroyed thousands of bombers, and we did not even know that it existed. This was the greatest failure of the ORS. We learned about Schräge Musik too late to do anything to counter it.
Smeed believed the crew's judgement was wrong. He thought a bomber's chance of being shot down by a fighter was far greater than its chance of colliding with another bomber, even in the densest part of the bomber stream. But he had no evidence: he had been too busy with other urgent problems to collect any. He told me that the most useful thing I could do was to become Bomber Command's expert on collisions. When not otherwise employed, I should collect all the scraps of evidence I could find about fatal and nonfatal collisions and put them all together. Then perhaps we could convince the aircrew that they were really safer staying in the stream.
There were two possible ways to study collisions, using theory or using observations. I tried both. The theoretical way was to use a formula: collision rate for a bomber flying in the stream equals density of bombers multiplied by average relative velocity of two bombers multiplied by mutual presentation area (MPA). The MPA was the area in a geometric plane perpendicular to the relative velocity within which a collision could occur. It was the same thing that atomic and particle physicists call a collision cross section. For vertical collisions, it was roughly four times the area of a bomber as seen from above. The formula assumes that two bombers on a collision course do not see each other in time to break off. For bombers flying at night over Germany, that assumption was probably true.
All three factors in the collision formula were uncertain. The MPA would be smaller for a sideways collision than for an up-and-down collision, but I assumed that most of the collisions would be up-and-down, with the relative velocity vertical. The relative velocity would depend on how vigorously the bombers were corkscrewing as they flew. Except during bombing runs over a target, they never flew straight and level; that would have left them sitting ducks for antiaircraft guns. The standard maneuver for avoiding antiaircraft fire was the corkscrew, combining side-to-side with up-and-down weaving. For predicting collisions, it was the up-and-down motion that was most important. From crew reports I estimated up-and-down motions averaging 40 miles an hour, uncertain by a factor of two. But the dominant uncertainty in the collision formula was the density of bombers in the stream.
I studied the crew reports, which sometimes described large deviations from the tracks that the bombers were supposed to fly. For the majority of crews, who reported no large deviations, there was no way to tell how close to their assigned tracks they actually flew. My best estimate of the density of bombers was uncertain by a factor of 10. This made the collision formula practically worthless as a predictive tool. But it still had value as a way to set an upper bound on the collision rate. If I assumed maximum values for all three factors in the formula, it gave a loss rate due to collisions of 1 percent per operation. One percent was much too high to be acceptable, but still less than the overall loss rate of 5 percent. Even if we squeezed the bomber stream to the highest possible density, collisions would not be the main cause of losses.
How common, really, were collisions? Observational evidence of lethal crashes over Germany was plentiful but unreliable. The crews frequently reported seeing events that looked like collisions: first an explosion in the air, and then two flaming objects falling to the ground. These events were visible from great distances and were often multiply reported. The crews tended to believe that they were seeing collisions, but there was no way to be sure. Most of the events probably involved single bombers, hit by antiaircraft shells or by fighter cannon fire, that broke in half as they disintegrated.
In the end I found only two sources of evidence that I could trust: bombers that collided over England and bombers that returned damaged by nonlethal collisions over Germany. The numbers of incidents of both kinds were reliable, and small enough that I could investigate each case individually. The case that I remember best was a collision between two Mosquito bombers over Munich. The Mosquito was a light, two-seat bomber that Bomber Command used extensively for small-scale attacks, to confuse the German defenses and distract attention from the heavy attacks. Two Mosquitoes flew alone from England to Munich and then collided over the target, with only minor damage. It was obvious that the collision could not have been the result of normal operations. The two pilots must have seen each other when they got to Munich and started playing games. The Mosquito was fast and maneuverable and hardly ever got shot down, so the pilots felt themselves to be invulnerable. I interviewed Pilot-Officer Izatt, who was one of the two pilots. When I gently questioned him about the Munich operation, he confessed that he and his friend had been enjoying a dogfight over the target when they bumped into each other. So I crossed the Munich collision off my list. It was not relevant to the statistics on collisions between heavy bombers in the bomber stream. There remained seven authentic nonlethal collisions between heavy bombers over Germany.
For bombers flying at night over England in training exercises, I knew the numbers of lethal and nonlethal collisions. After more than 60 years, I can't recall them precisely, but I remember that the ratio of lethal to nonlethal collisions was three to one. If I assumed that the chance of surviving a collision was the same over Germany as over England, then it was simple to calculate the number of lethal collisions over Germany. But there were two reasons that assumption might be false. On the one hand, a badly damaged aircraft over Germany might fail to get home, while an aircraft with the same damage over England could make a safe landing. On the other hand, the crew of a damaged aircraft over England might decide to bail out and let the plane crash, while the same crew over Germany would be strongly motivated to bring the plane home. There was no way to incorporate these distinctions into my calculations. But since they pulled in opposite directions, I decided to ignore them both. I estimated the number of lethal collisions over Germany in the time since the massive attacks began to be three times the number of nonlethal collisions, or 21. These numbers referred to major operations over Germany with high-density bomber streams, in which about 60,000 sorties had been flown at the time I did the calculation. So collisions destroyed 42 aircraft in 60,000 sorties, a loss rate of .07 percent. This was the best estimate I could make. I could not calculate any reliable limits of error, but I felt confident that the estimate was correct within a factor of two. It was consistent with the less accurate estimate obtained from the theoretical formula, and it strongly confirmed Smeed's belief that collisions were a smaller risk than fighters.
For a week after I arrived at the ORS, the attacks on Hamburg continued. The second, on July 27, raised a firestorm that devastated the central part of the city and killed about 40,000 people. We succeeded in raising firestorms only twice, once in Hamburg and once more in Dresden in 1945, where between 25,000 and 60,000 people perished (the numbers are still debated). The Germans had good air raid shelters and warning systems and did what they were told. As a result, only a few thousand people were killed in a typical major attack. But when there was a firestorm, people were asphyxiated or roasted inside their shelters, and the number killed was more than 10 times greater. Every time Bomber Command attacked a city, we were trying to raise a firestorm, but we never learnt why we so seldom succeeded. Probably a firestorm could happen only when three things occurred together: first, a high concentration of old buildings at the target site; second, an attack with a high density of incendiary bombs in the target's central area; and, third, an atmospheric instability. When the combination of these three things was just right, the flames and the winds produced a blazing hurricane. The same thing happened one night in Tokyo in March 1945 and once more at Hiroshima the following August. The Tokyo firestorm was the biggest, killing perhaps 100,000 people.
The third Hamburg raid was on the night of July 29, and the fourth on August 2. After the firestorm, the law of diminishing returns was operating. The fourth attack was a fiasco, with high and heavy clouds over the city and bombs scattered over the countryside. Our bomber losses were rising, close to 4 percent for the third attack and a little over 4 percent for the fourth. The Germans had learnt quickly how to deal with WINDOW. Since they could no longer track individual bombers with radar, they guided their fighters into the bomber stream and let them find their own targets. Within a month, loss rates were back at the 5 percent level, and WINDOW was no longer saving lives.
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Part I: A Failure of Intelligence
Prominent physicist Freeman Dyson recalls the time he spent developing analytical methods to help the British Royal Air Force bomb German targets during World War II.
By Freeman Dyson
Air War: A British Lancaster bomber is silhouetted against flares and explosions during the attack on Hamburg, Germany, on the night of January 30, 1943. (Credit: Imperial War Museum) Our editor in chief thinks you won't read this article online because long-form stories function better in print. Is he wrong? Tell us what you think.
I began work in the Operational Research Section (ORS) of the British Royal Air Force's Bomber Command on July 25, 1943. I was 19 years old, fresh from an abbreviated two years as a student at the University of Cambridge. The headquarters of Bomber Command was a substantial set of red brick buildings, hidden in the middle of a forest on top of a hill in the English county of Buckinghamshire. The main buildings had been built before the War. The ORS was added in 1941 and was housed in a collection of trailers at the back. Trees were growing right up to our windows, so we had little daylight even in summer. The Germans must have known where we were, but their planes never came to disturb us.
I was billeted in the home of the Parsons family in the village of Hughenden. Mrs. Parsons was a motherly soul and took good care of me. Once a week, she put her round tin bathtub out on her kitchen floor and filled it with hot water for my weekly splash. Each morning I bicycled the five miles up the hill to Bomber Command, and each evening I came coasting down. Sometimes, as I was struggling up the hill, an air force limousine would zoom by, and I would have a quick glimpse of our commander in chief, Sir Arthur Harris, sitting in the back, on his way to give the orders that sent thousands of boys my age to their deaths. Every day, depending on the weather and the readiness of the bombers, he would decide whether to send their crews out that night or let them rest. Every day, he chose the targets for the night.
"Bomber" Harris's entire career had been devoted to the proposition that strategic bombing could defeat Germany without the use of land armies. The mammoth force of heavy bombers that he commanded had been planned by the British government in 1936 as our primary instrument for defeating Hitler without repeating the horrors of the trench warfare of World War I. Bomber Command, by itself, was absorbing about one-quarter of the entire British war effort.
The members of Bomber Command's ORS were civilians, employed by the Ministry of Aircraft Production and not by the air force. The idea was that we would provide senior officers with independent scientific and technical advice. The experimental physicist Patrick Blackett had invented the ORS system in order to give advice to the navy. One of the crucial problems for the navy was to verify scientifically the destruction of U-boats. Every ship or airplane that dropped a depth charge somewhere near a U-boat was apt to claim a kill. An independent group of scientists was needed to evaluate the evidence impartially and find out which tactics were effective.
Bomber Command had a similar problem in evaluating the effectiveness of bombing. Aircrew frequently reported the destruction of targets when photographs showed they had missed by several miles. The navy ORS was extremely effective and made great contributions to winning the war against the U-boats in the Atlantic. But Blackett had two enormous advantages. First, he was a world-renowned scientist (who would later win a Nobel Prize), with a safe job in the academic world, so he could threaten to resign if his advice was not followed. Second, he had been a navy officer in World War I and was respected by the admirals he advised. Basil Dickins, the chief of our ORS at Bomber Command, had neither of these advantages. He was a civil servant with no independent standing. He could not threaten to resign, and Sir Arthur Harris had no respect for him. His career depended on telling Sir Arthur things that Sir Arthur wanted to hear. So that is what he did. He gave Sir Arthur information rather than advice. He never raised serious questions about Sir Arthur's tactics and strategy.
Our ORS was divided into sections and subsections. The sections were ORS1, concerned with bombing effectiveness; ORS2, concerned with bomber losses; ORS3, concerned with history. My boss, Reuben Smeed, was chief of ORS2. The subsections of ORS2 were ORS2a, collecting crew reports and investigating causes of losses; ORS2b, studying the effectiveness of electronic countermeasures; ORS2c, studying damage to returning bombers; ORS2d, doing statistical analysis and other jobs requiring some mathematical skill. I was put into ORS2d.
Two other new boys arrived at the same time I did. One was John Carthy, who was in ORS1; the other was Mike O'Loughlin, who shared an office with me in ORS2d. John had been a leading actor in the Cambridge University student theater. Mike had been briefly in the army but was discharged when he was found to be epileptic. John and Mike and I became lifelong friends. John was cheerful, Mike was bitter, and I was somewhere in between. In later life, John was a biologist at the University of London, and Mike taught engineering at the Cambridge Polytechnic. After retiring from the Polytechnic, Mike became an Anglican minister in the parish of Linton, near Cambridge.
The ORS consisted of about 30 people, a mixed bunch of civil servants, academic experts, and students. Working with us were an equal number of WAAFs, girls of the Women's Auxiliary Air Force, who wore blue uniforms and were subject to military discipline. The WAAFs were photographic interpreters, calculators, technicians, drivers, and secretaries. They did most of the real work of the ORS. They also supplied us with tea and sympathy. They made a depressing situation bearable. Their leader was Sergeant Asplen, a tall and strikingly beautiful girl whose authority was never questioned. The sergeant kept herself free of romantic entanglements. But two of her charges, a vivacious redhead named Dorothy and a more thoughtful brunette called Betty, became attached to my friends John and Mike. Love affairs were not officially discouraged. We celebrated two weddings before the War was over, with Dorothy and Betty discarding their dumpy blue uniforms for an afternoon and appearing resplendent in white silk. The marriages endured, and each afterwards produced four children.
My first day of work was the day after one of our most successful operations, a full-force night attack on Hamburg. For the first time, the bombers had used the decoy system, which we called WINDOW and the Americans called CHAFF. WINDOW consisted of packets of paper strips coated with aluminum paint. One crew member in each bomber was responsible for throwing packets of WINDOW down a chute, at a rate of one packet per minute, while flying over Germany. The paper strips floated slowly down through the stream of bombers, each strip a resonant antenna tuned to the frequency of the German radars. The purpose was to confuse the radars so that they could not track individual bombers in the clutter of echoes from the WINDOW.
That day, the people at the ORS were joyful. I never saw them as joyful again until the day that the war in Europe ended. WINDOW had worked. The bomber losses the night before were only 12 out of 791, or 1.5 percent, far fewer than would have been expected for a major operation in July, when the skies in northern Europe are never really dark. Losses were usually about 5 percent and were mostly due to German night fighters, guided to the bombers by radars on the ground. WINDOW had cut the expected losses by two-thirds. Each bomber carried a crew of seven, so WINDOW that night had saved the lives of about 180 of our boys.
The first job that Reuben Smeed gave me to do when I arrived was to draw pictures of the cloud of WINDOW trailing through the stream of bombers as the night progressed, taking into account the local winds at various altitudes as measured and reported by the bombers. My pictures would be shown to the aircrew to impress on them how important it was for them to stay within the stream after bombing the target, rather than flying home independently.
Smeed explained to me that the same principles applied to bombers flying at night over Germany and to ships crossing the Atlantic. Ships had to travel in convoys, because the risk of being torpedoed by a U-boat was much greater for a ship traveling alone. For the same reason, bombers had to travel in streams: the risk of being tracked by radar and shot down by an enemy fighter was much greater for a bomber flying alone. But the crews tried to keep out of the bomber stream, because they were more afraid of collisions than of fighters. Every time they flew in the stream, they would see bombers coming close and almost colliding with them, but they almost never saw fighters. The German night fighter force was tiny compared with Bomber Command. But the German pilots were highly skilled, and they hardly ever got shot down. They carried a firing system called Schräge Musik, or "crooked music," which allowed them to fly underneath a bomber and fire guns upward at a 60-degree angle. The fighter could see the bomber clearly silhouetted against the night sky, while the bomber could not see the fighter. This system efficiently destroyed thousands of bombers, and we did not even know that it existed. This was the greatest failure of the ORS. We learned about Schräge Musik too late to do anything to counter it.
Smeed believed the crew's judgement was wrong. He thought a bomber's chance of being shot down by a fighter was far greater than its chance of colliding with another bomber, even in the densest part of the bomber stream. But he had no evidence: he had been too busy with other urgent problems to collect any. He told me that the most useful thing I could do was to become Bomber Command's expert on collisions. When not otherwise employed, I should collect all the scraps of evidence I could find about fatal and nonfatal collisions and put them all together. Then perhaps we could convince the aircrew that they were really safer staying in the stream.
There were two possible ways to study collisions, using theory or using observations. I tried both. The theoretical way was to use a formula: collision rate for a bomber flying in the stream equals density of bombers multiplied by average relative velocity of two bombers multiplied by mutual presentation area (MPA). The MPA was the area in a geometric plane perpendicular to the relative velocity within which a collision could occur. It was the same thing that atomic and particle physicists call a collision cross section. For vertical collisions, it was roughly four times the area of a bomber as seen from above. The formula assumes that two bombers on a collision course do not see each other in time to break off. For bombers flying at night over Germany, that assumption was probably true.
All three factors in the collision formula were uncertain. The MPA would be smaller for a sideways collision than for an up-and-down collision, but I assumed that most of the collisions would be up-and-down, with the relative velocity vertical. The relative velocity would depend on how vigorously the bombers were corkscrewing as they flew. Except during bombing runs over a target, they never flew straight and level; that would have left them sitting ducks for antiaircraft guns. The standard maneuver for avoiding antiaircraft fire was the corkscrew, combining side-to-side with up-and-down weaving. For predicting collisions, it was the up-and-down motion that was most important. From crew reports I estimated up-and-down motions averaging 40 miles an hour, uncertain by a factor of two. But the dominant uncertainty in the collision formula was the density of bombers in the stream.
I studied the crew reports, which sometimes described large deviations from the tracks that the bombers were supposed to fly. For the majority of crews, who reported no large deviations, there was no way to tell how close to their assigned tracks they actually flew. My best estimate of the density of bombers was uncertain by a factor of 10. This made the collision formula practically worthless as a predictive tool. But it still had value as a way to set an upper bound on the collision rate. If I assumed maximum values for all three factors in the formula, it gave a loss rate due to collisions of 1 percent per operation. One percent was much too high to be acceptable, but still less than the overall loss rate of 5 percent. Even if we squeezed the bomber stream to the highest possible density, collisions would not be the main cause of losses.
How common, really, were collisions? Observational evidence of lethal crashes over Germany was plentiful but unreliable. The crews frequently reported seeing events that looked like collisions: first an explosion in the air, and then two flaming objects falling to the ground. These events were visible from great distances and were often multiply reported. The crews tended to believe that they were seeing collisions, but there was no way to be sure. Most of the events probably involved single bombers, hit by antiaircraft shells or by fighter cannon fire, that broke in half as they disintegrated.
In the end I found only two sources of evidence that I could trust: bombers that collided over England and bombers that returned damaged by nonlethal collisions over Germany. The numbers of incidents of both kinds were reliable, and small enough that I could investigate each case individually. The case that I remember best was a collision between two Mosquito bombers over Munich. The Mosquito was a light, two-seat bomber that Bomber Command used extensively for small-scale attacks, to confuse the German defenses and distract attention from the heavy attacks. Two Mosquitoes flew alone from England to Munich and then collided over the target, with only minor damage. It was obvious that the collision could not have been the result of normal operations. The two pilots must have seen each other when they got to Munich and started playing games. The Mosquito was fast and maneuverable and hardly ever got shot down, so the pilots felt themselves to be invulnerable. I interviewed Pilot-Officer Izatt, who was one of the two pilots. When I gently questioned him about the Munich operation, he confessed that he and his friend had been enjoying a dogfight over the target when they bumped into each other. So I crossed the Munich collision off my list. It was not relevant to the statistics on collisions between heavy bombers in the bomber stream. There remained seven authentic nonlethal collisions between heavy bombers over Germany.
For bombers flying at night over England in training exercises, I knew the numbers of lethal and nonlethal collisions. After more than 60 years, I can't recall them precisely, but I remember that the ratio of lethal to nonlethal collisions was three to one. If I assumed that the chance of surviving a collision was the same over Germany as over England, then it was simple to calculate the number of lethal collisions over Germany. But there were two reasons that assumption might be false. On the one hand, a badly damaged aircraft over Germany might fail to get home, while an aircraft with the same damage over England could make a safe landing. On the other hand, the crew of a damaged aircraft over England might decide to bail out and let the plane crash, while the same crew over Germany would be strongly motivated to bring the plane home. There was no way to incorporate these distinctions into my calculations. But since they pulled in opposite directions, I decided to ignore them both. I estimated the number of lethal collisions over Germany in the time since the massive attacks began to be three times the number of nonlethal collisions, or 21. These numbers referred to major operations over Germany with high-density bomber streams, in which about 60,000 sorties had been flown at the time I did the calculation. So collisions destroyed 42 aircraft in 60,000 sorties, a loss rate of .07 percent. This was the best estimate I could make. I could not calculate any reliable limits of error, but I felt confident that the estimate was correct within a factor of two. It was consistent with the less accurate estimate obtained from the theoretical formula, and it strongly confirmed Smeed's belief that collisions were a smaller risk than fighters.
For a week after I arrived at the ORS, the attacks on Hamburg continued. The second, on July 27, raised a firestorm that devastated the central part of the city and killed about 40,000 people. We succeeded in raising firestorms only twice, once in Hamburg and once more in Dresden in 1945, where between 25,000 and 60,000 people perished (the numbers are still debated). The Germans had good air raid shelters and warning systems and did what they were told. As a result, only a few thousand people were killed in a typical major attack. But when there was a firestorm, people were asphyxiated or roasted inside their shelters, and the number killed was more than 10 times greater. Every time Bomber Command attacked a city, we were trying to raise a firestorm, but we never learnt why we so seldom succeeded. Probably a firestorm could happen only when three things occurred together: first, a high concentration of old buildings at the target site; second, an attack with a high density of incendiary bombs in the target's central area; and, third, an atmospheric instability. When the combination of these three things was just right, the flames and the winds produced a blazing hurricane. The same thing happened one night in Tokyo in March 1945 and once more at Hiroshima the following August. The Tokyo firestorm was the biggest, killing perhaps 100,000 people.
The third Hamburg raid was on the night of July 29, and the fourth on August 2. After the firestorm, the law of diminishing returns was operating. The fourth attack was a fiasco, with high and heavy clouds over the city and bombs scattered over the countryside. Our bomber losses were rising, close to 4 percent for the third attack and a little over 4 percent for the fourth. The Germans had learnt quickly how to deal with WINDOW. Since they could no longer track individual bombers with radar, they guided their fighters into the bomber stream and let them find their own targets. Within a month, loss rates were back at the 5 percent level, and WINDOW was no longer saving lives.
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