Chapter Eight - Simple Math
"By April 1945 Oak Ridge had produced enough U235 to allow a near critical assembly...."ccxci
Richard Rhodes, author
The Making of the Atomic Bomb
(Accumulation of enough enriched uranium to achieve critical mass required one year. The uranium bomb prepared for Hiroshima barely three months after the first critical mass was accumulated contained almost three critical masses - author's note)
The determination to use Y-12's hard-won enriched uranium to power the Hanford reactors, like so many other decisions General Groves had to make in order to advance the program, must have been a finely balanced judgment, which is reflected in how he appears to have chosen to execute it. As has been outlined, only two options were scientifically feasible for creating a nuclear weapon before the war ended: a uranium bomb and a plutonium bomb. Technologies to achieve the bombs varied widely in some areas and were interchangeable in others but progress on all fronts was going forward.
Research had shown that probability-wise, economically and technically, plutonium was the better bet - faster, cheaper, easier. But the whole program was still a wager. Nothing was guaranteed. Even considering plutonium's appreciable promise, Groves could not afford to put all his eggs in one basket. To cover all eventualities, the imperative still was to achieve success with each weapon. He simply must be careful allocating resources along the way - ensuring he had enough of the necessary materials to make at least one of each bomb - and then he could weight any surplus resources in favor of the preferred plutonium prospect.
Such an intermingling of resources at this point, however, could prove to be problematic. Enriching uranium came at such a high price in every form of currency, whether it was money, time, or the energy exerted to achieve the endeavor. Consuming the hard-earned enriched uranium in an effort that failed would be anathema to those powerful men who had invested so much into it and were counting so much upon it. Should the plutonium bomb fall short of success for whatever unknown reason, and the uranium program require more fissile material to produce multiple bombs - which was believed the requirement to achieve victoryccxcii - both programs may have failed and the ambitions of all involved would be thwarted.
For Groves, the risks of taking enriched product originally intended for the uranium bomb and using it in the plutonium weapon must have seemed great, but worth taking. Especially if the intermingling could be camouflaged from the eyes of those who had a vested interest in the success of the overall program. If no one knew that one program had been put at risk for the other, if either program failed it would be considered to have failed on its own deficiencies.
While the brilliant brain trust he had hired was ciphering the universe of factors and exponents, of calculus and algorithms, Groves' decisions, though pressure-packed and frequently daunting, were usually solved using simple math and inspired resourcefulness. For example, each calutron required a given amount of magnetic force, and there was a given number of calutrons at any one time; therefore, a huge amount of silver was required for the electro-magnet windings of the calutrons. Eventually, over 13 tons of silver was required for the calutronsccxciii (copper windings were out of the question since hoarding every last bit of copper was essential for fulfilling conventional munitions demands). Groves borrowed 13,540 tons of silver, normally measured in troy ounces - in this case 395 million troy ounces worth over $300 million - from the United States Treasury.
Or Groves faced the decision of how many Alpha calutrons should be built and how many Beta calutrons? Through the course of time and the accumulation of experience he eventually settled on nine Alpha and three Beta calutrons.ccxciv And lastly, how should he allocate the enriched uranium between the plutonium bomb option and the uranium bomb alternative?
Probably the simplest, most natural solution was to split the enriched uranium originally dedicated to the uranium bomb, and to use half of the concentrated product in the plutonium reactors while saving half for its original purpose in the uranium bomb.
A second logical option took into account that critical mass for the uranium bomb finally had been calculated at approximately 15 kilograms.ccxcv He could have gauged the accumulation of enriched uranium so 15 kilograms, expected to be enough for one uranium bomb, would be on hand at a date early enough before the target drop date in August 1945.ccxcvi The bomb's enriched uranium could be reduced to metal, fabricated into its sub-critical slugs, and the bomb assembled in time for use when needed. And, of course, he would still need enough time to transport the weapon to the base of operations, from where it would be flown to its target for its deadly delivery.
Once he had made the calculations of how much enriched uranium per day would be required to accrue 15 kilograms by, say, 1 May, 1945, two months before the drop date objective, any surplus of the precious product could be invested in the favored plutonium-breeding reactors at Hanford. If everything went right, in August Groves could simply add the lone uranium bomb to his reserve of two or three plutonium bombs, which, once the more prolific plutonium started being produced using the enriched uranium, would grow by one bomb every two to three weeksccxcvii (compared to one uranium bomb every five monthsccxcviii). He simply had to choose now to fuel the reactors with the surplus enriched uranium.
Actually, both options merged well together. The rate of enriched uranium production as of the beginning of 1945 was setting a pace to be just at 30 kilograms around the beginning of May - 33 kilograms was actually achieved - according to the Beta Oxide Transfer Report that documented bomb-grade enriched uranium production.ccxcix If the plutonium bomb was granted half of the enriched uranium produced for the uranium bomb, by early May, 15 kilograms (33 pounds) could still be set aside for the uranium bomb - the amount needed for critical mass. Enough surplus enriched uranium would still be available for the plutonium project to receive 15 kilograms for feeding the Hanford reactors, providing a sizable boost to the more promising effort.
Supporting the suggestion that this path was chosen is a pair of references by author Richard Rhodes in his book The Making of the Atomic Bomb that, combined with two contemporaneous documents, reveals how the enriched uranium appears to have been used.
First, based on assumptions recorded by James Bryant Conant at the beginning of 1945, Rhodes calculated that if enrichment output was one kilogram per day, one bomb would be produced every six weeks. (Actually, from the beginning of 1945 through all but the last three weeks of its applicable wartime production, Oak Ridge averaged only one-third kilograms a day). From Conant's information Rhodes calculated that the uranium bomb would eventually need "about 42 kilograms - 92.6 pounds," which he then states was approximately 2.8 critical masses.ccc In other words, taking 42 kilograms and dividing it by the number of critical masses contained therein, 2.8, critical mass can be calculated to be about 15 kilograms.
At that time, nobody knew that three times that amount would actually be required for the uranium bomb, probably due to reduced efficiency due to contamination. Robert Serber, author of the quintessential textbook on Los Alamos, The Los Alamos Primer, which was the basis of all Los Alamos' scientists' orientation at the time, writes the amount actually used in the bomb was somewhat higher at approximately 50 kilograms.ccci Serber also validates the 15-kilogram critical mass figure in a footnote.cccii Rhodes stated later in his book that enough material was processed to achieve critical mass in April 1945.ccciii One can therefore conclude that critical mass was 15 kilograms (33 pounds), and that the amount for critical mass first became available in mid-April.
But Oak Ridge by this time had enriched roughly 30 kilograms of uranium to bomb quality according to the Beta Oxide Transfer Report - twice the amount Rhodes records was available at the time for the uranium bomb. In other words, half of the enriched material was gone and, outwardly at least, unaccounted for.
The second clue that suggests Groves was dividing the enriched uranium between the uranium bomb and plutonium bomb projects is found in a document written at Los Alamos. Eric Jette, the chief metallurgist at the New Mexico laboratory, wrote in a memo dated 28 December, 1944, that "At the present rate we will have 10 kilos about February 7 and 15 kilos about 1 May."ccciv Jette's 15 kilograms estimate by 1 May falls almost perfectly in line with when the uranium bomb program actually achieved that milestone in mid-April.
And the ratio of enriched uranium versus uranium metal to be produced as predicted by Jette, by the same 1 May, 1945 deadline is constant. In other words, all documentation and predictions that the author has found agree on this point: only half of the enriched uranium processed was accounted for and considered in the report that said enough material for critical mass had been produced. A third evidence of enriched uranium shared between weapons programs lies in a memorandum written by J. Robert Oppenheimer to Cyril Smith, Joseph W. Kennedy, Samuel K. Allison and Robert F. Bacher.
The document ties these men to enriched uranium usage despite their noted involvement with the plutonium bomb, not the uranium bomb. The memo, dated 28 July, 1945, four days too late to be discussing product used in the actual bombs dropped on Japan, is nonetheless interesting to this review as much for the four men to whom it is addressed as for the amounts of enriched uranium being shipped. (The quantity of product shipped becomes cogent information at a later point in this narrative.) With the exception of metallurgist Smith, who helped fabricate both the uranium and the plutonium bombs, each man in his own right was a driving force in the field of plutonium bomb development, having little to do with the uranium bomb.
Kennedy was a co-discoverer of plutonium and continued, with Emilio Segre, to research the radioactivity of the newfound element. Allison worked closely with Enrico Fermi on the first chain reacting pile in Chicago that made plutonium production a possibility and continued the bulk of his research in the field of breeder reactors as it related to making a plutonium bomb. And Bacher was dedicated to heading the group that studied the demanding requirements of detonating a plutonium bomb -- which was much more difficult than detonating a uranium bomb -- and was eventually credited with successfully leading the effort to develop the "implosion" method that was used, despite significant obstacles.
In the memorandum, Oppenheimer is reporting to these men the delivery schedule from Oak Ridge of uranium enriched to a level of 86.5 percent - Beta calutrons product.cccv While there may be a remote possibility these men were working together on some aspect of the uranium bomb project, such an instance is highly improbable given the contributions to the plutonium program they are known for, their backgrounds, and certain aspects of the communiqué. There seems to be no reason for Oppenheimer to have reported enriched delivery schedules to these men unless enriched uranium was an important component of the plutonium bomb project. The memo appears to be a very direct validation of production quantities of highly enriched uranium being used in the plutonium bomb project.
Metallurgical fabrication of uranium for both the uranium bomb itself and the uranium fuel slugs for the reactors was performed at Los Alamos. Given Smith's inclusion with the others in the memorandum, for even Smith's involvement was focused more on plutonium development than a uranium bombcccvi it appears the enriched material referred to is for use in the uranium slugs for the Hanford reactors. Reactor fuel is not composed of bomb-grade enriched uranium but normally is enriched to only between two and five percent; and it is unknown to what enrichment the war-time Hanford reactors may have been operated.
Neither the Alpha nor the Beta calutrons were so sophisticated at the time as to be able to control with any certainty their capacity to enrich uranium to a preset level; and considering the circumstances, it would have been risky and inefficient to produce anything but the highest enrichment possible. Instead, the managers of the calutrons must have found it most productive to make the highest-enriched product possible, then calculate the content of enriched versus raw uranium required in the uranium fuel to achieve the desired concentration, and mixed the two uranium stocks to suit. Such a controlled process, presumably, would have produced optimum results for plutonium output.
So in late 1944, General Groves appears to have split the
enriched uranium stocks between the weapons programs. Progress appeared
to be going well for Brigadier General Leslie R. Groves and the Manhattan
Then the first shoe dropped: As has been noted, sometime during the middle of April - Rhodes places the time between President Roosevelt's death on the twelfth and his funeral on the fifteenthcccvii - Otto Frisch reported to Robert Oppenheimer the staggering fact that one critical mass, the amount just becoming available as the bombing target date was fast approaching, would not be enough to fuel a viable uranium weapon.
No reason is given for the critical calculation correction but the culprit appears to be contaminants in the enriched material. At its best the uranium was enriched to 90 percent, leaving ten percent either U238 or other, mostly non-fissile, elements, any of which would obstruct the efficiency of the chain reaction. To overpower the neutralizing effects of these contaminants and produce an explosion that justified the expense and reliance that had been placed in its potential, the bomb required significantly more than the 15 kilograms that was the minimum amount of pure U235 initially thought to be required to create an explosion. As has been noted, the quantity ultimately used, according to Robert Serber, and indirectly but roughly supported by Rhodes' own calculations, was 50 kilograms - over three times critical mass.
Rhodes lightly dismisses the shortfall, however, suggesting that it "was now only a matter of time" before the deficit would be overcome. While the statement is obviously true, so it is true that time was a crucial matter - more so than Rhodes seems to have comprehended. Or else the Pulitzer Prize-winning author, despite his laudable achievement assembling the most comprehensive reference work ever compiled about the Manhattan Project, and for which he justly earned the Pulitzer and many other awards, fell short in one small but important measure.
While his historical references are extensively documented, footnoted and cross-referenced, he either fails to apply a similar standard for reconciling mathematical anomalies in his book; or he, like many other authors on the subject, chooses not to question unresolved discrepancies. Possibly he assumes any explanations for disparities are buried beyond the value of their pursuit, and the fact that history suggests they were resolved is explanation enough. Or, also understandably, he may have chosen not to pursue the incongruity as being outside the scope of his already massive work. Whatever the reason, the numbers, as has been demonstrated, do not add up.
Oak Ridge, splitting its enriched uranium allotments between the uranium bomb and the Hanford reactors, had taken almost a year to provide the 15 kilograms available for the uranium bomb by May 1945. In an effort to produce the balance of the 50 kilograms needed, even at its top production capacity in that spring of 1945, the uranium bomb program could only have produced seven or eight kilograms more between 1 May and 24 July.
The twenty-fourth of July is the date General Groves, himself, gave as the last delivery date of enriched uranium to Los Alamos, cccviii and this is corroborated elsewhere.cccix Seven or eight kilograms added to the 15 kilograms already stockpiled was still far short of the 50 kilograms actually required for the bomb. Even in a most drastic action, if contributions to the plutonium reactors had been discontinued and all enriched uranium produced had been committed to the uranium bomb effort, a strategy not likely to have been pursued given plutonium's superiority over uranium, especially considering the new tripling of the uranium bomb's material needs, the maximum possible enriched uranium available was just over five kilograms per month.
Accumulated over the next three months of May, June and July, the total of another 15 kilograms added to the original 15 kilograms would have made the material available for the bomb 30 kilograms. The 50-kilogram uranium bomb would still have been short its enriched uranium needs by fifty percent. A serious stumbling block had been dropped in the path of the uranium bomb.
The second shoe dropped just a few days later. On 18 April, Norris Bradbury, the man assigned the responsibility of overseeing assembly and final testing of the final plutonium bombcccx and who went on to become the post-war director of the Los Alamos National Laboratory, reported in a memo the program was experiencing serious problems with detonators. He then concluded:
(a) a much smaller number of tests than 300 (the scheduled number) will have been carried out;
(b) there is more than a bare possibility that the detonators will be unsatisfactory.
Particularly in the latter event it may be necessary to postpone final Raytheon tests until the detonator difficulty is unscrambled.cccxi
The detonator problem, the "Raytheon tests" and the timing of the memo itself all are cogent factors in a central premise of this book; that components from captured U-boat U-234 were employed to successfully complete both of the Manhattan Project's atomic bombs. The detonator problem had been a long-standing issue but those in charge thought it would have been overcome long before the spring of 1945. By now the faulty detonators as well as the delay of the Raytheon tests, combined with the shortage of enriched uranium, actually represented less the final shoe falling upon the program than one standing on the throat of the entire Manhattan Project.
Test detonations almost never went right. Getting all 32 firing points to discharge at the same instant using clumsy electro-mechanical circuits of cables, wires and connectors proved to be almost impossible. If the timing was off by a mere fraction of a millisecond at any one of the 32 firing locations, the mass of plutonium at the center would be shot out of the undetonated hole, like a bullet out of a gun.
The plutonium core would have been thrust out by the shock wave of all the other detonator explosions that fired on cue. Poor detonator timing could be caused by small inconsistencies in the quality of the cabling metal or a miscalculation of cable length of just fractions of an inch. According to none other than Luis Alvarez, even "the best detonators then available" were only achieving detonation waves spaced 10 to 20 feet apart, "rather than the required fraction of a millimeter."cccxii
The situation, so late in the game, openly was considered a crisis equal to the shortage of enriched uranium for the uranium bomb.cccxiii System quality was so poor that less than a week before Bradbury wrote his memo, a trial bomb proximity fuse had exploded barely following "bombs away" from the plane.cccxiv Whether the "proximity fuse" described refers to the same detonators that were causing the problems is unknown, but detonations were not simultaneous at best, and they were unpredictable at worst.
In either case, Oppenheimer, back in October, had aggressively pursued a resolution to the problem and had assigned a three-man committee to "consult on the procurement of detonators to insure that the designs are satisfactory...."cccxv The first man listed on the committee was Oppenheimer's old Berkeley buddy, physicist Luis Alvarez, who had transferred to the Manhattan Project from working on the development of radar and other high frequency wave applications.
Two other key high-ranking members of the Manhattan Project staff, Kenneth B. Bainbridge and a Lieutenant Colonel Lockridge accompanied Alvarez on the team. Alvarez would later be credited for developing a network of thread-like fuses that, when ignited simultaneously at the 32 detonator points, would instantly and evenly detonate the high explosives, each covering their assigned quadrant of the sphere in near-perfect unison.cccxvi
But for now, six months had passed since the creation of the detonator team - and only three remained before the Trinity test - and obviously the detonators were still a serious obstacle to success. Alvarez and his team had thus far failed. And this, compared to the "Raytheon" dilemma, appeared to be only a secondary problem, although the two look to have been inseparably interconnected.
According to General Groves, the main delay of the plutonium bomb was "the company manufacturing certain essential parts for a non-atomic assembly in the Fat Man (the code-name for the plutonium bomb) had been unable to meet delivery schedules."cccxvii Groves continues, explaining that the delayed part hindered testing of the bomb "until a critically late date."
The unidentified component over which he laments was the control unit for discharging the simultaneous firing signal for the detonators, known as "the X-unit." Raytheon, the unnamed manufacturer mentioned by Groves but referenced by name in Bradbury's memorandum above, was the maker of the X-unit. The device, which cost the equivalent of a Cadillac,cccxviii was a sophisticated conglomeration of cables, switches, transformers, wires, condensers, capacitors and relays.cccxix
The complexity of the instrument made it an engineer's nightmare. It appears that X-unit manufacturing was delayed further and made even more complicated because, as the brains of the detonation system, it required that the type of detonators to be used be integrated into the X-unit's design specifications, as seems is suggested in Bradbury's memo. Surely in as precise a piece of instrumentation as the X-unit, detonator selection must have been an important consideration. But as late as three weeks before the Trinity test, the detonator to be used still had not been selected, and modifications just prior to the Trinity test, as a result, were expected to be made on-site to the hardly-tested X-unit.cccxx
Whatever the case, the scientists struggled with the detonator and X-unit problem throughout the fall, winter and spring and still had not resolved it as the fateful summer of 1945 was unrolling. A raft of reports, memoranda and schedules, with addressees including not only Alvarez but those who received the enriched uranium schedule reviewed earlier, Bacher, Allison and Segre, flew from office to office as efforts were made to resolve the detonation problems. The communiqués show that as late as 9 April, 1945, the first in-flight tests for the X-unit were finally scheduledcccxxi to evaluate X-unit operation on an actual bombing run.
The tests proved, however, that the detonators were still unsafe in early May,cccxxii with only two-and-a-half months left until the Trinity test. One-and-a-half months later, on 20 June, with less than a month until Trinity and counting down, X-units were finally scheduled to be delivered to Los Alamos for the Trinity test, but even these were not prepared for their final use. Apparently detonators mysteriously had been obtained that could do the job, but for some unexplained reason modifications were still planned for the X-unit, even after delivery.cccxxiii
In a memorandum written by George Kistiakowsky dated 6 June, 1945, instructions were given that one X-unit was to be "modified, inspected, and made shippable to Trinity by 1 July. Two more units for Trinity should be on the Site (sic) by 1 July, and should be modified, and made shippable to Trinity by 7 July."
What was done to acquire the new detonators is unknown, as are the modifications made at the last minute to the X-units. But the timing of these important changes and the activities of Luis Alvarez during this same period may be very telling in regard to how the implosion-timing problem was resolved. Apparently, Luis Alvarez is the same Mr. Alvarez as the false "Commander Alvarez" who received Dr. Heinz Schlicke's proximity fuses from U-234.
And it appears that the same enriched uranium so desperately needed to complete the uranium bomb was received from the gold encased stocks of uranium labeled "U235" that Major Vance had taken from U-234. The facts appear to demonstrate that without the bomb materials surrendered with U-234, the United States' atomic bomb effort to win the war by mid-August would have failed. The question is; how did those powerful nuclear components fall into American hands?
ccxci Richard Rhodes, The Making Of The Atomic Bomb, p. 612
ccxcii Leona Libby, The Uranium People, p. 244; Richard Rhodes, The Making Of The Atomic Bomb, p. 691; Harlow Russ, Project Alberta, p. 55
ccxciii Richard Rhodes, The Making Of The Atomic Bomb, p. 490
ccxciv Herbert Childs, An American Genius, p. 350
ccxcvRichard Rhodes, The Making Of The Atomic Bomb, p. 614
ccxcvi Richard Rhodes, The Making Of The Atomic Bomb, p. 601
ccxcvii Leslie R. Groves, Now It Can Be Told, p. 309
ccxcviii Harlow Russ, Project Alberta, p. 66
ccxcix U.S. National Archives, Southeast Region, East Point, Georgia, Beta Oxide Transfer Report
ccc Richard Rhodes, The Making Of The Atomic Bomb, p. 601
ccci Robert Serber, The Los Alamos Primer, p. xv
cccii Robert Serber, The Los Alamos Primer, p. 33
ccciii Richard Rhodes, The Making Of The Atomic Bomb, p. 612
ccciv Eric Jette, memo, Production rate of 25, Los Alamos National Laboratory Archives, A-84-019-70-24
cccv J. Robert Oppenheimer, memo, Schedule for Delivery of X Material, Los Alamos National Laboratory Archives, A-84-019-70-24
cccvi Richard Rhodes, The Making Of The Atomic Bomb, p. 657
cccvii Richard Rhodes, The Making Of The Atomic Bomb, p. 614
cccviii Leslie R. Groves, Now It Can Be Told, p. 124
cccix Richard Rhodes, The Making Of The Atomic Bomb, p. 691
cccx George B. Kistiakowsky, memo, Organization of the X Division Participation at Trinity, Los Alamos National Laboratory Archives, A- 84-019-55-9
cccxi Norris E. Bradbury, memorandum to Norman Ramsey, Los Alamos National Laboratory Archives, A-84-019-82-16
cccxii Luis Alvarez, Alvarez, p. 133
cccxiii Robert Serber, The Los Alamos Primer, p. xv
cccxiv Max Morgan Witts, Gordon Thomas, Enola Gay, p. 113
cccxv Kenneth T. Bainbridge, memorandum, Minutes of a Meeting on the Electric Detonator Program, p. 2, Los Alamos National Laboratory Archives, A-84-019-14-11
cccxvi Robert Serber, The Los Alamos Primer, p. xvii
cccxvii Leslie R. Groves, Now It Can Be Told, p. 341
cccxviii Max Morgan Witts, Gordon Thomas, Enola Gay, p. 103
cccxix L. Fussell memorandum: Detonator Circuits Visit to Raytheon Co., Los Alamos National Laboratory Archives, A-84-019-41-11
cccxx F. Oppenheimer memorandum to N.E. Bradbury, June 21, 1945, Los Alamos National Laboratory Archives, A-84-019-55-9; also F. Oppenheimer memorandum to K. Greissen, D.E. Horning, E.J. Lofgren, June 26, 1945, A- 84-019-55-9
cccxxi Norman F. Ramsey, memorandum, 9 April 1945, Boosters for T-26, Los Alamos National Laboratory Archives, A-84-019-67-7
cccxxii William S. Parsons, minutes of 1 May 1945 Meeting On Detonators, Los Alamos National Laboratory Archives, A-84-019-82-16
cccxxiii George B. Kistiakowsky, memorandum 6 June 1945, X Units for Trinity, Los Alamos National Laboratory Archives, A-84-019-55-9
Back to Contents