Silicon Chip60 Years Of The Atomic Bomb - August 2005 SILICON CHIP
  1. Outer Front Cover
  2. Contents
  3. Publisher's Letter: Some people love valve amplifiers
  4. Feature: 60 Years Of The Atomic Bomb by Keith Walters
  5. Feature: Direct Petrol Injection by Julian Edgar
  6. Project: The Mudlark A205 Valve Stereo Amplifier by David Whitby
  7. Project: Programmable Flexitimer by Jim Rowe
  8. Project: Carbon Monoxide Alert by John Clarke
  9. Project: Serial LCD Driver by Graeme Matthewson
  10. Project: Enhanced Sports Scoreboard by Jim Rowe
  11. Salvage It: Washing machine pressure switches by Julian Edgar
  12. Vintage Radio: The AWA Radiola B32 transistor portable by Rodney Champness
  13. Feature: Hellschreiber Revisited by Silicon Chip
  14. Advertising Index
  15. Book Store
  16. Outer Back Cover

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Articles in this series:
  • The Mudlark A205 Valve Stereo Amplifier (August 2005)
  • The Mudlark A205 Valve Stereo Amplifier, Pt.2 (September 2005)
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  • Programmable Flexitimer main PCB [04108051] (AUD $12.50)
  • Programmable Flexitimer display PCB, DSE version [04108052] (AUD $12.50)
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  • Programmable Flexitimer front panel artwork (PDF download) (Free)
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  • PIC16F88-I/P programmed for the Carbon Monoxide Alert [cosensor.hex] (Programmed Microcontroller, AUD $15.00)
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On August 8th 1945, the world woke to the startling news that two days earlier, much of the Japanese city of Hiroshima had been destroyed by a single bomb dropped from a US aircraft. A few days later came the news that the city of Nagasaki had suffered a similar fate. Shortly after, the Japanese surrendered. 60 YEARS of the ATOMIC BOMB 8  Silicon ilicon Chip hip by Keith Walters siliconchip.com.au M uch has been written about the first atomic bomb to be used in warfare – and it is interesting to compare the newspaper reports of the time with more recent historical descriptions of the same event. Recent accounts reports tend to dwell on the terrible death toll . But that wasn’t really what the citizens of the time were so shocked about. After all, at that point in the war there were almost nightly raids on Japanese cities by huge fleets of B29 bombers, which inflicted similar amounts of damage with similar casualty figures. The after-effects of radiation and fallout are often mentioned these days but these weren’t really understood at the time. An awful realization No, the real shock was that here at last was an explanation for one of the greatest puzzles of WWII: What was the purpose of the V2 rocket? Toward the end of WWII the Nazis launched approximately 5,000 V2 rockets, mostly aimed at Antwerp and London. At first sight, the V2 sounds like a formidable weapon: carrying a one-tonne payload, it could climb to a height of about 100km and then fall back to Earth at supersonic speed, seemingly appearing out of nowhere before destroying one or at most, two buildings. As a military weapon, the V2 was ludicrously inefficient. They cost more to build than a conventional bomber, which could deliver much more explosive punch, far more accurately, and with a more than half-decent chance of coming back for another load! Terrifying though the V2 may have sounded, the vast majority of them simply failed to hit anything important. But after August 6th 1945, the whole world realised what the US and British military had known for some years: theV2 was merely one part of a radical new weapons system, the other part being the atomic bomb. Armed with a nuclear warhead, the V2’s targeting accuracy would cease to be an issue! Heinrich Himmler (in charge of Hitler’s dreaded SS) had actually made occasional references to such so-called “miracle weapons” which could “destroy London or New York with a single stroke.” Fortunately, as it turned out, building a workable nuclear weapon, particularly one that a V2 could carry, was far beyond the capabilities of the Nazi Military Industrial complex. But nobody had any way of knowing that at the start of the war. Manhattan Project As it was, the amount of industrial and scientific muscle that was applied in the USA to the top-secret “Manhattan Project” is simply unbelievable. Over half a million people worked on the project at one time or another, the vast majority having absolutely no idea what they were working on! The true cost will probably never be known, as several large corporations donated large amounts of time and resources at cost or for free, and the thousands of engineers and scientists were rarely paid overtime. An oftenquoted guesstimate is about $US30 billion (about $A42 billion) in today’s currency. Another little-appreciated fact is that the two bombs that were dropped used two completely different technologies. The Hiroshima device used relatively simple “gun-type” bomb construction but required a staggering amount of equipment and time to produce the highly enriched uranium it needed. This photograph of the damage to Hiroshima is also historically significant because it is signed by Col. Paul Tibbets, Pilot of the “Enola Gay” which dropped the first Atomic Bomb on Japan on August 6th, 1945. siliconchip.com.au August 2005  9 The Nagasaki device used plutonium, which costs far less to manufacture but the sophistication of the necessary implosion detonator device is, even to this day, far beyond the technological capabilities of most countries. Virtually all of this happened within a space of about three years, with most of the critical work done in the final 12 months! Why? Much has been written over the last 60 years about the actual reasons the atomic bombs were used on Japan, a large part of it being speculation presented as fact. One fact often overlooked is that the people making those decisions were all born in the much tougher world of the 19th century. They had already lived through one world war and the worst economic recession in recorded history. The world was a very different place then. At the time, most Americans knew virtually nothing about Japan or its people, apart from the single fact that the Japanese air force had launched an unprovoked attack on Pearl Harbour. The Allied Powers were also coming to terms with a massive humanitarian crisis in Europe, most of it the result of a drawn-out and futile war that the recently defeated Axis powers had effectively lost years before. So one of the factors would have been the growing realization that without an order of unconditional surrender from the Japanese Top Brass, there seemed little possibility of any quick end to hostilities in the Pacific. There was already a massive aerial bombing campaign under way that was expected to have destroyed all of Japan’s military manufacturing capability by early 1946, carried out by huge fleets of B-29 bombers. Although there was little question that the Japanese military would soon cease to be a major threat, there was no telling how it long it would be before the Pacific would again be safe for shipping. The Japanese soldiers’ (or probably more correctly, their officers’) “fight-to-the death” Bushido code was already resulting in unacceptably high Allied casualties just trying to secure some small Pacific islands; the death toll from an invasion of the Japanese 10  Silicon Chip mainland would be immeasurably higher. Hiroshima: August 6 1945 The only thing that seemed likely to change the situation was direct intervention by the Emperor, and the only thing that might prod him into such an unheard-of breach of protocol would be a massive display of overwhelming force. Originally a “demonstration” explosion in Tokyo harbour had been proposed but perhaps surprisingly this was rejected on the basis that it The blast from a nuclear bomb normally extends far probably would not look beyond the fire zone. But Hiroshima suffered from a all that impressive. It huge number of fires fed by gas leaks, exacerbated by the light construction of the majority of buildings. might sink a few boats and cause a mini-tidal wave, but overall the damage inflicted would plicity of the design, and the shortage probably be relatively slight. of further U235 supplies, they decided A list of potential military targets that testing of the Little Boy design was drawn up, the list gradually dwin- might be an unnecessary luxury. dling as city after city was destroyed The final “combat ready” Little by conventional bombing raids! Boy assembly was 3.2 metres long, By August 1945 there were only two 71cm in diameter and weighed about working atomic bombs actually avail- 4 tonnes, most of this being made able, one of each type, and although up by the steel tamper backplate. By there was some talk of reshaping mid-July the major bomb components Little Boy’s U235 core to make four had been shipped out to Tinian Island more implosion bombs, the War Office in several sections on the USS Indievidently decided it didn’t want any anapolis, under intense secrecy. The further delays. Due to the relative sim- uranium-containing sections were A few moments ago, there was a city under there. About 30 seconds after the explosion (8.15.15am local time on August 6, 1945), the Enola Gay circled Hiroshima at 30,000 feet – and the mushroom cloud was already above them. The city itself was already completely obscured by the thick black smoke seen at the bottom of the picture. siliconchip.com.au photographs was simply due to conventional fires caused by burning gas jets when large numbers of wooden factory buildings collapsed. More substantial brick and stone structures even directly under the blast were still left standing, although no one inside them would have survived. Actually the initial death toll wasn’t all that different from what had already been experienced in dozens of conventional bombing missions, although admittedly those didn’t have the added later complication of radiation exposure. Visitors to both sites reported that weeds and grass had started to sprout again within a few days, so the effect was more like that of a savage forest fire. Nagasaki: August 9 1945 Backup-plane view of the mushroom cloud over Nagasaki, August 9, 1945, Nagasaki was in fact the backup target, the primary target of Kokura being obscured by clouds. So too was Nagasaki – but it “earned” its place in history. flown out separately on three C-54 transport planes. The projected date of the first bombing mission was August 1 1945, with a second mission ten days later on August 11. However, bad weather delayed the first mission until August 6. Although their primitive on-board radar systems could establish the general location of a city, if there was substantial cloud cover, there was simply no way of finding your actual target! The B-29 “super fortress” finally selected was piloted by 30-year-old Colonel Paul Tibbets and christened “Enola Gay” after his mother. Tibbets is still alive incidentally; you can read a recent interview with him at www.guardian.co.uk/g2/ story/0,3605,769634,00.html You can also visit his website www. theenolagay.com The co-pilot was Captain Robert Lewis, and the weapons specialist supervising the bombing was US Navy Captain William “Deke” Parsons. The 12-man crew also included an assistant weaponeer, a bombardier, a navigator, two radar specialists, two flight engineers, a radio operator and a tail gunner. The bomb was assembled on Tinian Island and checked out on August 5th ready for a 2:45 AM takeoff the next day. It was supposed to be left in fullyoperational form but Parsons removed siliconchip.com.au the explosive charge from the gun for re-fitting immediately after takeoff, in case of a crash. The mission went off without a hitch, unlike the trouble-plagued Nagasaki mission a few days later. At 7:30AM Hiroshima was in plain sight and so the bomb’s electronic systems were activated. (Because of the enormous power drain of the valve-based electronics, the bomb could not be armed for much more than two hours before its intended use). At about 8AM local time the “aim point”, the Aioi Bridge, was lined up by Parsons. About 15 minutes later, Little Boy was released and when the Enola Gay was safely clear, a 1.3GHz arming signal was transmitted, switching on the bomb’s main control electronics. When the bomb fell below 7,000 feet, the onboard radar altimeters were enabled by the barometric safety switch and when they detected a height of 1,900 feet above ground, the cordite explosive charge was detonated. The U235 “bullet” then slammed into the tamper/target in less than six milliseconds, producing the nuclear explosion only about 150 metres short of the aim point. Most accounts of the event report that the city was completely destroyed by the initial explosion but this is something of an exaggeration. Most of the devastation seen on later The actual Fat Man bomb assembly was fitted into a relatively conventional bomb casing with the necessary remote control electronics and its batteries. The whole assembly was 3.25 metres long, 1.5 metres in diameter and weighed about 4.5 tonnes, more than half of this being the TNT explosive lens system. The B-29 selected for the mission was had already been named “Bocks Car” after Frederick C. Bock, the man who usually piloted it. It was piloted for the Nagasaki mission by Major Charles Sweeney. The intended target was the massive arsenal complex at the city of Kokura, where the bulk of Japan’s weapons R&D and manufacture was carried out. Things started to go wrong right from the start. (Ironically, the only thing that worked flawlessly was the bomb itself, despite the necessity of skipping many of its final checkout procedures due to the revised timetable)! Soon after takeoff they discovered that the fuel pump attached to the auxiliary tank was not working, and although this did not necessarily mean they had to abandon the mission, it severely limited the amount of time they could spend searching for their target. When they reached Kokura, the city was hidden in clouds so thick that they lost sight of the other two escort/decoy B29s. After three fruitless passes over Kokura, Sweeney decided to try for Nagasaki, the only other target in range. There was only enough fuel available for a single pass over Nagasaki, and since they would have to jettison Continued on P14 August 2005  11 ANATOMY OF THE ATOMIC BOMBS The basic theory of an atomic fission bomb is well known to most scientifically literate people these days, and was certainly understood by nuclear physicists by the late 1930s. Essentially, if a sizeable quantity of a suitably radioactive material could be suddenly crushed together into a small volume, the probability of any particular neutron colliding with another nucleus and releasing two or more further neutrons would be greatly increased. With a suitable “fissile” material the classic runaway chain reaction would take place resulting in almost instantaneous splitting of a large proportion of the nuclei and an enormous burst of heat and radiation. “Little Boy” At first, the only material that seemed workable for a bomb was the scarce uranium isotope U235, which has a nucleus consisting of 92 protons and 143 neutrons. Calculations showed it would need to be refined (that is separated from the other uranium isotopes) to at least 90% purity, otherwise the more radioactive U238 atoms would cause the critical mass to “jump the gun”, destroying the bomb after only a very small percentage of atoms had fissioned. It was quickly realised that the greater the amount of compression that could be applied to the fissile mass, the smaller the minimum amount that would be required to produce a true nuclear explosion. However the amount of compression that could be practically applied was heavily dependent on the physical properties of the strongest available materials at the time. The only workable approach envisioned in the early 1940s was a “gun” design where the fissile material is made in two separate pieces which are 12  Silicon Chip slammed together by an explosive charge. The limitations of tungsten carbide, the strongest workable material at the time, meant that a practical weapon would also need about 65kg of the 90% pure U235 – there was simply no conceivable method of applying sufficient compression to any smaller amount. As it turned out, only one such “gun type” uranium weapon was ever built, codenamed “Little Boy”, the design becoming obsolete before the weapon was ever tested. Bomb mechanism The actual bomb mechanism was made from a modified anti-aircraft gun. The 65kg fissile mass was made into two distinct sections: a 100mm diameter “plug” that would be fired down the barrel of the gun and a series of 100mm diameter rings (constructed like ferrite speaker magnets) that the plug would “collect” on the way. The 75mm barrel was machined out to 100mm and a conventional explosive charge would fire the U235 plug toward the “tamper”. The tamper consisted of a tungsten carbide plate mounted in a 2.5 tonne steel block. This steel block and the gun barrel had matching threads cut into them so they could simply be screwed together. When the explosive charge was fired the U235 plug and the collected uranium rings would smash into the tamper, producing a modestly compressed critical mass of uranium vapour, hopefully compact enough to start a runaway chain reaction. The “production” bomb’s control mechanism was amazingly sophisticated for something built 60 years ago. The bomb received its final arming signal (after it had been released from the aircraft), via a then state-of-the-art 1.3GHz radio control system. The bomb also contained a newly developed radar altimeter and a “fail-safe” atmospheric pressure switch, which prevented the bomb from detonating above 7,000 feet. Only one operational bomb of this type was ever produced, since by the time it was ready for combat use, the much more technically demanding but inherently more efficient plutonium implosion system had been successfully tested. Five complete “Little Boy” bomb mechanisms were actually built by August 1945 but there was only enough U235 for one of them. As far as operational safety was concerned, Little Boy was a ludicrously unsafe weapon! Anything that could have accidentally ignited the cordite charge (a plane crash or similar vehicle accident) could have set off a full-yield nuclear explosion. Although it was always transported with the explosive charge removed, it was only later realised that the design had no provision for waterproofing. Any water entering the device (in a shipwreck for example) could have acted as a crude moderator for the highly enriched uranium. While this could not produce a true nuclear explosion, it still would cause massive damage to the surrounding area as well as delivering a lethal dose of gamma rays and Here’s something you can never see again, because it disappeared in less than the blink of an eye. This is a photo of the actual “Little Boy” atomic bomb, ready for loading aboard the Enola Gay on Tinian Island, August 5, 1945. An interesting aside – one which would undoubtedly have changed history: would you believe that just four days after unloading its topsecret cargo on Tinian, the US aircraft carrier “Indianapolis” was sunk by a Japanese submarine? siliconchip.com.au neutrons to any crew members nearby. Created under the pressure of wartime emergency, the Little Boy bomb was a very inefficient design, in that less than 2% of the 65kg of U235 actually underwent useful fission. The superior compression system used on Fat Man allowed a similar explosive yield (18 - 21kt) using only about 6kg of plutonium. Another piece of history: “Fat Man” being transported to the B29 bomber “Bocks Car” for its oneway journey to Nagasaki, August 9, 1945 “Fat man” So the uranium bomb that was dropped on Hiroshima (Little Boy) was really something of an “orphan”. It was originally undertaken as the atomic fission device “most likely to work”, on the basis of what was known in the early 1940s. To the best of anyone’s knowledge at the time, the only material in existence that was suitable for building a fission bomb was uranium 235. However, as the initial research got underway, it was realized that a then-theoretical element with 94 protons and 145 neutrons might also be suitable. This was verified after a minute sample of the element was eventually created by bombarding U238 with a high-speed neutron beam from an early model cyclotron. Ultimately, this element was named “plutonium”. But while the scientists soon realized that it might still be possible to base a bomb design on plutonium, it would require the development of a vastly more sophisticated explosive trigger mechanism. No tamper made from any known substance would be anywhere near strong enough to withstand the force of the collision that would be necessary to initiate successful plutonium fission. The only solution was to shape the plutonium into a hollow sphere and completely surround it with a spherical layer of high explosive. To produce a precisely spherical shock wave, thousands of experiments were carried out with “explosive lenses” made from fast and slow-burning TNT mixtures. The individual explosions had to be synchronised to within nanoseconds, and so conventional hot wire electrical fuses could not be used. Instead, special “exploding wire” detonators were developed. These were combined with sophisticated spark-gap triggers driven from a newly developed portable regulated 8,000V DC power supply made by Raytheon. The spark gaps were all fed from a network of precision RC networks with exactly the same time-constant. 32 large high voltage capacitors were needed, and the capacitor/spark gap assembly alone weighed siliconchip.com.au over 200 kilograms! Apart from all this, the scientists and engineers had only a few months to learn the entire metallurgy of the brand-new element, plutonium. Initially they had problems with the plutonium sphere halves warping after casting and machining, until they discovered that an alloy of 3% gallium and 97% plutonium was dimensionally stable. Although, like uranium, plutonium 239 is only weakly radioactive in the “unmoderated” state, chemically it is an extremely toxic substance and spontaneously bursts into flame when exposed to air. All the machining had to be carried out in an atmosphere of nickel carbonyl gas, which plated any newly exposed surfaces with a protective layer of nickel. The final wartime implosion-type bomb used about 2.5 tons of TNT-based shaped charges precision-fitted around a series of nested shells of various materials. (See diagram). The entire assembly was housed in a spherical aluminium alloy shell about 100mm thick and 1,500 mm diameter. There were 32 separate explosive lens assemblies, 20 hexagonal and 12 pentagonal, in the same pattern as a soccer ball. Each assembly consisted of two precision castings of fast-burning and one casting of slow-burning explosive. The slow-burning segment fitted into a conical cavity in the larger of the fast-burning pieces, and a further piece of fast-burning explosive was fitted under this. The actual plutonium “pit” was machined into two precision hemispheres that formed a hollow sphere 90mm in diameter (about the size of a cricket ball). The 20mm polonium/beryllium neutron initiator fitted precisely inside the hollow centre. Surrounding the pit was a 70mm thick “tamper/reflector” made from natural uranium. Its purpose was mostly to keep the pit from rebounding before the full fis- sion reaction could be completed, but it also served as a neutron reflector to enhance the chain reaction. Also a small part of the “yield” of the bomb (about 20%) would come from fast fission of the tamper. Surrounding the tamper was a 115mm “Pusher/Neutron absorber” shell made from a boron/aluminium alloy. This was actually part of the mechanism that “tuned” the implosive shock wave, although what the neutron absorption function of the boron actually accomplishes has never been made entirely clear. The shock waves would move more slowly through the lightweight aluminium than they would through the uranium, and the timing was such that any reflected energy would be returned to the core just as the actual chain reaction began, something after the fashion of a Yagi antenna. For safety, a 20mm hole was cut through the plutonium pit and the pusher and tamper shells to allow the neutron initiator to be fitted just prior to combat use. For transport, a dummy sphere of cadmium removed any possibility of a chain reaction. Removable precisionmachined aluminium and uranium plugs allowed this to be withdrawn and the initiator fitted in its place. Each of the 32 exploding-wire detonators was connected to an SO239 “UHF” socket, the same type that is still found today on AM CB radios. (In those days, “UHF” meant pretty much anything above about 50MHz!) Since the detonators had to be fired within +/-10 nanoseconds of each other, 32 precisely matched lengths of coaxial cable were required. (Ironically, the necessary polythene dielectric co-ax was yet another technology that just “happened along” at the right time!) August 2005  13 Perhaps more by (bad?) luck than management, the Mitsubishi arms plant in Nagasaki became ground zero. Here’s what was left of it. the bomb anyway if they were going to make it back, the bombardier decided that if necessary they would attempt to aim the bomb using the onboard radar system. Nagasaki turned out to be covered in even thicker clouds than Kokura but just as they were about to release the bomb for a “pot luck” strike, a small opening appeared above a large industrial complex that turned out to be the Mitsubishi arms manufacturing plant. Although the bomb itself was of a completely different design from Little Boy, the arming sequence was exactly the same. The bomb was released, and when the plane was far enough away, the 1.3GHz arming signal was transmitted, activating the firing electronics. At about 7,000 feet, the barometric safety switch kicked in, allowing the radar altimeter/trigger to function. At 1,650 feet, the radar altimeter closed a contactor inside the 8,000V power supply, feeding this voltage to the RC spark gap array. A couple of milliseconds later, all 32 spark gaps arced over within 10 nanoseconds of each other, sending 32 identical high voltage pulses to the array of exploding wire fuses. An instant later 32 identical convex flame fronts were shaped and merged into a single spherical imploding shock wave. The various metal layers were vaporised as the wave travelled through them, the surface area of the spherical shock wave decreasing by a factor of about 16 times, thus increasing the pressure by a similar amount. The plutonium pit 14  Silicon Chip Nagasaki suffered less damage than Hiroshima, due largely to the city’s topography. was compressed by a factor of about 2.5 times, a remarkable figure for a virtually solid ball of metal! When the shock wave reached the centre, the neutron initiator assembly was instantly converted to a series of high pressure jets of beryllium/polonium vapour which mixed with the vaporised plutonium to “kick-start” the chain reaction. Once the chain reaction was under way a massive burst of high-speed neutrons struck the surrounding cloud of uranium vapour, fissioning some of the U238 atoms and adding about 20% to the explosive yield. The yield of the explosion was estimated at about 21,000 tonnes, completely destroying the largely corrugated iron structures of Mitsubishi plant, with an initial death toll estimated at about 70,000. As was the case with Hiroshima, the death toll would have been a lot lower if people had retreated to the simple but effective bomb shelters dug into the hillsides. Because of the small number of aircraft involved, they probably assumed it was a reconnaissance mission. It may seem incredible now, to think that it took the Japanese over a week to surrender after the massive devastation of the initial Hiroshima blast, but the sad fact was that communications were so poor at the time that most of the populace (military included) simply had no idea that the attacks had taken place! All that they knew at the nearby army bases was that all communication (radio, telephone or tele- graph) from the bombed cities abruptly ceased, all at the same moment. Petrol was only available for military use, and civilian transport between cities was virtually non-existent. There are numerous accounts from Japanese Air Force pilots who were sent to investigate and who simply had no idea what had happened, since there was no sign of the cratering seen on conventional bombardments. The immediate post-war period When the war ended on August 15 1945 obviously there was an abrupt change of priorities. Now that the plants were up and running, operating costs fell dramatically and so production of weapons-grade uranium and plutonium continued, but few actual working bombs were constructed. By October 1945 there were 60 Fat Man assemblies (without plutonium pits) available but by July 1946 there were still only seven fully operational Fat Man type weapons in the US arsenal. Presumably the US government had more pressing things to spend its money on at the time and so the nuclear weapons program was put on the back burner. However in 1949 the detection of traces of radioactive fallout drifting across from Siberia indicated that the Soviet Union had successfully tested a nuclear weapon of its own. As it turned out, this was basically a direct copy of Fat Man, constructed using information supplied by spies operating inside Los Alamos. From that point the Arms Race began in earnest. SC siliconchip.com.au 10 SECONDS IN THE LIFE OF AN ATOMIC BOMB This amazing series of photographs is of the world’s first atomic bomb blast – at Alamagordo, New Mexico, USA on July 16, 1945. (Photos in this feature courtesy atomicarchive.com) 6: The mushroom cloud starts to form – two seconds after detonation. 1: The early fireball, taken just sixteen milliseconds after detonation. 7: And grows – three seconds after detonation. 2: Another nine milliseconds later, (at 0.025s) not much appears to have changed. 8: Again at four seconds after detonation. 3: Here’s the fireball at 53 milliseconds. 9: The head starts to take on the familiar mushroom form – seven seconds after detonation. 4: And at 62 milliseconds it’s growing . . . 10: The mushroom head fully formed ten seconds after detonation. 5: Less than one tenth of a second after detonation. 5: And again at 90 milliseconds. siliconchip.com.au siliconchip.com.au August ugust 2005  15 2005  15 A