Math Skills Converting Amount To Mass Answers: Fill & Download for Free

Like with all jobs, how much you make street performing depends on a variety of factors:How skilled you areWhere you are performingHow many shows you doI'll go into more detail below, with a lot of actual data from three years of street performing, but for those interested in the short answer: as high as more than $1000/show and $80k/year, and as little as nothing.Our biggest show ever, £640.85.Now for the gritty details, going into depth on each of the three variables stated above.How skilled you areThis refers to how skilled you are at converting passersby into well paying customers, not how skilled you are at doing whatever you're performing. If you are truly amazing at convincing people en masse to stop, watch, and then pay you for the pleasure, it doesn't matter what you're doing or how good you are at it.To see how this plays out in real life, check out this graph:This shows the revenue per show since my brother and I started doing full street performing shows. Over three summers of performing, our average show revenue more than tripled ($165/show our first summer to $550/show at our most recent Fringe), while the tricks in our show stayed, by and large, exactly the same. This graph doesn't even take into account the actual first times we street performed, way back in 2005, because we didn't have anything you could call a show, we were just doing the tricks. This paid out something on the order of $10/hour.What does this mean? Did we just get better at swindling people out of their hard earned money? Or were we just bad at getting what we deserved when we first started? Neither. Our show wasn't very entertaining when we first started street performing. We got better at the transitions, at talking to people, and building a dedicated, engaged crowd, and at delivering all of our jokes in just the right way. One of the most important things we improved was our hat line (What are some of the most effective street performing "hat lines"?).We hope this is more entertaining than a burger!When it comes down to it, people think nothing of plopping down almost $15 (per person for families) to watch a movie that they might not even like. Paying $5 for a live, interactive show featuring some world class tricks, that you've already watched and know you liked? Seems like it makes a lot of sense. Even our best show ever, which topped $1000, probably only averaged around $2/person. That's less than an espresso at Starbucks, and I hope our show is more entertaining than a Venti coffee. So it's all about getting people to agree that what they just saw was worth something close to what you (the performer) think it is.This direct correlation between how much you make and how good you are is both a blessing and a curse. On the one hand, you don't have to rely on a boss to finally notice how much better you've gotten and give you a raise. This is awesome. On the other hand, if you have an off day where you're not feeling so hot, you make way less money. That sucks. More on what it's like to actually be out there doing this can be found here: What's it like to be a street performer? What are the perks, the hidden joys, and hidden pitfalls?Where you are performingThis encompasses two important factors: How many people are in the area, and why those people are there. You can think about the amount of money you'll generate in a show as:[math]E(Show)=P(Person Donating)*N*x[/math]where [math]E(Show)[/math] is the expected value of your show, [math]P(Person Donating)[/math] is the probability of an audience member donating after the show, [math]N[/math] is the number of people watching your show and [math]x[/math] is the average amount given for a given audience.The more people are walking through an area, the more that will stop and watch your show, plain and simple. The more people who watch your show, the more people will give you money afterwards, since you're increasing [math]N[/math] in the equation above.Why people are in that area affects [math]P(Person Donating)[/math]. If you're performing in a business district, for example, everyone passing by is likely to be in a rush to go somewhere, and unlikely to stay and watch your show (although they're all probably well off so [math]x[/math] will be a bit higher). If you're in a shopping area (like Faneuil Hall in Boston), people are in the mood to spend money and are generally just walking around. On the other hand, they're there to buy things, not experiences, so this variable could be higher. The best situation is in an area where people have time to kill, are in the mood to spend money, and are expecting to spend it on experiences (like the Edinburgh Fringe Festival).If your show's good enough, people will stick around to the end even if it's raining, especially in Scotland.Another important factor related to location is weather. Rain will ruin your show. You can go from an engaged audience of five hundred people to a soaking wet audience of ten if it starts to pour during your show. Some places are better for rain shows than others (Scottish people care less about standing out in the rain than people in Boston for instance), but a rainy show will almost always result in a small fraction of the revenue of a nice sunny day. A really hot or humid day usually results in a lackluster audience that doesn't really want to cheer or clap very much. A windy day can make nailing tricks more difficult. Since you'll inevitably encounter bad weather as a street performer, you need to take this into account when thinking about what your average show revenue will be.How many shows you doThis one seems obvious, but is actually pretty unique to street performing. When you're on a salary, every late night doesn't equate to a commensurate bonus. When you're a wage worker, you don't get to decide when you work overtime. When you're a street performer, if you want more money, you can go out and do more shows. It's that simple.You can only do this so many times in a day before you start getting tired and making dangerous mistakes.There's a flip side, of course. No one is out there expecting you to do a show, no boss to get on you about being late to work, no customers expecting products to be delivered on deadline, etc. You are completely responsible for getting out there and getting it done. There's also the fact that doing street shows is draining, both mentally and physically. Very few people can just pump out show after show (although you can design your show around this if you want), so with each successive show, it's likely that your energy levels will drop, along with the revenue of the show. This is extremely important when it comes to thinking about how much overall money you can make street performing.Miscellaneous ExpensesThere are also a lot of other factors to take into account that most people might not expect. Every extra person in your group means you split the revenue one more way. Almost everywhere you perform you're going to need public liability insurance, and usually a different kind for every place you go. Since no one wants to either perform or watch a street show in the depths of winter, if you want to make money you have to follow the seasons, which means travel expenses. The more props and equipment your show has (and some have a lot), the more you have to pay to ship them (and to keep maintained). Just like with any physical career, there's the ever-present possibility that an injury will put you out of work until you get better.The Bottom LineAt the end of the day, what does all this mean? Street performing is really hard work, but if you excel at it, you can make some pretty good money. A good street performer probably makes more money than people assume, but not more than makes sense if you actually think about it.PS: Here's an interesting graph showing the distribution of monetary denominations we received over two weeks at the fringe festival, compared to the total value of each denomination. Interesting how little of an effect all the denominations below £1 makes.

The invasion would have ended in a bloodbathAnd I have hard facts to corroborate my argument.This is one of the most complex questions I have ever answered because of the HUGE amount of data and facts that must be synthesized from various sources and presented in a logical manner to substantiate the opening statement. Truth be told, this answer does not contain all the relevant facts I have at my disposal. But because including all of them will result in a very long answer which may bore the readers and hence, I choose to include only the most representative facts to support the central argument. All the numbers and their associated significance/interpretation can be bewildering. But, I shall do my best to create a coherent and factually abundant answer to the readers.Acronyms and DefinitionsIt is necessary to define acronyms and terms that are too long to write conveniently:IJA: Imperial Japanese ArmyIJN: Imperial Japanese NavyUSN: US NavyRN: Royal NavyUSSBS: United States Strategic Bombing SurveyUSAAF: US Army Air ForceUSA: US ArmyUSM: US MarineMIS: Military Intelligence ServiceJIC: Joint Intelligence CommitteeUltra: decrypts of radio traffic of the Japanese militaryMagic: decrypts of encrypted Japanese diplomatic messagesJCS: Joint Chiefs of StaffsCINCPAC: Commander-in-Chief Pacific FleetAlso, an explanation concerning the IJA’s hierarchical organization of formations is necessary. In European armies and the USA, the hierarchical organization of formations arranged in ascending order by size was:regiment < division < corp < army < army groupBy contrast, the IJA’s hierarchical organization of formations arranged in ascending order by size was:regiment < division < army < area army < general armyThe IJA did not have corp. Hence, an IJA’s army was about the size of an corp in the USA and smaller than a USA’s army.ContextAfter Germany’s unconditional surrender in Europe in May 1945, the US military began transferring manpower and materials from Europe and the US homeland to the Pacific theater. The aim of this redeployment: defeating the remaining Axis Power - the Japanese Empire.Image source - Hell to Pay - D. M. GiangrecoOverview of Invasion planOn 25th May 1945, the JCS adumbrated a plan for the invasion of Japan. The details was to be fleshed out by subordinate commanders, starting with the top 2 commanders in the Pacific theaters: CINCPAC Chester W. Nimitz and Army commander General Douglas MacArthur.On May 28th, MacArthur issued his strategic plan for the invasion codenamed Downfall. His vision was to accomplish assigned aims by 2 successive operations. The two operations and their respective aim were:1/ Operation OlympicAimed at invading and securing southern part of Kyushu. The attack would be initiated on X-day which was decided tentatively to be 1st November 1945.2/ Operation CoronetAimed at invading and destroying the remaining Japanese forces in the Kanto Plain and Tokyo-Yokohama area on Honshu on Y-day tentatively decided to be 1st March 1946.As a side note, both MacArthur and the JCS by no means supposed that Operation Downfall would guarantee the end of hostilities in Asia. The US high command anticipated the contingency that fighting would last as long as needed to extinguish Japanese resistance in the central and northern of the Japanese home islands AND on the Asian mainland if required.Operation Downfall (Image source: Hell to Pay - D. M. Giangreco)US Order of BattleOne essential aspect of the invasion plan was the task of determining the amount of manpower, supplies and equipment needed to accomplish all objectives. This in turns depends on estimates of Japanese forces that would oppose the invasion.With regards to Olympic, US intelligence’s estimates of Japanese military strength on Kyushu varied by sources and with time. American intelligence’s originally estimated that the IJA had only 6 divisions, of which 3 were stationed in southern Kyushu and the other 3 were stationed in northern Kyushu.In May 1945, using information gathered by radio intelligence, MacArthur’s staff estimated that Olympic would be opposed by 8–10 IJA’s divisions. Then on June 18th, it was estimated a maximum of 350,000 Japanese troops would oppose the invasion.So all in all, the assumptions underlying the US invasion plan were:The maximum number of divisions the Japanese could deploy to reinforce Kyushu was 10. This was based on the assurance that absolute US air and naval superiority would prevent the Japanese from transporting large amount of equipment and manpower from Shikoku and Honshu to Kyushu across the sea lanes between these islands.Maximum Japanese troop strength was 350,000.Japanese air strength stood between 2,500–3,000 aircraft.The enemy would fight with the utmost fanaticism and that Allied forces would confront a “fanatically hostile population”.Using these estimates and the cardinal rule of warfare which emphasizes numerical superiority to guarantee victory, American military planners orders of battle for Olympic and Coronet were as follow:Operation OlympicThe invasion of southern Kyushu was entrusted to the USA’s 6th Army under the command of Prussian-born Lieutenant General Walter Krueger. The 6th Army was composed of 4 Corps, 12 divisions plus additional reserve units. The amounts of manpower, equipment and supplies allocated for Olympic were impressive:766,700 men134,000 vehicles1,470,930 tons of materialsThe invasion would begin with a typical heavy naval and aerial bombardment followed by amphibious landing supported by tactical air support. To sea-lift the 12 divisions, CINCPAC committed 1,315 amphibious vessels. The USN’s 3rd and 5th Fleets would operate jointly to support the invasion. The 3rd Fleet would render strategic support while the 5th Fleet would render tactical support. An impressive task force composed of 16 fleet + 6 light carriers of the USN and 6 fleet + 4 light carriers of the RN would provide the primary offensive power for the invasion force. The total number of carrier-borne aircraft was 1,914.Once US forces established stronghold on the island, they would construct forward bases and airfields in preparation for the 2nd operation. It was projected that 40 air groups and about 2,794 aircraft would operate from these bases to provide air cover for Operation Coronet.Plan for Operation Olympic and Estimated Japanese Strength and Dispositions as of May 1945. (Image source: Downfall - Richard B. Frank)Operation CoronetThis operation would be carried out by 23 US divisions plus 4 divisions held in reserve. The amounts of manpower, equipment and supplies were staggering:1,026,000 servicemen190,000 vehicles2,640,000 tons of materialUS military strength allocated for Olympic and CoronetIt was hoped that the Japanese would be subdued quickly (within 90 days) by bringing overwhelming forces and firepower to bear.The invasion of Japan would pose an enormous logistical challenge to the US military and the numbers bespoke this. In a series of meetings, logistical planners estimated that the amount of supplies deemed adequate to pursue the war in the Pacific for one year was 53,880,000 tons. This in turn posed the difficult problem of how to transport, store and deliver that massive amount through the vast expanse of the Pacific. Sea ports with large storage and handling capacity would have to be built which in turn required huge amount of construction labor and time which would severely hamper the invasion.Ultimately, planners decided against using intermediate bases. Instead, once stronghold on Kyushu was established, most supplies would be transported directly from the US mainland to Japan. Under this design, cargo vessels, 482 for Olympic and 700 for Coronet, would travel to US forward base at Ulithi atoll. From there, they would be directed to loading sites in Japan.However, the most dreadful problem for the planners of the invasion concerned casualties.How many casualties would we incur?This was a question that bedeviled those involved in the planning of Downfall. It mattered greatly because the American public was particularly averse to heavy casualties. The US had been involved in the war for 4 years. Many families had lost their sons, husbands, brothers. Despite some censorship, the military could not completely suppress casualty-related information released by the press. After victory in Europe, there was growing public demand for demobilization, partly motivated by war-weariness, partly by the desire to reunite with family members, and partly by the concern that the end of war would bring about lay-offs in American industry and those who returned home early had better chance of securing employment.Unfortunately, there was no simple answer to this question. Indeed, project casualties has always been immensely difficult because war is reigned by chaos, and uncertainty. Numerous unforeseen factors can conspire to produce surprising number of casualties. All unforeseen factors cast aside, casualties are affected by battlefield terrains as well as the strength, equipment, skill and resolve of the enemy.The statement that the invasion would inflict anywhere between 500,000 and 1,000,000 is so trite as to masks the many complex issues related to casualties projection. I think fresh information is needed.Planners of Downfall used various methods and context information to estimate potential casualties.One simplistic and dubious method applied casualty ratio derived from past campaigns to the number of men committed to Downfall.For example, a paper produced by the Surgeon General of the Army contained a table that showed casualty rates per thousands of men committed per day in the Pacific and European theater:(Image source: Downfall - Richard B. Frank)So for a Pacific campaign with the following parametersNumber of men committed: NNumber of days a campaign lasted: MThen estimated casualties for this campaign would be:WIA = [math]\frac{N}{1,000}\times M \times 5.50 [/math]KIA = [math]\frac{N}{1,000}\times M \times 1.78[/math]MIA = [math]\frac{N}{1,000}\times M \times 0.17[/math]Total casualties = [math]\frac{N}{1,000}\times M \times 7.45[/math]Applying the above formula for Olympic where N = 766,700 and M = 90, casualties would be:WIA=[math]\frac{766,700}{1,000}\times 90 \times 5.50 = 379516.5[/math]KIA=[math]\frac{766,700}{1,000}\times 90 \times 1.78 = 122825.34[/math]MIA=[math]\frac{766,700}{1,000}\times 90 \times 0.17 = 11730.51[/math]Total casualties = [math]\frac{N}{1,000}\times M \times 7.45 = 514072.35[/math]These numbers are consistent with the table below (the tables above show only casualties for ground troops, not sailors and airmen.)Image sources: Downfall - Richard B. FrankOn 13th May 1945, Admiral Nimitz presented a draft produced by his Joint Staff Study for Olympic which contains the following estimates for casualties during the first 30 days of Olympic:(Image source: Downfall - Richard B. Frank)A paper dated 15th June 1945 created by the JCS planner projected that the total casualties for both Olympic and Coronet would be 193,000.On 18th June 1945, a meeting was held in the White House whereby President Truman would inquire his military chiefs about casualty estimates. The record of the meeting reveals at least 5 markedly different estimates given to the President.Estimate 1 was derived from a set of casualty ratios derived from previous campaigns.Estimate 2 used a simple equation which multiplied a fixed casualty percent in any one particular campaign to the number of committed American troops to produce the estimate. Admiral Leahy used the casualty rate of 35% suffered in the battle of Okinawa to yield an estimate of 0.35 * 766,700 = 268,345 for Olympic.Estimate 3 given by George Marshall was very questionable in that Marshall claimed it would equal the 31,000 casualties incurred on Luzon.Estimate 4 given by Admiral Ernest King was equally dubious: casualties would be in the range [31,000 - 41,000] incurred in the battles of Luzon and Okinawa respectively.Estimate 5 given by Marshall was just as dubious: casualties would be 63,000 out of 190,000 “combatant troops.” Exactly what he meant by “combatant troops” was unclear.It must be noted that the aforementioned estimates were for Olympic only. President Truman postponed his inquiry for potential casualties incurred in Coronet.All in all, hopefully the readers can appreciate just how difficult it was to make a realistic and reasonably accurate estimate of the potential casualties the US forces would have suffered in Operation Olympic. Consequently, President Truman never got either an unambiguous or unanimous answer to his concern about casualties.HOWEVERAll disputes set aside, I encourage you to read carefully the rest of this answer filled with hard data and facts. Once you finish, you will be able to draw your own conclusion regarding potential casualties the US military would have incurred from the invasion of Japan.Japanese intention and order of battleIn 1945, the Empire of Japan was a defeated nation, as I have explained in this answer. The Pacific War was a naval war and hence which side controlled the sea won the war. In 1944, the USN had crippled the IJN in the battle of the Philippines Sea. Thereafter, despite there were still island battles to be fought, American victory in those battles was a foregone conclusion because the IJN could neither deliver supplies nor relieve the beleaguered Japanese garrisons.BUTThe logic that no victory meant defeat and that the war was lost did not apply to Japanese military leaders. Instead, as I understand it, they believed that no victory did not necessarily meant defeat and the war was lost. They were convinced that although they could no longer win, they could still avoid a defeat by exploiting one weakness of the US: American aversion to heavy casualties.Although Japanese military leaders demonstrated appalling strategic incompetence, a lack of understanding about the nature of modern total war and unwarranted contempt for their enemies, they understood very well that Americans were weary of the war and that they wanted to end the war quickly by an invasion of the Japanese home islands. It followed that if they could inflict extremely heavy losses on the Americans, they would be able to effect a negotiated peace with favorable terms for Japan, thereby avoiding total defeat.This understanding is best encapsulated in a statement in the Basic General Outline on Future War Direction Policy adopted at the June 6, 1945, Imperial Conference:The United States ... is confronted with numerous problems; such as, mounting casualties, the death of Roosevelt, and a growing war weariness among the people. .. . Should Japan resolutely continue the war and force heavy enemy attrition until the latter part of this year, it may be possible to diminish considerably the enemy’s will to continue the war.and in a statement made by General Korechika Anami 1945Diplomacy will have a better chance after the US has sustained heavy losses. We cannot pretend to claim that victory is certain, but it is far too early to say that the war is lost. That we will inflict severe losses on the enemy when he invades Japan is certain, and it is by no means impossible that we may be able to reserve the situation in our favor, pulling victory out of defeat.It was with this understanding that the Japanese government formulated and adopted a new strategic directive published on 20th January 1945 which declared the Home Islands a scene for a “final decisive battle” of the war. The Japanese armed forces were to construct defenses in the national defense sphere which encompassed the Bonin Islands, Formosa, the coastal region of East China and Korea. All Japanese servicemen were exhorted to:Fiercely resist the enemy.Reduce the enemy’s overwhelming advantage in the air, at sea, and on the ground with the support of suicide air units.Prevent the enemy from gaining a foothold.Shatter their morale.Repel the invasion of the home islands.To achieve these aims, the Japanese military extensively modified command structure to better organize and deploy existing assets, mobilize manpower and resources to raise and equip new combat formations.On 6th February 1945, an agreement between the IJA and IJN dictated that all air units in the home islands would be concentrated and deployed for suicide attacks. All IJA’s air units were subsumed into the so-called Air General Army. All IJN’s air units were organized into the 5th Air Fleet entrusted with defending the Kyushu-Ryukyu sphere and the 3rd Air Fleet entrusted with defending the rest of the Home Islands.Then on 8th April, the IJA’s staff officersFor the defense of Japan proper, the IJA created two theater of operations with respective commands:The 1st General Army headquartered in Tokyo; entrusted with defense of Central and Norther HonshuThe 2nd General Army headquartered in Hiroshima; entrusted with defense of Western Honshu, Shikoku and Kyushu.The 5th Area Army entrusted with the defense of Hokkaido.Then on 8th April 1945, the IJA’s staff officers in Tokyo completed a complex master plan for the forthcoming decisive battle entitled Ketsu-Go (Decisive Operation). In essence, Ketsu-Go envisioned that US forces would potentially invade 7 key areas. To crush the invaders, both the IJA and IJN would make every possible preparation to construct and strengthen defenses in those areas.The most salient aspect of Ketsu-Go was that the Japanese accurately predicted the areas most likely to be attacked by US forces: Kyushu and the Kanto-Tokyo areas. Accordingly, these two areas would receive a tremendous amount of manpower and resources required to inflict heavy losses on the American invaders.Preparation for Ketsu-Go were divided into 3 phases lasting from April to October. But preparation for Kyushu had to be completed by early June.There were 3 distinctive characteristics of Ketsu-Go1/ The emphasis on destroying enemy beachhead ASAPAfter mid 1944, the IJA recognized that water-edge defense (i.e fighting near or right on the beaches in the invasion areas) was futile due to overwhelming American naval and air power which could hurl fortifications skyward with massive 16-in naval shells. Hence, the IJA adopted inland defense designed to bring about attritional battles to wear down the American attackers and inflict small-scale casualties that would accumulate over the course of the battles. This strategy worked well on Iwo Jima and Okinawa, on which battles lasted much longer than anticipated and US casualties were high.But, inland defense had its downsides: it allowed the invaders to secure a foothold that could not be dislodged. This was acceptable on Iwo Jima and Okinawa because defeat on those islands were inevitable. Plus, the aim of those two battles were to prolong combat as long as possible to buy more time to strengthen the defenses in the Home Islands.However, the Home Island was different. This was the sacred soil of the Empire. This meant that the American invaders must never be allowed to secure a foothold as they did on Iwo Jima and Okinawa.Because it took a few days to gain such a foothold, it followed that the Japanese defenders had to destroy the American attackers within that window of opportunity. This in turn required rapid movements of IJA’s units to the invasion sites to counterattack the Americans. Due to the lack of mechanized means of transports and the mountainous terrains of Japan, the Japanese were constrained to move on foot to the invasion sites. It followed that IJA units had to be stationed reasonably close to the beachheads, not too close to avoid destruction by American naval and air units, but not too far as to give the invaders more time to secure a foothold.To prevent the enemy from advancing unchallenged inland, it was vital that the IJA opposed the enemy close to the beachheads to delay them and buy time for reinforcements to arrive.The solution to this dilemma? - forming Coastal and counterattack divisions.The 3 phases of Japanese mobilization plans (Image source: Downfall - Richard B. Frank)As you can see from the table above, the mobilization created two new formations:Static coastal-combat divisions: designed for close-quarter combat with the invaders a short distance inland from the water’s edge.Counterattack divisions: understrength field divisions designed to move swiftly from inland positions to reinforce IJA’s defense.2/ heavy use of suicide attack tactic2/ extensive mobilization of the civilian population to support combat operationsLet’s elaborate on the above characteristics.A disturbing revelation of IJA’s troop strengthIn the last 8 weeks of the war, from June to August, Olympic planners were in for a rude awakening because Ultra uncovered extremely disturbing information that invalidated all the initial assumptions and nullified the US battle plan. During this time span, radio intelligence gathered information that pointed to a massive increase in IJA’s troop strengths and disposition.To illustrate how massive such an increase was, I will let the numbers speak for themselves.MacArthur’s intelligence chief, general Charles A. Willoughby estimated that in March 1945, IJA’s troop strength in the Home Islands was 937,000 men of which 466,000 were combat troops organized into 11 combat and 14 training divisions.But as Japanese mobilization quickened, more units were formed and were detected by radio intelligence. In Mid July 1945, Willoughby estimated that IJA’s troop strength in the Home Islands was 1,865,000 - nearly double the estimate in March. By the end of July, MIS detected 27 new IJA divisions in the Home Island since the start of 1945. By Mid-August 1945, the MIS projected that the IJA could form between between 15–29 new divisions. By 1st January 1946, the total number of IJA divisions would be 54–70 divisions, according to the MIS’s assessment. This was a considerable increase from a total of 45–48 divisions Willoughby estimated in March 1945.Equally disturbing was the revelation concerning the deployment of these new formations. In particular, Olympic planners were alarmed by the fact that the Japanese accurately predicted where US forces would attack: in southern Kyushu and Kanto-Tokyo.It bears repeating that American intelligence originally estimated Japanese troop strength in Kyushu to be 350,000 men maximum and Japanese air strength between 2,500–3,000 aircraft. Therefore, by committing 766,700 American troops to Olympic, their leaders hope to overwhelm the Japanese defender and achieve victory quickly.But the influx of information gathered by radio intelligence shattered that confidence.By mid-July 1945, the MIS identified the presence of major units in Kyushu only suspected previously. Willoughby noted:a tremendous influx and organization of mobile units pouring into Kyushu, with positive identification of six divisions, as well as code names for at least two unidentified major units plus an artillery command.During the 2nd half of July, Willoughby identified 3 more divisions, 2 brigades, and 2–3 tank brigades on Kyushu. By July 21, the MIS provided a map in the Far East Summary which pinpointed 8 Japanese field divisions on Kyushu, 7 of which were stationed within the areas targeted by Olympic.By 2nd August 1945, the MIS identified 3 Japanese armies, 11 divisions, 1 brigade and 1 regiment on Kyushu. Estimated total troop strength was 545,000 - of which 445,000 were combat troops.By 7th August 1945, the MIS positively detected 2 more divisions on Kyushu, for a total of 13 divisions - 9 of which were stationed close to the targeted areas in southern Kyushu. Total troop strength were 560,000 men - of which 460,000 were combat troops.On 10th August 1945, the JIC estimated that by 15th October 1945, 56 field divisions and 14 training divisions would be present in the Home Islands. IJA’s troop strength would be 2.6 million men. On Kyushu, there would be 600,000 men in 13 field divisions. On 20th August 1945, the JIC issued the final revision of the initial estimates: the overall IJA’s troop strength on Kyushu would be 900,000 men and 14 field divisions. At least 9 of these divisions were stationed in southern Kyushu.Taking into account all of these numbers, the actual battle plan is visually depicted in the map below:Olympic invasion plan and IJA’s disposition and strength. (Image source: Downfall - Richard B. Frank)Moreover, the terrain of Japan in general and Kyushu in particular favored the defenders and negated a great deal of American advantage in mechanization.Coastal terrain common in Southern Kyushu. (Image source: Hell to Pay - D. M. Giangreco)Terraced rice fields on Kyushu were common and could not be bypassed easily. They were also highly defensible. (Image source: Hell to Pay - D. M. Giangreco)Rice paddies in the photo presented formidable barriers to mechanized units which would deny the attackers room for maneuvering and created ideal killing zones for the Japanese defenders. (Image source: Hell to Pay - D. M. Giangreco)A typical mountain village in central Honshu. With dwellings packed from hillside to hillside and extensive rice paddies extending from both ends, these areas were would have to be taken by assault by ground troops lacking sufficient armor support. (Image source: Hell to Pay - D. M. Giangreco)This disturbing revelation pointed to the dreadful prospect that instead of facing just 350,000 IJA’s troops, the 766,700 American servicemen committed to the invasion would face between 560,000 - 900,000 IJA troops. The attacker-defender ratio of 2:1 advantage was lost. The Americans would face much stiffer resistance. The IJA had stockpiled a huge amount of ammunition for Ketsu-go, including over 1,000,000 ballistic grenades for the humble Type 89 grenade discharger which had caused great casualties to US forces in Okinawa and Iwo Jima. Assuming that at each grenade would kill/maim 1 American, the expenditure of all 1,000,000 grenades would cause 1,000,000 American casualties.And the bloodshed on the ground would be rivaled by the slaughter at sea inflicted by incessant Japanese kamikaze attacks.Japanese Kamikaze attacksAmerican intelligence underestimate of IJA’s troop strength was matched by its own underestimate of Japanese air strength. If Olympic planners were stunned by the revelation of massive increase in IJA’s troop strength, they were equally stunned by the revelation of actual Japanese airpower.For Olympic, the original estimate of Japanese airpower was 2,500–3,000 aircraft. However, that number was refuted by the discovery of a much larger number of Japanese aircraft.The MIS discovered that the Japanese were employing the so-called “extreme conservation” strategy by:not deploying aircraft to challenge US bombersdispersing and concealing aircraft in hidden airfieldsconserving aviation fuelAs a result, the Japanese were able to amass a HUGE number of aircraft for suicide missions.Another reason for the increase in number of aircraft was the fact that the MIS found information hinting at the Japanese decision to commit trainer aircraft for suicide attack missions. The incorporation of trainer aircraft to the inventory of combat aircraft hugely increased the number of aircraft available for Ketsu-Go.Aerial reconnaissance discovered a huge number of aircraft shown in the table below.(Image source: Downfall - Richard B. Frank)Apart from the estimates of Ultra and the MIS, the CINCPAC, the USAAF and the USSBS contributed their own estimates of Japanese air strength.On 16th July 1945, the CINCPAC estimated that the Japanese had 11,190 aircraft of which 8,750 were available for the defense of the Home Island. On 13th August, the figures were revised to be 11,930 aircraft of which 10,290 would be available for the Home Island. Of these 4,880 were combat types and 5,410 were trainers.The USAAF estimated Japanese air strength to be 10,210 aircraft.A post-war examination of Japanese air strength revealed that the Japanese had a large number of aircraft reserved for kamikaze attacks. As shown in the table below:Postwar accounting of Japanese airpower by the USSBS (Image source: Downfall - Richard B. Frank)The Japanese had enough pilots trained for suicide missions. The USSBS estimated there were 18,600 pilots, 8,000 in the IJA and the rest in the IJN. Of the IJN aviators, 2,450 pilots were capable of day and night missions, 1,750 IJN were capable of dawn and dusk missions, and 5,950 required additional training. The IJN estimated that a pilot needed just 30-50 hours of flying time to man a trainer aircraft converted to kamikaze attack.The USSBS also established that the Japanese had sufficient aviation fuel to carry out these kamikaze attacks. At the end of the war, about 1,000,000 barrels of aviation fuels were uncovered. This would last for 7 months at the consumption rates of June and July 1945, and Japan still managed to produce about 25% of this low level of consumption.Now, unlike the kamikaze attacks around Okinawa which suffered heavy losses while inflicted a dismal fatality rate of only 1,78 per sortie, the kamikaze attacks around Kyushu enjoyed the following distinct advantages:Shorter travel distance: At Okinawa, fuel limitation constrained Japanese kamikaze units to fly in a relatively straight path that made their approach predictable to American interceptors. But around Kyushu, these units would fly much shorter distance, allowing them to fly in a circuitous route that made their approach less predictable and more difficult to intercept.Mountainous terrain: this masked low-flying kamikazes from search radars, giving US ship less time to spot and react to kamikaze aircraft.Secure communication: the battles would be conduct on Japanese soil which obviated the need for radio communication vulnerable to intercepts. Instead the Japanese would be able to use telephones to coordinate counterattacks and defense secure from the prying eyes of American radio intelligence.Element of surprise: during the kamikaze attacks around Okinawa, Japanese suicide aircraft had to fly relatively high to spot American ships before attacking. This made them vulnerable to detection by American radars which deprived them of the advantage of surprise. Both of these disadvantages would disappear around Kyushu. Mountains would shield kamikaze aircraft from radar; and Because American ships would operate close to the coast, there was no need for kamikaze units to fly far and high to find their targets. They could fly low to achieve the element of surprise. Hundreds of kamikaze aircraft attacking in mass could overwhelm American AA defense.Vulnerability of American troopships: A combination of cover afforded by the ground and mountainous terrain, surprise and short travel distance made it much easier for kamikaze units to attack the slow troop ships moving toward the landing zones.The advantages of trainer aircraft: while trainer aircraft were slow and could not lift a heavy bomb load, they had two distinct advantages over combat aircraft. They were made of wood and fabric which rendered them undetectable by radar AND invulnerable to proximity-fused shells fired by American shipboard AA guns.(Image source: Hell to Pay - D. M. Giangreco)(Image source: Hell to Pay - D. M. Giangreco)One of the most underrated weapons of WW2: the Yokosuka K4Y1 Training Seaplane. Made of wood and fabric materials, this aircraft could evade radar detection and proximity-fuzed shells.As shown in the estimates above, the Japanese had thousands of these trainer aircraft. They could inflict widespread destruction if used against supply vessels and troops landing craft.Imagine the carnage inflicted upon the American invaders by a large number of suicide aircraft and pilots operating with the aforementioned advantages.Fierce resistance from Japanese civiliansIn March 1945, the government implemented measures designed to prepare the civilian for Ketsu-Go. One measure involved establishing the Area Special Policing Units in every town and village. They would be subordinated to military commanders of an area. These units effectively integrated the civilian population into the military. governmental and civilian spheres. They would be employed to support combat units and perform other duties at the discretion of military unitsOn 27th March 1945, the government instituted a law which mobilized all citizens in the coastal areas to construct defenses, transport supplies and perform other duties as needed. Even young students above the 6th grade were mobilized (only 1st to 6th graders were exempted).On 23rd March 1945, the government established the Patriotic Citizens Fighting Corps which provided a mechanism for drafting able-bodied citizens for military service. All men between the ages of 15 to 60 and all women between the ages 17 to 40 were subject to conscription.All able-bodied civilians, regardless of age and gender, received basic training in how to kill the American invaders using whatever weapons available, including bamboo spears.A high school girl named Yukiko Kasai was drafted and given the following order:Even killing just one American soldier will do. You must prepare to use the awls for self-defense. You must aim at the enemy’s abdomen.Students trained to fight with bamboo spearsIJA officer trained civilians how to fight with bamboo spearsAs preposterous and unbelievable as all of these may seem to you, the IJA was serious about using bamboo spears to fight gun-wielding American soldiers as attested to by the recollection of a Japanese man who was drafted into the People’s Volunteer Corps when he was a young boy:His “equipment” consisted of a bamboo spear and a backpack filled with two large stones. He practiced huddling in a dank, stinking foxhole, waiting for the Americans. If the enemy approached, he would exchange his stones for a land mine. His mission was to destroy an enemy tank, and himself, with it. Reflecting back, the training, indeed the whole notion, was similar to something out of a demented cartoon. But, he emphasized, the military was serious. And if the Americans landed, he is certain he would have perished.This fusion of the civilian population and the military implied that any distinction of civilians from military personnel practically disappeared. It would be impossible for soldiers to determine who was an innocuous civilian warranting protection and who was a combatant in civilian clothes. One intelligence officer noted in a report:The entire population of Japan is a proper military target … there are no civilians in JapanJapanese fanaticism and confidence in Ketsu-GoMy research led me to the following conclusion which I want you to read very very carefully:The Japanese military was determined to fight to the death, even if that entailed utter national annihilation and sacrifice millions of Japanese lives.And the Japanese had unfailingly demonstrated that determination throughout the war. It was reflected both through incredibly high fatality rates of the IJA in all major battles and the words of Japanese military leaders.On Guadalcanal, US forces witnessed for the first time how the Japanese of all ranks literally chose death over surrender. US Marines trapped and annihilated an IJA’s detachment consisting of 800 men. Only 15 survived as POWs. A fatality rate of 98.1%.In May 1943, US forces fought the IJA in the battle of Attu. At the end of the battle, the 2,350-men Japanese garrison had only 29 men left, a fatality rate of 98.8%.In the battle on Gilbert Islands in November 1943, the Japanese garrison on Tarawa had 2,571 men at the outset of the battle. When the battle ended, only 8 men were captured alive: a fatality rate of 99.7%. On the nearby Makin island, of the 300-men garrison, exactly 1 was taken alive, a fatality rate of 99.67%.In the battle on the Marshalls Islands in February 1944, on Roi Namur, the Japanese garrison suffered 3,472 KIA. Only 51 were captured, a fatality rate of 98.6%. On Kwajalein island, the Japanese garrison suffered 4,938 KIA. Only 79 taken prisoner, a fatality rate of 98.4%.At the end of the battle of the Marianas Island during June and July 1944, the Japanese garrison of 30,000 on Saipan suffered 29,079 KIA. Only 921 became POWs: a fatality rate of 96.93%; and what shocked US marines even more was the spectacle of Japanese civilians taking their own lives by jumping off high cliffs or blowing themselves up with grenades after being told by the IJA the terrible fate that awaited them if they fell into American hands.Given that Japan’s warriors had consistently fought to the point of self-annihilation in the past and the fact that Ketsu-Go would take place on the sacred Home Island, Japanese fighting men would have fought with extreme zeal to repel the invaders.What’s more? Japanese military leaders were confident in final victory and were prepared to sacrifice millions of Japanese lives to achieve it:Admiral Takijirō Ōnishi:I can guarantee absolutely that Japan will not lose.. The war is just beginning. The expected Allied invasion would be repelled with acceptable Japanese casualties of 3 to 5 millions, With sufficient Japaneseness of spirit, the struggle might be maintained for years or even decades.If we are prepared to sacrifice 20 million Japanese lives in special attacks, victory will be ours.Army Minister General Korechika Anami:There were considerable chances of victory in the decisive battle in the homeland. Army officers universally believed in Japan’s victory in the “first decisive battle. He even believed that if Ketsu-Go managed to inflict extremely heavy casualties, Japan might be able to continue the war or avoid unconditional surrender.Lieutenant General Seizo Arisue, explained to his American interrogators after the war:If we could defeat the enemy in Kyushu or inflict tremendous losses, forcing him to realize the strong fighting spirit of the Japanese Army and People, it would be possible, we hoped, to bring about the termination of hostilities on comparatively favorable terms.Major General Masakazu Amano, Chief of Operation Division, assessed the outcome for Ketsu-Go as follows:We were absolutely sure of victory. It was the first and the only battle in which the main strength of the air, land and sea forces were to be joined. The geographical advantages of the homeland were to be utilized to the highest degree, the enemy was to be crushed, and we were confident that the battle would prove to be the turning point in political maneuvering.Captain Inoguchi Rikibei, Imperial Japanese Navy:Inasmuch as the Kamikaze attacks were the last means of any favorable results in the war and the only chance for breaking down American resistance a little, we did not care how many planes were lost. Poor planes and poor pilots were used, and there was no ceiling on the number of either available for use. . . . If enough damage could be done to American ships and enough American casualties resulted, perhaps there would be a ‘new deal’ later in which some form of victory might be salvaged from the war.Final ConclusionThe IJA still had millions of troops who would fight with the utmost zeal and bravery as their comrades had done during the war. They would be assisted by millions of loyal civilians enjoined to hurl themselves against American tanks and soldiers. Thousands of kamikaze aircraft would crash into troop ships loaded with men and ammunition. These millions of soldiers and civilians would be commanded by military leaders who were prepared to sacrifice millions of their own people to kill as many Americans as possible to force the US to the negotiation table.It is not difficult to imagine the gut-wrenching bloodbath brought about by the invasion of Japan. American casualties that resulted from the expenditure of huge stockpiles of Japanese ammunition, suicide air attacks and civilian suicide attackers would have been immensely heavy. Japanese casualties would have been far heavier.William B. Shockley, “Proposal for Increasing the Scope of Casualties Studies,” July 21, 1945If the study shows that the behavior of nations in all historical cases comparable to Japan’s has in fact been invariably consistent with the behavior of the troops in battle, then it means that the Japanese dead and ineffectives at the time of the defeat will exceed the corresponding number for the Germans. In other words, we shall probably have to kill at least 5 to 10 million Japanese. This might cost us between 1.7 and 4 million casualties including 400,000 and 800,000 killed.Maj. Gen. Graves B. Erskine, commanding general, 3rd Marine Division:Victory was never in doubt. Its cost was. ... What was in doubt, in all our minds, was whether there would be any of us left to dedicate our cemetery at the end, or whether the last Marine would die knocking out the last Japanese gun and gunner.It is a spine-chilling scenario to contemplate. I am certain that American leaders were tormented and horrified by the specter of this unprecedented butchery. In the face of an enemy that resolved to fight to the death, they were compelled to resort to the most drastic course of action: the atomic bombs the shock-and-awe effect of which forced the Emperor to surrender, thereby sparing millions of lives from the bloodshed that would have taken place on Japan.Reference(s)1/ Hell to Pay: Operation DOWNFALL and the Invasion of Japan - D. M. Giangreco2/ Downfall: The End of the Imperial Japanese Empire - Richard B. Frank3/ Werner Hermann's answer to What really caused Japan to surrender in WW2, the atomic bomb drop of Nagasaki or the Soviet invasion of Manchuria?

At least you are already above 60% of my high school, who don’t care if they pass the exam or not :)As someone who got a 5 on the AP Physics 1 exam two years ago (and did so rather easily, with more than half the time to check answers), I’m going to say it depends on how well you’ve mastered mathematical modeling. If you’re good at drawing force diagrams and then converting them into equations, you’re capable of getting a 3, at least. If you can intuitively understand what happens, then you’re going to breeze through to a 5.You see, the Physics 1 exam doesn’t test you on memorizing formulae or specific problem types. It evaluates you on your reasoning skills.You will get a formula sheet for the exam, so the key is understanding what each one does, not memorizing the symbols in each.Take a perennial favorite: What would happen to the gravitational acceleration at Earth’s surface if Earth’s radius doubled and its density halved? You could go find the trusty formula [math]F = \frac{Gm_{1}m_{2}}{R^{2}}[/math] and plug in [math]m_{1} = \frac{4}{3}\rho\pi R^{3}[/math], but this takes time, which can be limiting. Or, you could reason that mass is proportional to [math]R^{3}[/math] and density. So the mass quadruples. But, the gravitational force is inversely proportional to [math]R^{2}[/math], so the force remains the same, and therefore the acceleration is the same.So, here are my suggestions:Practice problems, and a lot. Don’t look back in the book for examples on how to do a specific problem. Only use the formula sheet, and the book if you don’t know what a particular formula does, or if you are missing some concept, like angular momentum.Learn your definitions. A lot of problems are easy points. One problem asked for the displacement of a projectile that landed 10 meters away. Correct answer: 10 meters. My answer: 14 meters, derived with an arc-length integral that took a good 10 minutes. What a waste.FORCE DIAGRAMS - Learn to read/create these; these are absolutely critical on the FRQs, you get so many free points for drawing these it isn’t funny.Modeling - Translating a force diagram/system into a set of equations is the HARD part. Practice this for the book problems, without looking back to see how the authors did it. Your calculator can do the solving.Dimensional analysis. If you have absolutely no clue how to do a problem, and have free time, just randomly multiply the measurements together until you get the correct units. Works like 50% of the time, especially in problems about proportions. Don’t do this while practicing, because it’s just tricking yourself, but definitely spend an hour or so on this before the exam. Learn the expressions of units like Newtons or Joules in base units. Your formula sheet often helps with this.Calculus - If you’re good at this, it helps a lot with re-deriving some equations quickly. But don’t actually study this.Energy/momentum - These have to be conserved. Put these equations all over your FRQs, with plugged-in numbers. If your answer doesn’t conserve these, then your answer is wrong (but make sure you’re testing for conservation in an isolated system). Know when to use; mechanical energy is not conserved in frictional processes. You can solve any conservation problem with kinematics, but these laws make it go a whole lot faster.Focus on the multiple choice. You can get a 3 just by doing the multiple choice and turning in a blank free-response. But with your cool force diagrams and equations, you’ll get at least half credit on the FRQ! Do a lot of these practice problems, and try to avoid using a lot of equations for these.Learn to use your calculator. Don’t be the one person who is always on the calculator, but can’t seem to get any closer to a solution. If you have a CAS, use its SOLVE feature. If its SOLVE feature doesn’t work for a problem, graph the equations and estimate their intersection.Finally, if you have to, cheat. Your calculator has a large amount of memory and can help you to remember certain things that aren’t easy to, like what do I do in rotational problems, or what the heck does a pendulum do. Don’t put the whole textbook on there; it’ll look suspicious. Just put a few worked examples.The multiple choice section is all about knowing your concepts. You won’t be expected to do any large computations here, so if you are, STOP. If you can’t figure out which concept is being applied, look at the equations. They can help you. But if you’re plugging in a bunch, you’re doing it wrong.Do sanity checks. If you said that the car would be moving at 220 m/s, think about what car can go at 500 MPH. If you find that the force on an object is 5000 N, it ought to be quite a large object. Falling objects should not go slower over time. An object always loses energy after a collision.Don’t be afraid to skip questions. The 5 threshold is actually pretty generous. Find the easy questions, do them, and then try the tricks above to solve the harder ones.But after your practice exams, make sure to do all the questions you skipped, correctly. Don’t look at the book unless you absolutely have to.The biggest thing to know about the FRQ is that you aren’t penalized for wrong information unless you provide contradictory information. So if you have no clue, write your knowns, unknowns, and some equations (with numbers plugged in), that might get you a majority of the credit.Finally, the day before, relax, get a good night’s sleep, and don’t do any studying longer than 30 minutes. It lets you approach the exam feeling confident and well-rested.P.S. If you’re going to be missing classes, make sure someone is covering for you on group projects… Nothing’s worse than going into the FRQ thinking “I’m definitely getting a C- on that project/lab, since they’re so clueless!” - Me on AP Econ/Physics lab.