Funny what a little Internet search can turn up (from 2 sources):
* The Lockheed P-38 was designed in response to a 1937 US Army Air Corps (USAAC) specification designated "Project X608" for a fast high-altitude twin-engine interceptor, capable of 580 KPH at an altitude of 6,100 meters (360 MPH at 20,000 feet). Five companies -- Consolidated, Curtiss, Douglas, Lockheed, and Vultee submitted proposals.
The Lockheed team was under the direction of Clarence "Kelly" Johnson, who would eventually design a string of famous aircraft up to the SR-71 Blackbird Mach 3 spy plane. Johnson's initial concepts for the new fighter covered a range of configurations, but the Lockheed team finally decided on a scheme with twin booms to accommodate the engines, and with the pilot and armament in a central nacelle. The aircraft was designated the "Lockheed Model 22". The engines were to be supercharged 12-cylinder, vee-inline, water-cooled Allison V-1710 engines.
When Johnson selected the Allison, it had not been rated at even 746 kW (1,000 HP), but it was really the only large inline engine available in the US at the time. The propellers would rotate in opposite directions to eliminate the effect of torque. The General Electric B-1 superchargers were positioned in the booms, behind the engines. Armament was to consist of four machine guns in the nose of the nacelle, clustered around a cannon. The design featured tricycle landing gear, making the aircraft one of the first with such a feature.
The Lockheed submission won the competition on 23 June 1938 and was awarded a contract to build a single "XP-38" prototype. The XP-38 was rolled out in December 1938 and first flew on 27 January 1939, with USAAC Lieutenant Benjamin Kelsey at the controls, who by no coincidence had helped drive Project X608 in the first place. Kelsey found he couldn't retract the flaps and thought of bailing out, but he managed to get back down on the ground safely. The problem was quickly fixed and later flights went much better, demonstrating the impressive performance of the type.
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The increasing tension in Europe, and the combined build up of the German and Japanese military forces, caused the United States to look at its own military condition. The fact was that the United States was lagging far behind other countries in military strategy and equipment. In order to address this problem, the military decided to initiate a design contest for a next generation interceptor. This aircraft would far exceed any other fighter currently in production in performance and armament.
The result of this desire for a new fighter was Specification X-608. In Specification X-608, the aircraft was required to maintain a top speed of 360 mph, whereas previously designed aircraft were only required to maintain a top speed of 300 mph. This aircraft would also be required to operate at altitudes of 20,000 and contain firepower three or four times higher than any other existing fighter aircraft. Essentially, this aircraft would be able to perform any mission any other fighter would be capable of, but not limited to any specific one.
At the time of this specification, the state of the aircraft in the United States military was lagging far behind any other country in Europe. The typical aircraft in service was limited to roughly 500 lbs. of armament. Usually this consisted of 2 machine guns and the ammunition. This new design would be the first of what would be considered modern aircraft. Vultee, Curtis, and Lockheed all submitted designs for this contest.
Hal Hibbard and Kelly Johnson headed the Lockheed team. Overall, there were only 50 engineers working on the new prototype. At this time, there were no indications of immediate war, and most of the designers and engineers were working on other designs, which were non-military related. The Lockheed team knew they would face stiff competition, but they believed their many innovations would set their design apart from the other entries. Hibbard and Johnson decided to build their prototype, the Model 22, around the new Allison V-1710 engine. This engine was capable of running at 1000 hp for over 150 hours. They immediately realized that a twin-engine fighter would be required to fulfill the X-608 requirements. Also new General Electric turbosupercharger development would enhance the high altitude performance of their new design. Johnson admired the Spitfire wing design, but realized that if he used a similar design, the Model 22 would not possess adequate long-range capabilities. In fact, early Spitfires contained 85 gallons of internal fuel, whereas the P-38 would eventually contain 400 once in operational status. The new Model 22 would be a heavy aircraft, and its wing characteristics were not considered acceptable for a fighter. The Lockheed design team felt that with the new engine development, turbosuperchargers, and their innovative design elements, it would indeed be an effective fighter. The design would also allow for a 23-mm Madsen cannon and four .50 caliber Colt MG-53 with 4,000 rounds of ammunition. Kelly Johnson was able to back up their designs with calculations, which would allow for accurate predictions about the aircraft performance. In June 1937, Lockheed was awarded the contract for the building of 1 prototype. If tests proved promising, Lockheed was informed they could expect an order for fifty others.