How did it happen that Hitler gave his blessing to a crash program to produce the V-2 in quantity? Hitler was not a fool. As a foot soldier in World War I he had survived some heavy artillery bombardments. Von Braun demonstrated his plans for the V-2 to Hitler in person in August 1941, and Hitler reacted with sensible objections. He asked whether von Braun had worried about the timing of the explosion, since a normal artillery shell arriving at supersonic speed would bury itself in the ground before exploding and do little damage. This was a serious problem, and von Braun had to admit that he had not thought about it. Hitler then remarked that the V-2 was only an artillery shell with longer range than usual, and the army would need hundreds of thousands rather than thousands of such shells in order to use them effectively. Von Braun agreed that this was true.It's still not exactly clear to me whether interservice rivalry is ever in any way efficient. Here's a 1957 Time story about the U.S. Army, Navy, and Air Force all jostling—much like in Dyson's story—to build their own missile programs. Much overlap ensues: "With the services competing hotly, the U.S. had upwards of 40 assorted missiles under development by 1950, when Defense Secretary George Catlett Marshall called in Chrysler Corp.'s gruff President K. T. Keller to bring order out of the chaos." Having all the services making basically the same damn thing jacked up costs enormously, outweighing whatever benefits competition might bring.
After the session with von Braun, Hitler ordered the army to plan production of hundreds of thousands of V-2s per year, but not to begin production until the bird had successfully flown. This decision seemed harmless at the time, but it played into the hands of the army rocketeers. The army leaders knew that the notion of producing hundreds of thousands of V-2s per year was absurd, but they accepted the order. It gave them authority to spend as much as they wanted on the program, without any fixed timetable. In August 1941 the war was going well for Germany. The army had won huge victories in the first two months of the Russian campaign, France was knocked out of the war, and America was not yet in. Hitler did not imagine that within three years he would be fighting a defensive war for the survival of the Reich. He did not ask whether the V-2 might be a toy that the Reich could not afford.
In Germany as in other countries, the main factor driving acquisition of weapons was interservice rivalry. The army wanted the V-2 because of rivalry with the Luftwaffe. The German air force was leading the world in high-technology weapons, developing jet aircraft and rocket aircraft and a variety of guided rocket missiles. The army had to have a high-technology project too. The V-2 was a high-technology version of artillery. It gave the army the chance to say to the air force, our rockets are bigger than your rockets.
Although Hitler was nominally a dictator, he was no more successful than political leaders of democratic countries in keeping rivalries between different branches of the military under control. He could fire military leaders, and did so from time to time, but he could not make them do what he wanted. The army leaders, with the help of von Braun, launched a crash program to produce the V-2. They produced a few thousand V-2s altogether, enough to outshine the air force but not enough to be militarily useful. Hitler could not force them to produce as many as he thought necessary, and he could not force them to stop the program and transfer its resources to the air force. The army and the air force continued to operate as independent principalities until the day Hitler died.