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In 1943 the increasing tempo of operations by the USAAF's 8th Air Force were proving to be difficult for the Luftwaffe to counter. Although by the end of the year they had managed to do serious damage to the bombing raids, the cost in fighter aircraft lost to the bomber's guns was enough to start a massive development effort to equip their fighters with considerably more powerful armament. Out of these projects came a number of heavy autocannon designs, air-to-air rockets, SAMss and the X-4.
Work on the X-4 began in June 1943, by Dr. Max Kramer at Ruhrstahl. The idea was to build a missile with enough range to allow it to be fired from well outside the range of the bomber's guns, while being guided with enough accuracy to guarantee a "kill". The X-4 met these specifications and more; its BMW 109-448 rocket motor got the missile up to a speed of over 1152km and kept it there during its "cruise", which lasted up to 4km (although 1.5 to 3.5km was more typical) while the defensive guns had a maximum effective range of about 1km. The rocket burned a hypergolic mixture of S-Stoff (nitric acid with 5% iron(3)chloride) and R-Stoff (an organic amine-mixture of 50% dimethylaminobenzene and 50% triethylamine called Tonka 250) as propellant, delivering 140kg thrust. There was no room for a fuel pump, so instead the fuels were forced into the engine by pistons inside long tubes, the tubes being coiled to fit inside the airframe. S-Stoff was so aggressive that it dissolved all base metals and was difficult to handle, and it was planned to replace the engine with a solid fuel design as soon as possible.
The missile was stabilized by spinning it slowly in flight, at about 60 RPM. This meant that any asymetrical thrust from the engine, or innaccuracies in the control surfaces, would be evened out as the missile spun. Signals were sent to the missile over two wires that were wound onto spools on the missile body, and corrected the direction of flight by operating control surfaces on the tail. A gyroscope kept track of "up" so that the control inputs from the pilot's joystick in the launch aircraft would be translated into yaw and pitch even as the missile rolled. Flares attached to two of the mid-section wings were used to keep the missile visible through the smoke of its engine.
The warhead consisted of a 20 kg fragmentation device that had a lethal radius of about 25 feet. It was thought that the guidance system would allow the pilot to get the missile into this range in terms of pitch and yaw, but at the ranges that the missile could operate at it would be almost impossible to judge range to anywhere near this accuracy. For this reason the missile mounted a proximity fuse known as Kranich, an acoustical system that was tuned to the sound of the B-17's engines in cruise. While approaching at high speed from the rear the Doppler effect would mean that the sound would be shifted to a higher frequency, but as the missile passed the bomber the shift would suddenly drop to zero and the warhead would be triggered.
History
The X-4 was designed to be easily assembled by unskilled labour. By early 1945, Ruhrstahl's Brackwede factory had produced over 1000 airframes (the number 1300 is typical), and were waiting for the rocket motors when the factory that produced them (BMW's Stargard factory) was bombed. It is possible that some X-4s were used in the closing weeks of World War II, although it was never delivered to the Luftwaffe.
X-4 air-to-air missile
X-7 anti-tank missile