Faster airplanes, however, need propellers with adjustable blades, able to increase the angle ("pitch") at which they "bite" into the air as the flight speed increases, so that they always face into the combined velocity v due to their own motion and that of the airplane. One can not compensate by increasing the speed v1 of the blade, because as the propeller tips reach the speed of sound, their efficiency drops markedly (and the noise they produce rises!)
Adjustable blades ("variable pitch propellers"), more expensive and complicated than one-piece propellers, have long been standard equipment on the faster propeller airplanes. But even they hit a limit. Suppose the airplane moves at the same speed as the propeller tip, that is, v2 = v1. The tip of the blade then needs to be rotated into the direction of motion by 45 degrees into the direction of motion (bottom drawing). Two disturbing trends now become evident.
First of all, as seen from the "vector addition triangle" and the theorem of Pythagoras, the total velocity v sensed by the blade is considerably faster (by about 41%) than either of its two component velocities, pushing it closer to the speed of sound and its associated problems. And secondly, the lifting force L on the blade is also rotated by 45 degrees! Only the component L1 pulls the airplane forward--the other component, L2, actually opposes the rotation of the propeller and demands extra power from the motor, power that serves no useful purpose.
Because of such problems, propeller-driven airplanes have never even approached the speed of the jets. The faster propeller-driven fighter airplanes of World War II flew at about 370-400 mph. The speed record for a purely propeller-driven airplane, 463 mph, was attained in Germany before the war (in 1939) and stood for decades. The current record is 528.33 mph, attained in 1989 by the "Rare Bear", a WW-II US Navy 8F8 "Bearcat" fighter, modified for high-speed racing. The airplane had crashed in 1962 and was lying in an Indiana cornfield, next to a runway, before Lyle Shelton in 1969 found it and restored it. He later replaced its 2400 HP engine with one of 4000 HP (getting less than 1 mile per gallon gas at top speed), replaced its propeller, and trimmed its weight. It is still flying. (Thanks to Dr. Eddie Irani for this information).
