http://en.wikipedia.org/wiki/Propeller_(aircraft)
A further consideration is the number and the shape of the blades used. Increasing the aspect ratio of the blades reduces drag but the amount of thrust produced depends on blade area, so using high-aspect blades can result in an excessive propeller diameter.
A further balance is that using a smaller number of blades reduces interference effects between the blades, but to have sufficient blade area to transmit the available power within a set diameter means a compromise is needed. Increasing the number of blades also decreases the amount of work each blade is required to perform, limiting the local Mach number - a significant performance limit on propellers.
A propeller's performance suffers as the blade speed nears the transonic. As the relative air speed at any section of a propeller is a vector sum of the aircraft speed and the tangential speed due to rotation, a propeller blade tip will reach transonic speed well before the aircraft does.
When the airflow over the tip of the blade reaches its critical speed, drag and torque resistance increase rapidly and shock waves form creating a sharp increase in noise. Aircraft with conventional propellers, therefore, do not usually fly faster than Mach 0.6. There have been propeller aircraft which attained up to the Mach 0.8 range, but the low propeller efficiency at this speed makes such applications rare.
There have been efforts to develop propellers for aircraft at high subsonic speeds.[4] The 'fix' is similar to that of transonic wing design. The maximum relative velocity is kept as low as possible by careful control of pitch to allow the blades to have large helix angles;
thin blade sections are used and the blades are swept back in a scimitar shape (Scimitar propeller);
a large number of blades are used to reduce work per blade and so circulation strength; contra-rotation is used. The propellers designed are more efficient than turbo-fans and their cruising speed (Mach 0.7–0.85) is suitable for airliners, but the noise generated is tremendous (see the Antonov An-70 and Tupolev Tu-95 for examples of such a design).
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We will find the proof of 4-blade vs 3-blade, sooner or later.
When a/c diving, it often creats a sharp increase in noise, which means tip of the blade reaches its critical speed.