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Chapter_8-The_Propeller

# Chapter_8-The_Propeller - Anderson Introduction Airplane...

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Unformatted text preview: Anderson Introduction Airplane wings and propellers have something in common: they are both made up of airfoil sections designed to generate an aerodynamic force. The wing force provides lift to sustain the airplane in the air; the propeller force provides thrust to push the airplane through the air. A sketch of a simple three-blade propeller is given in Fig. 8-1, illustrating that a cross section is indeed an airfoil shape. Fig. 8.1. The airplane propeller, emphasizing that a propeller cross section is an airfoil shape. However, unlike a wing, where the chord lines of the airfoil are essentially all in the same direction, a propeller is twisted such that the chord line changes from almost parallel to V ∞ at the root, to almost perpendicular at the tip. This is illustrated in Fig. 8-2, which shows a side view of the propeller, as well as two sectional views, one at the tip and the other at the root. This figure should be studied carefully. The angel between the chord line and the propeller’s plane of rotation is defined as the pitch angle β . The distance from the root to a given section is r . Note that β = β(r). 1 Fig. 8-2. Illustration of propeller, showing variation of pitch along the blade. The airflow seen by a given propeller section is a combination of the airplane’s forward motion and the rotation of the propeller itself. This is sketched in Fig. 8.3a, where the airplane’s relative wind is V ∞ and the speed of the blade section due to rotation of the propel is rω . Here, ω denotes the angular velocity of the propeller in radians per second. Hence, the relative wind seen by the propeller section is the vector sum of V ∞ and rω , as shown in Fig. 8-3b. Fig. 8-3. Velocity diagram for the flow velocity relative to the propeller. Clearly, if the chord line of the airfoil section is at an angel of attack α with respect to the local relative wind V , then lift and drag (perpendicular and parallel to V , respectively) are generated. In turn, as shown in Fig. 8-4, the components of L and D in the direction of V ∞ produce a net thrust T : φ φ sin cos D L T- = (8-1) 2 where φ = β – α . This thrust, when summed over the entire length of the propeller blades, yields the net thrust available T A which drives the airplane forward. Fig. 8-4. Generation of propeller thrust. This simple picture is the essence of how a propeller works. However, the actual prediction of propeller performance is more complex. The propeller is analogous to a finite wing that has been twisted. Therefore, the aerodynamics of the propeller is influenced by induced flow due to tip vortices. Moreover, due to the propeller twist and rotational motion, the aerodynamic theory is even more complicated. However, propeller theory has been extensively developed, although it is beyond the scope of this discussion.theory has been extensively developed, although it is beyond the scope of this discussion....
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Chapter_8-The_Propeller - Anderson Introduction Airplane...

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