The optimum condition is for О± to be just large enough to give the thrust required at the given W, but no larger. The net effect is that the propulsive efficiency of the propeller tends to decrease as the propeller is spun faster for a given flight speed V 0. Unfortunately, increasing W also increases the drag that resists propeller motion that requires more power from the motor to spin the propeller. Thus, simply revving the engine to make the propeller spin faster will generate more thrust. Since U is the vector sum (addition) of V 0 and W, both U and О± can be increased by increasing W, which increases with propeller rotation rate n (click on the different speed levels to see how changing n changes the forces on the propeller blade). Thrust can be increased by increasing, which can in turn be increased by increasing the oncoming flow speed ( U) and О± in the same way that lift on a wing is increased. This parallel force tends to reduce thrust and increase the work required from the motor, but for a well-designed propeller, this effect is small. There is also a 'drag' force on the blade parallel to the oncoming flow ( F ||). That is, work must be done by the motor to generate thrust. (Click here to review vector components.) Notice also that there is a vertical force component that resists the motion of the blade and must be overcome by the motor that spins the blade. (Here we call the 'lift' force generated by the blade instead of F L because is not perpendicular to the motion of the airplane as is the case for lift on a wing.) The horizontal component of points forward, giving the desired thrust ( F T). As with the wing, the propeller blade accelerates the oncoming flow away from it, generating force ( ) in a direction perpendicular to the oncoming flown as shown. Notice that the angle of the oncoming flow ( О±) is determined by (a) the speed of the aircraft ( V 0), and (b) the vertical speed of the propeller, namely, W = 2ПЂnr where n is the rotation rate of the propeller in revolutions per minute (rpm). In this view, the flow moves past the propeller blade in a manner similar to that illustrated for the wing above. On the right of the figure is the flow seen from the point of view of someone sitting on the propeller blade (relative motion is reviewed here). For future reference, let's say the chosen slice of the blade is a distance r from the hub (see the picture on the left in the figure).

Only a slice of the blade is shown so you can see the wing-like shape of the propeller blade moving through the oncoming flow. In the center of the figure below is a side view of a spinning propeller blade. Spinning the blade induces the fluid to flow over the blade in a manner similar to the flow over a wing, but rotated 90В° to generate thrust. The propeller blade must also be spun around its axis. Just rotating the wing 90В° isn't enough to turn lift into thrust. In this orientation, we call the wing a propeller 'blade'. The force on the wing is now pointed forward, creating thrust instead of lift. Now envision the above scenario rotated 90В° counter clockwise so that the top of the wing is facing forward. C L is called the lift coefficient and it depends on the wing geometry and О±. Where ПЃ is the fluid density, U is the upstream flow speed, and A is the wing area. If the angle of the wing relative to the oncoming flow (angle of attack, О±) is increased, the downward acceleration of the flow is enhanced and lift is increased (as long as О± is not too large). The vertical force acting on the wing is called lift and it is what keeps airplanes aloft. Both the process of catching the ball as it bounces up to your hand and throwing it back down to the ground exert a vertical force on your hand because your hand must change the motion of the ball from upward to downward. The process is analogous to the force required to bounce a ball on the ground. Because the flow is accelerated down (the direction of the fluid velocity is changed to the downward direction), NewtonвЂ™s Third Law requires there be an upward reaction force on the wing. The net effect is a change in flow direction from upward to downward by the wing. Near the front of the wing, the curvature of the top of the wing adds to this effect because the flow must curve up as it approaches the wing in order to flow smoothly over the hump on the top of the wing. As a result, the fluid flowing over the wing tends to flow down and away from the wing as it passes the end or 'trailing edge' of the wing. In the figure above it can be seen that near the back a wing has a slightly steeper slope on the top as compared to the bottom.

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