Calculation of Twist in an Airplane Propeller Suppose you are designing the propeller of a radio-controlled model airplane. The overall diameter of the propeller is 34.0 cm, and the hub assembly diameter is 5.5 cm (Fig. 14–53). The propeller rotates at 1700 rpm, and the airfoil chosen for

Question

Calculation of Twist in an Airplane Propeller

Suppose you are designing the propeller of a radio-controlled model airplane. The overall diameter of the propeller is 34.0 cm, and the hub assembly diameter is 5.5 cm (Fig. 14–53). The propeller rotates at 1700 rpm, and the airfoil chosen for the propeller cross section achieves its maximum efficiency at an angle of attack of 14°. When the airplane flies at 30 mi/h (13.4 m/s), calculate the blade pitch angle from the root to the tip of the blade such that α = 14° everywhere along the propeller blade.

Accepted Answer

We are to calculate blade pitch angle θ from the root to the tip of the propeller such that the angle of attack is α = 14° at every radius along the propeller blade.
Assumptions 1 The air at these low speeds is incompressible. 2 We neglect the secondary effects of swirl and acceleration of the air as it approaches the propeller; i.e., the magnitude of [latex] \vec{V}_{ ext {wind }} [/latex] is assumed to equal the speed of the aircraft. 3 The airplane flies level, such that the propeller axis is parallel to the wind velocity.
Analysis The velocity of the air relative to the blade is approximated to first order at any radius by using Eq. 14–27. A sketch of the velocity vectors at some arbitrary radius r is shown in Fig. 14–54. From the geometry we see that

Pitch angle at arbitrary radius r: [latex] heta=\alpha+\phi [/latex] (1)

[latex] \vec{V}_{ ext {relative }} \cong \vec{V}_{ ext {wind }}-\vec{V}_{ ext {blade }} [/latex] (14–27)

and

[latex] \phi=\arctan \frac{\left|\vec{V}_{ ext {wind }} ight|}{\left|\vec{V}_{ ext {blade }} ight|}=\arctan \frac{\left|\vec{V}_{ ext {wind }} ight|}{\omega r} [/latex] (2)

where we have also used Eq. 14–26 for the blade speed at radius r. At the root [latex] \left(r=D_{ hub } / 2=2.75 cm ight) [/latex], Eq. 2 becomes

[latex] heta=\alpha+\phi=14^{\circ}+\arctan \left[\frac{13.4 m / s }{(1700 rot / min )(0.0275 m )}\left(\frac{1 rot }{2 \pi rad } ight)\left(\frac{60 s }{ min } ight) ight]= 8 3 . 9 ^ { \circ } [/latex]

[latex] u_{ heta}=\omega r [/latex] (14–26)

Similarly, the pitch angle at the tip [latex] \left(r=D_{ ext {propeller }} / 2=17.0 cm ight) [/latex] is

[latex] heta=\alpha+\phi=14^{\circ}+\arctan \left[\frac{13.4 m / s }{(1700 rot / min )(0.17 m )}\left(\frac{1 rot }{2 \pi rad } ight)\left(\frac{60 s }{ min } ight) ight]= 3 7 . 9 ^ { \circ } [/latex]

At radii between the root and the tip, Eqs. 1 and 2 are used to calculate θ as a function of r. Results are plotted in Fig. 14–55.
Discussion The pitch angle is not linear because of the arctangent function in Eq. 2.

Question 14.7: Calculation of Twist in an Airplane Propeller Suppose you ar...

Related Answered Questions

Design of a New Geometrically Similar Pump After graduation, you go to work for a pump manufacturing company. One of your company’s best-selling products is a water pump, which we shall call pump A. Its impeller diameter is DA = 6.0 cm, and its performance data when operating at nA = 1725 rpm ...

Verified Answer:

Verified Answer:

Turbine Specific Speed Calculate and compare the turbine specific speed for both the small (A) and large (B) turbines of Example 14–13. ...

Verified Answer:

Application of Turbine Affinity Laws A Francis turbine is being designed for a hydroelectric dam. Instead of starting from scratch, the engineers decide to geometrically scale up a previously designed hydroturbine that has an excellent performance history. The existing turbine (turbine A) ...

Verified Answer:

Verified Answer:

The Effects of Doubling Pump Speed Professor Seymour Fluids uses a small closed-loop water tunnel to perform flow visualization research. He would like to double the water speed in the test section of the tunnel and realizes that the least expensive way to do this is to double the rotational ...

Verified Answer:

Verified Answer:

Verified Answer:

Verified Answer:

Verified Answer: