Airfoil Spar Design Procedure

Airfoil Spar Design Procedure

ME3227 Project

Objective

Set up a procedure to design an internal box beam to support aerodynamic and fuel weigh loads using as the example NACA 653-018.

Description

An internal box beam will be used as the main structural support member for a specified airfoil. A sketch of a cross-section for the design is shown in Figure 1. The weight of the airfoil skin and the foam fill can be neglected.

Figure 1. Airfoil Box Beam Support Geometry

The geometry of the outside airfoil skin for NACA 653-018 is given in Figure 2. The box beam width, height and thickness must be sufficient to support the aerodynamic loads and the weight of the fuel for two cases: 1) when the fuel tank is completely filled at take-off and 2) when the tank is assumed to be empty at landing. The weight of the fuel can be found from the literature or the internet. The aerodynamic loads are a function of the airfoil speed in the air. Three loads should be considered: 1) the lift acting up in Figure 1, 2) the drag acting to the right in Figure 1, and 3) a pitching moment acting clockwise in Figure 1. The forces and the moment are given by:

, (1)

, (2)

Figure 2: Airfoil Geometry

Figure 3a. Lift and Quarter Point Moment Coefficient

Figure 3b. Drag Coefficient and Aerodynamic Center

and

(3)

where r is the density of air (1.205 kg/m3 at sea-level), L and D are the lift and drag respectively, M is the moment for the lift and drag acting at the quarter chord (c/4), z is wing span location (i.e., the distance from the root of the wing to the tip, and is the coordinate perpendicular to the plane of Figures 1, c is the chord length as shown in Figure 1, is the lift coefficient shown in Figure 3a, cd, is the drag coefficient shown in Figure 3b, and is the pitching moment coefficient as shown in Figure 3a. Note that the coefficients, cd and are functions of the Reynolds number, Re, which is given by

(4)

where n is the kinematic coefficient of viscosity (take the room temperature value of 1.511x10-6 m2/s).

The quantities dL/dz, dD/dz and dM/dz are the lift force, drag force and pitching moment per change

in span length, z. Hence the total lift, L, drag, D, and pitching moment ,Mc/4, are given by

, (5)

, (6)

and

, (7)

where a is the wing span. For a rectangular wing (see Figure 4) the chord length does not vary and the total lift, L, drag, D, and pitching moment ,Mc/4, are given by , , and respectively. For the trapezoidal wing in Figure 4 only the chord length is a function of z, or . Hence the forces and the moment are distributed along the length of the box beam, and beam bending theory and torsion theory must be extended to distributed forces and moments and variable cross-section geometry.

Note that the total lift must be equal to the total weight of the airplane plus (or minus) the ascending (or descending) acceleration. This correction, if necessary, can be found from the sine of the slope angle times the weight. Use for the weight a fully loaded Boeing 747.

Figure 4. Non-Tapered and Tapered Wings

The bending and torsion stresses must be combined, for example using Mohr’s circle, and should not exceed either the yield, rupture, fracture, or fatigue limits divided by a safety factor. As an example, take the safety factor to be 1/0.85. The deflections and twist must be small enough to keep the lift sufficient, the drag small, and, of course, to prevent interference with the ground. Note that the lift, drag and moment vary with the angle of attack (i.e., the angle between the direction of the velocity and the chord). Figure 3b clearly shows that to large an angle of attack will remove the lift (i.e., the airfoil stalls) and the airplane will descend catastrophically.

There are two parts to the project:

In Part 1 develop a procedure to find the dimensions of the box beam and the material for a non-tapered

planform.

In Part 2 develop a procedure to find the dimensions of the box beam and the material for a tapered

planform. For this case you must decide how the box beam cross-section should change with the span

location.

The final report should be written in a professional manner, including: abstract, introduction, sections on the details of the procedure, conclusions, references and appendices if necessary. The project report must be less than ten pages, back-to-back, not counting references. The part 1 and Part 2 interim reports are brief summaries on the procedure and results, and must be less than one page.