Condition A represents Va, the design maneuvering speed. From the previous posts, the load factor, n, is +3.8, and the airspeed is 85 kts. The aircraft weight is 1200 lbs. One new piece of information we need today is that the wing weight is estimated at 220 lbs. This acts at the wing CG which I've estimated at 26.6% of the chord length back from the leading edge. This weight includes 90 lbs of fuel (7.25 gallons per side), the tanks and fittings and half of the strut weight in addition to the basic airframe and covering.
To get the loads on the front spar, we add all the twisting forces acting around the rear spar, and divide by the distance between the front and rear spars to find the force required by the front spar to keep things in equilibrium. There are four forces/moments at work in our simplified (CAM 04 Appx IV) analysis:
1) Force of lift acting at 25% of the chord
2) Force of drag acting at 25% of the chord
3) Pitching moment of the airfoil
4) Weight of the wing acting at the wing CG
;)
The lift force is defined as follows:
...where Cl_local is the local coefficient of lift, A is the wing planform area, and q is the dynamic pressure:
...which works out to 24 psf for this speed at sea level. FAR 23, Appendix A in paragraph A23.7(e)(1) states that we need to increase the positive loads by 5%. We also need to account for the angle of attack, as the diagram above illustrates. Multiplying the resulting lift force by the moment arm (distance from the rear spar to the aerodynamic center) gives us the moment about the rear spar due to lift. Using the chord length instead of the area in the equation above, and dividing the result by the moment arm of the front spar gives the force per unit length in the front spar. The equation looks like this, where rac and rfrontspar are the moment arms for the aerodynamic center and the front spar, respectively, about the rear spar:
Drag is made up two components, form drag and induced drag. The equation for the combined drag coefficient for our example looks like this:
AR is the aspect ratio of the wing, Cd0 is the zero-lift drag coefficient from the airfoil data (0.011), and Cl is the wing coefficient of lift. Coefficient of lift can be calculated using the following equation:
S is the gross wing area (135 sf), Wgross is the max gross weight of the aircraft (1200 lbf). This Cl computes to 1.4 which should, and does, come out pretty close to the max wing coefficient of lift of 1.38. Substituting that result into our drag coefficient equation gives a Cd of 0.105.
The equation to find the required reaction in the front spar due to the contributing component of the drag force is as follows:
To be continued...
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