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Unified Engineering Spring 2004 Fluids Problems F3–F
F3+F4. A symmetric airfoil has a trailing edge flap, with the hinge at xh/c = 0 .75, with the flap set at some small downward deflection angle ∂.
a) Define and sketch the camberline-slope dZ/dx, both versus x and versus α.
b) Use Thin Airfoil Theory to determine the airfoil’s c� and cm,c/ 4 , as functions of � and ∂.
c) Important quantities for an airplane-control designer are the flap control derivatives
�c� (^) , �cm,c/ 4 �∂ �∂
Determine these for the present flapped airfoil. Note: You may wish to check your results with Xfoil. The GDES menu allows you to set a flap deflection.
F5. An experimentalist determines that the downwash velocity for a rectangular wing of span b approximately obeys the relation
w = L 2 π V b^2
a) Assuming w is constant across the span, determine how CDi depends on CL for this wing.
b) Determine the wing’s CL(�) relation, and compare its dCL/d� to the 2-D value of 2 �. Hint: Start with the relation CL = 2 ��eff.
F6. Anderson Chapter 5, p 416. Problems 1. and 2. (closely related).
Unified Engineering Spring 2004 Problem M Draw loading, shear and bending moment diagrams for the following beam under the
loading shown. Label all key values (i.e. where changes in magnitude or slope occur).
Maintain the convention shown below for positive shear forces and bending moments:
Problem M The spar in a wing is modeled as a 10 m long beam. The combination of lift and self-weight
is modeled as resulting in a load distribution varying linearly from 5kN/m at the root to zero
at the tip. The beam has a rectangular cross section, height, h, of 100 mm and breadth, b, of
50 mm. Calculate the maximum bending stress in the beam, stating its location(s) and
calculate the deflection of the tip of the beam
mass?. Assume that failure will occur when the maximum bending stress equals the strength of the material.
c) For the materials listed in the table below, identify the material(s) that you would choose to meet the criteria of part (a) and part (b). What other factors should be considered in selecting a material for this application?.
d) Square solid sections are structurally not very efficient – “I” beams or hollow “box” beams are much more efficient – why is this? What other factors would need to be considered in selecting a material if a “box” cross-section was to be considered in (c)?.
Material Density, r , Modulus, E, CTE, a, Price , p, Tensile Strength, (Mg/m^3 ) (GPa) x 10 -6^ K -1^ ($/Mg) s f ,^ (MPa) Stainless Steel 17-7 PH 7.9 193 12 1500 1435 Aluminum alloy (2000 series) 2.8 71 24 1500 350 Titanium alloy Ti-6Al4V 4.5 120 9.0 8000 850 Carbon fiber composite* 1.5 70 3.0 100000 700 Wood (e.g spruce)* 0.6 12 4.0 300 300 Silicon Carbide (SiC) 3.0 410 4.0 50000 300
- These materials are anisotropic. You can assume that the values given are available in the requisite directions for this problem.
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