Step 1: Cruise condition at Mach 0.8.
Civilian transport aircraft generally cruise in the transonic regime (\(M \approx 0.8\)). Conventional airfoils (like A and B) produce strong shock waves on the upper surface, leading to wave drag rise. Thus, an airfoil that reduces or delays shock formation is required.
Step 2: Characteristics of supercritical airfoil.
- Flattened upper surface: reduces local flow acceleration, delaying shock to further aft.
- Aft camber on the lower surface: maintains lift while keeping upper-surface pressure distribution favorable.
- Blunt leading edge: improves low-speed handling.
- Thin trailing edge: aids smooth pressure recovery.
Step 3: Eliminate other options.
(A) Conventional airfoil: suffers early shock formation.
(B) Strongly cambered: even worse drag divergence at transonic speeds.
(C) Very thin symmetric: lacks sufficient lift at cruise \(C_L\).
(D) Matches supercritical features: best suited for Mach 0.8 cruise.
Final Answer:
\[
\boxed{\text{Option (D) is aerodynamically best suited.}}
\]
For a NACA 4415 airfoil, the location of maximum camber, as a fraction of the chord length from the leading edge, is _________.
Two designs A and B, shown in the figure, are proposed for a thin-walled closed section that is expected to carry only torque. Both A and B have a semi-circular nose, and are made of the same material with a wall thickness of 1 mm. With strength as the only criterion for failure, the ratio of maximum torque that B can support to the maximum torque that A can support is _________ (rounded off to two decimal places).
A thin flat plate is subjected to the following stresses: \[ \sigma_{xx} = 160 \, {MPa}; \, \sigma_{yy} = 40 \, {MPa}; \, \tau_{xy} = 80 \, {MPa}. \] Factor of safety is defined as the ratio of the yield stress to the applied stress. The yield stress of the material under uniaxial tensile load is 250 MPa. The factor of safety for the plate assuming that material failure is governed by the von Mises criterion is _________ (rounded off to two decimal places).
A prismatic vertical column of cross-section \( a \times 0.5a \) and length \( l \) is rigidly fixed at the bottom and free at the top. A compressive force \( P \) is applied along the centroidal axis at the top surface. The Young’s modulus of the material is 200 GPa and the uniaxial yield stress is 400 MPa. If the critical value of \( P \) for yielding and for buckling of the column are equal, the value of \( \frac{l}{a} \) is __________ (rounded off to one decimal place).
A uniform rigid bar of mass 3 kg is hinged at point F, and supported by a spring of stiffness \( k = 100 \, {N/m} \), as shown in the figure. The natural frequency of free vibration of the system is ___________ rad/s (answer in integer).
A jet-powered airplane is steadily climbing at a rate of 10 m/s. The air density is 0.8 kg/m³, and the thrust force is aligned with the flight path. Using the information provided in the table below, the airplane’s thrust to weight ratio is ___________ (rounded off to one decimal place). 