Question

Problem 7 (4 marks) Consider a light, single-engine, propeller-driven airplane similar to a Cessna Skylane The airplane weight is 2950 lb and the wing reference area is 174ft2. The drag coefficient of the airplane Co is a function of the lift coefficient CL, such that C 0.025+0.054i a) For a steady level flight at sea level, where the ambient atmospheric density is 0.002377slug/ft3, plot on a graph the variation of Cu, CD, and the lift-to-drag ratio (L/D) with flight velocity ranging between 70 ft/s and 250 ft/s b) Make some observations about the variation of these quantities with velocity.

Answer 1

problem 7:

Solution:

Find the coefficient of lift using, 2W Here, Weight of the a Density at sea level is ρ rplane is W, Wing reference area is S, Coefficient of drag is Cp and Substitute 2950 lb for W, 0.002377 kg/m3 for ?, 70 m/s for V, and 174 ft for S in the equation, 2W pVes 2x2950 0.002377x70x174 -2.911

Find the coefficient of Drag using, C,-0.025 + 0.054G 2 Substitute, 2.911 for C in the equation, C0.025+0.054C, 0.025+0.054x2.911 0.483

Find a relation between lift and drag using coefficient of lift and coefficient of drag equation, of drag equation 7S 2W 14625 since,Cp 0.025+0.054Ci) L C D CD Substitute, 2.911 for C, and 0.483 for Cp in the equation L C D CD 2.911 0.483 -6.03

The values of C, is calculated for different velocities at the interval of 10 m/s calculated from the range 70 m/s to 250 m/s and Cn value These values are calculated for the velocities ranging between 70 m/s to 250 m/s and a table is ratio are calculate and tabulated D CD plotted as shown here.

Velocity (ft/s) DCD 70 2.911 0.483 6.03 1.761 0.192 9.17 90 110 1.179 0.100 11.79 130 0.844 0.063 13.40 150 0.634 0.047 13.49 170 0.494 0.038 130 190 0.395 0.033 11.97 210 0.323 0031 10.42 0.270 0.029 9.31 250 0.2280.028 8.14

The graph between Lift coefficient ( C) and velocity (V) is drawn 3.5 Lift coefficient Vs Velocity 2.5 1.5 0.5 0 0 50 V 150 200 250 300

The graph between Drag coefficient C)and velocity (V) is drawn 0.6 Drag coefficient Vs Velocity 0.5 0.4 CD 0.3 0.2 0.1 0 0 50 100 V 150 200 250 300

( - The graph between velocity (V) and Lift - Drag is drawn 16 14 12 10 Lift-to-Drag Vs Velocity LUD 50 100 150 200 250 300 The following results are obtained from the graphs. The lift coefficient decreases continuously as V increases lift coefficient with veloci decreases as the velocity increases