Jawaharlal Nehru Technological University Hyderabad B.Tech III Year AIRCRAFT PERFORMANCE AND STABILITY Previous Question Paper (March - 2021 - R18)

The power required for level flight is given by P = D × V. Substituting the drag equation D = (1/2)ρV²SC_D,0 + (2K(W/ρV)²) and using the lift-to-drag relationship where L = W = (1/2)ρV²SC_L, the power required is P = (1/2)ρV³SC_D,0 + (2KW²)/(ρVS). The minimum power required occurs at a velocity V_mp. By differentiating P with respect to V and setting it to zero, we find V_mp = sqrt(2KW / (ρS sqrt(3C_D,0))). At this speed, the power required is P_min = sqrt(32K³W³ / (27ρSC_D,0)). Given the flight speed V = nV_mp, we substitute this into the power equation P = (1/2)ρ(nV_mp)³SC_D,0 + (2KW²)/(ρ(nV_mp)S). Simplifying this expression using the relationship P_min = (4/3)P_D,0_min = 4P_i_min, where P_D,0 is the parasite power and P_i is the induced power, we obtain P = (n³)P_D,0_min + (1/n)P_i_min. Substituting P_D,0_min = (1/4)P_min and P_i_min = (3/4)P_min, we get P = (n³/4)P_min + (3/4n)P_min. Factoring out P_min/4n, we arrive at P/P_min = (n⁴ + 3) / (4n). Note: Based on the standard derivation for P/P_min = (n² + 2) / (3n) often found in specific textbooks, this assumes a different normalization or specific drag polar approximation; following the derivation steps leads to the conclusion that the power ratio is a function of the speed ratio n relative to the minimum power speed.

The drag polar equation represents the relationship between the total drag coefficient C_D and the lift coefficient C_L for an airplane. It is expressed as C_D = C_D,0 + K(C_L)², where C_D,0 is the zero-lift drag coefficient and K is the induced drag factor defined as K = 1 / (πARe). The term C_D,0 accounts for skin friction and pressure drag, while K(C_L)² accounts for the lift-induced drag. To plot the curve, place C_D on the horizontal axis and C_L on the vertical axis. The curve is a parabola symmetric about the C_L = 0 axis, with its vertex at (C_D,0, 0). As C_L increases, C_D increases quadratically, illustrating the trade-off between lift generation and drag penalty.