Question

In an analysis, the maximum endurance in cruise of a jet airplane is used to measure its performance. If just the parasite drag coefficient is reduced by 19 %, determine if this increases or decreases its performance, and if so determine by how much.

Answer 1

Given:

parasite Drag Coefficient,$C _{D}$ is reduced by 19% or 0.19 times

Solution:

Using Breguet's Endurance Eqn:

$E = t_{2} - t_{1} = - \int_{W_{1}}^{W_{2}}\frac{dW}{c_{t}D}$

or

$E = \frac{1}{c_{t}}\frac{C_{L}}{C_{D}}\ln\frac{W_{1}}{W_{2}}$             (1)

From eqn (1), other terms being constant, then

$E = K\frac{1}{C_{D}}$

or

$E\propto\frac{1}{C_D}$

Therefore, the above relation shows that when drag coefficient $C _{D}$ decreases performance increases and vice-versa due to inverse relation between the.

So, 19% decrease will result in:

$E = \frac{1}{0.19}$ = 5.26 times increase in performance