Question

A wing designer comes up with two wing designs with different efficiency factors for a highaltitude
reconnaissance aircraft. The aircraft flies in steady, level flight at low subsonic cruise
speeds so that it can obtain better images of the ground underneath. If the weight, engine
thrust, aircraft speed and altitude are fixed, and induced drag is always the same fraction of
the total drag, derive a relationship between wing span and efficiency factor.

Answer 1

The coefficient of the drag is gvien by

Cd o : shape / parasitic drag which is property of the shape / geometry and reynolds number also.

Cd_i : The induced drag which is manisfesation of a lift .  

Now we have given that is constant so it implies and

Drag force is given by

and at cruise  

and we have  altitude( implies density) , velocity , Thrust (imlies drag ) fixed

so must be constant

-->

--> as alpha is constant

-->

----->

-->  

--A

Now we have

as mentioned above L=W fixed , and we have  altitude( implies density) , velocity fixed

so --B

from equation A and B we have

is the required relation ANS