Question

1. From an earlier presentation (Module 2B) we learned how to calculate g-loading from a known bank angle (g loading=1/cosφ $TbFwAAAABJRU5ErkJggg==$ ). Consider an aircraft weighing 40,000 lbs. and using the examples provided in the presentation slides, what will be the imposed load on the aircraft wings for the following bank angles: 15°, 30°, 45°, and 60°? If we desire to include a Factor of Safety of 1.50, what will be the allowable stress (material strength required) for the overall wing structure that experiences a 60° bank angle?

Answer 1

The Load factor of an aircraft is a measure of forces acing on the whole system. The load factor of g loading are same thing and depends on the bank angles by the following relation:

   (1)

GL = Cosy

Where, $\varphi$ is Bank angle.

(A) We have the mass of the aircraft,

mg = 40000 lbs

(i) For ,

y = 15

Imposed load,

  

F1 = mass x Acceleration x Load factor = mass x g Force

F1 = ma X GL X 9 = 40000 x 32.174 x = 1332359.03 lbf

(ii) For ,

4= 30°

Imposed load,

F2 = ma X GL X g = 40000 – x 32.174= 1486053.4 lbf

(iii) For ,

6= 45°

Imposed load,

F3 = ma X GLX g = 40000 x - X 32.174 = 1820036.28 lbf

(iv) For ,

= 60

Imposed load,

F4 = m, X GLX g = 40000 x x 32.174=2573920 lbf

(B) Case-I: If the value of material strength is given then

  

om = material strength psi

Now when the aircraft has to experience a Bank angle of ,then

= 60

  

allowable = Oall = working stress

(2)

material strength = Om = F.O.S. x gall x Load Factor = N X Om X GL

   (3)

= Om = N * Oall X GL = 1.2 x - x all = 30 all

   (4)

Om 1 > Call = N X GL 3

Hence the allowable stress or the working stress in the airplane must be 1/3rd of the material strength of Aircraft for Bank angle of and Factor of Safety, FOS=1.5 for overall wing structure.

= 60

CASE-II: When the material strength is not given, let us assume the the total wing effective area or working area be $A_{w}$

Now for wing angle , we have,

= 60

  

F4 = 2573920 lbf

hence allowable stress,

1715946.67 _F4F4 Wall Au * FOS Au X FOS 2573920 1.5.Aw -psi

For known working area $A_{w}$ we can get the value of allowable stress at the aforementioned condition.