Calculation of the reduced stiffness of a simple suspension

[Semat10]

Hello,

I have a problem with reducing a stiffness of a front suspension. Unfortunately I don't understand how to get the reduced stiffness on the right side in the picture. (k_f=k/cos^2E)

Thanks in advance for your help.

Many greetings,
Semat10

 

[Lnewqban]

The vertical stroke equals the inclined stroke times the cosine of angle ε.

 

[Semat10]

Hello,

I was thinking the same thing but I don't know where the square came from?

Many greetings

 

[Lnewqban]

The force of the vertical spring must be less than $N_f*cos (ε)$ ; therefore, the vertical stroke must be proportionally smaller $(cos (ε))$ than the inclined one (accounted for twice).

$k_{vertical} = N_f / {Vertical~stroke} = N_f / {Inclined~stroke}*cos (ε)$

$k_{vertical}/k_{inclined}=?$