Date: Thu, 25 Jan 1996 16:09:22 -0500
From: Phillip.Johnson@Lockheed.on.ca (Phillip Johnson)
Subject: Re: Cabin Width

     Bill Kleb Writes,
     
     >  i was actually more worried when i heard the spar thickness was 
     >  increased 20% from the cozy to the cozy iv!  the standard 
     >  beam-bending stiffness equation goes as thickness^4---so this 
     >  simple analysis says the wing spar is 2 times stiffer!  a stiffer 
     >  wing is not always better since the wing root moments can now be 
     >  much higher since the wing is not able to "unload" lift through 
     >  deflection.
     
     The relationship described here is the relationship for a solid beam, 
     i.e. if you took the spar cap in isolation, a 20% increase in thickness 
     would yield a doubling in stiffness. If however you take two spar caps 
     and separate them by a value that is large compared to the individual 
     thickness of the spar caps, the strength increases enormously as with 
     the standard spar configuration. Now, if you take two separated spar 
     caps and increase their thickness a small amount, not the separation, 
     when I say a small amount I mean an amount that does not contravene the 
     large separation requirement, the stiffness and strength of the 
     structure increase linearly with the increasing thickness of the spar 
     caps. 
     
     The simple analysis given above does not take into account any 
     stiffening resulting from the shear web but is intended to illustrate 
     that Nat's 20% increase in thickness will strengthen the spars by only 
     20% which I believe was his intent. So the nominal 1700lb gross for the 
     MK III now becomes 2040 lbs for the MK IV. The number is close enough 
     to 2050 lbs to use this figure.
     
     Wow did I actually agree with Nat ;-) maybe there is hope for me.
     
     Phillip Johnson