Scaling test results to winchproof RC glider spar
-------------------------------------------------
Mark Drela 
Feb 15 00


This spar sizing procedure is based on the test data 
obtained by loading spar samples to destruction.



Typical two-meter glider example...

Sparcap thickness  :     Tc =  0.028 in  (4 plies, commonly sold as 0.030 in)
Design cap stress  :  sigma = 140000 psi (still may be conservative I think)
Design shear stress:    tau =  12000 psi (50% safety margin included)
Allowed core stress:  sig_C =    500 psi (50% safety margin for 4 lb balsa)

Heavier balsa can withstand proportionately larger sig_C.

Note: The bottom spar cap is in tension, and can surely tolerate
at least 200000 psi or even 300000 psi stress.  The bottom cap 
thickness can therefore be 0.021 in (3 plies) or even 0.014 in (2 plies).


Conditions at wing root:

wing span   :  b = 78 in
wing load   :  F = 160 lb        (winch line force)
spar height :  h = 0.9 in        (9% airfoil with 10 in chord)
cap modulus :  E = 2.0x10^7 psi  (for common T-300 carbon fiber)

bending mom.:  M = b F/8 = 1560 lb-in
cap load    :  P = M/h   = 1733 lb
shear load  :  S = F/2   = 80 lb

required cap area   :  Ac = P / sigma = 0.0124 in^2
required cap width  :   w = Ac / Tc   = 0.44 in

required shear area :  As = S / tau   = 0.0067 in^2
required skin thick.:  Ts = As / 2h   = 0.0037 in   (2 layers of 1.5 oz glass)

estimated core compressive strength:  sig_C = tau As / h w  =  200 psi
                                                            (no problemo!)

estimated tip deflection:  d = b^2 sigma / (4 E h) = 12 in
                                                     (yikes!)

This particular case may call for a reduction in the allowable 
stress sigma to get proportionately lower tip deflection.  
The spar will then be stronger than necessary but that 
has to be accepted.



Ideally one wants to taper the spar dimensions so as to maintain constant 
sigma and tau.  This will give minimum weight for a given strength.

Assuming the cap thickness Tc and spar height h are roughly constant, 
the relative spar width and shear skin thickness should taper as follows:

       center  ..     midspan  ..     tip
       -----------------------------------
 w  ~  1.0    0.56    0.25    0.06    0.0
 Ts ~  1.0    0.75    0.50    0.25    0.0

Simple linear taper of w is OK, but gives unnecessary strength 
(and weight) outboard.  Ts will obviously need to be stepped ---
from 2 layers in the middle dropping to 1 layer at midspan.

If w is constant, then the sparcap thickness Tc should taper the same
way as w above.




Sizing wood spars
-----------------

The sizing example above can also be followed for sizing 
spar caps and shear webs in traditional I-beam wood wings.  
The following minor definition changes must be made.  
I got the wood properies out of an old book on wood 
aircraft structures.

h  =  spar height measured between cap section midpoints
   =  total height  -  single cap thickness

As =       wood shear web area
Ts = As/h  wood shear web thickness

E = 1.3x10^6 psi  (spruce)

tau   =  200 psi  (for 4 lb balsa.  Scale up for larger densities.)
sigma = 5000 psi  (spruce)

Notes: 

* tau and sigma are values at failure.  Reduce these to get 
some safety margin.  

* The same ideal spanwise taper rates apply.  Typical existing
wood spars are grossly oversized outboard relative to the center.

* Much more modest winch loads will need to be chosen with wood,
else the spar will end up wider than the airfoil chord!