1/4 Scale Pioneer 3 Spar Calculations by Chuck Clemans

The spar design calculations are my first attempt at that sort of thing so
comments are welcome.

Case 1. Based on winch line load at full zoom launch...
Assumptions:
Winch load of 160 lbs.
Load at MAC located 27.2" outboard of wing joiner.
Spar caps of 0.060" x 0.5" carbon laminate with full balsa shear web.
Cap strength 160,000 psi
Airfoil thickness at spar of 1.359" including 1/16" D tube sheeting based on th 9.3% BW 05 02 09 airfoil.
Bending Moment:
Mb = Load/Ma = (160/2)(27.2) = 2176 in lbs
h = 1.359 - 2(0.0625) - 0.060 = 1.174"
Load in spar cap at wing joiner.
P = Mb/h = 2176/1.174 = 1854 lbs
Cap area required:
Ar = P/160,000 = 1854/160,000 = 0.012 in2
Cap area available:
Aa = 0.5 * 0.060 = 0.03 in2
Margin of Safety
MS = (Ah/Ar) -1 = (0.03/0.012) - 1 = 1.5

Case 2, Based on model weight.
Assumptions same as Case 1. except as noted.
:
Total weight of model 4lbs at 10g (equivalent to moderate winch load of 40 lbs)
Spar caps of 0.030" x 0.05" carbon laminate with full balsa shear web.
Mb = (4/2)(27.2)(10) = 544 in lbs
h = 1.359 - 2(0.0625) - 0.030 = 1.204 in
P = 544/1.204 = 452 lbs
Ar = 452/160,000 = 0.0029 in2
Aa = 0.5(0.030) = 0.015 in2
MS = 0.015/0.0029 -1 = 5.17
Reduction of spar cap to 3/8" x 0.030" would provide:
Aa = 0.375(0.030) = 0.01125 in2
MS = 0.01125/0.0029 - 1 = 2.8
Spar cap .25" x 0.030"
Aa = 0.25(0.030) = 0.0075 in2
MS = 0.0075/0.0029 -1 = 1.5

Case 3. Based on model weight.
Assumptions same as Case 2. except as noted.
Spar caps are 0.125" x 0.75" spruce with full balsa shear web
Cap strength is 5100 psi
h = 1.109"
P = 544/1.109 = 491 lbs
Aa = 0.125(0.75) = 0.0975 in2
Ar = 491/5100 = 0.96 in2
MS = 0.0975/0.96 -1 = 0.01

Conclusions:
Case 1 is extreme, but can be handled easily with 0.5" x 0.060" carbon spar caps. Zoom launches are not necessary for a scale glider, but extra strength might be of interest if aero tow is planned. Bottom cap could be 0.030 carbon.
Case 2 can be handled by 0.25" x 0.030" carbon spar caps, but extra width at root might be needed for joiners.

Case 3. Spruce spar caps even if 0.75" x 0.125" at root do not provide adequate margin of safety.
Plans:
I plan on a spar which is 3/8" to 1/2" wide at the joiner and tapering to 1/4" by quarter span and remaining 1/4" wide to the tip.
Spars will be built external to the wing with either carbon laminate blades or hardened 5/16" Dia. steel rod wing joiners. Spar cap width at root will be determined by wing joiner requirements, but will taper to 0.25" at tip. Spar caps could be tapered in thickness, but I probably won't. I haven't found tapered carbon longer than 48".
Completed spars with caps and shear web will be wrapped with Kevlar thread to prevent delamination of caps and web prior to insertion in wing structure.
Spars could be constructed using the same process as used on the Marske Pioneer 3, but for a one off build it's hard to beat balsa webs and carbon caps and I like the idea of avoiding the complexity of a mold. As long as it looks like the Pioneer 3 on the outside that's good enough for me. If the emperor has clothes and can fly, that's cool.