Max Bending, Stress, Deflection:

$$ M_{max}=PL\\\\ $$

$$ \sigma(L)=\frac{-ML}{I_{z}} $$

$$ \delta_{max}=\frac{-PL^3}{3EI_{z}} $$

Carbon Tube Mechanical Properties [1][2]:

$E\approx70GPa=7e+10Pa$

$\sigma_{max}\approx1.8GPa=1.8e+9Pa$

Verify OTS Carbon Tube:

1. Input: $P,\ L,\ D,\ d$
   1. If needed, change $E,\ \sigma_{max}$
2. $\sigma(L) \leq1.8GPa$
   1. $F.S.=\frac{1.8GPa}{\sigma(L)}$
3. $\delta_{max}\leq\frac{L}{40}$

References:

[1] Fleuret, C., Andreani, A., Laine, E., Grandidier, J., L'Heritier, S., Gorge, A. "Complex wing spar design in carbon fiber reinforced composite for a light aerobatic aircraft." Mechanics and Industry, vol. 17, no. 6, article 614, 2016. [2] Mechanical Properties of Carbon Fibre Composite Materials, Fibre / Epoxy resin (120°C Cure). Mechanical Properties of Carbon Fibre Composite Materials. (n.d.).