Determining the fuselage thickness (basics)
An article by ScienceInsight
Article AV127
The wall thickness of aircraft fuselages depends on various load factors:
- Aerodynamic forces (pressure, air resistance)
- Mechanical loads (vibrations, shocks, take-off/landing forces)
- Internal pressure (e.g. in high-speed drones or stratospheric flights)
To calculate the wall thickness of a cylindrical CFRP hull (e.g. aircraft or drones), we use the layer-by-layer theory (Classical Lamination Theory, CLT). CFRP (carbon fiber reinforced plastic) is an anisotropic material whose mechanical properties also depend on the fiber orientation. To simplify, we will first derive wall thickness taking into account the bending moment, elastic modulus and allowable strain.
Basic formula for minimum wall thickness
$t = \frac{\sigma \cdot D}{2 \cdot F}$
t = required wall thickness [mm]
σ = permissible bending stress of the material (CFRP: approx. 700–1000 MPa)
D = diameter or characteristic fuselage width [mm]
F = safety factor
Sandwich structures
${t_{\text{eff}}} = {\sum t_{\text{i}}}$ := applies to structured hulls with sandwich core
${t_{\text{i}}}$ := Thickness of each material layer
Bending stress in the cylindrical body
$\sigma = {\frac{M \cdot y}{I}}$ $\:\: \land \:\:$ $y = {\frac{t}{2}}$
${I ≈ \pi \cdot R^3 \cdot t}$
(approximately for a thin-walled cylindrical hull: t≪R)
$\sigma_{\text{zul}} = {E \cdot \epsilon_{\text{zul}}}$ $\:\: \land \:\:$ $\sigma < \sigma_{\text{zul}}$
Assumption: t $\propto$ R
$\Rightarrow$ $\sigma = {\frac{M}{2 \cdot \pi \cdot R^2 \cdot t}}$
σ := Bending stress of the material
$\sigma_{\text{perm}}$ := Permissible bending stress given by the material properties
M := Bending moment acting on the cylindrical body
y := Distance from the neutral fiber (a symmetrical structure y=t/2)
I := Area moment of inertia of the cross section
E := Elastic modulus of the CFRP in the fiber direction (depending on the layering)
$\epsilon_{\text{perm}}$ := Maximum permissible elongation of the material
t := Wall thickness of the CFRP wall
R := Radius of the cylindrical body