Hydrogen Type IV COPVs, Carbon-Fiber Filament Winding & 54.74° Netting Analysis
Filament-Wound Vessel Netting Analysis (54.74°) Formula
Calculate Exact Balanced Netting Winding Angle ATAN(SQRT(2)) = 54.74°, Axial-Governed Dry Fiber Thickness (mm), Hoop-Governed Dry Fiber Thickness (mm), and Total Composite Shell Thickness (mm).
Why every single-angle composite hydrogen tank and rocket motor case winds fibers at 54.74°—TAN²(alpha) = 2 matches 2:1 hoop-to-axial stress!
In a closed cylindrical pressure vessel of radius `R` (mm) at Burst Pressure `P` (MPa), Circumferential Hoop Running Load `N_theta = P * R` (`N/mm`) is **EXACTLY TWICE** Axial End-Cap Running Load `N_phi = (P * R) / 2`! Under Composite **Netting Analysis** (conservatively neglecting micro-cracked epoxy matrix stiffness so continuous carbon tows at +/-`alpha` from the cylinder axis carry `100%` of burst load at Allowable Fiber Stress `sigma_f`), axial equilibrium requires Dry-Fiber Thickness `t_f,axial = N_phi / (sigma_f * COS²(alpha))` while hoop equilibrium requires `t_f,hoop = N_theta / (sigma_f * SIN²(alpha))`! Setting `t_f,axial = t_f,hoop` yields `SIN²(alpha) / COS²(alpha) = TAN²(alpha) = N_theta / N_phi = 2` -> **`alpha_opt = ATAN(SQRT(2)) = 54.7356° ≈ 54.74°`**! Winding off-angle wastes carbon fiber on whichever direction governs `MAX(t_f,axial, t_f,hoop) / V_f`!
Verify on a 700-bar (`70` MPa) Type IV Hydrogen Storage Tank Cylinder—Liner_Radius `R` = 180.0 mm (B2), Design_Burst_Pressure `P` = 70.0 MPa (B3), Helical_Winding_Angle `alpha` = 54.74° (B4 -> Theoretical Magic Angle = `54.74°` in E2), Design_Fiber_Stress `sigma_f` = 2,400.0 MPa (B5), and Cured_Fiber_Volume_Fraction `V_f` = 0.60 (B6): Axial Dry-Fiber Demand equals `7.88` mm (E3), Hoop Dry-Fiber Demand matches at `7.87` mm (E4), requiring Minimum Total Carbon/Epoxy Composite Wall `t_comp = 13.13` mm (E5)!
| COPV Netting Analysis KPI (R=180 mm, P=70 MPa, alpha=54.74° vs 45°, Vf=0.60) | Formula | Verified Output |
|---|---|---|
| Balanced Netting Angle (deg) | ATAN(SQRT(2)) * (180 / PI()) | 54.74° (universal 2:1 biaxial optimum) |
| Axial Dry-Fiber Thickness (mm) | (0.5 * P * R) / (sigma_f * (COS(alpha)^2)) | 7.88 mm (5.25 mm @ 45° over-axial) |
| Hoop Dry-Fiber Thickness (mm) | (P * R) / (sigma_f * (SIN(alpha)^2)) | 7.87 mm (10.50 mm @ 45° hoop deficit!) |
| Governing Composite Wall (mm) | MAX(tf_Axial, tf_Hoop) / Fiber_Vol_Vf | 13.13 mm (17.50 mm = +33% heavier @ 45°!) |
Netting Analysis Axial vs Hoop Fiber Equilibrium & Composite Shell Thickness Formula
Validate `Radius R > 10` mm, `Burst_Pressure P > 0` MPa, `Helical_Angle alpha` in `[15°, 80°]`, `Fiber_Stress > 100` MPa, and `Fiber_Volume_Fraction V_f` in `[0.35, 0.75]`!
=LET(rd_m, B2, pr_m, B3, an_r, B4 * (PI() / 180), sf_m, B5, vf_r, B6, ta_f, (0.5 * pr_m * rd_m) / (sf_m * (COS(an_r) ^ 2)), th_f, (pr_m * rd_m) / (sf_m * (SIN(an_r) ^ 2)), IF(OR(rd_m <= 10, pr_m <= 0, B4 < 15, B4 > 80, sf_m <= 100, vf_r < 0.35, vf_r > 0.75), "Invalid COPV Input", ROUND(MAX(ta_f, th_f) / vf_r, 2)))Naive 45.0° Winding-Angle 33% Weight Penalty Check (Set Winding Angle B4 = 45.0°)
Wind the vessel at `45.0°` (`B4 = 45`, optimal for pure torsion shafts, NOT `2:1` pressure vessels!): Axial Fiber Demand E3 drops to `5.25` mm while Hoop Demand E4 jumps to `10.50` mm, forcing Governing Composite Shell Thickness E5 up `+33.3%` from `13.13` mm to `17.50` mm unless dedicated `90°` hoop plies are added!
=IF(ISTEXT(E5), E5, ROUND((B3 * B2) / (B5 * (SIN(B4 * (PI() / 180)) ^ 2)), 2))Try the example
Use the original values or change them to test your understanding.