Your geometry is actually very “wave-relevant” because the bottom rectangle (about 74 ft x 50 ft) is not tiny compared to common short-period wind-wave wavelengths. Using your numbers, each leg appears to be a 24 ft member at 45°, giving about 17 ft horizontal and 17 ft vertical projection (which matches the bottom rectangle offsets from the 40 ft x 16 ft top).
A common misconception is “big waves are long, so all corners rise together.” That is often true for long-period swell, but shorter-period wind waves (which can be only moderate height) can have wavelengths comparable to your structure footprint, creating corner-to-corner phase differences that can unload some cables while loading others.
Deep-water wavelength approximation:
L(m) ≈ 1.56 * T^2
L(ft) ≈ 5.12 * T^2
| Wave period T (s) | Approx. wavelength L (ft) | Comparison to your ~74 ft length / ~89 ft diagonal |
|---|---|---|
| 4 s | ~82 ft | Comparable to length and diagonal → corners can be near different phases |
| 5 s | ~128 ft | Bigger than footprint → more “in-phase,” but still not perfectly |
| 6 s | ~184 ft | Usually “mostly together” |
So you do not need a 20 ft breaking wave to see differential heave/pitch/roll that unloads some members. A 4–6 s sea with modest height can create fast relative motions and cable load cycling. This is a primary reason offshore moorings and tension members almost always incorporate compliance and/or pretension margins.
For a given cable, slack occurs when the structure motion shortens the end-to-end distance more than the cable’s elastic extension from pretension. In simplified form:
Slack risk if: ΔL_shortening > (T0 / k_total)
where:
T0 = pretension in the cable
k_total = axial stiffness of cable + any inline spring element (N/m or lb/ft)
Steel wire rope is very stiff (high k), so T0/k is small: you get small elastic stretch for a given pretension.
That makes it easier for motion to “eat up” the stretch and drive a member toward slack unless pretension is high
(or you add compliance).
If a cable goes slack and then re-tensions quickly, the peak load can greatly exceed the quasi-static load. The peak depends on relative velocity at re-tension and on stiffness. Energy-wise, a simplified snatch estimate is:
Peak snatch tension scale: T_snatch ~ v_rel * sqrt(m_eff * k_total)
v_rel = relative end velocity when slack is taken up
m_eff = effective mass participating in that mode (structure + added mass)
k_total = axial stiffness (higher stiffness = higher snatch peak)
Two strong design conclusions follow:
ΔL_allow ≈ T0/k_total.Compliance