Inputs
Advanced constants (weights, drag, damping, cost…)
Tradeoff Table — 3 Leg Profiles (same displaced volume, 10′ chord)
| Leg Profile | Fits 45′ HC? | Waterplane Area (Total Sq Ft) |
Restoring Force (Lbs per ft water height) |
Natural Heave Period Tn (s) |
Est. Speed @ 10.0 kW (Knots) | Heave w/o Stabilizer, 5.0′ wave (ft) | Stab Force, 3 fins (Total Lbs) | Stab Influence (Ft Equivalent) |
Heave WITH Stabilizer (Final Motion, ft) |
Heave Reduction |
Est. Weight of Each Leg (Marine Aluminum) |
Est. Cost: 1 Leg + 1 Stabilizer (Marine Aluminum) |
|---|
Profile sizing: NACA 0030 is your stated baseline (L 39′, draft 19.5′, chord 10′, width 3′). NACA 0040 / 0025 keep the 10′ chord and are re-lengthened to hold the same displaced volume (so buoyancy & payload are identical across rows). Container checks assume legs lie lengthwise; nested pair = 2×width + 0.1′ across the 7.7′ width.
Heave vs Wave Period (current inputs)
Solid = heave without stabilizer · dashed = final heave with stabilizer · gray dashed line = full following (water rise = H/2) · white marker = current wave period. Smaller-waterplane legs (0025) sit lower on this chart — less motion for the stabilizer to cancel — but they also go slower, which weakens fin force.
Model, Formulas & Assumptions
- Geometry. Prismatic NACA 4-digit legs: section area
A = 0.685 · chord · width(exact integral of the NACA thickness form). 0040/0025 re-lengthened at constant volume:L = V₀/A, draft = L/2. - Buoyancy. Half of each leg submerged: displacement
= 3 × ½V × 64 lb/ft³(≈76,900 lb for all three rows). - Waterplane & restoring force. For a vertical prism,
dV/dz= section area, so total waterplane= 3Aand restoringk = 3A × 64lb per ft of water-height change. - Your ramp heave model. Crest raises the water H/2 over Tw/4. Treating the seastead as spring-mass (k above, mass = displacement × (1+added-mass)), the response to a ramp start-up is
f = 1 − (sinφ/φ) · e−δφ, withφ = (π/2)(Tw/Tn),Tn = 2π√(m(1+added)/k). Heave w/o stabilizer= f × H/2. δ (default 0.12) stands in for heave-plate + radiation damping; result clipped to [0, 1.05]×H/2. Slow waves (Tw >> Tn) → f→1 (follows fully); fast waves → f→0 (ignores them). Smaller waterplane → softer spring → lower f → less motion for the stabilizer to remove. - Speed. Thrust
ηP/vbalances drag½ρv²K, givingv = &cuberoot;(ηP / (½ρK))withK = cd(t/c)·chord·draft·3 legs·kint + Cf(ITTC, Re)·Swet;cd = 0.005 + 0.011(t/c);Swet= foil perimeter × submerged depth × 3. Iterated for Reynolds-corrected friction. Excludes wave-making and dinghy drag (lumped into kint). - Stabilizer. Fin lift
F = N × ½ρv² · (span×chord) · CL— works better when going faster. Authority in feet= F/k(your “force ÷ (waterplane × 64)” conversion). Final heave= max(0, heave₀ − F/k). Assumes fins hold CL without stalling and react within the T/4 ramp. - Weight & cost. Shell area = foil perimeter×length + 2 end caps; weight
= area × plate × 168 lb/ft³ × (1 + frame allowance). Fin = both faces + root. Cost = pounds × fabricated $/lb (order-of-magnitude; yard quotes vary widely). - Battery aside. 25 % of displacement in LFP at ~140 Wh/kg pack-level ≈ .
- Levers on stabilizer authority: more span, higher CL (flapped foil), more fins, more power (speed), or softer springs (thinner legs) — but thinner legs slow the boat, which cuts fin force. The table nets that out per profile.
- Not modeled: pitch/roll (assumed stiff triangle), diffraction/excitation phase, slamming, mooring & dinghy drag, thruster-housing drag beyond kint, solar/battery mass placement. Treat outputs as comparison-grade, not naval-architecture-final.