Analysis: 1/6 Scale Triangular Seastead Model Test
Based on video: Watch Scaled Video (Froude Corrected)
SCALING PARAMETERS (Froude Scaling, Scale Factor λ = 6)
--------------------------------------------------------
Length Scale (λ) : 6
Time Scale (√λ) : 2.449
Velocity Scale (√λ) : 2.449
Acceleration Scale (1) : 1.0 (Same g's in model and full scale)
Force/Mass Scale (λ³) : 216
Frequency Scale (1/√λ) : 0.408
Wave Height Scale (λ) : 6
Wave Period Scale (√λ) : 2.449
MODEL SPECIFICATIONS (Measured)
--------------------------------
Triangle Side Length : 10 ft (3.048 m)
Float Diameter : 8 in (0.203 m)
Float Length (Draft Max) : 4 ft (1.219 m)
Float Waterline Area (each): π * (4 in)² ≈ 50.3 in² (0.0324 m²)
Total Waterline Area (A_wp): ~151 in² (0.0973 m²) @ 1/3 draft
Displaced Volume (Model) : A_wp * Draft = 151 in² * 16 in ≈ 2416 in³ (0.0396 m³)
Model Mass (Est. ρ=1000) : ~39.6 kg (87 lbs) -- Very Light!
Target Draft (2/3) : 32 in (Waterline Area unchanged)
Target Displaced Volume : ~4832 in³ (0.0792 m³)
Target Mass (Ballasted) : ~79.2 kg (175 lbs)
FULL SCALE SPECIFICATIONS (λ = 6)
----------------------------------
Triangle Side Length : 60 ft (18.3 m)
Float Diameter : 4 ft (1.22 m)
Float Length : 24 ft (7.3 m)
Draft (Current 1/3) : 8 ft (2.44 m)
Draft (Target 2/3) : 16 ft (4.88 m)
Waterline Area/Float : π * (2 ft)² = 12.57 ft² (1.167 m²)
Total Waterline Area : 37.7 ft² (3.5 m²)
Displacement (Current) : ~19.5 tonnes
Displacement (Target) : ~39 tonnes
1. Wave Environment Estimation
Since I cannot watch the video directly, the following is a methodology for you to apply while watching the Froude-scaled video, followed by typical estimates for "waves from a tripod on shore" (likely wind chop / fetch limited).
How to Measure from Video:
- Pause on a frame where a wave crest passes the bow float.
- Reference: The float diameter is 8 inches (0.667 ft) model scale.
- Estimate wave height (trough to crest) in "float diameters".
- Multiply by 6 for full scale height.
| Observed Model Wave Height | Model Height (ft) | Full Scale Height (ft) | Sea State Description (Full Scale) |
|---|
| 0.5 x Float Dia (4 in) | 0.33 ft | 2.0 ft | Slight (Sea State 2) |
| 1.0 x Float Dia (8 in) | 0.67 ft | 4.0 ft | Moderate (Sea State 3) |
| 1.5 x Float Dia (12 in) | 1.0 ft | 6.0 ft | Rough (Sea State 4) |
| 2.0 x Float Dia (16 in) | 1.33 ft | 8.0 ft | Very Rough (Sea State 5) |
Typical "Shore Chop" Guess:
Waves generated near shore by wind (fetch limited) are usually steep and short. If the model floats (8" dia) are moving up/down roughly half their diameter (4 inches), the model waves are ~0.33 ft.
→ Full Scale Equivalent: ~2.0 ft (0.6 m) Significant Wave Height (Hs).
If the boat is really rocking, and waves are 1 float diameter high (8"), Full Scale = 4 ft (1.2 m).
Wave Period (Critical for Resonance Check)
In the slowed video (which represents Full Scale Time), time the period between crests passing a fixed point (or the boat pitching cycle).
- Full Scale Period ~ 3-4 sec: Short, steep wind chop. High excitation frequency.
- Full Scale Period ~ 6-8 sec: Typical coastal swell/chop mix.
- Full Scale Period > 10 sec: Long swell.
Heave Natural Period (Target Draft 16ft): Tn_heave ≈ 2π √(Mass / (ρg Aw)) ≈ 3.2 - 3.5 seconds.
Pitch Natural Period: Estimated 4.5 - 5.5 seconds (Waterplane Inertia ~ 3 * (1.167 m²) * (9.15m/√3)² ≈ 300 m⁴; Mass ~ 39,000 kg; GM_L ~ 1.5m).
Resonance Risk: If the video shows periods of 3-4 seconds (full scale time), you are near
Heave Resonance. If periods are 5-6 seconds, near
Pitch Resonance. The current light draft (8ft) raises natural frequencies (stiffer), potentially moving them away from typical chop, but reducing stability.
2. Motion Comparison: Tri-Seastead vs. 50ft Catamaran vs. 60ft Monohull
Assumption: Full Scale Sea State 3-4 (Hs = 3-5 ft, Tp = 4-6 sec). Target Ballasted Condition (Draft 16ft, Disp 39t).
| Metric | Tri-Seastead (60ft Side, 39t) | 50ft Catamaran (e.g. Lagoon 50) | 60ft Monohull (e.g. Swan 60) |
|---|
| Displacement |
~39,000 kg |
~25,000 - 30,000 kg |
~40,000 - 50,000 kg |
| Waterplane Area (Aw) |
3.5 m² (Tiny) |
~30 - 40 m² (Large) |
~25 - 30 m² (Medium) |
| Heave Stiffness (ρgAw) |
~34 kN/m |
~300 - 400 kN/m |
~250 - 300 kN/m |
| Heave Natural Period |
~3.3 sec |
~1.6 - 1.8 sec |
~1.7 - 1.9 sec |
| Pitch Inertia (Iyy) |
~2.5e6 kg·m² (Wide stance) |
~1.5e6 kg·m² |
~3.0e6 kg·m² (Deep ballast) |
| Pitch Stiffness (ρg∇GM_L) |
~550 kN·m/rad (Low GM_L) |
~1,500 kN·m/rad (High GM_L) |
~2,000 kN·m/rad (High GM_L) |
| Pitch Natural Period |
~5.0 sec |
~2.0 - 2.5 sec |
~2.5 - 3.0 sec |
| Motion Character |
Slow, Large Amplitude |
Quick, Snappy, Small Amp |
Moderate Period, Mod Amp |
Qualitative Motion Description
Tri-Seastead (Column Stabilized / Semi-Sub)
- Heave: Very compliant (soft spring). In 4ft waves, heave amplitude approaches wave amplitude (RAO ≈ 0.8 - 1.0). You follow the water surface. Low acceleration, large displacement.
- Pitch/Roll: Long natural period (~5s). If wave period is 4-5s, significant resonant amplification possible (RAO 1.5 - 2.5+). Motion feels "slow motion," "floating," "gentle giant." Deck accelerations are low unless hitting pitch resonance.
- Phase: Motions are largely in-phase with wave elevation (heave) or slope (pitch). No "slamming" or "hobby-horsing" typical of high waterplane vessels.
50ft Catamaran (High Waterplane, Low Inertia)
- Heave/Pitch: Very stiff (High Aw). Natural periods ~1.7s (well below wave energy). RAO < 0.5 usually.
- Feel: "Stiff," "jerky," "bouncy." High vertical accelerations (often 0.2g - 0.4g RMS in 4ft seas) because the boat tries to stay level while waves pass under hulls.
- Bridge Deck Slamming: Major source of high-frequency shock (impulse acceleration > 1g).
- Roll: Very high stiffness (wide beam), snappy roll, uncomfortable for some.
60ft Monohull (Ballasted, Medium Waterplane)
- Heave/Pitch: Stiffer than Tri, softer than Cat. Natural period ~2s.
- Feel: "Rhythmic," "rolling." Significant coupled Roll-Pitch (corkscrew motion).
- Accelerations: Vertical accel lower than Cat (0.1g-0.2g RMS), but Lateral/Transverse accel higher due to roll.
- Slamming: Bow emergence/immersion cycles cause impacts.
3. Acceleration Analysis
Key Physics: Froude scaling preserves accelerations (g's). Model Accelerations (g) = Full Scale Accelerations (g).
Estimating from Video (Model Scale)
- Track a corner of the triangle (or CG) vertically frame-by-frame.
- Fit $z(t) = A \sin(\omega t)$.
- Acceleration $a = -\omega^2 A$.
- In Model Time: $\omega_m = 2\pi / T_m$.
- In Full Scale Time (Video is already slowed): $\omega_{fs} = \omega_m / \sqrt{6}$. Amplitude $A_{fs} = 6 A_m$.
- Check: $a_{fs} = \omega_{fs}^2 A_{fs} = (\omega_m^2 / 6) * (6 A_m) = \omega_m^2 A_m = a_m$. Matches.
Predicted Full Scale Accelerations (Target Ballasted Condition, Hs=4ft, Tp=5s)
| Degree of Freedom | Est. RAO (Response Amplitude Operator) | Motion Amp (ft) (Half Wave Height) | Angular Freq (rad/s) (ω=2π/5) | RMS Accel (g) | Peak Accel (g) |
|---|
| Heave |
0.95 |
1.9 ft (0.58 m) |
1.26 |
0.046 g |
0.065 g |
| Pitch (at corner, L/2≈30ft from CG) |
1.8 (Near Resonance) |
3.6° (0.063 rad) |
1.26 |
0.051 g |
0.072 g |
| Roll (at corner) |
1.5 |
3.0° |
1.26 |
0.042 g |
0.060 g |
| Combined Corner (Vector Sum) |
- |
- |
- |
~0.08 g RMS |
~0.12 g Peak |
Comparison of RMS Vertical Acceleration (g) at Deck Level
| Vessel | Sea State 3 (Hs~3ft) | Sea State 4 (Hs~5ft) | Sea State 5 (Hs~8ft) |
|---|
| Tri-Seastead (Ballasted) | 0.03 - 0.05 g | 0.05 - 0.09 g | 0.08 - 0.15 g |
| 50ft Catamaran | 0.10 - 0.15 g | 0.15 - 0.25 g | 0.25 - 0.40 g (+ Slams) |
| 60ft Monohull | 0.06 - 0.10 g | 0.10 - 0.18 g | 0.18 - 0.30 g |
Conclusion on Comfort (ISO 2631 / MIL-STD-1472):
- Tri-Seastead: **"Not Uncomfortable" to "A Little Uncomfortable"** (0.05 - 0.1g RMS). Excellent for living/working. Caveat: Low frequency motion sickness (sopite syndrome) possible for sensitive individuals at 0.05-0.1Hz.
- Catamaran: **"Fairly Uncomfortable" to "Very Uncomfortable"** (0.15 - 0.3g RMS). High frequency vibration + slams cause fatigue.
- Monohull: **"A Little" to "Fairly Uncomfortable"**. Roll induces lateral acceleration; correlated with seasickness incidence.
4. Ballast Correction Prediction: Current (1/3 Draft) vs Target (2/3 Draft)
You asked: "Estimate if we had twice the weight and same waterline area what the accelerations would have been."
Physics Changes (Mass x2, Aw Constant, Draft x2)
- Mass (m): 2x
- Waterplane Area (Aw): Same (Columns vertical).
- Heave Stiffness (ρgAw): Same.
- Heave Natural Freq (ω_n): $\sqrt{k/m} \rightarrow \omega_{new} = \omega_{old} / \sqrt{2} \approx 0.707 \omega_{old}$.
- Heave Natural Period: Increases by $\sqrt{2} \approx 1.414$ (e.g., 2.3s $\rightarrow$ 3.3s model time).
- Inertia (Iyy): Mass doubles. CG lowers (ballast low in columns). Radius of Gyration ($k_{yy}$) likely similar or slightly larger. $I_{yy} \approx 2 \times I_{old}$.
- Pitch Stiffness (ρg∇GM_L): Displacement (∇) doubles. BM_L (Waterplane inertia / ∇) stays same (Aw same, ∇ double). KB rises slightly. KG drops significantly (ballast low). GM_L increases significantly (2x to 3x).
- Pitch Stiffness: Increases ~2.5x - 3x.
- Pitch Natural Freq: $\sqrt{K_{pitch}/I_{yy}} \rightarrow \sqrt{2.5 / 2} \approx 1.12 \times \omega_{old}$. Period drops slightly (~10% faster).
Acceleration Prediction: Current (Light) vs Ballasted (Heavy)
Assumption: Wave excitation frequency ($\omega_{wave}$) is fixed by the ocean (e.g., Full Scale Tp=5s, $\omega=1.26$ rad/s).
| Parameter | Current Model (1/3 Draft, Light) | Ballasted Model (2/3 Draft, 2x Mass) | Effect on Accel |
|---|
| Heave Nat Period (Full Scale) |
~2.3 sec |
~3.3 sec |
Moves away from typical chop (3-4s), closer to swell. Detuning. |
| Heave RAO @ Tp=5s (ω=1.26) |
~1.3 (Near Resonance!) |
~0.95 (Sub-resonant) |
Motion Amp ↓ ~27% |
| Pitch Nat Period (Full Scale) |
~4.0 sec (Est. Low GM) |
~5.0 sec (Higher GM) |
Moves closer to typical Tp=5-6s? Slight risk. |
| Pitch RAO @ Tp=5s |
~1.2 |
~1.8 (Potentially Higher!) |
Motion Amp ↑ ~50% (If hitting resonance) |
| Net Heave Accel (g) |
Higher (Resonant) |
Lower |
Improvement |
| Net Pitch Accel (g) |
Lower |
Potentially Higher |
Risk Area (Needs Damping) |
Specific Prediction for Your Next Test (Model Scale)
If you ballast to 2/3 draft (2x weight):
- Heave Motion (Vertical translation of CG): Amplitude will decrease by ~25-30%. The model will feel "heavier," less "bouncy" in heave. Accelerations (g) will DECREASE.
- Pitch Motion (Rotation): Amplitude will likely INCREASE by 20-50% because the natural period shifts from ~4.0s to ~5.0s (Full Scale), moving closer to the peak energy of typical wind waves (Tp=4-6s). The higher GM provides stiffness, but the mass increase dominates inertia less than stiffness increases.
- Visual Observation: The model will sit lower (obviously). In waves, it will heave less but pitch/roll more visibly. The corners will trace longer arcs.
- Accelerometer Data (Vertical at Corner): Heave component drops. Pitch component rises. Net Vertical Acceleration (g) at corners: ROUGHLY SIMILAR or SLIGHTLY HIGHER. (Heave down 30%, Pitch up 40% -> Vector sum ~ +5-10%).
- Phase: Heave will lag waves more (mass dominated). Pitch will be closer to in-phase with wave slope (stiffness dominated near resonance).
Recommendation: You MUST add damping (heave plates on bottom of columns, or flared bases) to control the Pitch RAO at resonance. Without damping, the ballasted version might feel "wallowy" in pitch in 4-6s waves.
5. Summary & Next Steps
- Wave Estimate: Measure float-diameter displacement in video. 1 Dia = 4ft Full Scale.
- Motions: Tri-Seastead = Low Frequency, Large Displacement, Low Acceleration (mostly). Superior comfort if pitch resonance damped.
- Cat/Mono: High Frequency, Small Displacement, High Acceleration. Fatiguing.
- Ballast Effect: Fixes Heave Resonance (Good). Risks Pitch Resonance (Bad). Add Heave Plates / Damping Skirts on column bottoms before next test.
- Instrumentation: Put an IMU (Arduino/ESP32 + MPU6050 or BNO055) on the model CG and one on a corner. Log at 50Hz. This gives you exact RAOs and Phase to validate these predictions.
Disclaimer: This analysis uses strip theory / simplified rigid body dynamics estimates. Actual performance depends on exact CG, VCG, damping (viscous + wave), mooring stiffness (tripod on shore), and wave directionality. The "Tripod on Shore" mooring adds significant stiffness/restraint not present in free-floating full scale.