Helical Mooring Screw Installation Analysis

Dinghy-Driven "Circle Method" for Prototype Seastead (Caribbean Sand)

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1. Core Physics & Assumptions

Dinghy Thrust & Torque Generation

Parameter	Value	Notes
Engine Power	10 HP (7.5 kW)	Standard portable 4-stroke
Prop Diameter / Pitch	~9.25" x 8" - 10"	Typical for 10 HP
Bollard Pull (Static Thrust)	~220 – 260 lbs	Empirical: ~22–26 lbs/HP. We use 250 lbs for calcs.
Lever Arm Length	10 ft	User specified
Max Theoretical Torque @ Anchor	2,500 ft-lbs	250 lbs × 10 ft
Realistic Avg. Torque (Slip, Angle, RPM drop)	1,500 – 1,800 ft-lbs	Dinghy circles at 2–3 kts; prop slip ~30-40%; lever angle < 90°.

Soil Profile: "Typical Caribbean Sand"

• Type: Carbonate sand (crushed coral/shells), often medium dense ($N_{60} \approx 10–30$).
• Friction Angle ($\phi$): $32^\circ–36^\circ$ (higher than silica sand due to angular particles).
• Unit Weight ($\gamma'$): ~60–70 pcf (submerged).
• $K_t$ Factor (Torque-to-Capacity): 7–10 ft^-1 for Type SS (Square Shaft) or small Pipe Shaft. We assume 9 ft^-1 for 1.5" sq bar (6" helix) and 7 ft^-1 for larger shaft (12" helix).
• Helix Pitch: Standard **3 inches** (1 ft per 4 revs).

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2. Case A: 6-inch Diameter Helix → 7 ft Embedment

Torque Profile vs Depth

Depth (ft)	Est. Torque Req'd (ft-lbs)	% of Dinghy Max (2,500)	Status
1	150	6%	Easy
3	450	18%	Easy
5	750	30%	Moderate
7 (Target)	~1,050	42%	Comfortable

*Calc: $T \approx 2.0 \times 6^2 \times z / 144 \times 12 \approx 1.0 \times 36 \times z / 12 \dots$ simplified to ~150 ft-lbs/ft depth for 6" in this sand.*

Time Estimate

Step	Calculation	Time
Total Revolutions	7 ft × 12 in/ft ÷ 3 in pitch = 28 Revs	--
Circle Radius	~12 ft (Lever 10ft + Dinghy offset)	--
Circle Circumference	2 × π × 12 ≈ 75 ft	--
Dinghy Speed (Low Gear)	~2.5 knots ≈ 4.2 ft/sec	--
Time per Revolution	75 ft / 4.2 ft/s ≈ 18 seconds	--
Pure Driving Time	28 revs × 18 sec = ~8.5 minutes	8.5 min
Setup / Reposition / Restarts	Anchor starting, rope handling, alignment	+ 10–15 min
TOTAL ESTIMATE		15 – 25 Minutes

Lever Bar Spec (6-inch Helix)

Property	Recommendation
Max Bending Moment (at eye)	2,500 ft-lbs (30,000 in-lbs)
Material	Schedule 80 Steel Pipe (Black Iron) or Solid Round Bar
Option 1: Schedule 80 Pipe	2.5" Nominal (OD 2.875", Wall 0.276") Section Modulus $Z \approx 1.06$ in³ → Stress = 28 ksi (Safe, $F_y=36$ ksi)
Option 2: Solid Round Bar	1.75" Diameter (45 mm) $Z = \pi d^3/32 \approx 1.31$ in³ → Stress = 23 ksi (Very Safe)
Weight (10 ft length)	Pipe: ~36 lbs | Solid Bar: ~55 lbs
Eye Connection	Weld 1/2" plate lug with 1.5" hole to pipe end; reinforce with gussets. Critical failure point.

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3. Case B: 12-inch Diameter Helix → 11 ft Embedment

Torque Profile vs Depth

Depth (ft)	Est. Torque Req'd (ft-lbs)	% of Dinghy Max (2,500)	Status
1	450	18%	Easy
3	1,350	54%	Working Hard
5	2,250	90%	Stall Risk High
7	3,150	126%	IMPOSSIBLE
9	4,050	162%	--
11 (Target)	~4,950	198%	IMPOSSIBLE

*Calc: Torque scales with Area ($D^2$). 12" helix has 4x area of 6". Torque ~600 ft-lbs/ft depth.*

Why it fails

• Physics Limit: A 10 HP prop simply cannot generate 5,000 ft-lbs of torque at the anchor. You would need ~20 HP at the prop (or a 20 ft lever arm, which is unmanageable).
• Stall Behavior: At ~5 ft depth, the dinghy will spin its prop (cavitate) or the engine will lug down and die. The anchor stops advancing.
• Caribbean Sand Variability: If you hit a dense layer ($N>30$) or coral rubble at 3 ft, it stalls immediately.

Lever Bar Spec (12-inch Helix) — *If attempting*

Since torque demand is ~2x the 6" case, the bar must be significantly stronger. The dinghy connection becomes the weak link.

Property	Recommendation
Design Torque (Target)	5,000 ft-lbs (60,000 in-lbs)
Option 1: Schedule 80 Pipe	3.5" Nominal (OD 4.0", Wall 0.318") $Z \approx 2.75$ in³ → Stress = 22 ksi (Safe). Weight: ~75 lbs (10 ft). Heavy to handle on dinghy.
Option 2: Solid Round Bar	2.5" Diameter (63 mm) $Z \approx 3.8$ in³ → Stress = 16 ksi (Very Safe). Weight: ~110 lbs (10 ft). Requires 2 people to lift.
Eye Connection	Must be forged/upset end or heavy welded lug (1" plate). Standard weld on pipe OD will fail at 5,000 ft-lbs. Consider a commercial Kelly Bar adapter (used in mini-piling).
Lever Length	Keep at 10 ft. Longer lever = more torque but slower circles & higher bending moment on bar.

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4. Lever Bar Design Deep Dive

The "Eye Connection" Problem

The highest stress is not in the middle of the bar, but at the weld/joint connecting the bar to the anchor eye. This sees the full 2,500–5,000 ft-lbs moment plus eccentric prying loads.

• Don't: Drill a hole in the end of a pipe and put a bolt through it. The pipe wall will ovalize/tear.
• Don't: Weld a simple 1/2" plate tab to the end of a Schedule 40 pipe for 5,000 ft-lbs.
• Do (DIY): Slide a 12" long piece of heavy wall tube (e.g., 3" OD x 0.5" wall) over the end of your lever bar. Weld it fully around (360°) with 3/16" fillets. Drill the 1.5" hole through this thick sleeve. This moves stress into thick material.
• Do (Pro): Buy a "Square Drive Kelly Bar" section (e.g., 1.5" or 2" Square) from a foundation supply house (e.g., PierTech, Hubbell, MacLean Dixie). They have forged square sockets on one end and pin holes on the other. Weld a round sleeve on the other end for your lever. Cost: ~$150–$300. Guaranteed strength.

Ideal Bar Material Summary

Helix Size	Best "DIY" Bar	Weight	Best "Pro" Bar	Cost Est.
6-inch	2.5" Sch 80 Pipe (10 ft) + 3"x0.5" wall sleeve at eye	~40 lbs	1.5" Solid Square Bar (Kelly Bar section)	$80 (Pipe) / $200 (Kelly)
12-inch	3.5" Sch 80 Pipe (10 ft) + 4"x0.5" wall sleeve at eye	~80 lbs	2" Solid Square Bar (Kelly Bar section)	$180 (Pipe) / $350 (Kelly)

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5. Operational Procedure & Safety Checklist

1. Pre-Set Anchors: Screw all 6 anchors in by hand/diver to 2–3 ft (past the "wobble zone") before hooking dinghy. Ensures they start vertical.
2. Rigging: Use a 5/8" Dyneema/Spectra rope (breaking strength > 20,000 lbs, near zero stretch). Nylon stretches 20% → stores dangerous energy if bar snaps or anchor breaks free.
3. Rope Attachment: Connect rope to lever bar end via soft shackle or spliced eye. No metal shackles at the lever end (missile hazard if failure).
4. Dinghy Setup: Attach rope to a stern-mounted tow bridle (two points on transom), NOT a single cleat. Prevents dinghy spin-out.
5. Driving Pattern: Drive wide, slow circles. Keep rope tension high. If engine lugs (RPM drops >20%), STOP. You are at torque limit. Do not "power through."
6. Monitoring: Have a spotter watch the anchor shaft (if visible) or a tell-tale on the rope. Count revolutions (pitch = 3") to track depth.
7. Safety Zone: NO ONE in the "snap-back zone" (cone 90° behind lever bar). If rope/bar fails, it recoils at lethal speed.
8. Retrieval Plan: How to get the bar off the anchor eye at 11 ft depth? Design the eye connection so a diver can pull a pin, or the bar lifts straight off (T-handle top).

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6. Recommendation for Your Prototype

1. Use 6-inch Helices (Target 7 ft). They install in 20 mins with your 10 HP dinghy. Buy 3x per corner (6 total) to match the 12" capacity.
2. Fabricate 2x Lever Bars from 2.5" Sch 80 Pipe (10 ft) with heavy sleeves at the eye end. Weight ~40 lbs each—manageable by one person on a dinghy.
3. Buy 200 ft of 1/2" Dyneema (SK78). Low stretch, floats, UV resistant.
4. Test in Sandbox First: Drive one anchor at the boatyard/dock in 5 ft sand. Verify torque/rpm behavior before going to site.
5. Scale Up Later: For the full-scale seastead (27,500 lbs disp), you will need a hydraulic drive head (skid steer / mini excavator / dedicated anchor drive) on a barge. The dinghy method does not scale to 12"/14" helices at 20+ ft depths.