⚓ Hydrodynamics & Under Keel Clearance
Advanced Ship Squat & UKC Calculator
Professional hydrodynamic estimation of dynamic ship squat, dynamic draught, and under keel clearance (UKC) based on validated Dr. C.B. Barrass & PIANC guidelines.
🌊 1. Barrass Formula (Standard / Express)
For open deep water or standard confined fairway (divisor 100 or 50). Minimum input data required.
📐 2. Advanced (Channel Blockage Factor S)
Precise channel cross-section accounting: S = As / Ac via Dr. Barrass (2004) hydrodynamic formula.
🚢 Passage & Vessel Particulars
kn
Vessel speed through water (STW). Squat increases proportionally to the square of ship speed (V²)!
m
Actual water depth accounting for charted depth and height of tide (Charted Datum + Tide).
m
Maximum static draught in resting condition (deepest draught between bow and stern) in current water density.
Cb
Leave blank to auto-calculate from Lwl, B, Δ or check Navlib reference ↗
Hull fullness coefficient (0.80–0.88 for tankers/bulkers; 0.55–0.70 for container vessels). If Cb > 0.70, vessel squats by the head!
In confined waters, hydrodynamic bottom suction is approximately twice as high as in open deep water at identical speed.
m
Average cross-sectional bed width of the channel used to calculate fairway area Ac = Bc × H.
m
Length of the ship at the operating waterline. Used for Cb auto-calculation.
m
Moulded breadth of the ship at midship section. Required to determine midship submerged cross-section As.
t
Vessel displacement in metric tonnes. Sea water density is assumed at 1.025 t/m³.
Cm
Midship section coefficient. Typically 0.98 for commercial merchant vessels.
Safe Navigational Margin
Dynamic under keel clearance satisfies international safety recommendations.
Maximum Squat
0.00 m
Via Barrass Formula
Dynamic Draught
0.00 m
Static: 0.00 m
Dynamic UKC
0.00 m
Static: 0.00 m
Trim Tendency
By the Bow
For Cb > 0.70
📊 Dynamic Squat & UKC Cross-Section Profile
Scalable Vector View
📋 Comprehensive Hydrodynamic Protocol
| Hydrodynamic Factor | Symbol | Calculated Value | Navigational Assessment |
|---|---|---|---|
| Applied Block Coefficient | Cb | 0.820 | Full-form hull (Tanker/Bulker) → Trim by the bow |
| Critical Shallow-Water Wave Speed | Vcr | 24.2 kn | Safe subcritical speed range |
| Froude Depth Number | Fnh | 0.43 | < 0.60 (Linear hydrodynamics zone) |
| Channel Blockage Factor | S (As / Ac) | 0.245 | Moderate fairway restriction |
| Static Under Keel Clearance | UKC stat | 2.50 m | At rest condition (H - T) |
| Dynamic Under Keel Clearance | UKC dyn | 1.65 m | 12.2% of static draught (Meets criteria) |
📚 Navigator's Guide: Ship Squat Physics & UKC Criteria (Click to Expand)
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1. Physical Nature of Ship Squat
When a vessel moves through shallow water or a restricted fairway, water displaced by the hull rushes backwards along the sides and underneath the keel at accelerated velocity (return flow). In accordance with Bernoulli's theorem, this velocity increase causes a sharp drop in hydrodynamic pressure beneath the hull, generating a downward suction force and vertical sinkage.
2. Hull Geometry Influence on Trim (Dr. Barrass Trim Rule)
- Cb > 0.72 (Tankers, Bulk Carriers): The center of maximum pressure drop is located forward of amidships. The vessel experiences Bow Squat (trim by the head), drastically reducing clearance under the bulbous bow.
- Cb < 0.68 (Container ships, Ro-Ro, Passenger liners): Due to fine forward waterlines, maximum suction concentrates aft. The vessel experiences Stern Squat (trim by the stern).
- 0.68 ≤ Cb ≤ 0.72: Symmetrical sinkage occurs approximately on an Even Keel.
3. Critical Wave Speed & Froude Depth Number (Fnh)
The velocity of a shallow water gravity wave is defined by Vcr = √(g · H). As vessel speed approaches 0.70 · Vcr (Fnh > 0.65), the ship enters the transcritical speed regime: wave resistance surges exponentially, squat approximately doubles, and severe steering instability can occur. It is strongly recommended to maintain V < 0.60 · Vcr.
4. Recommended UKC Safety Criteria (IMO / PIANC)
- Open Sea / Coastal Waters: Dynamic UKC ≥ 20% of static draught (or minimum 1.5–2.0 m).
- Canals & Port Approaches: Dynamic UKC ≥ 10% of static draught (or minimum 1.0 m).
- IMPORTANT: In the presence of swell or ship rolling/pitching, additional clearance equal to maximum motion amplitude must be added to dynamic draught!
Navigational Notice: This calculator is a supplementary passage planning aid. The Master and Officer of the Watch (OOW) retain ultimate responsibility for safe navigation, adequate under keel clearance (UKC), and accounting for swell, roll, squat, and water density variations (STCW / Bridge Procedures Guide).
Hydrodynamics Core Hub
PIANC // DR. BARRASS MODELS
Hydrodynamic Ship Squat & Dynamic Under Keel Clearance (UKC) Estimation
Navigating in confined shallow fairways, canals, and port approaches introduces severe grounding hazards resulting from hydrodynamic sinkage (Ship Squat)[cite: 5, 6]. In compliance with SOLAS Chapter V (Regulation 34), IMO Resolution A.893(21) for Voyage Planning, and the ICS Bridge Procedures Guide, navigating bridge teams and marine pilots must continuously verify depth-to-draft ratios (H/T) and determine dynamic bodily sinkage along each shallow transit leg[cite: 5].
The NavLib Squat & UKC Calculator provides marine professionals with an empirical hydrodynamic computation engine based on validated formulations by Dr. C.B. Barrass and PIANC guidelines (World Association for Waterborne Transport Infrastructure)[cite: 5]. The module computes dynamic bodily sinkage, longitudinal trim tendencies (Bow vs. Stern Squat), shallow-water critical wave speed (Vcr), and net dynamic under keel clearance margins[cite: 5].
Barrass Hydrodynamics
Open & Confined Formulations
Rapid evaluation via standard Barrass formulas for open waters (divisor 100) and restricted fairways (divisor 50) scaled directly by the square of vessel speed.
Restricted Waterways
Blockage Factor Engine
Advanced channel constriction modeling resolving blockage factor S = As / Ac using immersed midship cross-section, channel breadth, and midship coefficient Cm[cite: 5].
Safety Auditing
PIANC & Froude Verification
Automated auditing of depth Froude number (Fnh < 0.60), critical shallow-water wave speed (Vcr), and net dynamic UKC against statutory Company SMS criteria[cite: 5].
Frequently Asked Questions: Ship Squat & UKC (FAQ)
Should Speed Through Water (STW) or Speed Over Ground (SOG) be used for calculating squat?
Always use Speed Through Water (STW). The Bernoulli suction effect and pressure drop beneath the flat bottom are entirely generated by the relative velocity of water flowing around the hull. If a vessel maintains an SOG of 8 knots against a 3-knot head current, the flow rate around the hull is 11 knots, and squat must be calculated using 11 knots.
How does the hull block coefficient (Cb) govern dynamic trim tendencies?
According to Dr. Barrass's empirical trim rule:
- Cb > 0.72 (Tankers, Bulk Carriers): full forward lines concentrate hydrodynamic suction in the forward third. The vessel trims by the bow (Bow Squat).
- Cb < 0.68 (Container Ships, Passenger Liners): fine forward lines allow smooth water displacement, while run lines accelerate flow aft. The vessel trims by the stern (Stern Squat).
- 0.68 ≤ Cb ≤ 0.72: bodily sinkage occurs nearly parallel to the baseline (Even Keel).
What is critical shallow-water wave speed (Vcr) and the trans-critical regime?
The propagation speed of a gravity wave on depth H is:
Vcr = square_root(g * H), where g = 9.81 m/s² and H is water depth in meters. The depth Froude number is Fnh = V / square_root(g * H). If vessel speed exceeds 0.65–0.70 * Vcr (Fnh > 0.60), the ship enters the trans-critical zone: wave drag escalates dramatically, stern sinkage deepens abruptly, and steering control degrades. Safe seamanship mandates keeping transit speed well below 0.60 * Vcr.
What are the standard industry benchmarks for safe Under Keel Clearance (UKC)?
Standard maritime safety criteria prescribed across Company SMS manuals and PIANC publications:
- Open Sea and Coastal Waters: dynamic UKC ≥ 20% of static maximum draft;
- Approach Channels, Canals, and Fairways: dynamic UKC ≥ 10% of static draft (or minimum 1.0–1.5 meters of clear water);
- Alongside Berth during Cargo Ops: static clearance of not less than 0.3–0.5 meters accounting for low water tides.
What is the most effective immediate countermeasure if UKC drops dangerously?
The fastest and most effective action is immediately reducing engine RPM. Because squat scales with the square of speed (V²), reducing transit speed by just 2 to 3 knots decreases squat sinkage by 40% to 50%, instantly restoring water clearance beneath the keel.
Regulations:
SOLAS V/34, IMO Res. A.893(21), PIANC MarCom WG 121
Models:
Dr. C.B. Barrass (Open Water, Confined Canal, Blockage S)
Reporting:
Isolated DOM Print (A4), Excel (.CSV), Clipboard Log
