Calculate simplified bulb geometry, bulb-to-displacement volume ratio, and Kracht-style nondimensional bulb parameters for preliminary hull-form studies.
Selected model: —
Protruding bulb volume VPR: — m³
Elliptical base area at FP ABASE: — m²
Volume-centroid position forward of FP xV: — m
Volume ratio VPR / ∇: —
Volume ratio as percentage: — %
Protruding bulb volume VPR: — m³
Dimensionless volume ratio VPR / ∇: —
Percentage of displaced volume: — %
Breadth parameter CBB: —
Length parameter CLPR: —
Depth parameter CZB: —
Cross-section parameter CABT: —
Lateral-area parameter CABL: —
Volumetric parameter CVPR: —
Volumetric parameter as percentage: — %
A bulbous bow is a shaped underwater extension of the forebody. Its hydrodynamic effect depends on how the pressure and wave systems generated by the bulb interact with those of the main hull.
Bulb performance cannot be described by volume alone. Protruding length, breadth, vertical position, transverse area, integration with the forebody, draft and operating speed all affect the result.
This page calculates simplified geometry and nondimensional bulb parameters. It does not predict resistance reduction or identify an optimum bulb.
| Symbol | Meaning | Usual unit |
|---|---|---|
| LPR | Length of the bulb protruding forward of FP | m |
| BB | Maximum bulb breadth used by the model | m |
| HB | Total height of the modelled bulb base section | m |
| ZB | Height of the foremost bulb point above the baseline | m |
| ABT | Transverse bulb area at FP | m2 |
| ABL | Area of the protruding bulb in the longitudinal centreplane | m2 |
| VPR | Bulb volume protruding forward of FP | m3 |
| ∇ | Ship displaced underwater volume | m3 |
Protruding volume: VPR includes only the part forward of FP. A real bulb may also require fairing volume aft of FP where it merges into the main hull.
The geometry tab represents the protruding bulb with a flat elliptical base at FP and a forward tip at LPR. It provides two idealised shapes.
VPR = πLPRBBHB / 6
Abase = πBBHB / 4
xV = 3LPR / 8
VPR = πLPRBBHB / 8
Abase = πBBHB / 4
xV = LPR / 3
The paraboloid contains less volume than the half-ellipsoid for the same length, breadth and height. Neither model reproduces the complete fairing of a real bulb into the forebody.
Consider the following simplified protruding bulb:
VPR = π/6 × 5.0 × 3.2 × 2.6 = 21.782 m3
Abase = π/4 × 3.2 × 2.6 = 6.535 m2
xV = 3/8 × 5.0 = 1.875 m forward of FP
VPR/∇ = 21.782 / 15,000 = 0.001452
The protruding model volume is 0.1452% of the ship's displaced volume.
The volumetric parameter compares the bulb volume protruding forward of FP with the vessel's displaced underwater volume:
CVPR = VPR / ∇
Some references report this value as a percentage:
CVPR,% = 100VPR / ∇
A ratio is a useful comparison quantity, but it does not show where the volume is placed or how the bulb interacts with the main-hull wave system.
Kracht's bulb description uses nondimensional parameters so that bulbs can be compared between ships of different size.
| Parameter | Formula | Description |
|---|---|---|
| CBB | BB / B | Bulb breadth relative to ship breadth |
| CLPR | LPR / LPP | Protruding length relative to ship length |
| CZB | ZB / TFP | Vertical bulb position relative to forward draft |
| CABT | ABT / AMS | Bulb area at FP relative to midship section area |
| CABL | ABL / AMS | Longitudinal bulb area relative to midship section area |
| CVPR | VPR / ∇ | Protruding bulb volume relative to displaced volume |
Use the following ship and bulb data:
CBB = 3.2 / 20 = 0.1600
CLPR = 5 / 120 = 0.04167
CZB = 3 / 8 = 0.3750
CABT = 6.535 / 156.8 = 0.04167
CABL = 12 / 156.8 = 0.07653
CVPR = 21.782 / 15,000 = 0.001452
Expressed as a percentage, CVPR = 0.1452%.
Descriptor, not recommendation: these coefficients report the entered geometry. Selecting an optimum set requires resistance evidence for the vessel's intended drafts and operating speeds.
The geometric model calculates the area of its full elliptical base. That result is not automatically identical to the ABT required by the Holtrop–Mennen method.
Holtrop ABT is the relevant immersed transverse bulb area at the position where the still-water surface intersects the stem. The correct value depends on the actual bulb section and waterline.
Holtrop also uses hB, the height of the centroid of that transverse area above the keel. This is different from the Kracht depth parameter ZB, which describes the vertical position of the foremost bulb point.
A bulb changes the forebody pressure field and wave pattern. A geometry that performs well at one speed and draft may provide less benefit, or additional resistance, under another condition.
A design assessment should therefore consider the vessel's operating profile rather than only one nominal design point.
Changes in loading condition can alter:
A simplified protruding model represents an additive volume forward of FP. A real bulb may instead be integrated into the complete forebody, redistributing volume aft of FP as part of a faired hull surface.
The same protruding volume can therefore belong to several different sectional-area curves and hull shapes.
This calculator can determine:
It cannot determine:
Design limitation: bulb design is a hydrodynamic hull-form problem. Geometry calculations are useful for defining candidates, but resistance performance should be checked with an appropriate prediction method, model tests, CFD or validated parent-vessel data.
NauticalSolver calculators are intended for preliminary engineering, study and independent checking. Use vessel-specific geometry and validated hydrodynamic analysis for final bulbous-bow design.