Ship Stability, Theory and Practice • Volume One: Foundations of Ship Stability

Chapter 5 — Fresh Water Allowance, Dock Water Allowance and the Load Lines

The density story reaches the rule book

Learning objectives

By the end of this chapter you will be able to:

  1. sketch the load line mark and name every line: deck line, ring, TF, F, T, S, W and WNA;
  2. state what the statutory freeboard is and where it is measured;
  3. calculate the fresh water allowance from FWA = ∆Summer ÷ (4 × TPCSW) and explain where the formula comes from;
  4. calculate the dock water allowance from DWA = ((1025 − ρDW) ÷ 25) × FWA;
  5. explain the seasonal marks and the one forty eighth seasonal allowance;
  6. solve dockside loading problems: how much cargo may be loaded so that the ship floats at her permitted mark on reaching the sea;
  7. relate every figure to the MV Ninja load line data in the booklet.

Chapters 1 and 4 established the physics: a ship floats deeper in lighter water, and every tonne moves her a calculable number of centimetres. This chapter is where the physics meets the law. The load line mark on the ship's side is the visible edge of the Load Line Regulations, and the two allowances of this chapter, one for fresh water and one for dock water, are what let an officer load legally in a river or a dock and still be exactly at the permitted mark when the ship reaches the sea.

5.1 The load line mark

Amidships on each side every ship carries the load line mark: a ring 300 mm in outside diameter with a 25 mm band and a horizontal line 25 mm thick through its centre, a deck line above it, and forward of the ring a vertical line with the seasonal lines on its forward side and the fresh water lines on its after side. The upper edge of the line through the ring marks the summer load waterline, and the statutory freeboard is the vertical distance from the upper edge of the deck line down to it: 3920 mm for MV Ninja. The letters beside the ring identify the assigning authority. The ship must never be submerged beyond the line applicable to the zone, the season and the water she floats in.

The load line mark of MV Ninja deck line summer freeboard 3920 mm N A TFFTSW FWA 216 mm 1/48 of summer draught 200 mm The ring is 300 mm outside diameter with a 25 mm band; the horizontal lines are 25 mm thick. The upper edge of the line through the centre of the ring marks the summer load waterline, and the statutory freeboard is measured from the upper edge of the deck line down to it. The letters beside the ring identify the assigning authority.
Figure 5.1   The load line mark of MV Ninja. The upper edge of the line through the ring is the summer load waterline; the comb carries the seasonal and fresh water marks. There is no separate WNA line: it is marked, 50 mm below W, only on ships of 100 m or less in length, and MV Ninja is 148 m.

5.2 The fresh water allowance

Load the ship to her summer mark in salt water and then float her in fresh: Chapter 1 tells us she sinks, because a greater volume must be displaced to carry the same weight. The distance she sinks, at the summer displacement, is the fresh water allowance, and the F mark is painted exactly one FWA above the S mark so that an officer loading in fresh water can load to F, knowing the ship will rise precisely to S as she reaches the sea.

The F mark is the summer mark's fresh water twin F S Salt water: loaded to the S mark F S Fresh water: loaded to the F mark same ship, same displacement FWA 216 mm Loaded to F in fresh water, the ship rises exactly to S as she reaches the sea: the F mark sits one fresh water allowance above the summer line.
Figure 5.2   Loaded to the F mark in fresh water, the ship rises exactly to the S mark in salt water. The gap between them is the FWA.

The allowance comes from comparing the volumes the same displacement requires in the two waters. The extra volume in fresh water is a thin slab, waterplane area times FWA, and when the slab is equated to the volume difference and the waterplane written in terms of the salt water TPC, everything cancels except two figures the officer already has:

FWA = ∆Summer ÷ (4 × TPCSW)   (mm) MCA formula sheet, September 2020
Where the formula comes from fresh water line salt water line slab of volume = Aᴡ × FWA The displacement is the same in both waters, so the extra volume needed in fresh water is: ∆÷1.000 − ∆÷1.025 = ∆ × 25 ÷ (1000 × 1025) That volume is the shaded slab, Aᴡ × FWA. Setting the two equal, and writing Aᴡ in terms of the salt water TPC, the areas cancel and only ship figures remain: FWA = ∆ˢᵘᵐᵐᵉʳ ÷ (4 × TPCˢᴡ) answer in millimetres; MCA formula sheet, September 2020 For MV Ninja: FWA = 30456 ÷ (4 × 35.28) = 216 mm, exactly the figure printed in her data booklet and exactly the distance from the S mark up to the F mark.
Figure 5.3   Where the formula comes from: the slab of extra volume in fresh water, with the waterplane area written as the TPC.
Worked example 5.1

Calculate the fresh water allowance of MV Ninja (summer displacement 30456 t, salt water TPC at the summer draught 35.28 t), and compare it with the data booklet.

FWA = ∆Summer ÷ (4 × TPCSW) = 30456 ÷ (4 × 35.28) = 30456 ÷ 141.12 = 215.8 = 216 mm

The booklet prints 216 mm, and its F row confirms the geometry: the F freeboard of 3704 mm is exactly the summer freeboard of 3920 mm less one FWA.

5.3 The dock water allowance

Most loading berths are neither ocean nor river but something in between: dock water. The permitted submergence of the summer mark then lies proportionally between the two extremes, nothing at 1025 kg/m³ and the full FWA at 1000, and the interpolation is a straight line:

DWA = ((1025 − ρDW) ÷ 25) × FWA MCA formula sheet, September 2020
The dock water allowance is a straight line between two known points 100010051010101510201025 054108162216 fresh water: full FWA = 216 mm salt water: no allowance dock water 1010: DWA = 129.6 mm dock water density ρᴅᴡ (kg/m³) allowance (mm) DWA = ((1025 − ρᴅᴡ) ÷ 25) × FWA
Figure 5.4   The DWA is a straight line interpolation between no allowance in salt water and the full FWA in fresh.
Worked example 5.2

MV Ninja loads in dock water of density 1010 kg/m³. By how much may her summer mark be submerged on completion of loading?

DWA = ((1025 − 1010) ÷ 25) × 216 = (15 ÷ 25) × 216 = 129.6 mm

She may float 129.6 mm deeper than the S mark in this dock, and will rise exactly to the mark in salt water.

Worked example 5.3

What maximum mean draught may MV Ninja have on sailing from the dock of Worked example 5.2, if she is to be at her summer marks at sea?

maximum draught = summer draught + DWA = 9.600 + 0.1296 = 9.730 m

5.4 The seasonal marks

The comb carries more than S and F. The winter mark W sits one seasonal allowance, one forty eighth of the summer draught, below S; the tropical mark T the same distance above it. For MV Ninja the seasonal allowance is 9.600 ÷ 48 = 0.200 m, so W is at 9.400 m and T at 9.800 m. The tropical fresh mark TF sits one FWA above T, just as F sits one FWA above S. A Winter North Atlantic line, WNA, is marked 50 mm below W only on ships of 100 m or less in length; on MV Ninja, at 148 m, it coincides with W and is not marked. Which mark governs depends on the load line zone the ship is in and the season of the year: the zones divide the world's oceans by the weather that may be expected there, and the deepest permitted loading for a voyage is set by the most restrictive zone it crosses.

The world's load line zones, in schematic a simplified band picture: the real chart of zones and seasonal dates is in the Load Line Regulations Winter zone (north)Summer zoneTropical zoneSummer zoneWinter zone (south) equator a voyage crossing zones must comply with each zone's mark as it enters that zone In a winter zone the W mark applies; in the tropics the T mark; and the season of the year moves some boundaries. Plan the deepest loading around the most restrictive zone of the voyage.
Figure 5.5   The load line zones in schematic. The applicable mark changes as the ship crosses from zone to zone.

The complete load line data of MV Ninja, from the booklet, now reads as one connected family: the salt water marks spaced by the 200 mm seasonal allowance, and each fresh mark one FWA above its salt twin. At a fresh water mark the ship carries the displacement of its salt water twin, 30456 t at F and 31164 t at TF, because she rises exactly to S or T on reaching the sea: her mass is fixed and it is the volume of displacement that grows. The salt water column of the hydrostatic table at 9.816 m or 10.016 m does not apply, since she is not in salt water at those draughts.

MV Ninja's load line data, from the booklet salt water marks are spaced by the seasonal allowance of 200 mm; the fresh marks sit one FWA (216 mm) above their salt twins TF Tropical fresh draught 10.016 m ∆ = 31164 t F Summer fresh draught 9.816 m ∆ = 30456 t T Tropical draught 9.800 m ∆ = 31164 t S Summer draught 9.600 m ∆ = 30456 t W Winter draught 9.400 m ∆ = 29751 t Which mark applies depends on the zone, the season and the water: the ship must never be submerged beyond the applicable line at sea.
Figure 5.6   MV Ninja's five load lines. Every spacing in this ladder comes from two numbers: the seasonal allowance of 200 mm and the FWA of 216 mm. At F and TF the ship is in fresh water and carries the displacement of S and T respectively, 30456 t and 31164 t.
Worked example 5.4

Using the booklet, state MV Ninja's maximum permitted draught and the corresponding displacement (a) in a winter zone and (b) in a tropical zone, both in salt water, and (c) verify the tropical fresh draught.

(a) Winter: draught 9.600 − 0.200 = 9.400 m, displacement 29751 t.

(b) Tropical: draught 9.600 + 0.200 = 9.800 m, displacement 31164 t.

(c) Tropical fresh: TF = T + FWA = 9.800 + 0.216 = 10.016 m, exactly the booklet figure. The whole comb is generated by two allowances.

5.5 Loading in dock water: the complete problem

Everything in this chapter now assembles into the classic dockside question: the officer reads where the water stands against the mark, works out how much deeper the ship may legally go, and converts those millimetres into cargo through the TPC, corrected for the dock water. Watch the pieces of Chapters 4 and 5 mesh:

Worked example 5.5

MV Ninja is completing loading in dock water of RD 1.015. The water surface stands 60 mm below the upper edge of her summer mark. How much more cargo may she load so as to float at her summer marks in salt water? (Salt water TPC at the summer draught 35.28 t.)

DWA = ((1025 − 1015) ÷ 25) × 216 = 86.4 mm

permitted sinkage = 60 + 86.4 = 146.4 mm = 14.64 cm

TPCDW = (TPCSW ÷ 1025) × ρDW = (35.28 ÷ 1025) × 1015 = 34.94 t

cargo = 14.64 × 34.94 = 511.5 t

Every line of this working came from an MCA sheet formula: the DWA, the TPC conversion, and sinkage = w ÷ TPC run backwards. This is the form the question takes in examinations, and at real loading berths.

How much more can she load? Reading the answer at the mark F S highest permitted waterline in this dock upper edge of S mark water level now 60 mm still below S DWA 86.4 mm (dock RD 1.015) 146.4 mm total sinkage available sinkage available = 60 + 86.4 = 146.4 mm = 14.64 cm cargo = 14.64 × TPC in the dock water (34.94 t) = 511.5 t
Figure 5.7   Worked example 5.5 at the ship's side: 60 mm still to go to the mark, plus 86.4 mm of dock water allowance, gives 146.4 mm of legal sinkage.
Worked example 5.6

In the same dock (RD 1.015), the water surface stands 30 mm above the upper edge of the summer mark. Is MV Ninja overloaded, and how much cargo may she still load?

She is not overloaded: in this dock the mark may legally be submerged by the DWA of 86.4 mm, and only 30 mm of it is used.

permitted further sinkage = 86.4 − 30 = 56.4 mm = 5.64 cm

cargo = 5.64 × 34.94 = 197.1 t

A submerged summer mark in dock water is not by itself a sign of overloading. The test is the mark plus the allowance, never the mark alone.

Interactive: the allowance calculator

Enter any ship's summer displacement and salt water TPC, then slide the dock density: the FWA and DWA are computed from the two MCA formulas.

FWA = – mm ρDW = 1010 kg/m³ DWA = – mm

Interactive: the dockside loading laboratory

MV Ninja lies at the berth. Set the dock water density and where the water stands relative to the S mark (negative means below the mark, positive means the mark is already submerged). The laboratory finds the cargo she may still load, and the mark drawing responds.

ρ = 1015
DWA = – mm Sinkage available: – mm TPC in dock water: – t Cargo she may load: – t
F S

Chapter summary

Self test questions

Work each question with pencil, paper and the MV Ninja data booklet first. Your score appears in the bar below.

Chapter 5: FWA, DWA and the Load LinesSelf test score: 0 / 10