A draft survey weighs bulk cargo by measuring how much deeper the ship sits in the water after loading. This calculator takes the six standard draft readings, forms the trim-corrected quarter mean, applies the dock water density correction to the hydrostatic displacement, and reports cargo as the difference between the initial and final surveys.
How it works
The six drafts are combined into a single corrected mean, displacement is read from the ship’s tables at that mean and scaled for water density, and cargo is the change in net displacement:
mean fwd/aft = (forward + aft) / 2
mean midship = (port + starboard) / 2
quarter mean = (forward + aft + 6 × midship) / 8
corrected disp = table displacement × (actual density / 1.025)
cargo = |final corrected disp − initial corrected disp|The 6× weighting on the midship reading in the quarter mean compensates for hull hogging or sagging, which bends the ship between the perpendiculars and would otherwise bias the mean draft.
Why the quarter mean, not a simple average
A ship’s hull flexes under its own weight and the distribution of cargo. In hogging, the midship section rises relative to the ends; in sagging, it dips. A simple average of forward and aft drafts ignores this deflection and gives a biased displacement. The quarter mean, with its 6× midship weighting, was derived to minimise this error by giving proportional weight to the body of the ship where most displacement occurs.
Worked example
Suppose an initial survey reads: forward port 5.41 m, forward starboard 5.39 m (mean fwd 5.40 m), aft port 6.81 m, aft starboard 6.83 m (mean aft 6.82 m), midship port 5.95 m, midship starboard 5.97 m (mean mid 5.96 m).
Quarter mean: (5.40 + 6.82 + 6 × 5.96) / 8 = (5.40 + 6.82 + 35.76) / 8 = 47.98 / 8 = 5.998 m
From the ship’s hydrostatic tables at 5.998 m, displacement might read 22,850 tonnes at salt water density 1.025. The dock water hydrometer reads 1.018. Corrected displacement: 22,850 × (1.018 / 1.025) = 22,694 tonnes.
Repeat the calculation for the final survey after loading (which will show a deeper mean draft and higher corrected displacement), then subtract deductibles (ballast, fresh water, fuel, lubricating oil, constants) from each. The difference between final and initial net displacements is the cargo loaded.
Reading the draft marks accurately
Draft marks on ocean-going vessels are typically painted or welded in 100 mm or 200 mm intervals, with the bottom of each numeral sitting at the metric depth it represents. Reading to the nearest centimetre requires a steady eye at water level — ideally a licensed surveyor reading from a launch or a pilot ladder, not from the ship’s rail. Any error of even 20 mm in the midship draft translates to a multi-hundred-tonne error in cargo on a large Capesize bulker.
Deductibles: the step that turns displacement into cargo
Corrected displacement includes everything aboard: the ship itself (lightship weight), all liquids in tanks, stores, crew effects, and cargo. To isolate cargo, you subtract:
- Ballast water — measured by ullage or soundings
- Fresh water — bunker FW and distilled water in tanks
- Fuel oil and diesel — density-corrected by fuel grade
- Lubricating oil — often a standard constant
- Ship’s constants — agreed figure for miscellaneous items not separately measured
A disciplined survey verifies each deductible independently. Disputes about cargo weight between shipper and receiver almost always trace to disagreements over deductibles rather than the draft readings themselves.