This appendix provides a practical, step-by-step guide to performing a draft survey calculation. While the theory is discussed in Chapter 7, this section is designed to be a hands-on reference for ship’s officers responsible for this critical task. The worked example uses a fictional bulk carrier to illustrate the application of corrections and the overall process.

Part 1: Step-by-Step Calculation Procedure

A draft survey consists of two distinct sets of calculations: one for the vessel’s condition before cargo operations (Initial Survey) and one for the condition after cargo operations (Final Survey). The difference determines the weight of the cargo. The following steps are performed for both the initial and final surveys.

Step 1: Data Collection & Recording

Meticulously measure and record all variable data.

  1. Read Drafts: Read all six draft marks: Forward Port (FP), Forward Starboard (FS), Midship Port (MP), Midship Starboard (MS), Aft Port (AP), and Aft Starboard (AS). Read as close to the water as possible to avoid parallax error.
  2. Measure Water Density: Take a representative sample of the dock water from a depth of approximately half the ship’s draft. Use a calibrated hydrometer and record the density (e.g., 1.018 t/m³).
  3. Sound All Tanks: Accurately sound or ullage all tanks containing liquids:
    • All Ballast Water tanks.
    • All Fuel Oil tanks (HFO, LSMGO/VLSFO – settling, service, storage).
    • All Fresh Water tanks (potable, boiler feed).
    • All other tanks containing significant weights (Lube oil, sludge, bilge water, etc.).
  4. List Other Deductibles: Note down any other weights on board that are not part of the ship’s lightship weight (e.g., crew and effects, stores, provisions, any temporary equipment). The total of these items is often assumed to be part of the “Ship’s Constant.”

Step 2: Calculate Mean Drafts and Trim

  1. Calculate Mean Draft at each Perpendicular:
    • Mean Fwd Draft (Fm) = (FP + FS) / 2
    • Mean Mid Draft (Mm) = (MP + MS) / 2
    • Mean Aft Draft (Am) = (AP + AS) / 2
  2. Calculate Apparent Trim:
    • Apparent Trim (App. Trim) = Am - Fm (Positive if by the stern, negative if by the head).
  3. Calculate Quarter Mean Draft (DM): This is the mean draft corrected for hog or sag, used to enter the hydrostatic tables.
    • DM = (Fm + Am + 6 * Mm) / 8

Step 3: Calculate Net Corrected Displacement

This step involves taking the displacement from the ship’s tables and applying a series of corrections.

  1. Find Initial Values from Hydrostatic Tables: Using the Quarter Mean Draft (DM) calculated in Step 2, enter the ship’s hydrostatic tables to find the following values (you may need to interpolate):
    • Displacement (Δ) for standard density (usually 1.025 t/m³)
    • Tonnes per Centimetre Immersion (TPC)
    • Moment to Change Trim by One Centimetre (MTC or MCT1cm)
    • Longitudinal Centre of Flotation (LCF) from midships (AP/FP datum).
  2. First Trim Correction (TC1): This corrects for the displacement change due to the vessel’s trim.
    • TC1 (tonnes) = (App. Trim (cm)) * (TPC) * (LCF (m from midships)) / (Length Between Perpendiculars - LBP (m))
    • Sign of Correction: This correction is added if trim by the stern and LCF is aft of midships, OR if trim by the head and LCF is forward of midships. It is subtracted otherwise.
  3. Second Trim Correction (TC2): A smaller correction for the change in the waterplane shape due to trim.
    • TC2 (tonnes) = (App. Trim (cm))² * (50 * dMTC/dz) / LBP (m)
    • Where dMTC/dz is the difference in MTC values for drafts 50cm above and 50cm below the current mean draft.
    • This correction is always added to the displacement.
  4. Density Correction: This corrects the standard saltwater displacement for the actual measured dock water density.
    • Corrected Displacement = Displacement from Tables * (Actual Density / 1.025)
    • Alternatively: Density Correction (tonnes) = Displacement from Tables * ((Actual Density - 1.025) / 1.025)
    • The result is added or subtracted accordingly.
  5. Calculate Net Corrected Displacement:
    • Net Corrected Displacement = Displacement from Tables + TC1 + TC2 + Density Correction

Step 4: Calculate Total Deductible Weights

  1. Using the sounding/ullage figures from Step 1 and the ship’s tank calibration tables, calculate the weight of liquids in each tank. Be sure to apply corrections for trim and list as provided in the tables.
  2. Sum the weights of all liquids (Ballast, Fuel, FW, etc.).
  3. Add the standard weight for other items (crew, stores, etc.) to get the Total Deductible Weight.

Step 5: Determine Initial or Final Vessel Weight

  1. Vessel Weight = Net Corrected Displacement – Total Deductible Weight
  2. If this is the Initial Survey, this figure is the Weight Before Loading. If it is the Final Survey, it is the Weight After Loading.

Step 6: Calculate Cargo Weight

  1. Cargo Loaded = Weight After Loading – Weight Before Loading

Part 2: Worked Example

Vessel: MV Bulk Star (Fictional) LBP: 185.0 m Initial Survey (Before Loading):

  1. Data Collection:
    • Drafts: FP: 3.40m, FS: 3.50m; MP: 4.15m, MS: 4.25m; AP: 4.90m, AS: 5.00m
    • Density: 1.015 t/m³
    • Deductibles (from tank soundings):
      • Ballast Water: 10,500 MT
      • HFO: 850 MT
      • MGO: 120 MT
      • Fresh Water: 250 MT
      • Others (Stores, etc. + Ship’s Constant): 350 MT
      • Total Initial Deductibles = 12,070 MT
  2. Mean Drafts & Trim:
    • Fm = (3.40 + 3.50) / 2 = 3.450 m
    • Mm = (4.15 + 4.25) / 2 = 4.200 m
    • Am = (4.90 + 5.00) / 2 = 4.950 m
    • App. Trim = 4.950 – 3.450 = 1.50 m (150 cm) by the stern.
    • DM = (3.450 + 4.950 + 6 * 4.200) / 8 = 4.200 m
  3. Calculate Initial Displacement:
    • From Hydrostatic Tables at DM = 4.200 m:
      • Displacement (Δ) = 17,250 MT
      • TPC = 45.50 t/cm
      • MTC₁ (at 3.70m) = 280.0 t-m/cm
      • MTC₂ (at 4.70m) = 290.0 t-m/cm
      • LCF = 2.50 m Aft of Midships
    • TC1 = (150 cm * 45.50 * -2.50 m) / 185.0 m = -92.23 MT (Negative sign for LCF is aft, so correction is subtracted for trim by stern).
    • TC2 = (150² * 50 * (290.0 – 280.0)) / (100 * 185.0²) = +3.30 MT (Note: some formulas divide by LBP, some by 100*LBP^2, always use ship’s specific formula. This is an example).
    • Initial Displacement Corrected for Trim = 17,250 – 92.23 + 3.30 = 17,161.07 MT
    • Density Correction = 17,161.07 * ((1.015 – 1.025) / 1.025) = -167.42 MT
    • Net Corrected Initial Displacement = 17,161.07 – 167.42 = 16,993.65 MT
  4. Determine Initial Vessel Weight:
    • Weight Before Loading = 16,993.65 MT – 12,070 MT = 4,923.65 MT

Final Survey (After Loading):

  1. Data Collection:
    • Drafts: FP: 11.80m, FS: 11.90m; MP: 12.10m, MS: 12.20m; AP: 12.40m, AS: 12.50m
    • Density: 1.016 t/m³ (re-measured)
    • Deductibles (from tank soundings):
      • Ballast Water: 200 MT (remains in one small tank)
      • HFO: 840 MT (10 MT consumed)
      • MGO: 118 MT (2 MT consumed)
      • Fresh Water: 245 MT (5 MT consumed)
      • Others + Constant: 350 MT (assumed unchanged)
      • Total Final Deductibles = 1,753 MT
  2. Mean Drafts & Trim:
    • Fm = (11.80 + 11.90) / 2 = 11.850 m
    • Mm = (12.10 + 12.20) / 2 = 12.150 m
    • Am = (12.40 + 12.50) / 2 = 12.450 m
    • App. Trim = 12.450 – 11.850 = 0.60 m (60 cm) by the stern.
    • DM = (11.850 + 12.450 + 6 * 12.150) / 8 = 12.150 m
  3. Calculate Final Displacement:
    • From Hydrostatic Tables at DM = 12.150 m:
      • Displacement (Δ) = 58,150 MT
      • TPC = 55.20 t/cm
      • MTC₁ (at 11.65m) = 590.0 t-m/cm
      • MTC₂ (at 12.65m) = 610.0 t-m/cm
      • LCF = 3.50 m Aft of Midships
    • TC1 = (60 cm * 55.20 * -3.50 m) / 185.0 m = -62.66 MT
    • TC2 = (60² * 50 * (610.0 – 590.0)) / (100 * 185.0²) = +1.05 MT
    • Final Displacement Corrected for Trim = 58,150 – 62.66 + 1.05 = 58,088.39 MT
    • Density Correction = 58,088.39 * ((1.016 – 1.025) / 1.025) = -510.37 MT
    • Net Corrected Final Displacement = 58,088.39 – 510.37 = 57,578.02 MT
  4. Determine Final Vessel Weight:
    • Weight After Loading = 57,578.02 MT – 1,753 MT = 55,825.02 MT
  5. Calculate Cargo Loaded:
    • Cargo Loaded = (Weight After Loading) – (Weight Before Loading)
    • Cargo Loaded = 55,825.02 MT – 4,923.65 MT = 50,901.37 MT

Part 3: Key Formulae at a Glance

  • Quarter Mean Draft (DM): (Fwd + Aft + 6 * Mid) / 8
  • First Trim Correction (TC1): (Trim_cm * TPC * LCF_m) / LBP_m
  • Second Trim Correction (TC2): (Trim_cm)² * 50 * dMTC / (100 * LBP_m²)
  • Density Correction: Displacement * ((Actual Density - Standard Density) / Standard Density)
  • Net Corrected Displacement: Table Displacement ± TC1 + TC2 ± Density Correction
  • Cargo Weight: Final Net Weight - Initial Net Weight (where Net Weight = Corrected Displacement – Deductibles)

Accuracy Tips

  • Always apply trim corrections if >50 cm.
  • Use consistent and calibrated instruments.
  • Measure tank soundings before and after operations.
  • Take density samples at multiple points.
  • Confirm tank contents are stable before soundings.

Disclaimer

This guide is for instructional and reference purposes only. The specific hydrostatic data, tank calibration tables, and approved calculation methods provided in your vessel’s official and Class-approved Stability Booklet and Loading Manual must always be used for all official draft survey calculations. The accuracy of any draft survey is wholly dependent on the accuracy of the initial measurements and the correct application of the ship’s specific data.

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