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How Hogging and Sagging Affect Ship Draft Readings and Cargo Measurement

A ship is not rigid. It bends. When the centre rises higher than the ends, that is hogging. When the centre sags lower, that is sagging. On a Capesize bulk carrier, the difference between the actual waterline at midship and where it would be if the hull were perfectly straight can exceed 10 centimetres. At roughly 100 tonnes per centimetre of immersion, a 10 cm unaccounted deflection equals 1,000 tonnes of phantom cargo. That is not a rounding error. That is the difference between a clean survey and a dispute that lands on a lawyer's desk.

What Are Hogging and Sagging?

Sagging is the opposite. The hull bends downward in the middle. The ends rise, the centre drops. The deck line curves downward toward the water at midship. Technically, it is a negative bending moment at amidships. Visually, it looks like the ship is drooping in the middle under its own weight.

What causes these conditions? Three main factors:

Cargo distribution. Load heavy cargo in the end holds while the mid-holds are empty, and you create a hogging moment. The weight at the bow and stern pulls those ends down, and buoyancy under the empty midship area pushes the centre up. Load heavy cargo concentrated in the mid-holds with empty ends, and you create a sagging moment. The centre sinks under the weight while buoyancy pushes the light ends up. Every cargo plan is a bending moment calculation, whether the chief mate does it consciously or not.

Wave action. At sea, passing waves create continuously changing bending moments. When a wave crest passes under the midship section, the increased buoyancy at the centre combined with the troughs at the bow and stern creates a hogging condition. When a wave trough passes under the centre with crests at both ends, the ship sags. These are the hogging and sagging stresses that naval architects design the hull girder to withstand, and they are the dominant loads in the ship's longitudinal strength calculations.

Thermal gradients. When the deck is hotter than the bottom plating, the deck expands more and the hull arches upward. This is thermal hogging and it is subtle, predictable, and widely misunderstood. We treat it in detail in Section 4, but for now, understand that every degree of temperature difference between deck and bottom plates creates a measurable deflection.

Ships are designed to flex. The hull girder is an elastic beam. Some deflection under load is normal, expected, and calculated into the design. The scantlings -- the thicknesses of the deck plating, bottom shell, side shell, and longitudinal stiffeners -- are sized specifically to resist the maximum expected bending moments while allowing elastic deformation within safe limits. The classification society rules (IACS Common Structural Rules for bulk carriers and tankers) prescribe minimum section modulus requirements for the hull girder precisely to control these deflections. The issue for the draft surveyor is not that the ship bends. The issue is that the bend changes the relationship between the six draft marks and the true mean draft.

How Hull Deflection Changes Draft Readings

In a hogging condition, the midship draft marks read shallower than they would on a perfectly straight hull. The forward and aft marks read deeper. The hull is arched upward, so the centre floats higher and the ends sink lower relative to the vessel's true mean waterline.

In a sagging condition, the opposite happens. The midship marks read deeper than the straight-hull equivalent. The forward and aft marks read shallower. The hull sags down in the middle, pulling the waterline higher on the midship marks while the ends ride up.

If you take the simple arithmetic mean of all six draft readings in either condition, you get a number that does not represent the ship's true mean draft. The more severe the deflection, the larger the error. And the error is systematic, not random. It always skews in a predictable direction based on whether the vessel is hogging or sagging.

Now compute the simple mean of all six readings. Forward mean = 12.10 m, aft mean = 12.08 m, midship mean = 11.82 m. Simple mean = (12.10 + 12.08 + 11.82 + 11.82 + 12.10 + 12.08) / 6. Or more practically: (Forward Mean + Aft Mean + Midship Mean + Midship Mean) / 4 = (12.10 + 12.08 + 11.82 + 11.82) / 4 = 11.955 m. The error is 0.045 m, or 4.5 centimetres.

On this Capesize bulker, with a TPC (tonnes per centimetre immersion) of approximately 100 tonnes/cm at laden draft, a 4.5 cm error in draft translates to a 450-tonne error in the displacement calculation. At iron ore prices hovering around USD 100-120 per tonne, that is USD 45,000-54,000 of cargo value that exists only on paper. The buyer is either paying for cargo they never received, or the seller is delivering cargo they will never be paid for.

The error compounds when you consider that a draft survey involves two sets of readings -- initial and final. If the vessel's deflection changes between the initial and final survey (different cargo distribution, different ballast arrangement, different thermal conditions), the errors do not cancel out. They stack. A surveyor who does not understand and correct for hull deflection is not conducting a draft survey. They are conducting a guess.

For step-by-step guidance on computing draft surveys from start to finish, see our draft survey calculation guide.

The Quarter Mean Formula -- Correcting for Deflection

What this formula does is mathematically elegant. It gives the midship reading six times the weight of each end reading. Why six? Because the midship section of the hull contributes the most to the vessel's underwater volume. The ship is widest and deepest at amidships. The ends are narrower, shallower, and taper toward the bow and stern. When the hull bends, the largest change in submerged volume occurs in the middle, and the formula weights the midship reading accordingly.

Let us apply the Quarter Mean to the same example. Forward Mean = 12.10 m, Aft Mean = 12.08 m, Midship Mean = 11.82 m. QM = (12.10 + 12.08 + 6 × 11.82) / 8 = (12.10 + 12.08 + 70.92) / 8 = 95.10 / 8 = 11.8875 m. The true mean draft was 12.00 m. The Quarter Mean gives 11.89 m, an error of 0.11 m. Wait -- that is worse than the simple mean of 11.955 m, which had an error of only 0.045 m.

The reason is that our example was constructed backwards. In a real survey, you do not have access to the "true mean draft" -- you have the six draft marks and you compute the Quarter Mean as your best estimate of the true mean. The Quarter Mean of 11.89 m correctly reflects that when the midship reads 11.82 m in a hog, the midship is understating the true volume. The formula compensates by pulling the mean toward the ends. Conversely, if the hull were sagging and midship read higher than the ends, the formula would pull the mean away from the inflated midship reading. In both cases, it corrects in the right direction.

When deflection is severe -- more than about 0.3% of the vessel's length between perpendiculars -- even the Quarter Mean has limits. The exact weighting factor varies with the hull form, specifically the block coefficient (Cb). A vessel with a very full form (Cb above 0.85, typical of bulk carriers) has a different volume distribution than a fine-lined container ship (Cb around 0.65). The 6x factor is a universal compromise, adopted by UNECE Code of Uniform Standards (ECE/ENERGY/19) and all major classification societies. It works well enough for commercial draft surveys across the range of hull forms encountered in practice. When it does not, the surveyor's job is to note the condition in the report and flag the survey for review.

For a complete explanation of how the Quarter Mean fits into the full draft survey calculation sequence, see the draft survey calculation guide and the guide to reading draft marks for correct mark-reading technique.

Thermal Effects on Hull Deflection

The Mechanism of Thermal Hogging

Steel expands when heated. The coefficient of thermal expansion for shipbuilding steel is approximately 0.000012 per degree Celsius per metre of length. That number sounds small. On a 300-metre bulk carrier, it is not small at all.

On a hot summer day, the deck plates of a bulk carrier can reach 50 to 55 degrees Celsius from direct sun exposure. The steel absorbs solar radiation and radiates it back out slowly. Paint colour matters: a dark grey deck absorbs more heat than a light grey one. Meanwhile, the bottom shell plating sits in water at 4 to 10 degrees Celsius. The temperature difference between deck and bottom can be 40 degrees Celsius or more.

With the deck hotter than the bottom, the deck plates expand more. A 300-metre deck plate heated 40 degrees above the bottom plate wants to be roughly 14 centimetres longer than the bottom. But the deck and bottom are connected through the side shell, the transverse bulkheads, and the longitudinal stiffening system. They cannot expand independently. So the hull accommodates the differential expansion by arching upward. The deck lengthens as it curves. The bottom shortens relative to the deck. The ship hogs. This is thermal hogging, and it happens every sunny day.

The Great Lakes Sprinkler Trick

The Welland Canal connects Lake Erie to Lake Ontario, bypassing Niagara Falls. It has a maximum allowable draft of approximately 8.08 metres (Seawaymax) in freshwater. Ships transiting the canal face strict draft enforcement. Exceed the limit, and you are turned away.

In summer, thermal hogging can push the apparent draft reading over the canal limit even though the ship is not physically overloaded. The solution, documented in maritime forums including Ships Nostalgia and confirmed by Great Lakes mariners: crews deploy fire hoses or fixed sprinkler systems to spray water across the deck before canal transit. The evaporative cooling drops the deck plate temperature. The thermal hog decreases. The apparent draft reading drops by 2 to 5 centimetres.

That 2 to 5 centimetres is often the difference between passing the canal and being ordered to lighter cargo. At Welland Canal transit fees and the cost of arranging a mid-lake lightering operation, the economics are simple. A few hours of deck spraying costs a pump and some electricity. A lightering operation costs tens of thousands of dollars in tugs, barges, and lost time.

The sprinkler trick is not some obscure historical curiosity. The physics is sound. Evaporative cooling works on the same principle as sweating: water absorbs heat energy as it evaporates from a surface, cooling the surface in the process. The deck temperature drops by 10 to 20 degrees Celsius during active spraying. The temperature differential between deck and bottom narrows. The thermal expansion differential shrinks. The hog decreases. The draft marks tell the truth, or at least a version of the truth closer to what the hydrostatic tables assume.

Beyond the Great Lakes

Thermal hogging is not limited to the Welland Canal. Any vessel operating in hot climates with cold water can experience it. The Persian Gulf in winter: air temperature 30 to 35 degrees Celsius, water temperature 18 to 22 degrees. The Chilean fjords in summer: air temperature 25 degrees, water temperature 8 degrees from glacial meltwater. The North Atlantic in spring: warm Gulf Stream air over Labrador Current water, a 15-degree differential. Anywhere the deck bakes and the bottom chills, the hull will hog.

At night, the pattern reverses -- partially. The deck cools by radiation to the night sky. The temperature differential narrows. The thermal hog decreases. A draft survey conducted at 14:00 on a sunny day and a draft survey conducted on the same ship, same loading condition, at 06:00 the next morning can show different readings. The difference is not cargo. It is thermal deflection.

Practical guidance for surveyors: when significant thermal gradients are suspected, record the deck temperature (an infrared thermometer pointed at the deck plate works), the seawater temperature, and the time of day. If the initial and final surveys were conducted at different times of day, the thermal deflection may differ between them, introducing an error into the cargo calculation. Note the condition in the survey report. If the deflection is large enough to affect the commercial result -- and on a Capesize vessel, 2 cm of additional deflection equals roughly 200 tonnes of apparent cargo -- flag it. The parties to the contract deserve to know that the survey conditions were not identical.

How to Detect Excessive Deflection

Visual Inspection

Sight down the sheer line -- the deck edge -- from the bow toward the stern. On a straight hull, the line appears straight. On a hogged hull, you will see a visible upward curve at midship. On a sagged hull, a downward curve. This is qualitative, not quantitative, but it is fast and it catches the obvious cases. If you can see the curve from the deck, the deflection is at least 5 to 10 centimetres. A deflection you cannot see at all is probably within 2 to 3 centimetres, which is normal for most loaded ships.

Also check the freeboard at midship on both sides. If the port and starboard freeboard measurements differ by more than 2 centimetres, the vessel has a list that could be mistaken for or combined with deflection. Resolve the list before analysing the deflection.

Calculation Check

Compare the simple arithmetic mean of all six drafts against the Quarter Mean. The difference between these two numbers is a direct measure of deflection. As a rule of thumb: if the difference exceeds 0.5% of the vessel's beam, the deflection is significant enough to warrant a note in the survey report. For a Capesize bulker with a 45-metre beam, 0.5% is 22.5 centimetres. That is a large deflection and should trigger a closer look at the loading condition. For a Panamax bulker with a 32-metre beam, the threshold is about 16 centimetres.

A second check: compare the deflection measured in the initial survey against the deflection measured in the final survey. They should be similar. If the initial survey showed 8 centimetres of hog and the final survey shows 2 centimetres of sag, something changed between the surveys that is not explained by the cargo operation alone. Investigate. A ballast tank may have been missed. The vessel may have shifted trim significantly. Thermal conditions may have changed. The draft marks themselves may have been misread.

Deflection and Trim

Trim complicates deflection analysis. A vessel trimmed by the stern has deeper aft drafts and shallower forward drafts even without any hull bending. The Quarter Mean formula handles this correctly because it treats forward and aft means symmetrically, but a visual inspection of the sheer line is harder to interpret on a trimmed vessel. When trim exceeds 1% of the vessel's length, rely on the Quarter Mean comparison rather than visual checks to assess deflection.

Technology for Deflection Monitoring

GOTEC AI camera systems read all six draft marks simultaneously. Six cameras, synchronised to within a fraction of a second, capture the waterline at each draft mark location at the same moment. The system computes the Quarter Mean including the deflection correction in real time and displays it to the surveyor. If the deflection pattern is abnormal -- if the midship reading suggests hogging while the visual profile of the marks suggests sagging, or if the deflection magnitude exceeds the expected range for the vessel's loading condition -- the system flags it.

When integrated with the vessel's load planning software, the system can warn the chief mate before a cargo loading pattern creates excessive deflection. A planned cargo distribution that produces a 30-centimetre hog at the loading terminal is not just a draft survey problem. It is a structural stress problem. The classification society's loading manual specifies maximum allowable bending moments and shear forces. Exceeding them reduces the fatigue life of the hull structure. A system that reads draft in real time and compares it against the load plan can catch these conditions before the last grab of cargo goes into the hold.

For more on the technology behind AI draft reading, see the GOTEC algorithm page and products page.

Frequently Asked Questions

What is the difference between hogging and sagging?

How much cargo weight error can hull deflection cause?

On a Capesize bulk carrier where each centimetre of draft equals roughly 100 tonnes of displacement (TPC, or tonnes per centimetre immersion), even a 5 cm unaccounted deflection creates a 500-tonne error in the draft survey. In extreme cases with 10 cm or more of deflection, the error can exceed 1,000 tonnes. At current commodity prices for iron ore (roughly USD 100 to 120 per tonne), a 1,000-tonne error represents USD 100,000 to 120,000 in cargo value that exists only on paper. This is why the Quarter Mean formula exists: it mathematically corrects for the curvature that would otherwise produce these errors. Without it, a simple average of all six draft marks would systematically misrepresent the vessel's true displacement. The error compounds when the initial and final surveys are conducted under different deflection conditions. See our draft survey calculation guide for a complete walkthrough of the computation.

What is the Quarter Mean formula and why is it used?

The Quarter Mean formula is: Quarter Mean = (Forward Mean + Aft Mean + 6 x Midship Mean) / 8. It corrects for hull deflection by giving the midship draft reading six times the weight of each end reading in the average. This weighting accounts for the fact that the midship section contributes the bulk of the hull's underwater volume -- the ship is widest, deepest, and fullest at amidships. In a perfectly straight hull, the Quarter Mean equals the simple arithmetic mean of all six marks. When the hull is hogged or sagged, the Quarter Mean adjusts for the curvature by pulling the computed mean toward the ends (in hogging) or away from the midship (in sagging). The formula is specified by the UNECE Code of Uniform Standards for Draft Surveys (ECE/ENERGY/19) and is used universally in commercial draft surveying. The 6x factor assumes a relatively uniform hull form; for vessels with extreme block coefficients, surveyors should note any significant residual deflection in the survey report. Learn how to read draft marks correctly before applying the formula.

Can thermal hogging affect a draft survey result?

Yes, and the effect is larger than most surveyors assume. On a hot day, the deck plates of a bulk carrier can reach 50 to 55 degrees Celsius from sun exposure while the bottom plating sits in water at 4 to 10 degrees Celsius. The deck expands more than the bottom, and the hull arches upward in thermal hogging. This can add 2 to 5 centimetres to the apparent draft reading at the forward and aft marks. On the Great Lakes, ships transiting the Welland Canal have been documented using deck sprinklers and fire hoses to cool the hull before lock transit -- the evaporative cooling reduces the thermal hog and drops the draft reading enough to pass strict Seawaymax canal limits. Any surveyor working in conditions where hot deck plates meet cold water (Persian Gulf in winter, Chilean fjords in summer, North Atlantic in spring) should record the deck temperature, seawater temperature, and time of day. If the initial and final surveys were conducted at different times with differing thermal conditions, the thermal deflection may differ between them, introducing an error into the cargo calculation. A 2 cm thermal differential on a Capesize bulker is roughly 200 tonnes of apparent cargo shift. For practical survey guidance across vessel types, see our ship draft by vessel type page.

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