The mean of means, also called the quarter mean draft, is a weighted average used in ship draft-survey and Hindship calculations. It gives greater weight to the midship draft so the final working draft better represents the ship’s underwater form when hogging or sagging may be present.
Quick answer: Mean of Means formula
(F + A + 6M) ÷ 8
Where F is the mean forward draft, A is the mean aft draft and M is the mean midship draft.
How to calculate it step by step
1. Find the mean draft at each position
If port and starboard readings are available, average each pair first:
- F = (Forward Port + Forward Starboard) ÷ 2
- A = (Aft Port + Aft Starboard) ÷ 2
- M = (Midship Port + Midship Starboard) ÷ 2
2. Apply the weighted formula
Multiply the mean midship draft by 6, add the forward and aft means, and divide the total by 8:
Mean of Means = (F + A + 6M) ÷ 8
Worked example
Assume the corrected mean drafts are:
- Forward mean draft, F = 7.980 m
- Aft mean draft, A = 8.610 m
- Midship mean draft, M = 8.330 m
(7.980 + 8.610 + 6 × 8.330) ÷ 8
= 8.32125 m
The mean of means is therefore 8.32125 m, normally rounded only as required by the vessel’s calculation procedure or examination question.
Why is the midship draft multiplied by 6?
A simple forward-and-aft average does not reflect hull deflection at midships. The mean-of-means formula gives six of the eight weighting parts to the midship draft. This makes the working draft respond to the difference between the midship reading and the mean of the end drafts, which is important when the vessel is hogged or sagged.
Mean draft versus mean of means
| Calculation | Formula | Purpose |
|---|---|---|
| Mean draft | (F + A) ÷ 2 | Simple average of the end drafts |
| Mean of means | (F + A + 6M) ÷ 8 | Weighted working draft using the midship reading |
Common mistakes
- Using individual port or starboard readings instead of the mean at each position.
- Forgetting to multiply the midship draft by 6.
- Dividing by 3 instead of dividing the weighted total by 8.
- Using uncorrected drafts when the question requires corrections to the perpendiculars first.
- Rounding the drafts too early and carrying the error into later calculations.
Frequently asked questions
What is another name for the mean of means?
In draft-survey work it is commonly called the quarter mean draft. Some training notes may also describe it as the corrected mean draft used for entering the hydrostatic tables.
When should the mean of means be calculated?
Calculate it after obtaining the corrected forward, aft and midship mean drafts. It is then used as the working draft for the next stage of the draft-survey or Hindship problem.
Can I calculate it without a midship draft?
No. The weighted formula requires a midship draft. If only forward and aft drafts are available, you can calculate the ordinary mean draft, but not the mean of means.
For the basic forward-and-aft calculation, read How to Calculate Mean Draft of a Ship. You can also browse the growing Maritime Quick Answers library.
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