The Art of Dredging

Dredging and shipping

Vertical squat


Vertical squat is not extra draught due to shallow water effect. (Ships would sink, if this was true.) 

Vertical squat is due to waterflow being restricted under the ship's hull (and in a channel; also along the sides of the ship). It's called Bernouilli's Law, whatever.

  • Waterflow is restricted
  • Waterspeed is increased
  • Waterpressure drops
  • Waterlevel drops

This lowering of the waterlevel around the ship causes the ship to move downwards towards the seabottom, and causes a smaller Under Keel Clearance(UKC).  



Gerardus Mercator sailing in an shallow channel.  UKC is about two metres. Ship's speed 10 knots. You see the extreme bowwave, and the lowering of the waterlevel midships.  Sand is loosened up by the propellers. 

(This photo was taken during the Pusan New Port Project in Korea. Initial depth of the accesschannel was 13 metres. During the project, the channel deepened about 1.5 metres, due to the agitating effect of our propellers.)


The same idea in a computermodel: the waterlevel is lowered around midships.





Different situations:


Ship in open sea; no interaction with sides of channel.

Ship in restricted channel: ship experiences extra squat.

OK, for people who get itchy when they see a formula, just hang in:

Here is a formula for calcualting squat. It's an empirical formula, which means that it's more or less correct, but not entirely. Result of the formula is squat in meter.




Speed of ship in knots




Block coefficient





Velocity return factor = S / (1 - S)



Blockage factor = As / Ac (0.10 to 0.30)



Midship immersed cross-sectional area of the ship



Cross-sectional area of the channel = h * W



Water depth (meters)




draught (meters)





breadth (meters)





Underkeel clearance (meters)



Width of channel (meters)




Width of influence = 7.7 + 45 *  (1 - Cw)^2



Water plane area coefficient





Well, this is just one squat formula. There are hundreds of squat formulas, and all of them are empirical, none of them is exactly correct.

Check this out: Squat-calculation.exe (download 35kB) by Jan Bertrem, ir.

IThis file contains 15 different squat formulas.

You can fiddle away with the parameters and get a feeling of the influence on UKC for a ship sailing in shallow water. 

The really important thing about this formula (and all the other squat - formulae, which all look-alike) is what happens with ship's speed.

Fill in a ship's speed of 5 knots, or 10 knots, the result of the formula is 25 versus 100.

Double speed gives four times higher squat. 

Put it in a graph and it looks like this: ship's speed is what it's all about.











               Blockcoefficient of the underwater ship is also a pretty important factor.

Left Gerardus Mercator, with a full body. Right Juan Sebastian De Elcano, with a slightly more elegant shape. 

Mercator has more buoancy in the bow; thus Juan will trim more forward when sailing in shallow water.  


OK, what's the deal ?

The squat-formulae gives a good way to control a ship's draught and speed in shallow water, optimising load of the ship, without comprimising safety.

When a dredger has to sail through an access channel, or has to pass a shallow patch, with a loaded ship, and is tide-restricted, you can take a squat-formula and turn it into a squat-calculator, in an excel-file, for example.

Suppose your dredger has to sail in a channel, and the ship is tide-restricted.

The mate on duty has two major problems, every time he wants to sail into that channel: 

  1. "I am on the dredging area and I need to enter the access channel, with this ETA and this tidal height. What is my maximum draught possible to sail in that channel ?"                                                           
  2. "Ok, i f*cked up on the dredging area. My draught is now this, larger than I planned at (1).  Can I still sail in that channel with this draught without touching the seabottom ?   And what speed should I sail to keep it safe then ?"

We made a squat-caluclator for "Gerardus Mercator":

Squat-calculator.xls  (download19 kB)

                      and it looks like this:

This is a calculator for TSHD Gerardus Mercator !  You cannot use it for other ships, as the ship's dimensions are not correct. Don't blame this website if your ship runs aground, you have been warned.

If you start optimising load / draught / tidal height and ship's speed,  you better play it safe at the start, and keep a few metres between your ship's keel and the seabed.

In textbooks about squat, the advice is always to keep 10-15 % of your draught as Under Keel Clearance (UKC). In certain cases, we narrowed this to 5% (that's 0.5 meter UKC  when sailing !).

And you should consider the position of fueltanks onboard: if they are in vulnerable places, not protected by void spaces or cofferdams, you may risk rupture of a fueltank when you run aground. Just think twice before narrowing UKC !

When you start feeling confident about this way of calculating squat, and when you notice that echosounder readings match your calculations, you may narrow the UKC margin.

And we became highly confident in the results of the spreadsheet.

One time, a chief mate loaded the ship 20 cm deeper and sailed 2 knots faster than the values advised by the squat-calculator. The ship's keel scraped bottom. That was the margin we achieved.

Warning: every ship reacts different in shallow water, concerning trim, list during turning, steering capabilities, course stability.

And you have to be really sure about some values:

  • waterdepth in the channel: that means the channel has to be multibeamed completely, and the depth of the shallowest part has to be measured beyond any doubt.  Nothing less will do..
  • Tidal height has to be an actual measurement, not simply an astronomical (calculated) tidal height. You'll need realtime online tidal height onboard.
  • The ship's draught sensors have to be reliable, accurate and exact,
  • and don't forget to adjust the density of the seawater in your loadcomputer.

 Good luck,  and try to keep Murphy out of this one.


Marc Van de Velde


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