This is one the most important functions used to help keep the integrity of a  large ship.

In the Neosho Class Oiler Early Days, the level of fuel in any one tank was found by
clipping a float
to a 50 ft. tape measure and the person could "feel" the level
of the tank - not exact, but good to about a 1/4 of an inch,
 when you know what you are doing.

The float was made of lightweight material  - oil and water resistant.
Tom Wickert  AM2 told me about it over the phone on december 20, 2011.
He had made many soundings on the Kawishiwi.
This how he described it.

A jury rigged type paddle was found on the Hassampa by Captain Patraick Moloney on a SCAVENGER HUNT he had on Nov. 15, 2011.
He found the paddle [below], I had asked for, in the Cargo Lab. It still smelled like cargo. It's about 6" diameter.
It clips onto a 50 foot spool tape measure for gauging fuel depth in tanks.

The process is really called: Outage (Ullage)
The depth of the space in a tank not occupied by oil. Same as ullage. It is measured from the flange of the ullage hole [Bung Hole] to the surface of the oil. Also the space left in a petroleum product container to allow for expansion as a result of temperature changes during shipment and use.

There are several articles about this on the web.
Military RulesLawWine WorldDefinition;
  WikipediaCoast Guard Test, Item 69.

The experiences of Kawishiwi's 1976 era
Liquid Cargo Officer
LTJG Lary Harris
Explains the process well:
In my day we would have the SRF (Ship Repair Facility) or the tender fabricate these "bobs" out of aluminum plate - heavy enough to pull the tape down, non sparking, and they made a loud SPLASH as they hit the oil in the tank.

Gauging the tank in this manner is properly called "ULLAGE" (Ullage is synonymous with "outage") because what you are measuring in this manner is how much cargo is out of the tank, not how much is in the tank.  The formula on the web page then shows how to convert ullage to innage (how much cargo remains in the tank).

As I remember, we did not actually need to do the math to accomplish this. Instead we had an Ullage Table for each tank, which would convert the ullage figure (in feet and inches) directly into barrels of cargo remaining in the tank.  Typically we would have one guy from the Supply division and one guy from the K (cargo) division go around together and take ullages on each tank - to make sure that supply and K divisions agreed on the recorded figures.  Then I would use the ullage tables to compute how much cargo remained in the tanks.  There was also a correction factor for temperature, to bring the recorded soundings back to a corrected figure for oil at a standard temperature, which as I remember, was about 72 degrees.  Typically in the WESTPAC area, the cargo was so close to this temperature that no correction was needed.  In the Persian Gulf or the Aleutians where it was much hotter or cooler, the correction was applied, as the cargo oil could expand or shrink by as much as 4 or 5 percent.

We always needed to have extra tape measures and ullage bobs on hand, as these were fragile and the tape tended to break off right at the bitter end, leaving the ullage bob in the tank.  The tapes, as I remember, were also very expensive.
We would also regularly use a conventional sounding bob to take readings on the tanks to check for water contamination.  We would put water indicating paste on the bottom two or three inches of the sounding bob and then let it sit at the bottom of the tank for a moment.  When it was pulled up, if the water indicating paste changed color it indicated that there was water at the tank bottom.  It then would be necessary to use the "Stripping Pump" which had a low capacity but pulled from a small suction foot at the lowest part of the tank, to pump out this water and transfer it to the "Slop Tanks".  Water contamination was particularly critical in JP-5, as expensive airplanes have a tendency to fall out of the sky if they are fed contaminated fuel.  Our standard was "Water white to light straw color, and clear enough to read a newspaper through a quart glass bottle of JP-5"
A milkshake appearance was a sure indication of water contaminated JP-5. The contaminated mixture of DFM, JP-5 and water in the slop tanks would be allowed to settle out and sometimes we would use the better part of this slop for Kawishiwi bunker fuel (we were not as fussy a customer as some folks were), or keep it until the next time inport when we could pump it back ashore to the tank farm for processing. Sometimes we jokingly threatened to quietly open up the suction valves on the slop tanks and give the worst of it to a customer ship that had been a particular thorn in our side (either because they were inept or because they were needlessly fussy about fuel quality).  I do not, however, remember actually doing this. (at least that's my story.)

In calm weather, getting an accurate reading was a simple evolution, but in a rough sea it was a challenge, as the cargo would be sloshing around with considerable enthusiasm as the ship rolled and pitched.  It was necessary to take several readings and average them out to get an approximate reading, which might not be closer than three or four inches to the true level in the tank.  We did the best we could.  In really rough weather it was also possible to encounter boarding seas on the cargo deck, so life jackets and a minimum of two men at a time was the rule in these conditions.  I don't recall that we had any close calls with anyone being washed over the side, but the ullage men often returned soaked from head to food after sounding the tanks. 

The trim of the ship also affected the readings.  When fully loaded, the Kawishiwi rode pretty level, but as product was discharged and she became progressively lighter, she got higher and higher at the bow, while the draft aft was only reduced a bit, so the cargo in the tanks was now at a slant from fore to aft and a true reading was not possible because of this tilt.

There was also the "tension" of how to distribute the cargo in the tanks.  Having all the tanks at the same level produced the least amount of stress on the hull, but as more and more cargo was discharged, and all of the tanks became low, we could not pump very fast because there was less "head" pushing the oil towards the pump suction inlet.  We could pump a lot faster from a full tank than an empty one. Time was always critical, especially when unreping a carrier, as they were always senior and always in a hurry.  I remember that once in a while, if the weather was fair, we would transfer cargo around to produce a couple of full tanks if we anticipated a carrier unrep.  This would put the stress / strain computer in the Liquid Cargo office (this analog device computed the stress and strain on the hull based on how full or empty each tank was) right up against the RED "do not exceed" area, but would reduce the unrep time by 20 or 30 minutes. 

Sometimes we did not have much control over this - for instance if we were not unreping any carriers, we might be selling a lot of DFM (diesel fuel, marine) to the other ships but not getting rid of much JP-5 (Jet fuel), so the JP-5 tanks would be full to the brim while the surrounding DFM tanks had a much lower level, creating stress and strain.  Again, we did the best we could.  The 143 class oilers seemed to be robustly constructed and I never saw any evidence of hull or tank damage due to improper loading or bad weather.  This was not true of some of the other oilers.  I remember that, near the end of her life, the Taluga had many broken frames and braces in her cargo tanks and needed a special letter of dispensation from BU SHIPS or ABS or someone in order to continue to remain in service.                           Lary Harris  LTJG 1975 -1978    30 Dec. 2011

HOG  and  SAG

The terms that are used for the stress and strain on an oilers hull caused by load distribution is "hog" when the hull is bowed up caused by the tanks in the middle (We are talking fore and aft.) are lightly loaded and the most forward and most aft tanks are loaded heavy. When the tanks are loaded heavily in the middle and the tanks most forward and aft are loaded lightly the hull is in a "sag" condition. We had a manual hog and sag calculator in the log room when i was cargo officer in 68 and 68 that after all the tanks were measured you plugged in all the numbers and determined hog and sag.

One skipper during my tour was very firm that he had the hog and sag report immediately after every carrier unrep. No "ifs", "ands", or "buts" about it.

Like Lary says the Kawishiwi never showed any visible signs that hog and sag affected hull intergrity like cracked deck plates. I have heard that some of the Cimmaron class had those problems.  Andy 12-31-2011

The image left, came from a military report named "LONGITUDINAL STRENGTH AND MINIMUM WEIGHT"

Definition from: Sea Talk

You are probably well aware that many of the more colorful and expressive words in the English language were first used aboard ships at sea. In a very real way sailor talk was a dialect, a provincial language with a specific and very distinct usage.

Incidentally, there were no women on board those ships, at least not at first, so the language of the sea is a thoroughly male language.

Hog : Describing a vessel that is sagging at the ends when hauled or careened indicating that the ship is losing integrity in its timbers, and that the ship has not been braced well.

Sag: A droop in the middle of a ship because it is water logged and losing integrity. or To droop in the middle, as a ship that is rotten and losing integrity. To droop in the middle because the vessel is inadequately supported amidships when hauled or careened.

The digram below comes from the paper,

I haven't seen diagrams like those in over 40 years at Liquid Cargo Officer school.     Andy 1-1-2012

Modern day sounding tapes look like this.
The operation is much different. Read SOUNDING.

Today there is also a fuel gauge located on the bridge, forward bulkhead

From Rainier tour: