We have been involved in quite a number of lost container cases in the last few years, especially on large (12,000 TEU plus) container vessels. Some of these cases show various deficiencies, but in other cases it appears that the lashings simply are not strong enough for normal vessel operations.
That has led us down the lashing requirements rabbit hole, and there are real indications that lashing calculations have been extended along a path to failure. That is not unusual, new failure mechanisms often show up when complex systems are scaled up, and this may be the case with regard to load assumptions on lashings on large container ships..
In that regard I started to ponder wind loads when I came across two videos showing empty container stacks that were blown over during storm Eunice in Rotterdam where windspeeds apparently reached 90 mph.
What struck me is that these containers were so readily peeling away on the lee side of the stack and it made me wonder if this failure mode relates to shipboard container losses.
As near as I can figure the videos shows two different stacks and each provides some interesting insights.
These are some screen shots (the video itself disappeared from YouTube):
There actually is a line that is tied to the top downwind container. Before the line snaps the containers in the middle of the stack are already sliding out
It looks like there is substantially elevated pressure in the gap between the container stacks (and suction on the exposed face).
The line snaps and the whole stack slides away while rotating.
Then the next stack starts to rotate away. It is unclear what the actual wind direction is, but I think it is coming over the left shoulder of the videographer.
The second video provides a better indication wind direction.
The below screen shot shows the stacks simply being sucked off the leeward side.
At a certain stage, top containers simple evenly slide off the top, which pretty clearly indicates the tumbling stacks are squarely on the leeside of the pile of containers.
I suspect that the containers in the later pictures are sliding because there no longer is a nice suction face behind a full stack with all the jumbled containers behind the next stack (similar to a tapered tail on a car).
Looking at this information I realized that I never think in terms of negative pressure (suction pressure) in drag situations. I deal with drag and lift forces all the time, but think in terms of drag coefficients and lift coefficients in the context of the total drag and lift that is produced by the wind on the total object that is a free body (ship, sailboat or airplane). I never really cared what part of these coefficients provides pressure force and what part provides suction force. (The only place where this occurs is on propellers and cavitation, but I never spent much time delving into that subject.)
The internet provided some interesting information, and it comes from civil engineering since buildings are stationary (aerospace engineers call them stationary targets) with pressure and suction sides, and that information opened an engineering window that I had never fully considered.
Building codes show that suction coefficients can be as high as -0.8. Taking into account that the stagnation pressure coefficient is 1.0, that means that the combination of stagnation pressure (completely stalled flow on the windward face) and a suction coefficient on the backside can start to work towards a drag coefficient total of 1.8. That is just order of magnitude thinking, since you cannot have full stagnation on the windward side and suction on the leeward side, because then there will be no flow around the building to produce suction at the leeward side, but let’s go on.
I reached for Hoerner’s Drag, and, yes, this hefty incredibly useful 1965 reference has 2 pages (out of hundreds of other drag discussions) on building leeward side suction and I copy the illustrations here.
Since I don’t do buildings, I must have ignored those pages in my younger days.
Then I started to wonder how I could have missed this important physical issue and reached for my EIT training manual (Lindeberg 6th edition). This manual only provides whole drag coefficients, but now, when I study the table with this newfound knowledge, it provides a deeper understanding that I never appreciated before.
It shows that (higher Reynolds number) flat plate drags are higher than stagnation pressure, starting at 1.16 and can reach 2.0 for infinitely long plates. In other words, for an infinitely long flat plate, it produces full stagnation pressure on the windward side plus the same suction (negative pressure) on the leeward side. In retrospect that makes sense and I can only expect the engineers that developed lashing calculations on container vessels are aware of these concepts and took that into account in their calculations.
What works for smaller container vessels may not work for larger container vessels. Calculations become reliable once there is proof in the pudding and for many years the pudding looked pretty good, but recently things have gotten a little weird. There are other factors that may have ruined the pudding for large containers ships, but let’s just follow this one a little deeper into the rabbit hole.
Windspeeds increase with increasing altitudes. Due to drag from the ground there is a wind gradient where windspeeds near the ground are much lower than further away from the ground. This is called the wind gradient. Wind gradient is a huge and complex issue in large racing sailboat design and I spent a lot of time thinking about it in my America’s Cup design days.
Hoerner provides a clever graphic depiction of the effect of wind gradients.
What this graphs shows is that if a container stack is 50 % higher, the dynamic pressure (and suction) is about 20 percent higher at a certain recorded wind speed.
In other words, if one were to use a certain assumed wind speed for container lashings, but now my container stack is 50% higher my suction pressure will be 20% higher (Note that is pressure; the suction force on the whole stack will be 1.2 x 1.5 = 1.8 times larger). For the same wind speed suction pressures will be higher on taller container ships. A 20% increase in suction pressure is not a huge increase, but there are a number of other factors that are gradually eroding the design safety factors on large container ship lashings using conventionally accepted calculation approaches. I will only discuss the aerodynamic assumptions here, but there are also other assumptions that no longer make sense.
Due to the existence of wind gradients, when performing a forensic analysis, it is significant to take note of the height of the anemometer of the vessel that lost the containers. A large container ship that records 60 mph sustained winds, was probably in somewhat lighter conditions than a smaller container ships that records 60 mph sustained winds.
Aerodynamically I am gut estimating that the suction pressure increase is larger than 20 % for a 50% taller stack of containers on a container ship.
When a container ship rolls into a beam wind, for the same roll period, the maximum apparent beam wind (free flow wind speed plus the wind of the object moving through the wind) across the top of the container stack will be higher on the taller ship than the lower ship. The longer arm from the roll center to the top of the stack at the same rotational speed will result in a higher velocity at the top of the container stack. That velocity then needs to be added to the assumed windspeed used in the lashing calculations. It will not hugely increase the windspeed, but wind force increases with the square of the total windspeed and, as such, this motion will be another straw added to the camel’s back.
It is also significant to note that the suction Cd is not even from the tips to midspan on a flat plate. At midspan the local suction pressure can be higher than at the ends. Since a ship is loaded with individual container cells, one cannot assume that a single independently secured cell is exposed to an average Cd, and instead it should be assumed that it could be exposed to the maximum Cd, which, as noted above, would be in the range of -1.0.
Moreover, in large waves, the wind gradient is more pronounced above the wave tips than it is in the wave troughs. Smaller container vessels will have a larger portion of their exposed side sheltered in these troughs. Combined, these factors may very well result in suction pressures that are occasionally 50% higher than can be reasonably assumed for smaller container vessels.
“Traditionally” we have seen container losses in the stern or bow of containers ships (ignoring other securing failures), because these locations can be most heavily exposed to waves (bow) or unusual motion combinations of heave and roll (stern). Losses such as those seen on ONE APUS have left me rather baffled, because the failures were mostly midship, but midship is where one can expect the highest suction loads on ships like this, and if these loads are underestimated, the midship securings can became inadequate.
Please note that these are just wind load considerations and our work on these issues is showing there are manifold other issues and assumptions that are resulting in bad lashing pudding.
Generally technical societies start discussions when unusual failures are occurring. In this case I am surprised that, as near as I can figure, the silence on this subject by lashing engineers has been deafening. Hopefully this will start a deeper discussion and we all will learn more.