A "sudden strong wind": the worst excuse Ever Given?

The Suez Canal is an artery of world trade, connecting the Mediterranean with the Red Sea, and providing an avenue for vessels to pass between Asia and the Middle East and Europe. The main alternative, a passage round the Cape of Good Hope at the southern tip of Africa, takes considerably longer.

On average, nearly 50 vessels per day pass along the canal, although at times the number can be much higher - accounting for some 12% of world trade. It is particularly important as an avenue for oil and liquified natural gas, enabling shipments to get from the Middle East to Europe.

- BBC

A study by German insurer Allianz said the blockage could cost global trade $6 billion to $10 billion a week.

Evergreen Marine said the ship "was suspected of being hit by a sudden strong wind, causing the hull to deviate from waterway".

I really wondered if the orders of magnitudes in question were realistic at all, so I decided to quickly run the numbers.

This is a quick-and-dirty analysis, aimed at being understandable by anyone, with or without a background in physics.

Every time I need to take an assumption, I always pick the side that goes in favour of the wind theory. That way, the result will be an upper bound.

Wind exposure area

The Ever Given is 33m-tall, with 14.5m of this height submerged in water.

Looking at the container stack, and using the standard 2.6m height for each container, the pile should be about 26m-high.

This gives us a total above-the-water height of 44.5m.

The ship is 400m-long.

Simplifying things for the worst, we assume the side area is a rectangle. Its area is this 17,800m^2, i.e. 1.78 hectare.

This is big: ~2.5x the area of a football pitch, or ~200x your average sailing boat sails area.

Air mass & momentum

Let's be extremely generous and say that the wind is blowing at 100km/h. Constantly.

Let's also assume that it is blowing perfectly perpendicular to the boat, and that it is giving away 100% of its momentum to the ship - this is a very strong assumption.

100km/h is about 27.8m/s.

At standard temperature and pressure (0°C and 100 kPa), dry air has a density of 1.2754 kg/m^3. Pretty sure it is not 0°C in Egypt right now, but let's keep a margin for some potential humidity and/or anticyclone pressure.

It means that in 1s, 17,000*27.8*1.2754kg of air are hitting the side of the ship.

That's about 603t of air per second.

Forces calculation

The ship's mass is 224,000t.

The wind's lateral force - again, if fully transferred to the ship - is 603t/s * 27.8 m/s, i.e. ~16.8 million Newtons.

Using Newton's second law of motion, we can deduct the ship's resulting lateral acceleration 16,800/224,000 = 0.075m/s^2

That isn't much. At all.

Gravity average acceleration at the Earth's surface is 9.81m/s^2, i.e. 131 higher.

BUT, let's unchecked, acceleration compounds.

Trajectory simulation(s)

Let's assume the ship was sailing dead in the middle of the canal.

The ship is 59m-wide.

The canal is 200m-wide.

That leaves us ~70m between the ship and the bank on each side.

Let's make one last very strong assumption: the water displaced laterally is not opposing the ship's lateral movement generated by the wind. This is wrong because the ship's lateral section is huge - in the same order of magnitude as a football pitch, again - and absolutely not optimized aerodynamically for this type of lateral translation: a ship is supposed to sail bow-first, not laterally like a crab.

But, this type of friction is usually proportional to the movement speed, which would remain reasonably low for most of the trajectory - as we will check retrospectively.

If the ship starts with no lateral motion, then integrating the acceleration equation twice gives us an impact after 43s.

The resulting lateral speed would be ~3.2m/s, i.e. ~11.5km/h. This is not enough to ignore water resistance, but not very high either considering this would be the absolute maximum speed for the whole trajectory.

The wind's force is not linear to its speed: it increases with the square of its speed.

For a 70km/h constant wind speed, the impact happens after 62s at an end lateral speed of 2.3m/s (8.2km/h).

For a 50km/h constant wind speed, the impact happens after 86s at an end lateral speed of 1.6m/s (5.8km/h).

Let's not forget the angle either: a mere 30-degree (vs. a perfectly perpendicular wind) would decrease the wind force by 25%, everything else being equal. 45 degrees would decrease it by 50%.

Finally, this is in case the wind never falters and, obviously, the ship's captain does not start any avoidance manoeuvre.

Sensitivity analysis

The wind's force is not linear to its speed: it increases with the square of its speed.

For a 70km/h constant wind speed, the impact happens after 62s at an end lateral speed of 2.3m/s (8.2km/h).

For a 50km/h constant wind speed, the impact happens after 86s at an end lateral speed of 1.6m/s (5.8km/h).

Let's not forget the angle either: a mere 30-degree (vs. a perfectly perpendicular wind) would decrease the wind force by 25%, everything else being equal. 45 degrees would decrease it by 50%.

Such angles would increase the time-to-impact by a third, or multiply it by 2, respectively.

Finally, this is in case the wind never falters and, obviously, the ship's captain does not start any avoidance manoeuvre.

Conclusion

Even without strong hypotheses, it does seem like an extremely strong wind could in theory bring the ship dangerously close to the bank.

Even if the ship's captain managed to steer early enough, the bank effect - the marine version of the aeronautics ground effect - could take care of the last meters and bring us to the catastrophic situation we all know about.

I must say that it goes against my initial intuition, so I am glad I did the math.

Hope you found it entertaining as well.