Technical thinking: Bigger is better, but more dangerous, too

By Mark Jones

The cause of the Francis Scott Key Bridge collapse seems clear. The Dali, the cause of the bridge’s demise, sits grounded with parts of the bridge strewn across its bow. Drifting after losing power, the ship hit one of the bridge’s supports, bringing it down in an instant. Removal of the support gave gravity the advantage. Entropy and gravity, enemies of the bridge since it was constructed, won. Cut and dry as that seems, there are things to learn and a surprising reason the bridge is on the bottom of the Patapsco River.

There have been lots of reporting about the size of the Dali, about how much bigger it is than ships at the time the bridge was constructed. There has been no reporting I’ve seen on why ships keep getting bigger. No reporting on what is being optimized as ships get ever more gargantuan in scale.

The Dali is a container ship, built to carry shipping containers. These are counted in twenty-foot equivalent units, abbreviated TEU. The first container ship, Ideal-X, a retrofitted tanker, first sailed in 1956 with a cargo of 58 containers. It was the brainchild of Malcolm McLean, who saw the efficiency of containerized shipping. Containerized shipping continues to grow, as does the size of the ships. The Dali is a Neopanamax container ship built in 2016. She is a big boat, 984 feet long with a beam of over 158 feet, capable of carrying nearly 10,000 TEUs. There are now almost 6,000 container ships riding the waves. The biggest carry 24,000 TEUs, more than double the size of the Dali. For all her size, 21 sailors are all that is needed to sail her.

Scale is an important driver in the chemical industry. I wrote an article about the importance of scale in chemical production, even including an origami demo to show the source of the economies of scale. In building chemical plants, material — metal — is used to construct largely cylindrical vessels. The cost of these vessels dominates the capital expenditure. Doubling the volume of a cylindrical vessel doesn’t double the amount of material needed for the walls. It only increases by about a factor of 1.5. The increase in capital is given by the increase in capacity raised to the 0.6 power. I guessed the 0.6 factor was similarly driving the ships to get bigger. The origami cup used in my demo looks a little like a ship — maybe the math was the same.

Bigger ships cost more than smaller ones, as bigger chemical plants cost more than smaller ones. The cost per capacity drops as scale increases. The cost per capacity for a ship drops more slowly as size is increased than for a chemical plant, more than for a perfect cylinder. Ships tend to grow in length more than width is one explanation. Whatever the reason, the impact on increasing scale is less than I anticipated. The cost of a ship increases by the capacity raised to ~0.8 power. Still, for an investment in the $100 million range, with a 25-year lifetime, CAPEX is a major driver.

The surprise was fuel, by far the biggest contributor to operating expenses. Fuel consumption per ton transported drops as ships get bigger. Hydrodynamic drag is proportional to the area. Given the shape of container ships, the area moving through the water increases very little as the ships get longer. Doubling the size of the ship doesn’t double the fuel use. That means emissions drop too. That is a good thing since the emissions from maritime shipping are actually quite large: an estimated 858 million metric tons of CO₂emissions globally, 3% of global emissions.

Scale reduces the three big cost drivers in shipping, capital, labor, and operating expenses. It is a win all around and explains why decades of growth in vessel size is sure to continue. Ships are destined to get bigger, putting more bridges in peril.