The Dali container ship appeared to move slowly before hitting the Francis Scott Key Bridge in Baltimore on Tuesday. However, it delivered such great force that a reasonable comparison would be to launching a rocket.

How can something that travels slower than a casual cyclist have such a devastating impact? The answer lies in its mass: about a third to half that of the Empire State Building.

It could take months or even years for engineers to perform careful simulations of this disaster that take all variables into account. But we used the limited data available to begin to understand the force of the collision.

And even our most simplified calculations show that the impact was enormous.

Our lowest estimate of how much force would be needed to slow the Dali if it were fully loaded is about 12 million newtons, about a third of the force needed to launch the Saturn V rocket for the Apollo lunar missions.

And our most advanced estimates, reviewed by several civil engineering experts, suggest that it is realistic to estimate the force of the impact on the pier at more than 100 million newtons.

“It’s on a higher energy scale than you can really imagine,” said Ben Schafer, a professor of civil and systems engineering at Johns Hopkins.

Comparing very large forces

EXAMPLE | APPROXIMATE STRENGTH (IN NEWTONS) |
---|---|

Fully loaded 18-wheeler crashing into bridge at 80 mph | 1 million |

Force needed to decelerate fully loaded Dali in 38 seconds | 12 million |

Saturn V rocket thrust at launch | 35 million |

Earth’s gravitational force on 100 female blue whales | 110 million |

Force required to decelerate fully loaded Dali in 4 seconds | 115 million |

Force required to decelerate fully loaded Dali in 2 seconds | 230 million |

Experts disagreed on whether it was reasonable for any bridge pier to withstand a direct collision with a huge container ship.

“Depending on the size of the container ship, the bridge doesn’t stand a chance,” said Nii Attoh-Okine, an engineering professor at the University of Maryland. He said that Baltimore’s Key Bridge was working perfectly before the accident occurred and that he thought 95 to 99 percent of the bridges would be damaged if such a container ship struck them.

But Sherif El-Tawil, an engineering professor at the University of Michigan who reviewed our calculations, said it was feasible to design a pier that would remain standing after such an impact. “If this bridge had been designed to current standards, it would have survived.”

Modern bridges, designed in the era of “ultra-large” containers, are typically built with stronger piers or protective systems around the piers that can absorb or deflect the force of ship collisions.

But the Key Bridge was completed in 1977, when standards were different and ships were much smaller.

## Doing the math

To work on our estimate, we start with an equation familiar to anyone who has taken a physics class.

Our first task, and a major source of uncertainty, was to find these numbers.

**First, dough: **

We estimate the Dali’s mass to be somewhere between 195,000 metric tons fully loaded and 78,000 metric tons empty, based on ship records and maritime standards on how much weight a typical container ship can carry. We know the ship was carrying at least some cargo, so even with a light load her mass was probably at least 100,000 metric tons, our lowest estimate.

**Next, acceleration:**

To estimate how quickly the ship slowed, we pulled data from two ship tracking websites, MarineTraffic and My Ship Tracking, which provide regular snapshots of ship movements.

Before the collision, data indicates that the ship was moving at about 12.5 kilometers per hour. (The ship’s speed is measured in knots, but we converted the numbers.) The next data point we find, 38 seconds later, shows it moving at 4 km/h.

In the absence of definitive data from the ship’s black box, let’s plug these numbers into our formula.

Based on these numbers, we estimate that the average force needed to slow the ship is between 6 and 12 million newtons.

**Here’s the problem, however.** This calculation assumes that the spacecraft slowed down at a fairly consistent rate during those 38 seconds.

In reality, we think that the ship’s speed dropped precipitously in the first moments of the collision, as it came into contact with the pier. Videos of the collapse indicate that most of the action occurred in just a few seconds, from the moment the ship hit the pier to the moment the pier tipped over, triggering the collapse of the bridge.

The ship probably did *majority* of its deceleration in those first seconds. (The data and photos suggest that it continued to travel some distance, but not much, after making contact with the pier.) But for now, we can only use video evidence to guess exactly how long that part of the collision lasted. .

“I think this is the biggest uncertainty,” said Themistoklis Sapsis, a professor of ocean engineering at MIT who reviewed our calculations. Based on video footage, he estimated the collision time was probably between one and four seconds.

You can see below how much our force calculation varies depending on the duration of the collision and the amount of cargo the ship is carrying.

At one end of the spectrum, if the deceleration occurred for four seconds and the Dali was lightly loaded, the average force experienced by the ship would have been about 60 million newtons.

But a full Dali and a quick one-second deceleration would mean a force in excess of 400 million newtons.

Somewhere in between, assuming that most of the deceleration occurred over two seconds, we are left with an estimated force of 120 million to 230 million newtons.

We tried one more method: using a formula for calculating ship collision force published by the American Association of State Highway and Transportation Officials, the industry organization that publishes bridge safety standards. If we plug in our numbers for Dali’s mass and velocity, we get 142 million newtons.

Engineering experts have warned that while this formula provides a rough estimate based on the limited data we have, it is also an oversimplification with a lot of uncertainty.

Our own calculations are also an oversimplification. We didn’t try to take into account the ship’s rotation, the angle of the collision, and exactly how and where it collided with the pier (a smaller force applied in the wrong place can be more damaging than a large force applied elsewhere). The container ship would also have dragged a considerable amount of water with it, which would have added its own momentum.

But the thing is: even the widest reasonable range is on the order of tens to hundreds of millions of newtons – an astonishingly large force by any estimate.

## What this means for bridges

Instead of designing a pier to withstand an impact of tens or hundreds of millions of newtons, the engineers said, you can help protect a bridge by creating protective systems — such as “fenders,” artificial islands or structures called dolphins — that would spread force, slow the ship before impact or divert it from the dock.

Safety standards could also be revised to require tugs to accompany large ships for longer periods until they are safely away from infrastructure.

In 1980, a ship collision caused the collapse of the Sunshine Skyway Bridge in Tampa Bay, Florida, and in the decade following that disaster, the industry approved guidelines that bridges or their protective structures should withstand greater forces.

Collisions between ships and bridges that cause this level of damage are extremely rare, El-Tawil said. Still, he said he was surprised a protection system hadn’t been added to the Key Bridge.

“The protection system would have diverted the ship from the docks, protected the bridge, protected the community from the loss of a critical bridge and protected the ship itself,” he said.