Erin Schaff/The New York Times
Force of Ship Impact Was on the Scale of a Rocket Launch
The container ship Dali appeared to move sluggishly before striking the Francis Scott Key Bridge in Baltimore on Tuesday. Yet it delivered a force so large that one reasonable comparison is to a rocket launch.
How could something traveling slower than a casual bike rider cause such a devastating impact? The answer lies in its mass: roughly a third to a half of the Empire State Building.
It may be months or even years before engineers conduct careful simulations of this disaster that take into account all the variables. But we used the limited available data to start to understand how strong the collision might have been.
And even our most oversimplified calculations show the impact was enormous.
Our lowest estimate of how much force it would take to slow the Dali, if it were fully loaded, is around 12 million newtons, about a third of the force it took to launch the Saturn V rocket for the Apollo moon missions.
And our higher-end estimates, reviewed by several civil engineering experts, suggest it is realistic to put the force of the impact with the pier at upward of 100 million newtons.
“It’s at a scale of more energy than you can really get your mind around,” said Ben Schafer, a professor of civil and systems engineering at Johns Hopkins.
EXAMPLE | APPROXIMATE FORCE (IN NEWTONS) |
|---|---|
| Fully loaded 18-wheeler colliding with a bridge at 80 m.p.h. | 1 million |
| Force required to slow the fully loaded Dali over 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 slow the fully loaded Dali over 4 seconds | 115 million |
| Force required to slow the fully loaded Dali over 2 seconds | 230 million |
Figures for the Dali container ship are initial estimates based on preliminary and incomplete data.
Experts disagreed on whether it was reasonable for any bridge pier to withstand a direct collision with a massive container ship.
“Depending on the size of the container ship, the bridge doesn't have any chance,” said Nii Attoh-Okine, a professor of engineering at the University of Maryland. He said that Baltimore’s Key Bridge had been performing perfectly before this accident occurred, and that he thought 95 to 99 percent of bridges would be damaged if such a container ship were to strike 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 stay standing after such an impact: “If this bridge had been designed to current standards, it would have survived.”
Modern bridges, designed in the age of ultralarge shipping containers, are typically built with stronger piers or protection systems around the piers that can either absorb or deflect the force of ship collisions.
But the Key Bridge was completed in 1977, when standards were different and ships were far smaller.
Doing the Math
To work through our estimate, we started with an equation familiar to anyone who has taken a physics class.
Our first task, and a major source of uncertainty, was finding those numbers.
First, mass:
We estimate the mass of the Dali to be somewhere between 195,000 metric tons fully loaded and 78,000 metric tons empty, based on ship records and maritime standards for how much weight a typical container ship can take on. We know the ship was carrying at least some cargo, so even with a light load its mass was probably at least 100,000 metric tons, our low-end 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 the movements of ships.
Sources: MarineTraffic and My Ship Tracking. Note: Data points are represented as circles. Lines are intended as guides only. (That is: We don’t know the true speeds in between our data points.)
Before the collision, the data indicates that the ship was moving around 7.8 miles per hour. (Ship speed is measured in knots, but we converted the numbers.) The next data point that we could find, 38 seconds later, shows it moving at 2.5 m.p.h.
In the absence of definitive data from the ship’s black box, let’s plug these numbers into our formula.
For the actual calculation, we used metric units.
Based on these figures, we estimate that the average force required to slow the ship is between 6 million and 12 million newtons.
Here’s the catch, though. That calculation assumes the ship slowed at a pretty consistent rate over those 38 seconds.
In reality, we think the ship’s speed dropped precipitously in the first few moments of the collision as it made contact with the pier. Videos of the collapse indicate that most of the action took place in just a few seconds, from when the ship first struck the pier to when the pier toppled, kicking off the bridge collapse.
The ship probably did most of its slowing down in those first few seconds. (The data and photos suggest it continued to travel some distance, but not far, after first making contact with the pier.) But for now, we can only use video evidence to make a guess at exactly how long that part of the collision took.
“I think this is the biggest uncertainty,” said Themistoklis Sapsis, a professor of ocean engineering at M.I.T. who reviewed our calculations. Based on video footage, he estimated that 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 how much cargo the ship is carrying.
Data sources: My Ship Tracking and MarineTraffic (speed), Vessel Finder (ship deadweight) and The Maritime Engineering Reference Book (cargo estimates).
On one end of the spectrum, if the deceleration took place over four seconds and the Dali was lightly loaded, the average force experienced by the ship would have been around 60 million newtons.
But a full Dali and a quick one-second deceleration would have meant a force above 400 million newtons.
Somewhere in the middle, assuming most of the slowdown took place 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 to calculate the ship collision force published by the American Association of State Highway and Transportation Officials, the organization that publishes bridge safety standards. If we plug in our numbers for the mass and speed of the Dali, we get 142 million newtons.
Engineering experts warned that while this formula provides a ballpark estimate based on the limited data that we have, it is also an oversimplification with a lot of uncertainty.
Our own calculations are also an oversimplification. We don’t try to account for 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 have also dragged a sizable amount of water with it, which would add its own momentum.
But the point is: Even the widest reasonable range is on the order of tens to hundreds of millions of newtons — a mind-bogglingly large force, by any estimate.
U.S. Army Corps of Engineers via Reuters
What it means for bridges
Rather than designing a pier to withstand an impact of tens or hundreds of millions of newtons, engineers said, you can help safeguard a bridge by creating protective systems — such as “fenders,” artificial islands, or structures called dolphins — that would spread out the force, slow the ship prior to impact or divert it from the pier.
Safety standards could also be revised to require that tug boats 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 in Florida, and in the decade following that disaster, the industry passed guidelines that bridges or their protective structures should withstand larger forces.
Collisions between ships and bridges causing this level of damage are exceedingly rare, Mr. El-Tawil said. Still, he said he was surprised that a protection system had not been added to the Key Bridge.
“The protection system would have diverted the ship away from the piers, protected the bridge, protected the community from the loss of a critical bridge, and protected the ship itself,” he said.