How Do You Stop a Massive Ship?

Image: NTSB. From the NTSB Drone Video of the Dali collision with the Francis Scott Key Bridge.

It was a tragedy. There was a loss of life, huge economic impact as well as damage to infrastructure. Yes, I’m referring to the to collision between the DALI cargo ship and the Francis Scott Key Bridge in the port of Baltimore. The ship appears to have lost power which resulted in a loss of control. This lead to a collision and a collapse of the bridge.

Although this is indeed a disaster, there’s still some very important physics here. In particular, how do you stop a massive cargo ship? Not just any ship, a vessel that weighs somewhere around 93,000 tons moving at about 2 miles per hour. That’s not going to be easy to stop. There are actually two different ways to make this calculation. I could estimate the distance it takes to stop or I could estimate the time.

Stopping and Time

If the ship is moving with an initial velocity (v_1) with a mass (m), what backwards pushing force (F) will stop it if we know the time interval (Δt)? Let’s assume that there is a constant force over the time interval. In this case, we can use the momentum principle. It looks like this:

Here, the momentum (p) is the product of mass and velocity. So, if the ship stops (with a final velocity of 0 m/s), then we can solve for the magnitude of the force. Note: just to make things simpler and since the momentum and forces are in…