Stopping and Time

Let’s consider a ship traveling with an initial speed (v_1) and a mass (m). What backward force (F) is necessary to bring it to a stop over a time period (?t)? Assuming a constant force throughout this time frame, we can apply the momentum principle, which can be expressed as follows:

The momentum (p) is defined as the product of mass and velocity. Thus, if the ship comes to a halt (final velocity = 0 m/s), we can calculate the force needed to stop it. For simplification, we can represent this as a scalar equation, acknowledging that force and momentum are vectors.

However, estimating the time of the collision (?t) is complex. Fortunately, we can employ an alternative method to compute the force involved.

Stopping and Distance

Assuming the ship has mass (m) and moves with an initial velocity (v_1), it will stop over a distance (?r). A backward force (F) is necessary to decelerate and halt it. Below is a diagram depicting this scenario. Numerical values will be added shortly.

Given that we are dealing with force and distance, the Work-Energy principle is most applicable here. This principle states that a force acting on an object performs work, which we can define as:

While force (F) and displacement (?r) are vectors, work is a scalar quantity. If the force opposes the displacement (acting backward), the angle is 180 degrees, resulting in negative work. This work alters the energy of the system, which, in this context, is solely the ship. The kinetic energy (KE) of the ship is expressed as:

With a final velocity of zero, the kinetic energy at that point is also zero. Thus, the change in energy amounts to -1/2mv². Combining these concepts allows us to derive an expression for the force acting on the ship.

This leads us to an interesting observation: while the momentum principle indicates that the force required to stop the ship depends on its mass and velocity, the work-energy principle shows that it is influenced by the mass and the square of the velocity.

Estimating Stopping Force

Let’s delve into some numerical calculations now. The Dali's reported mass is 93,000 tons, which we’ll interpret as long tons, equivalent to 9.3 x 10³ kilograms. The reported speed at the time of the collision was 6.8 knots, translating to approximately 3.5 meters per second.

Estimating the stopping distance is challenging, but using available images from the NTSB, we can make an informed guess. Assuming standard 40-foot shipping containers, we can measure the distance the ship traveled past the bridge. Utilizing Tracker Video Analysis, I estimate this distance to be around 49 meters. However, the actual distance the Dali traveled during the impact is likely closer to 30 meters.

Now, integrating these values into calculations yields an impact force of approximately 1.42 x 10⁷ Newtons, or around 32 million pounds. This calculation is based on a conservative estimate of stopping distance. However, it's worth noting that this assumes a constant impact force, which is likely an oversimplification; in reality, the force would likely spike during impact.

[How Do Ships Stop Without Brakes? - YouTube]

This video explores the mechanisms behind how ships can come to a stop without traditional braking systems, shedding light on the physics involved.

Just for comparison, consider attempting to stop a 93,000-ton vessel traveling at 6.8 knots without a bridge. Would it be feasible to use a rocket engine for this purpose?