When I first heard the term naval architecture I thought it was the artistic practice of designing beautiful boats. It turns out it’s a proper scientific discipline dedicated to the engineering of ships.
Over the course of this article we’ll go over different aspects of naval architecture. I’ll explain how ships are propelled, what makes them stay afloat, and how they’re carefully designed to not tip over even in dynamic conditions:
To understand why a ship rocks side-to-side in the wavy ocean waters, we first have to understand that it’s water itself that’s responsible for all of the ship’s behaviors. We’ll start with a simple device – a water-filled syringe.
You’ve probably seen a syringe before. When its plunger is pressed, the contents of the syringe comes out on the other end. In the demonstration below we have a syringe connected through a thin hose to another container that has a spring in it. The entire system is filled with water. As you increase the force on the plunger observe the little spring being compressed at the other end of the hose:
By applying force on the plunger we increase the pressure in the fluid, which in turn pushes the little piston and compresses the spring. We can measure that pressure using a pressure gauge. In the demonstration below the sliders allow you to control the applied force and the area of the plunger:
Observe that the pressure P on the gauge is proportional to the perpendicular input force F, but it’s inversely proportional to the area A. We can tie these three values using the following equation:
In metric system pressure is expressed in pascals (Pa) named after Blaise Pascal, while in the imperial system pounds per square inch (psi) are commonly used.
Notice that we no longer have any spring to compress. Even though we’re applying a force the plunger doesn’t move since water, unlike air, is minimally compressible. It’s easy to squeeze an empty, tightly screwed plastic bottle, but when filled to the brim with water the bottle won’t budge much. At the pressures we’re applying here, water practically doesn’t change its volume.
With a syringe, we’ve directly applied a force by pushing on the plunger, however, we could recreate that experiment by putting a heavy, tightly fitting weight on top of water in a container. In the demonstration below you can control how heavy the weight is to see how it affects the pressure read by the gauge:
Note that even when we remove the weight the pressure meter shows a non-zero read. The water itself also has weight so its mass above the point of measurement contributes to the readout as well.
Let’s try to quantify the force exerted by the water. Firstly, notice that the shape of the water above the measurement forms a cylinder with height h and a base surface area A:
The mass m of that cylinder of water is just its volume V times the density ρ of the contained water:
That highlighted volume V, however, can also be expressed as the area of the base A times the height h which we can plug into the equation for mass m:
The force of gravity F acting on that water is equal to its mass m times the gravitational acceleration g:
If we now plug all these values to the equation for pressure P = F / A we get:
Which we can simplify by reducing the area A to obtain the final equation for pressure P of liquid with density ρ at a depth h under surface:
Note that the resulting pressure P is independent of the base area, it’s only affected by the height h and density ρ of the water above:
In general the density ρ of water is not constant and depends on temperature and salinity, but at the scales we’re interested in we can assume its value doesn’t change.
If you recall our first demonstration of a loaded syringe, you may remember that the pressure applied to the plunger “travelled” through the hose to act on a spring, which was quite distant from the syringe itself. The very same rules apply here. Observe the pressure shown by the gauge two different spots of this L-shaped container: