25.03.2021

Why Are Ships So Slow?

Ships have a reputation for being large bulky lumps that slowly plot around the world even a passage from San Francisco to Southampton on a modern ocean liner now takes the best part of a week. What is it about ships that makes them so slow? In terms of physical size ship’s engines are enormous. They are so big that the larger ones are typically known as cathedral engines – the Emma Maersk is powered by one of these. She is an E-Class container vessel almost 400 meters long and was the largest container ship when she was launched back in 2006.

Of course, since then Maersk have introduced the Triple E Class which is slightly wider and longer and other companies have bought out ships even bigger; still her engine weighs more than three hundred tons and pumps out a whopping 109000 horsepower. Now, it is easy to compare that to a car as they all publish the horsepower of their engines. The typical cars you are looking at about hundred horsepower depending on the configuration you have chosen. At the extreme end, you have got Formula 1 cars which can be pushing a thousand horsepower.

It is a little trickier to compare that to an aircraft as they use jet engines which produce thrust instead of the mechanical horses that we use anywhere else. The math is complex, but the best estimates are found - the typical 747 engines are 150000 HP mark. So, for power it makes sense that the plane is the fastest but the ship comes second and she is still slower that the car. So there must be more to it than just the horses.

With movement and things another factor always makes an appearance – mass – it is in the energy formula with kinetic energy being half MV squared and it forms acceleration force being mass times acceleration. So, how we can add mass into this discussion? We can look at horsepower per ton instead. For the plane we can take the 474 – they come in anywhere between three and five hundred tons and are powered by four of those jet engines. A crude power gives the power per ton, let’s say, 1200 horsepower per ton. The car we said was around 100 horsepower typically and you can assume in normal car weighs between one and two tons, and averaging that out gives you about 75 HP per ton.

Of course, with F1 cars they are somewhat lighter and more powerful, so their figures are closer to the figures we got for the airliner. Now the ship, fairly obviously, she will weigh the most. The fully loaded Emma Maersk will weigh around 200000 tons, with her engines delivering 109000 HP, we will calculate the power per ton as 0.5 HP/ton. The vehicles are now starting to settle in the correct order. The plane is still ahead, the car is second and the ship is training a long way behind. But fir the ship, from here it only gets worse.

Do you remember working out terminal velocity at school – is when the force produced by an engine matches the resistance force from the medium. The object is moving through. For example, you drop a ball and it will fall faster than if you drop a feather, the wind resistance of the feather is much greater so its velocity ends up being slower. The same applies with vehicles. The plane experiences air resistance, the car – a combination of air resistance and friction with the ground, but the ship is moving through water a comparatively dense medium. This means she is experiencing the greatest force against her.

The drag equation explains that drag is proportional to a cross-sectional area and the square of the speed. The cross-section will get from the breadth of the ship times its draft, which we can assume to e a constant for most ships. Of course, if you reduce the draft, like when there is no cargo, the ship will be able to go faster as there is less drag. Otherwise, drag is determined by the square of the speed. You double the speed, you quadruple the drag. You can sort of assume the force produced by the engine is constant. There are variations due to the water flow, but we can ignore those for now.

All the while the engine produces more force than the resistance. The ship will accelerate as she speeds up. The drag increases according to the square of the speed. Once the drag force matches the engine force, no more acceleration occurs. The ship has reached terminal velocity. For the Emma Maersk this is around 25 knots and that is typical for most large ships. For smaller ships, this is typically slower and that is because their engines produce more power. But crucially the cross-section does not reduce in proportion to that change in engine power.

There are ferries that do go significantly faster than normal ships, some of them are called fast cats, which is short for fast catamaran and a catamaran is just a boat that has two hulls. Instead of a single box-shaped hull the cat has two thin hulls. The separation between them produces the transverse stability that they need and the buoyancy is just produced by the combined underwater volume of both hulls. Clearly, there is less buoyancy which means less carrying capacity which is why they are usually only passenger ships. They key here is that you have drastically reduced the cross-section that produces the underwater drag. Reduce the drag and you will increase the theoretical maximum speed add on a few jet turbines and you’ve got yourself a ferry that is capable of speeds far higher than a typical ship.

And what about small speed boats? Well again, they reduce the cross-sectional area allowing higher speeds but rather than change the shape of the hull, they are designed to rise above the water instead of pushing through it. We call it planing above a certain speed the water flow lifts the hull, reducing the cross-section reduces the drag and increasing the speed. Hydrofoils do a similar thing except they have an underwater wing to produce the lift. At slow speeds the whole hull creates resistance; as the speed increases, lift is generated lifting most of the hull clear, reducing the cross-section and increasing the speed.