Pirates of the Caribbean 5: there be some good science in that there film

It’s hard to believe, but it has been more than 13 years since the first Pirates of the Caribbean film set sail on our screens. The fifth instalment, out this week, is Pirates of the Caribbean: Dead Men Tell No Tales.

Like the third film in the series, it opens with a powerful scene showing an emotional father-son reunion following events of the previous films.

Dead Men Tell No Tales introduces a new nemesis for the iconic Captain Jack Sparrow (played by Johnny Depp), in the Spanish Navy ghost captain Armando (played delightfully evil by Javier Bardem). He’s not the only villain, with Australian actor David Wenham adding to his growing list of villainous roles as well.

Salazar leads a ghost crew intent on eliminating every pirate on the seas. Jack, aided by the feisty astronomer Carina Smyth (Kaya Scodelario), scrambles to find the magical Trident of Poseidon with which he may defeat Salazar.

The Pirates films have always deftly combined a basis in the “Golden Age of Piracy” with supernatural fantastical themes and regular departures from reality.

In this science review, I’ll examine some of the phenomena shown in the film to see whether the filmmakers have gone for entertainment (always understandable), realism or both. But beware, there be moderate spoilers ahead.

How ships turn

Salazar has a good reason to want his revenge on Sparrow. During an encounter in Jack’s youth, he tricked Salazar into following his ship into danger, only to lasso a nearby rock outcrop and execute what on land would be called a bootleg turn.

Sneaky Jack Sparrow executes a bootleg turn. (Walt Disney Studios)

During the bootleg turn, Jack’s ship leans inwards. Water vessels behave very differently during turns, depending on a number of factors, and some will lean inwards during a turn, others outwards.

Executing a bootleg turn in a ship. (123rf.com/rustamank/Daria Yakovleva/blueringmedia/Michael Milford)

When a ship turns, there is a centrifugal force that appears to act on the ship (red arrow in the animation, above). The only force available to counteract this one is the reaction force from the water the ship is immersed in.

Tilting inwards or outwards during a turn. (123rf.com/Miro Kovacevic/Michael Milford)

A ship has a centre of gravity (shown by the black and white circle, above) that stays in the same position relative to the structure of the ship, unless cargo is moved around inside the ship. The centre of gravity is the point where one can consider the gravitational force to act on the ship.

A ship also has a centre of buoyancy (shown by the red and white circle, above) that moves around depending on the tilt of the ship hull. It represents the location of the centre of gravity for the volume of water that the hull displaces.

In the left image, the water reaction force pushes in a line that passes below the centre of gravity. This force is trying to twist the ship hull in an anti-clockwise direction, tilting it to the left. The buoyancy force counteracts this, trying to twist the ship hull back in a clockwise direction.

In the right image, the water reaction force pushes in a line that passes above the centre of gravity. This force is trying to twist the ship hull in a clockwise direction. So the ship has tilted to the right, so that the buoyancy force can counteract it.

This is a bit of a simplification, in part because this is a dynamic process where the centre of buoyancy moves around as the ship tilts.

In Dead Men Tell No Tales, Jack throws a rope out to lasso the rock and turn his ship around. The rope is attached to the ship fairly high up, pulling at the ship most likely above its centre of gravity, and hence tilting the ship towards the rock. So that’s a plus for the science plausibility.

Robbing the bank

Jack hatches an audacious plan to hitch horses to a one tonne safe and drag it out of the bank. The plan comes undone when the safe doesn’t budge and the horses drag the entire bank building through town instead.

But can 12 horses pull a one tonne safe along the ground? What about an entire bank building?

I initially thought the one tonne safe was plausible but the building was ridiculous. But horses are incredibly strong, with pairs of draft horses pulling up to 50 tonnes.

This video (below) shows two draft horses pulling about 5.4 tonnes. For 12 to pull a building along a street isn’t so far outside the realms of possibility.

Whirling guillotine

In possibly the most memorable scene of the film, Jack is just about to be executed by guillotine when a cannonball smashes into it. What follows is the farce of the guillotine blade getting closer and then further away from his neck as the entire guillotine spins in the air.

Don’t try this at home kids. (123rf.com/Milosh Kojadinovich/Michael Milford)

If you’ve ever spun something attached to a string, you know that if you spin it fast enough, the string stays taut.

To avoid the guillotine chopping Jack’s head off, it has to spin fast enough so that the acceleration of the cutting bit outwards at least counteracts the acceleration of gravity. Let’s say the guillotine is four metres tall, which is the radius r. We can work out the time period it takes to do one revolution, T:

acceleration = 4 × π² × r / T²

T² = 4 × π² × r / acceleration

T² = 4 × π² × 4 / 9.81

T = 4.012 seconds

The guillotine would need to spin in a full circle at least once every four seconds. In the film it appears to be spinning much more quickly so Jack surviving is plausible.

Longitude by chronometer

While navigating on the ship, astronomer Carina uses a chronometer, a highly accurate time piece developed over a long time period in the 18th century.

Efficient navigation at sea requires knowing both your latitude and longitude, and the chronometer was one of the critical technological developments in seafaring history.

Latitude is easy to find, for example by looking at the altitude of the sun at noon (its highest point). Longitude was much harder to find at sea, and required the combination of a knowledge of the stars and the time at a reference location, such as in Greenwich, England.

The chronometer kept time accurately, enabling sailors to navigate much more efficiently and reliably than ever before. The long race to win this technological race is a fantastic story and has been the subject of an award winning book, Longitude by Dava Sobel.

It’s quite refreshing to see the film accurately portray some of the aspects of navigating on the open seas hundreds of years ago, a big plus for the science.

The verdict

The film itself is a lot of fun, with several moments of genuine pathos which were missing from some of the recent instalments.

Depp, Rush and Bardem are great as always. Kaya Scodelario does well, although she’s hamstrung by scripting at times.

Like all long running film series, it also benefits from the stronger familiarity and emotional investment by the audience in key characters - whether bringing them back or killing them off.

In terms of the action and the science, the film has a surprising amount of both. Much of it is explicit, usually through astronomer Carina, who at various times re-calibrates an astronomical telescope or uses a chronometer to work out their longitude. Other aspects are implicit in the many chases and fight scenes.

Also surprisingly, a lot of the science stacks up reasonably well.

As to the science behind ghost sharks? Well, we already have those in chimera (also known as ghost sharks), even if they aren’t quite as snappy as the ones in this new film.

Acknowledgements: The author thanks Ross McAree, Peter Jacobs and Alexander Klimenko at the University of Queensland for their assistance with some of the theory. Any mistakes are entirely the fault of the author.