# Star Wars Episode IV

# The Movie

“Star Wars Episode IV: A New Hope” premiered in 1977 and started one of the greatest movie series ever. It’s full of space movie math, some of which we’ll investigate here.

## Math Situation 1: Hanger Storage

The rebel base is on a planet and their space ships are stored in some kind of hanger. Military and civilian aircraft are also often stored in aircraft hangers, or inside aircraft carriers, where space is restricted.

In the movie, approximately 30 rebel fighters were deployed to assault the empire’s death star – the fighter shown above is a similar-sized one.

If we assume that a fighter measures 12.5 metres long and 13 metres long, and we pack them in a regular square pattern (see the image below), how big a hanger do we need to store them?

First we can work out the area that one ship takes up:

*Area one ship = width x height*

*Area one ship = 13 x 12.5*

*Area one ship = 162.5 m ^{2}*

But there are 30 ships, so we need to multiply the area for one ship by 30:

*Total area required = #ships x area per ship*

*Total area required = 30 x 162.5 m ^{2}*

*Total area required = 4875 m ^{2}*

A small block of land that a house sits on is about 400 square metres. So the hanger would take up about as much land area as 12 small house blocks.

## Math Situation 2: Staffing the Death Star

The Death Star was an enormous space station built the Empire, measuring approximately 120 km in diameter. It was so gigantic, that Obi Wan Kenobi said this famous line, “That’s no moon. It’s a space station.”

Staffing this huge station with personnel would require a lot of people – but how many exactly? We can look at the largest vessels we have in real life, and attempt to scale up their staffing requirements to estimate what the Death Star would need.

* Narongsak Nagadhana / Vadimmmus / 123rf.com.*

The largest vessels we have in real life are aircraft carriers. The Nimitz class aircraft carriers are the largest, measuring 333 metres long and weighing over 100,000 tonnes. They have about 5000 people on board, and they are often nicknamed a “floating city”.

A reasonable assumption might be that the staff per volume of ship is the same for both the carrier and the space station.

We can approximately model the aircraft carrier as a triangle-based prism, 333 metres long and with a triangle cross-section:

*Carrier volume = cross-sectional area × length*

*Carrier volume = 30 × 77 × 333*

*Carrier volume = 769230 m ^{3}*

And then work out the staff density:

*Staff per cubic metre = 5000 / 769230*

*Staff per cubic metre = 0.0065*

Now for the Death Star:

*Death Star volume = 4/3πr ^{3}*

*Death Star volume = 4/3π × (60km) ^{3}*

*Death Star volume = 904779 km ^{3}*

Now the personnel calculation:

*Death Star staff = volume in cubic metres × staff / cubic metre*

*Death Star staff = 904779 × 1000 ^{3} × 0.0065*

*Death Star staff = 5,881,000,000,000*

That’s almost 6 trillion staff – which seems perhaps a little high.

What about if the staff are only in the outer 0.1 km shell of the Death Star? We can recalculate:

*Death Star outer skin volume = 4/3π(r _{outer}^{3} – r_{inner}^{3})*

*Death Star volume = 4/3π × (60 ^{3} – 59.9^{3})*

*Death Star volume = 4516 km ^{3}*

Which gives us a staff calculation of:

*Death Star staff = volume in cubic metres × staff / cubic metre*

*Death Star staff = 4516 × 1000 ^{3} × 0.0065*

*Death Star staff = 29,354,000,000*

That’s still 29 billion staff!

The actual figures given for the Death Star staff are usually in the range of a few hundred thousand to a couple of million – much fewer than our calculation. This probably means that staff aren’t distributed over the entire station, but rather only in certain sections.

## Real Life Example – Civilian Plane Storage

Airports and companies also need to store aircraft in hangers. Let’s say you need to store a reserve fleet of 5 A380s at all times in one hanger in one long row.

*Alexander Zelnitskiy / Nils Weymann / 123rf.com.*

To store them safely, let’s leave a safety buffer of 10 metres around each plane where nothing else can go (including another plane’s safety buffer). How big an area will your hanger need to cover? The A380 is 73 metres long with an 80 metre wingspan.

To work out the area each plane will take, we need to add a 10 metre buffer (twice) to both the length and the width:

*Plane storage area including safety buffer = (plane width + 2 × safety buffer) × (plane length + 2 × safety buffer)*

*Plane storage area including safety buffer = (80 + 2 x 10) × (73 + 2 x 10)*

*Plane storage area including safety buffer = 100 x 93*

*Plane storage area including safety buffer = 9300 m ^{2}*

But there are 5 planes, so we need to multiply this area by 5:

*Total area required = #planes × plane storage area including safety buffer*

*Total area required = 5 × 9300 m ^{2}*

*Total area required = 46500 m ^{2}*

## Air Conditioning for the Hanger

Maintenance on these aircraft is often performed in these hangers. If we say the **average** height of the hanger roof is 30 metres (the A380 is 24 metres high), what volume of air is stored in the hanger that needs to be cooled?

To calculate the volume of the hanger, we need to multiply its floor area (which we just calculated) by the average height of the roof:

*Hanger volume = floor area × average height*

*Hanger volume = 46500 × 30*

*Hanger volume = 1395000 m ^{3} *

Wow – that’s 1.4 **million** cubic metres of air.