“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 cover here. Here’s a snippet from the final rebel assault on the Death Star:
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.
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 need to cover about 12 times as much area as that.
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.
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 x safety buffer) x (plane length + 2 x safety buffer)
Plane storage area including safety buffer = (80 + 2 x 10) x (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 x plane storage area including safety buffer
Total area required = 5 x 9300 m^2
Total area required = 46500 m^2
Air Conditioning for the Hanger
Often maintenance on these aircraft is 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: