If you have been on the internet, you surely have seen this website showing the sizes of different starships. Way cool. Here is a small sample – but it doesn’t do the site justice. You really need to go browse around.
Of course, I can’t let something like this just go. One of the things I always think is interesting is to consider objects of different size. Perhaps the general idea is that you can just scale stuff up or down as you like. But, it doesn’t work this way. Let me start with my own spaceship. It is a sphere with a thruster on the back. It just holds one person.
Now, what happens if I want to make a bigger version. Let me go ahead and get some related points out of the way.
What does the thruster do?
Great question. Really, what do they do? In real spacecraft, these thrusters are used to change the momentum of the spacecraft. You could think of these as exerting a force on the craft which would make it accelerate. What if you kept the thruster on for a long time? You would keep accelerating. Do you see the problem? Most of these ships in the science fiction shows fly with their thrusters on at constant speed. This is what would happen if you have some resistive force (like air resistance).
The point is: I am going to assume that the thruster accelerates the ship – which may not agree with the movie. Moving on.
I know someone is going to point out some of these issues (even though I am stating now that they are assumptions). Some of these might not be completely valid – but it will be close enough to show my point.
- Force from the thruster is proportional to the area of the thruster. I know – you could come up with all sorts of reasons why this would not be true, but I am still going with this assumption.
- The density of big and small starcrafts are about the same. Yes, maybe the walls of a ship are the same thickness, and this would make bigger ships have a lower density – but then they have more internal walls also.
- Small starcraft and large starcraft have thrusters to produce the same (or similar) acceleration.
- The following all mean the same thing: space ship, starship, starcraft, space craft, etc…
Let me look at my small craft above. If the only force on it is from the thruster, then:
If Fthrust is the only force on the ship, then the acceleration and the thrust are always in the same direction. This means I can just look at the magnitude of thrust and acceleration. In my above ship, it is a sphere with a radius R. The thruster is circular with a diameter L. If thrust is proportional to the area of the thruster, I can say:
Where K is some constant. The mass is related to the density and the volume so that:
Here, C is another constant (not to be confused with the konstant K). C includes info about the shape and the density – both of which are not too important. This means:
One more thing – let me get L as a function of R.
Notice – I made a new constant (alpha). Just because.
A bigger spherical ship
I am now going to build an even bigger spherical ship. It is going to be 10 times the radius of the first one. It is going to have about the same density and be capable of the same acceleration. How big would it’s thruster be? If the constant alpha is the same, and I increase R by a factor of ten then:
Increasing the radius by a factor of 10 means I would have to increase the diameter of the thruster by a factor of 31.6ish. So, it wouldn’t “look” the same. This is what it would look like.
Bigger ships need way bigger thrusters.
An example in Star Wars
The Star Wars universe has two ships that are a great “case study”. These are the Star Destroyer and the Super Star Destroyer. What makes these two ships great for a comparison? Well, they are in the same universe. They have the same shape. I can safely assume that they have similar densities. Finally, if they are going to be in the same fleet, it seems reasonable that they would have similar accelerations. Here is a side by side partial comparison (also from Jeff Russell’s starship dimensions page)
Apparently, there are some others debating the size of the Super Star Destroyer. I will go with the dimensions from Jeff Russell’s diagram. This gives the Star Destroyer with a length of 1.6 km and the Super Star Destroyer with a length of 19.0 km.
What about the thrusters? According to this page at theforce.net, there are 13 thrusters on the back of the Super Star Destroyer. And there are 3 on the back of the plain old Star Destroyer.
I will first calculate the constant alpha for the Star Destroyer. I know it is not a sphere, but here R is like the length. So how big are the thrusters? By examining Jeff’s diagram, I get the length of the thruster is L = 0.126 km. This gives:
Note the square root of 3. That is because the three thrusters increase the thrust by three. If I increased the length of a thruster by a factor of three, the area would increase by a factor of 9. Now. if I assume 13 identically sized thrusters on the back of the Super Star Destroyer, how big should they be? Using the same alpha for the Star Destroyer and R = 19.0 km:
How big are the Super Star Destroyer (SSD) thrusters according to Jeff’s diagram? From my measurements, they are 0.42 km wide. Let me fix the diagram so that it has a thruster that is 2.48 km wide.
Go ahead. I am sure you could think of some valid reasons why this is wrong. I agree with you. I drew they thrusters as being 20 times wider. Maybe they are only 15 times wider. Still big.
I am not saying don’t comment. But here is my prediction for comments.
- Leave George Lucas alone!
- Dude, get a life. Why don’t you go outside or get a date or something
- Are you serious? Don’t you know this is a movie? It is not even science fiction, it is science fantasy
- I have just placed a large bounty on your head
- Bounty hunters? We don’t need this scum
- Well, actually according to the Star Wars Universe, the Super Star Destroyer has super thrusters. This is why it is called super. They stole this technology from the Ewoks
- Speaking of Ewoks, the battle on Endor was staged. There is no way rocks could penetrate storm trooper armor. The Emperor set it up.
- I have checked your figures and you are way off. I get an alpha of 0.13342 instead of your value of 0.108