Space Ship Analysis

More often that not, I win by landing. In almost all the games I have ever played I have either launched a full maxed out space ship or the 15S/3*2C/1*3M ship that is ideal for OCC.

Recently I was faced with the very unusual situation of having my 15S/3*2C/1*3M ship ready in an OCC game while my rivals were not even close to discovering space flight. I wondered about making a bigger ship with 2 sets of modules but how many extra structurals would I need for that? How fast would it go? As far as I know no one has yet analyzed the situation so that the answer will be known apriori. That is when I decided to perform this analysis.

Let
s stand for Space Ship Structural
c for Space Ship Components (Propulsion and Fuel)
C for connected pairs of Space Ship Components (one Propulsion and one Fuel)
m for Space Ship Modules (Habitation, Life Support, and Solar Panel)
M for the Mass of the space ship
F(C) for the speed factor (described later)
Y for the travel time in years

Then
M = 100*s + 400*c + 1600*m
Y= M*5.6/F(C)

F() is a function of C. I could show it as a combination of log based 2 and floor. But since C can only be an integer from 0 to 8 it is easier to simply present a table:
F(0)= 100
F(1)= 1100 F(2)= 2100 F(3)= 3100 F(4)= 4100
F(5)= 6100 F(6)= 8100
F(7)=11100 F(8)=14100

While you can make a space ship with any number of structurals, components, and modules only connected pairs of components contribute to your speed and only connected triples of modules contribute to your score. Thus you need to make sure all your components and modules are connected.

Let SC() stand for the number of Structurals it takes to have a given number of pairs of Components connected.
S(0)= 0
S(1)=S(2)=S(3)=15
S(4)=17
S(5)=21 S(6)=25 S(7)=29 S(8)=33

Let SM() stand for the number of Structurals it takes to have a given number of triples of Modules connected.
S(0)= 0
S(1)=15
S(2)=23 S(3)=31 S(4)=39

Finally, let S(x,y) stand for the number of Structurals it takes to have x pairs of Components and y triples of Modules connected.
S(x,y) = Max(SC(x),SM(y))

Observation: four/three/two pairs of components are almost 4/3/2 times as fast as one pair of components. After that the ratio is higher: five pairs are almost 6 times as fast, six pairs 8 times as fast, ...

In OCC because you have a single city it takes at least one turn for each space ship part. The objective is always to finish as quickly as possible since if you wait rivals will either annihilate you or build a faster space ship and catch yours.

Typically you want the leanest ship, where there are only one triple of modules. The ideal ship here has 3 pairs of components, because with one pair it takes 36 years, 2 pairs 21 years, 3 pairs 15 years, 4 pairs 13 years, ...
The first three each need 15 structurals thus if you can build your components in one turn 3 pairs is faster than 2 pairs which is faster than 1. But 4 pairs takes 17 structurals and thus requires at least another 4 turns for a saving of two years in arrival time. It gets worse with more pairs of components.

If you can afford to send two triples of modules up, then the best ship for OCC is 23s/5*2c/2*3m this ship takes 15 extra turns to build but arrives a turn earlier (14 years vs 15).

For three and four triples of modules the OCC ships are 31s/7*2c/3*3m and 39s/8*2c/4*3m.

Thanks!

Well done, Ali !
No excuse for building the wrong parts from now on

Excellent work determining those relationships.

For me when playing OCC the overriding goal is to achieve the earliest landing possible. One other factor comes in with the number of years per turn that are passing once I build Apollo and start on ship parts. If 10 years are passing with each turn, building second and third sets of Components sometimes does not make sense: a 15-1-1-1-1-1 ship will get there in 36 years, but 20 years passes before I'm ready to launch a 15-2-2-1-1-1 ship which takes another 21 years. If it is down to 5 years per turn or below it is worth building a faster ship, but once I get more than 3 of each (as you mentioned) the number of required Structurals goes up so I burn up more turns.

Should I be playing for points instead then priorities will be different. Now that we have some formulas I'm sure somebody (StuporMan?) will turn that into a spreadsheet for serious number crunching. But it looks like you have laid out the basic considerations plainly.

I'm about to put up a "How to Buy your Spaceship" thread I've been working on...

Rather than making people download a spreadsheet I'll post it this way. I'll let someone else work on the associated flight times.

I hope I interpreted the information in the original post correctly - I have not verified any of of the numbers.

Thank you for the table above Tim. The info in it is indeed correct.

ElephantU, is this the spread sheet you were asking for?

Heh, another thing I need to print out and add to my impossibly large stack of Civ2 game info when I get home.

A spaceship with 3 module sets, 8 components sets and 33 structurals, travel time will be 9.5 years so it's gonna take 9 years.

Tigui, you are correct. In all cases, travel time is reported with a digit after the decimal but truncated in practice.