How many rockets per minute would you need to fill an Express Transport Belt with Spidertrons?
There are multiple vehicles in Factorio. There are cars, tanks, trains, and then there's the ultimate Spidertron.
Spidertrons are incredibly versatile and useful. Creating one is difficult. Automating them is even harder.
Why? It's not because of normal material requirements. At this point in the game,
everything required for a Spidertron should be fully automated...
...Except for fish.
Fish do not respawn.
The only way to automate fish is to launch a rocket.
Endgame bases are measured in rockets per hour.
So how many rockets per hour would you need to fill an express transport belt with Spidertrons?
First, we need to know how many spidertrons we get out of one rocket.
We can launch a rocket with 100 space science packs to get 100 fish, giving us \(\mathrm{\frac{100\ fish}{1\ rocket}}\),
which, given an excess of other materials, can directly translate to \(\mathrm{\frac{100\ spidertron}{1\ rocket}}\).
The spidertron demand for a full belt is \(\mathrm{\frac{45\ spidertron}{1\ second}}\), which is equivalent to \(\mathrm{\frac{162000\ spidertron}{1\ hour}}\).
Now we can calculate the number of rockets per hour to satisfy this requirement.
$$\mathrm{\frac{162000\ spidertron}{1\ hour}\times\frac{1\ rocket}{100\ spidertron}=\frac{1620\ rocket}{1\ hour}}$$
That's a lot of rockets!
But we're not finished yet. What throughput of raw materials would it take to fulfill this rocket demand?
First, let's quantify some recipes. \(\mathrm{1\ rocket\ part=10\ LDS+10\ RCU+10\ rocket\ fuel}\).
LDS is low density structure, and RCU is a rocket control unit.
Now, \(\mathrm{1\ LDS=20\ copper+5\ plastic+2\ steel}\), \(\mathrm{1\ RCU=32.5\ copper+15\ iron+10\ plastic+1\ blue\ circuit}\), and \(\mathrm{1\ rocket\ fuel=110\ light\ oil}\).
Let's put it all into one big equation. First, the complex materials for each rocket.
$$\mathrm{
\frac{1620\ rocket}{1\ hour}\times
\frac{100\ rocket\ part}{1\ rocket}\times
\left(
\frac{10\ LDS}{1\ rocket\ part}+
\frac{10\ RCU}{1\ rocket\ part}+
\frac{10\ rocket\ fuel}{1\ rocket\ part}
\right)
}$$
Now, let's separate the materials out into their raw components.
$$\mathrm{
\frac{1620\ rocket}{1\ hour}\times
\frac{100\ rocket\ part}{1\ rocket}\times
\left(
\left(\frac{10\ LDS}{1\ rocket\ part}\times\frac{(20\ copper+5\ plastic+2\ steel)}{1\ LDS}\right)+
\left(\frac{10\ RCU}{1\ rocket\ part}\times\frac{(32.5\ copper+15\ iron+10\ plastic+1\ blue\ circuit)}{1\ RCU}\right)+
\left(\frac{10\ rocket\ fuel}{1\ rocket\ part}\times\frac{110\ light\ oil}{1\ rocket\ fuel}\right)
\right)
}$$
What a massive equation! Let's simplify.
$$\mathrm{
\frac{1620\ rocket}{1\ hour}\times
\frac{100\ rocket\ part}{1\ rocket}\times
\left(
\frac{200\ copper+50\ plastic+20\ steel}{1\ rocket\ part}+
\frac{325\ copper+150\ iron+100\ plastic+10\ blue\ circuit}{1\ rocket\ part}+
\frac{1100\ light\ oil}{1\ rocket\ part}
\right)
}$$
$$\mathrm{
\frac{1620\ rocket}{1\ hour}\times
\frac{100\ rocket\ part}{1\ rocket}\times
\frac{
150\ iron+
525\ copper+
150\ plastic+
20\ steel+
10\ blue\ circuit+
1100\ light\ oil
}{1\ rocket\ part}
}$$
$$\mathrm{
\frac{1620\ rocket}{1\ hour}\times
\frac{
15000\ iron+
52500\ copper+
15000\ plastic+
2000\ steel+
1000\ blue\ circuit+
110000\ light\ oil
}{1\ rocket}
}$$
$$\mathrm{
\frac{
24300000\ iron+
85050000\ copper+
24300000\ plastic+
3240000\ steel+
1620000\ blue\ circuit+
178200000\ light\ oil
}{1\ hour}
}$$
That's how many raw materials you would need per hour for rockets to automate a full belt of Spidertrons!
Let's convert to seconds and ticks to get a better sense of scale.
$$\mathrm{
\frac{
6750\ iron+
23625\ copper+
6750\ plastic+
900\ steel+
450\ blue\ circuit+
49500\ light\ oil
}{1\ second}
}$$
$$\mathrm{
\frac{
112.5\ iron+
393.75\ copper+
112.5\ plastic+
15\ steel+
7.5\ blue\ circuit+
825\ light\ oil
}{1\ tick}
}$$
Is this insurmountible? I mean... if a bunch of players can get together and make a
1 million science per minute base,
who knows what's possible?