"Excuse the fact that I'm WAY too into Miner's Haven"
Ok, first off there is a page called the Miner's Haven Calculator, where you can download something onto your computer and it will do all this stuff for you.
But knowing me, I hate downloading stuff onto my computer gradually making it slower. So, I'm here to show you exactly how to calculate the minimal conveyor time you can get while maximizing your ore value, all on any calculator.
Route One. "The Spray and Pray method"
Ok. first you will need to know what value your ore starts at. You can either put it over a Basic Furnace or just look it up on this wiki.
Then, in the calculator, put whatever number that is. Let's say 600 for a giant iron mine.
Now, what % does your upgrader upgrade by? Let's go with 35% for an upgrader that doesn't upgrade ore past 3,000,000 (3M).
With those numbers, you are going to put it in the calculator like so.
600(The value of your ore) * (times) 1.35 (The % upgraded, add a 1 if it has less than 3 digits.) ^ (Raise it to a power) 10 (Make a guess on how many you think it will upgrade by.)
Now I got 12K. But wait, THAT'S NOT 3M!?!
If it isn't past the cap, go back to where you started with 600 * 1.35 ^ __ then add a higher number (15)
I got 54K. Obviously, we need to get a bigger jump in powers.
600 * 1.35 ^ 35 = 21M
WHOOPS! too high. Now you'd slowly decrease your power (^ 35) until you reach JUST BELOW 3M, then you add 1 and that's how many upgraders, exactly, you need.
Route Two "The Up the Tree method"
Ok, back with our $600 ore. Now, again we need to do 35% to 3M. In this way, you set it up in the calculator like so.
600 (Ore value) * (Times) 1.35 (The percent of the upgrade, plus one if it has 1 or 2 digits and no power).
That gets me $810.
Now, I will plug in the new ore value into the same thing, like so.
810 (New ore value from the previous upgrade) * 1.35
And get my new value.
I will continuously do this until my value goes from under 3M to over 3M, then I count the number of times I multiplied by 1.35.
Route Three "The Direct Method"
Once again, let's go back to our $600 ore and the 3M limit. Divide the 3M limit by the value of the ore, $600. Divide the logarithm of the quotient by the logarithm of the multiplier and round the number up if it is a decimal. That's it. You now have the minimum number of upgraders you need to use to reach the limit. This is what it looks like on a calculator:
log(3,000,000 / 600) / log(1.35) = 28.380749...
Round 28.380749 up and you get 29 upgraders.
OH NO! you're done for!
1e+12 is actually really simple, but when NOT calculating the maximum ore value, ( With the Schrödinger method) it's hard to work with.
Here is how to do it:
Let's say your ore value is 5B (5,000,000,000). You would plug in that HUGE number, right?
Instead, you just put 5. yes, 5, but that 5 symbolizes 5,000,000,000.
And when calculating the number, you must remember that your first digit is actually 5B.
Now, you still might get 1e+12.(10^12)
Here is how you find out what 1e+12 is.
Take that 1, add 12 zeros behind it.
BOOM! You got the huge number and exactly what you need.
Now it may not be just 1e+12, it could be stuff like
and any possible number.
In that way, simply move the decimal 15 slots back, (or whatever is after the +) and make lots of zeros on the end.
And bam. you got it all calculated.
Give yourself a pat on the back.