Science (math) For The Win!!

So I was playing around with a VERY basic excel sheet trying to model nitrate buildup and removal. Literally, 2 columns of variables replicated over say 20 weeks. Long story short, I came to the following outcome:

Max Nitrate concentration (ppm, pre-WC, assuming stable tank) can be expressed as the weekly new nitrate buildup times the inverse of the percent of water changed. Note that for calculations, percent will be expressed as a decimal, or proportion of 1. Also, I can't do subscripts, so blue text is subscript.

NO3max = NO3weekly increase x (1 ÷ WCamount)

Examples:
A. If your tank adds 5ppm/week of nitrates (cycle output minus plant uptake), and your change 1/4 (0.25) of your water in the same interval, your max NO3ppm will be 5 x 4 (4 being the inverse of 0.25) = 20ppm.



B. If your tank adds 10ppm/week of nitrates (double of above), and your change 1/2 (0.5) of your water in the same interval (also double of above), your max NO3ppm will be 10 x 2 (2 being the inverse of 0.5) = still 20ppm.

C. If your tank adds 10ppm/week of nitrates, and your change only 1/5 (0.2) of your water in the same interval, your max NO3ppm will be 10 x 5 (5 being the inverse of 0.2) = 50ppm.

D. If your tank adds 3ppm/week of nitrates, and your change 1/3 (0.33) of your water in the same interval, your max NO3ppm will be 3 x 3 (3 being the inverse of 0.33) = 9ppm.

Now, what are the practical applications of this? I have some ideas, but what say you?
Also, what do we name this principle/formula? Points for relevant acronyms!!

Eg. Calculating Interval Calculations (Helpfully), Like nItrates, by David (my real name) = CICHLID

 

Cool! Also helpful.

 

Can we call it made my head hurt. Lol. Nitrate schedule?

 

Can we call it made my head hurt.

I always felt that repetition made learning easier. So I give many examples. Sorry.
And I had to put in the table itself, because "show don't tell".
And I award you no points for "made my head hurt".

 

Love it. name ideas

Parameter Output Occumulation (bad spelling stretch) chart (POO chart)

Pristine Water Chart tool (PWC tool)

Seriously Helpful Interval Tool chart (nuff said)

I mean after all, that's what nitrates are

 

EXpected MAXimum NO3
=
EXMAXiN


PREMAXiNi
=
PREdicted MAXImum Nitrates

 

Poo chart. I love it. Lol

 

I've been thinking of ways to use this relationship/model.
1. I can't help but see similarities with the EI method for planted tanks. This uses a 50% weekly WC to keep fert concentrations in check. Using the Poo chart (doesn't make the most sense, but clearly is the catchiest, thx @jenloli42), we could understand that the rate of fert in the tank will never exceed twice the dosage. Ie, after dosing, the rate in the tank will be 2x the dosage, which is the max, and the min (before WC) would be the dosage itself. This assumes once-weekly dosing, which is not always the case, but let's not get derailed by trivial details. For me, it's one thing to read it, its another thing entirely to see it happen.
2. It can also help us understand what our actual bioload might be, in terms of ammonia inputs. I've read elsewhere that ammonia:nitrites:nitrates is basically 1:1:1. That makes sense, because a single molecule of each has a single nitrogen atom (NH3, NO2 and NO3). So if we understand the level of nitrates, we're also understanding the inputs of ammonia. Even with liquid tests, it's hard to be precise on nitrates. Is it actually 5ppm? Maybe 5-10, but closer to 10? Not over 40, but maybe as low as 10ppm? By knowing that we're testing at the max level (eg pre-WC), taking regular water change amounts into account, and knowing where the nitrate levels have tested out in the past, we can do a better job of estimating NO3 levels, and thus also know ammonia inputs.
Here's an example: using my spreadsheet and fixing the WC amount at 33% (close to my actual WC amount), I can fiddle with NO3 input variable, and see what I would read under different bioloads, and compare that to what I actually test (kinda like a cheap sensitivity analysis):
- 3ppm of new NO3/week gives pre-WC max of 9ppm of nitrates
- 5ppm of new NO3/week gives pre-WC max of 15ppm of nitrates
- 10ppm of new NO3/week gives a pre-WC max of 30ppm of nitrates
I know from my occasional testing that my nitrates are just shy of 10ppm. So I can infer that my bioload should be around 3 ppm weekly of ammonia (after plants have done their part of the job).
I haven't done an ammonia-based fishless cycle, but those of you that have will have an understanding of how to prep a tank for that nitrogen processing capacity.

 

Practical application? Unless you change 50% or more of tank water, your nitrates, before the next water change will always be more, never less than the week before. Assuming you have no plants, stock and feeding schedule stays the same and there is no nitrates in tap water.

I believe that a fully stocked tank will add more than 20 ppm NO3/week.