If you assign additional military factories to produce equipment or reassign existing military factories, you will notice that the new production line of new equipment starts at a low production efficiency before slowly climbing to the production efficiency cap. Unfortunately, the daily change in production efficiency, known as Daily Production Efficiency Growth, changes after the elapse of every 24 hours. This change is substantial in the beginning and diminishes over time. Because it is not linear, it is difficult from the onset to foresee how much equipment that military factory will produce. We have a daily rate that is changing every day.
The Wiki has a formula on determining how many days it will take to reach a particular production efficiency. Using that formula, I have arrived at a formula that provides Production Efficiency as a function of time in days. PE with subscript t is the future production efficiency after a number of t days. PE with subscript i is the initial, starting production efficiency. On January 1st, 1936 at 1200 hours, creating a new line will give you a base production efficiency of 10.05%. PEcap is the Production Efficiency Cap. In 1936, this will be 50.05%.
As you can see, it is a square root function. This does not surprise me because the software development that goes into game engines tends to use square roots. I'm looking at you too, Mojang. 2^6=64.
Using this, you can calculate the total quantity of production accrued over a period of t days using this summation function encapsulating the square root function (see below). Because production efficiency changes on a daily bases and not continuously, the summation function exists to calculate the area under this "curve," which, if you graphed it out, would not actually look like a curve, because it is a step function.
S is what is going to be added to your stockpile, equipment in the field, garrisons, operations, or whatever you have assigned in your Logistics and Recruitment tabs. K is the constant that represents the aggregate combination of all your modifiers from industry research and stability. It should be a mixed number greater than 1 and not a %. PC is the per-unit production cost of that piece of equipment.
Congratulations, this formula will tell you how much one military factory will provide after a certain amount of time. Every newly assigned military factory will have its own curve and you would have to run another separate calculation for it. When a new modifier is introduced, you will have to stop and change the k value to reflect that modifier, replace the n value with the current t value in terms of time elapsed since that factory began producing, and provide a new t value that is the difference between the old t value and your current t value.
Edit: After 1936, when you have already started researching things like Dispersed Industry, Machine Tools, and etc, those modifiers will strew your math. However, the formula is flexible enough to accommodate those changes. For example, after researching Machine Tools, replace the Production Efficiency Cap (PEcap) value with 60.05% instead of 50.05%. You will also have to alter the t and n values to reflect the period of time where the modifier was absent and add that to the remaining period of time where that new modifier has an effect. This will result in two summations.
This is probably too time-consuming and impractical for even a pacifist minor to undertake. As Germany, you could theoretically grab a friend to play co-op, devoting his or her entire attention to forecasting production and basically becoming your Albert Speer (if he's into that kind of thing I guess).
The Wiki has a formula on determining how many days it will take to reach a particular production efficiency. Using that formula, I have arrived at a formula that provides Production Efficiency as a function of time in days. PE with subscript t is the future production efficiency after a number of t days. PE with subscript i is the initial, starting production efficiency. On January 1st, 1936 at 1200 hours, creating a new line will give you a base production efficiency of 10.05%. PEcap is the Production Efficiency Cap. In 1936, this will be 50.05%.
As you can see, it is a square root function. This does not surprise me because the software development that goes into game engines tends to use square roots. I'm looking at you too, Mojang. 2^6=64.
Using this, you can calculate the total quantity of production accrued over a period of t days using this summation function encapsulating the square root function (see below). Because production efficiency changes on a daily bases and not continuously, the summation function exists to calculate the area under this "curve," which, if you graphed it out, would not actually look like a curve, because it is a step function.
S is what is going to be added to your stockpile, equipment in the field, garrisons, operations, or whatever you have assigned in your Logistics and Recruitment tabs. K is the constant that represents the aggregate combination of all your modifiers from industry research and stability. It should be a mixed number greater than 1 and not a %. PC is the per-unit production cost of that piece of equipment.
Congratulations, this formula will tell you how much one military factory will provide after a certain amount of time. Every newly assigned military factory will have its own curve and you would have to run another separate calculation for it. When a new modifier is introduced, you will have to stop and change the k value to reflect that modifier, replace the n value with the current t value in terms of time elapsed since that factory began producing, and provide a new t value that is the difference between the old t value and your current t value.
Edit: After 1936, when you have already started researching things like Dispersed Industry, Machine Tools, and etc, those modifiers will strew your math. However, the formula is flexible enough to accommodate those changes. For example, after researching Machine Tools, replace the Production Efficiency Cap (PEcap) value with 60.05% instead of 50.05%. You will also have to alter the t and n values to reflect the period of time where the modifier was absent and add that to the remaining period of time where that new modifier has an effect. This will result in two summations.
This is probably too time-consuming and impractical for even a pacifist minor to undertake. As Germany, you could theoretically grab a friend to play co-op, devoting his or her entire attention to forecasting production and basically becoming your Albert Speer (if he's into that kind of thing I guess).
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