Clock speed

Production and power buildings, such as Miners, Constructors or Biomass Burners, can have their clock speed set to any percentage between 1.0000% and 250.0000% with four decimals. For production buildings, this allows them to operate slower or faster at the cost of greatly reduced or increased power usage. For power buildings the maximum power output and accompanying fuel consumption can be increased in tandem, granting more utility from a single building. Overclocking and underclocking both have utility in optimizing a factory, helping to synchronize production, increase energy efficiency and smooth out the peaks in factory power consumption.

Terminology
Clock speed is the speed of operation of a building. 200% clock speed means the building will operate twice as fast, 50% means half operation speed, however, this is not the case for power generators, see below.

Overclocking refers to setting the clock speed above 100%.

Underclocking refers to setting the clock speed below 100%. Underclocking does not require any Power Shards.

Usage
To change a clock speed, interact with a building and look at its lower left of the UI. Underclocking can be done freely, however overclocking requires Power Shards, which are crafted from Power Slugs. Up to three power shards can be placed into a building, each allowing the maximum clock speed to be increased by 50%. The clock speed can be changed in increments of 1% using the slider or by directly typing in the desired value for either Clock speed or Target production rate.

In any case below, the overclocking percentage will be rounded to 4 decimal places: The actual clock speed saved into that machine can be checked by re-open the UI. Typing in an arbitrarily high value will be rounded down to the nearest valid value (such as 250%), while non-numeric inputs are ignored. Setting clock speed below 1% will result in 1% clock speed instead; this is visible when the machine UI is re-opened.
 * Input the desired item production per minute
 * After the clock speed percentage is saved into the machine, the item per min will be re-evaluated to 2 decimal places.
 * Input the Clock Speed percentage directly
 * Typing simple equation in either the item per minute or clock speed
 * Keep in mind just like the calculator available in quick search it evaluates right to left so multiple step equations may not give the expected result

There is an issue where the round down applies to 5 and below, and round up only applies to 6 and above.

Clock speed for miners and extractors
Overclocking Miners and Oil Extractors is highly beneficial as it allows you to extract more ore/oil per node. In terms of energy per ore/oil extracted, an overclocked miner/extractor on a higher-purity node can also be more efficient than a non-overclocked one on a lower-purity node. Defining the energy efficiency as the energy required per ore or oil extracted: More generally, stepping up the node purity by one level while simultaneously multiplying the clock speed by $$ 2^{5/3} \approx 3.175$$ results in the same energy efficiency (energy requirement per ore or oil extracted).
 * mining a pure node at 250% has the same energy efficiency as mining a normal node at 78.74% or an impure node at 24.80%
 * mining a normal node at 250% has the same energy efficiency as mining an impure node at 78.74%

Since, for the same clock rate, higher-purity nodes require significantly less energy per ore or oil extracted, a simple strategy for reducing power consumption associated with extraction is: A more optimal approach is detailed below, but the power savings relative to this simple strategy are generally modest.
 * 1) fully overclock pure nodes (or, for Miner Mk.3, overclock pure nodes to 162.5%, due to the Mk.5 belt limit) before extracting anything from normal nodes, then
 * 2) fully overclock normal nodes before extracting anything from impure nodes.

Optimization
When you have access to more than enough nodes to satisfy your extraction requirements, the most power-efficient way of extracting ore or oil involves taking a lot from the pure nodes, a moderate amount from the normal nodes, and a tiny amount from the impure nodes, so that the energy efficiency per ore or oil extracted is the same across all nodes. Suppose that you have access to and that you will be tapping each node with an extractor with a base extraction rate of $$ B $$ as described below: If your target extraction rate is $$ X $$ ore or oil per minute, the most energy-efficient clock rates can be determined as follows   Calculate the power consumption required for the simple approach described above (overclocking high purity before tapping lower purity). This is an optimistic upper bound on the power you could save by fully optimizing the clock speeds - does it seem like a lot to you? If not, then you shouldn't bother with this optimization.  Solve for $$ c $$ as: $$ c = \frac{X}{B (2 \cdot n_\text{p} + \underbrace{2^{-5/3}}_{\approx 0.315} \cdot n_\text{n} + \underbrace{2^{-13/3}}_{\approx 0.0496} \cdot n_\text{i})} $$  Assuming no belt or clock limits, the ideal clock rates would be: Unfortunately, this operating point will not always be realizable, either because: In these cases, the pure extractors should be set to the highest usable clock rate (162.5% for Mk.3 miners with Mk.5 belts, 250% for Oil Extractors with Mk.2 pipes) and then the algorithm should be repeated to determine how best to use the normal and impure nodes to gather the balance of the ore or oil. If this second solution requires the normal extractors to be set to a clock rate over 250%, then the normal extractors should be set to 250% and the impure extractors should be set to whatever rate is required to gather the balance of the ore or oil. If this again requires a clock rate over 250%, then X is too high for given nodes.
 * $$ n_\text{p} $$ pure nodes
 * $$ n_\text{n} $$ normal nodes
 * $$ n_\text{i} $$ impure nodes
 * $$ 100% \cdot c $$ for each pure node
 * $$ 100% \cdot c / 2^{5/3} \approx 31.5% \cdot c $$ for each normal node
 * $$ 100% \cdot c / 2^{10/3} \approx 9.92% \cdot c $$ for each impure node
 * it requires the pure extractors to operate at a clock speed over 250%, or
 * it requires the pure extractors to exceed the Mk.5 belt limit of 780 items/min or the Mk.2 pipe limit of 600 fluid/min



For example, if you would like to extract 1800 oil from a combination of 2 pure nodes, 3 normal nodes, and 5 impure nodes, then This would require 582.83 MW, a savings of 110.3 MW.
 * $$ B = 120$$ oil/min for an oil extractor
 * $$ n_\text{p} = 2$$, $$n_\text{n} = 3$$, and $$ n_\text{i} = 5$$
 * $$ X = 1800$$ oil/min
 * The simple way to achieve this extraction rate is to fully overclock both pure nodes (1200 oil/min) and then tap and fully overclock just two normal nodes (600 oil/min). This would require 4 fully overclocked Oil Extractors, which would consume 693.14 MW. This is therefore the optimistic upper bound on the power savings. It seems worthwhile, although we should remember that this is an optimistic estimate and our actual savings will likely be lower.
 * The calculation gives $$ c = 2.889 $$, so
 * The pure extractors should be operated at 288.9%. This exceeds 250%, so we instead must assume that the 2 pure extractors operate at 250%, collectively producing 1200 oil/min
 * As a sub-calculation, we repeat with $$ n_\text{p} = \mathbf{0}$$, $$n_\text{n} = 3$$, $$ n_\text{i} = 5$$, $$ X = \mathbf{600}$$ oil/min. This gives $$ c= 4.19$$, so
 * The normal nodes should be operated at 132.0%
 * The impure nodes should be operated at 41.58%

Clock speed for production buildings
For production buildings, the craft time is directly proportional to the clock speed, but the power required changes polynomially. As the item production rate increases, the ingredient consumption rate increases as well. The table below shows five different clock speeds on a Constructor, for example, producing Iron Rod that takes 4 seconds.

The formula for power usage is:

where $$clock\ speed$$ is a number with up to 4 decimals between 1 and 250, and both $$power\ usage$$ and $$initial\ power\ usage$$ are measured in MW. For relative energy usage per item produced, subtract the exponent factor by 1, that is,
 * $$power\ usage = initial\ power\ usage \times \left( \frac{clock\ speed}{100} \right )^{1.6}$$
 * $$power\ usage = initial\ power\ usage \times \left( \frac{clock\ speed}{100} \right )^{1.321928}$$

Underclocking Constructors and Assemblers in early game is highly beneficial. It can yield considerable fuel (Biomass) savings. With Splitters and Mergers available, fuel savings can be accompanied with zero loss to production rate. Miner Mk.1 with two Smelters operating at full clock speed can produce over 570 ingots from normal node with the energy of one stack of leaves. Miner Mk.1 with nine Smelters operating at 22% clock rate yields to over 900 parts with same amount of energy. Net production rate will be virtually identical and the energy saved can be used elsewhere.
 * $$energy\ usage = initial\ energy\ usage \times \left( \frac{clock\ speed}{100} \right )^{0.6}$$
 * $$energy\ usage = initial\ energy\ usage \times \left( \frac{clock\ speed}{100} \right )^{0.321928}$$

It should be noted that production buildings use the full calculated value, and as such the rounded value listed in-game is not always accurate.

Production buildings that're underclocked to have active power consumption below the idle rate of 0.1MW will still use 0.1MW while idle.

Clock speed for power generators
Overclocking power generators does not affect the fuel-to-power ratio, both the fuel burn rate and power output are increased proportionally.

The table below shows different clock speeds set on a, while the rates also apply for and. Note that a 250% overclock does not give 250% power as the in-game target MW value suggests. The true production values are listed with the generator's fuel. Furthermore, note how energy per Coal does not change with the clock speed.


 * The percentage for 200% generator capacity can be also memorized as, which can be entered into the clock speed field.
 * scale differently with overclocking. They use 1.321928 instead of 1.3 as the exponent and root number. At 250% clock speed, one operates 2.00000009951 times faster compared to 100% clock speed.
 * cannot be overclocked at all.

Fuel burn time formula
$$fuel\ burn\ time = initial\ fuel\ burn\ time \times \sqrt[1.3]{\frac{100}{clock\ speed}} $$

where $$clock\ speed $$ is a number with up to 4 decimals between 1 and 250, and both $$fuel\ burn\ time $$ and $$initial\ fuel\ burn\ time $$ are measured in seconds.

Power capacity/fuel consumption rate formula
$$power\ capacity = initial\ power\ capacity \times \sqrt[1.3]{\frac{clock\ speed}{100}} $$ where $$clock\ speed $$ is a number with up to 4 decimals between 1 and 250, and both $$power\ capacity $$ and $$initial\ power\ capacity $$ are measured in MW. replace $$power\ capacity $$ and $$initial\ power\ capacity $$ with $$fuel\ consumption\ rate $$ and $$initial\ fuel\ consumption\ rate $$ measured in parts per minute or to get the fuel consumption rate.

Desired clock speed for an operating rate formula
(The formula for finding the clock speed to set a power generator to for a desired operating rate)

$$clock\ speed = 100 \times \left( \frac{operating\ rate}{100} \right )^{1.3} $$ where $$clock\ speed $$ is a number with up to 4 decimals between 1 and 250, and $$operating\ rate $$is the desired percentage of the normal operating rate. $$operating\ rate $$can be gotten by dividing the desired $$power\ capacity $$ or $$fuel\ consumption\ rate $$ by the $$initial\ power\ capacity $$ or $$initial\ fuel\ consumption\ rate $$ and multiplying by 100.

Examples: $$ (rounded to 4 digits) $$ which would mean that power capacity is $$150 \times \sim2.0235 =\ \sim303.52814\ MW $$ and fuel consumption rate is $$12 \times \sim2.0235 =\ \sim24.2823\ m^3/min $$ (all rounded to 4 digits, multiplier used up to 13 digits) $$ (rounded down to 4 digits, gives you 199.999948% operating) $$ (rounded to 4 digits) $$
 * At 150% clock speed for a fuel generator burning normal fuel, the burn time would be $$5 \times \sqrt[1.3]{\frac{100}{150}} = \ \sim3.66029\ seconds
 * At 250% clock speed for a fuel generator, the multiplier for power capacity and fuel consumption rate would be $$\sqrt[1.3]\frac{250}{100} =\ \sim2.0235
 * To achieve 200% operating rate of a normal generator, the clock speed would be: $$100 \times \left( \frac{200}{100} \right )^{1.3} =\ \sim246.2288%
 * To achieve 75% operating rate of a normal generator, the clock speed would be: $$clock\ speed = 100 \times \left( \frac{75}{100} \right )^{1.3} =\ \sim68.7986%
 * If you wanted to burn 4 fuel per minute for a fuel generator using normal fuel, you would need an operating rate of $$clock\ speed = 100 \times \left( \frac{4}{12} \right )^{1.3} =\ \sim23.9741%
 * If you had 246 fuel to burn you would need $$\frac {246}{12} = 20.5\ generators$$ which means you would need 20 generators at 100% operating rate and 1 generator at 40.6126% (see above) operating rate.

Experimental
Experimental The operating rate of power generators scales linearly with their clock speed. A generator set to 250% will operate 2.5 times faster, thus consuming 2.5x as much fuel (and Water) and producing 2.5x as much power.

History

 * Patch 0.7.0.0:
 * Changed production building and extractor exponent from 1.6 to 1.321928
 * Changed power generators' operating rate to match their clock speed, thus scaling linearly
 * Patch 0.4.0.4: Fixed overclocking not showing the correct value when pasting settings in some situations
 * Patch 0.4.0.3: Changed the number of decimals in overclocking from 1 to 4
 * Patch 0.4.0.0: It is now possible to set decimal percentages as clock speed, the game no longer rounds it to the nearest whole percentage