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{{version|1.29}}
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{{version|1.11}}
 
A '''force limit''' is a soft limit on how many [[ships]] or [[regiments]] a [[country]] can possess. It can be exceeded at a monetary price.
 
A '''force limit''' is a soft limit on how many [[ships]] or [[regiments]] a [[country]] can possess. It can be exceeded at a monetary price.
  
If a country goes past its force limit, the maintenance cost per unit will increase by twice as many percent as they are above the force limit, eventually making further expansion of the army or navy prohibitively expensive.
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If a country goes past its force limit the maintenance cost per unit will increase by as many percent as they are above the force limit, eventually making further expansion of the army or navy prohibitively expensive.
  
 
There are two independent force limits, one for naval units and one for land units, but both operate largely the same.
 
There are two independent force limits, one for naval units and one for land units, but both operate largely the same.
  
 
== Computing force limit ==
 
== Computing force limit ==
{{SVersion|1.29}}
 
  
 
===Province modifiers===
 
===Province modifiers===
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{{SVersion|1.18}}
 
Provinces contribute to the force limit through their development level and through the following modifiers and buildings. Note that only coastal provinces may contribute to a country's naval force limit.
 
Provinces contribute to the force limit through their development level and through the following modifiers and buildings. Note that only coastal provinces may contribute to a country's naval force limit.
  
{|class="mildtable sortable"
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{|class="wikitable sortable"
 
! Condition
 
! Condition
! Land force limit
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! Tech Level
! Naval force limit
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! Land Force Limit
 +
! Naval Force Limit
 
|-
 
|-
| Per development || {{green|+0.1}} || {{green|+0.1}}
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| Per development || || {{green|+0.1}} || {{green|+0.1}}
 
|-
 
|-
| Trade good bonus: [[Trade_goods|Grain]] <br> <small>(only with {{icon|rom|24px}} [[Rights of Man]])</small> || {{green|+0.5}} || 0
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| [[Regimental Camp]] || Mil 8 || {{green|+1}} || 0
 
|-
 
|-
| Trade good bonus: [[Trade_goods|Naval supplies]] <br> <small>(only with {{icon|rom|24px}} [[Rights of Man]])</small> || 0 || {{green|+0.5}}
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| [[Conscription Center]] || Mil 22 || {{green|+2}} || 0
 
|-
 
|-
| [[Regimental Camp]] || {{green|+1}} || 0
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| [[Shipyard]] || Dip 6 || 0 || {{green|+2}}
 
|-
 
|-
| [[Conscription Center]] || {{green|+2}} || 0
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| [[Grand Shipyard]] || Dip 19 || 0 || {{green|+4}}
 
|-
 
|-
| [[Shipyard]] || 0 || {{green|+2}}
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| [[Important center of trade]] || || 0 || {{green|+2}}
 
|-
 
|-
| [[Grand Shipyard]] || 0 || {{green|+4}}
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| Being in [[trade company]] || || 0 || {{green|+0.5}}
 
|-
 
|-
| [[Important center of trade]] || 0 || {{green|+2}}
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| [[Local autonomy]] (per 1%) || || {{red|-1%}} || {{red|-1%}}
|-
 
| Being in [[trade company]] || 0 || {{green|+0.5}}
 
|-
 
| [[Local autonomy]] (per 1%) || {{red|-1%}} || {{red|-1%}}*
 
 
|}
 
|}
  
 
===Country modifiers===
 
===Country modifiers===
{|class="mildtable"
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{|class="wikitable"
 
! rowspan = "2" | Condition
 
! rowspan = "2" | Condition
! colspan = "2" | Force limit modifier
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! colspan = "2" | Force Limit multiplier
 
|-
 
|-
 
! Land !! Naval
 
! Land !! Naval
 
|-
 
|-
| Base for every nation || {{green|+6}} || {{green|+12}}
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| Independent nation || {{green|+6}} || {{green|+12}}
|-
 
| Army Organizer [[advisor]] || {{green|+10%}} || 0
 
 
|-
 
|-
| Subject nation || {{red|-3}} || {{red|-6}}
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| Subject nation || {{green|+2}} || {{green|+4}}
 
|-
 
|-
| [[March]] nation || {{green|+30%}} || {{green|+30%}}
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| March nation || {{green|+2 / +30%}} || {{green|+4 / +30%}}
 
|-
 
|-
| ''Trading in'' bonus: [[Trade_goods|Grain]] || {{green|+20%}} || 0
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| Trade good bonus: [[Trade_goods|Grain]] || {{green|+10%}} || 0
 
|-
 
|-
| ''Trading in'' bonus: [[Trade_goods|Naval supplies]] || 0 || {{green|+20%}}
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| Trade good bonus: [[Trade_goods|Naval supplies]] || 0 || {{green|+10%}}
 
|-
 
|-
 
| Being the [[revolution]] target || {{green|+40%}} || {{green|+40%}}
 
| Being the [[revolution]] target || {{green|+40%}} || {{green|+40%}}
 
|-
 
|-
 
| Being an [[Jan Mayen|invading nation]] || {{green|+100}} || {{green|+100}}
 
| Being an [[Jan Mayen|invading nation]] || {{green|+100}} || {{green|+100}}
|-
 
| Fortified House [[Native council#Unique native buildings|unique native building]] || {{green|+10}} || 0
 
|-
 
| Per large [[colonial nation]] || {{green|+5}} || {{green|+10}}
 
|-
 
| Per state of the [[Holy Roman Empire]]<br><small>(Emperor only)</small> || {{green|+0.5}} || 0
 
|-
 
| Per Officer's Mess (trade company investment) || {{green|+5}} || 0
 
|-
 
| Per Admiralty (trade company investment) || 0 || {{green|+5}}
 
 
|}
 
|}
 +
 +
===Updating force limits===
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 +
Force limits are normally recalculated by the game on the first day of each month. To force an update in the middle of a month, you can activate a [[privateer]] mission and wait one day for the force limits to refresh. This may be necessary if one changes local autonomy levels in the middle of the month for example.
  
 
== More sources of force limit ==
 
== More sources of force limit ==
{{SVersion|1.29}}
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===Ideas and policies===
 
===Ideas and policies===
 
{{SVersion|Timeless}}
 
{{SVersion|Timeless}}
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=== Government ===
 
=== Government ===
====Land force limit====
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{{SVersion|1.18}}
{| class="mildtable sortable"
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 +
'''Land force limit'''
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{| class="wikitable sortable"
 
|-
 
|-
 
! Type !! Modifier
 
! Type !! Modifier
 
|-
 
|-
| [[Steppe nomads]] || {{green|+10%/+20%/+30%}} depending on government level
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| [[Steppe nomads]] || {{green|+10%/+20%/+30%}}
 
|-
 
|-
 
| [[Government#Tribal governments|Tribal Federation]] || {{green|+10%}}
 
| [[Government#Tribal governments|Tribal Federation]] || {{green|+10%}}
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|-
 
|-
 
| [[Revolutionary republic]] || {{green|+20%}} if the [[factions#revolutionary_republic|Girondists]] are in power
 
| [[Revolutionary republic]] || {{green|+20%}} if the [[factions#revolutionary_republic|Girondists]] are in power
|-
 
| [[Japan#Daimyo_.26_Shogunate|Shogunate]] || {{green|+0.5}} land force limit per subject daimyo if Sword Hunt decision has been taken (only with {{icon|moh}} [[Mandate of Heaven]])
 
|-
 
| [[Japan#Daimyo_.26_Shogunate|Daimyo]] || {{red|−2}} if subject to the Shogun who has taken the Sword Hunt decision (only with {{icon|moh}} [[Mandate of Heaven]])
 
 
|}
 
|}
  
====Naval force limit====
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Additionally, the [[Holy Roman Empire|Holy Roman Emperor]] gets {{icon|land force limit}}{{green|+0.5}} land force limit per member state.
{| class="mildtable sortable"
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 +
'''Naval force limit'''
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{| class="wikitable sortable"
 
|-
 
|-
 
! Type !! Modifier
 
! Type !! Modifier
 
|-
 
|-
 
| [[Dutch Republic]] || {{green|+10%}} if the Statists are in power
 
| [[Dutch Republic]] || {{green|+10%}} if the Statists are in power
|-
 
| [[Pirate Republic]] || {{green|+50%}}
 
 
|}
 
|}
  
=== Subjects ===  
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=== Subjects ===
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{{SVersion|1.18}}
 +
* [[Vassal]]s and [[client state]]s give {{icon|land force limit}}{{green|+1}} land force limit to their master.
 +
* [[March]]es give {{icon|land force limit}}{{green|+2}} land force limit to their master.
 +
* Large (more then 10 provinces) [[colonial nation]]s give {{icon|land force limit}}{{green|+5}} land force limit and {{icon|naval force limit}}{{green|+10}} naval force limit to their master.
 +
* Junior partners in a [[personal union]] and [[protectorate]]s don't increase the land force limit of their masters.
  
* [[Vassal]]s and [[client state]]s give {{icon|land force limit}}{{green|+1}} + {{green|10%}} of their land force limit to their master.
+
*Following ideas and policies that increase force limits increased by subjects
* [[March]]es give {{icon|land force limit}}{{green|+1}} + {{green|20%}} of their land force limit to their master.
 
* Large (10 or more provinces) [[colonial nation]]s give {{icon|land force limit}}{{green|+5}} land force limit and {{icon|naval force limit}}{{green|+10}} naval force limit to their master.
 
* Junior partners in a [[personal union]] don't increase the land force limit of their masters.
 
 
 
Following ideas and policies increase land force limits increased by subjects.
 
 
 
For example, an increase of {{green|100%}} would mean that all above mentioned bonuses would be doubled (2 + 40% instead of 1 + 20% land force limit from marches or 10 instead of 5 from colonial nations).
 
  
 
{{bonus table|vassal forcelimit bonus}}
 
{{bonus table|vassal forcelimit bonus}}
  
 
== Effect on maintenance ==
 
== Effect on maintenance ==
{{SVersion|1.29}}
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{{SVersion|1.11}}
If a country has more land or naval units than the corresponding force limit, maintenance for those units will be multiplied by the ratio of units to the force limit, with the units over the force limit counting twice<ref name=defines> See in {{path|defines}} </ref>.
+
If a country has more land or naval units than the corresponding force limit, maintenance for those units will be multiplied by the ratio of units to the force limit. For example, being at twice the force limit will double the maintenance for each unit.
<math>\text{Maintenance increase} = \frac{\text{Force limit}+\text{Number of units over the force limit}\cdot 2}{\text{Force limit}}</math> <br>
 
  
For example, having 12 regiments of infantry while at a force limit of 10 will increase maintenance for all regiments by 40%, independent of the type of unit.
+
Light Ships suffer increased cost as well, which squares the effect on their maintenance.
  
As can be seen, going over the force limit will very quickly increase the maintenance costs and should only be done when absolutely necessary. Going over the land force limit will not increase the costs for naval units and vice versa.
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== Strategy ==
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{{SVersion|1.11}}
 +
For purposes of this section, assume the ''average base maintenance'' per unit—that is, the maintenance cost of a unit before force limit modifiers—is constant. Define the ''force limit ratio'' as
 +
 
 +
<math>\text{force limit ratio} = \frac{\text{number of units}}{\text{force limit}}</math>
  
 
=== Total maintenance cost ===
 
=== Total maintenance cost ===
  
The total maintenance cost of an army or navy is:
+
The total maintenance cost of an army or navy is
  
<math>\text{total maintenance cost} = \text{average base maintenance}\cdot\text{number of units}</math>
+
<math>\text{total maintenance cost} = \text{average base maintenance}\cdot\text{number of units}\cdot\text{max(force limit ratio, 1)}</math>
  
Or, when above force limit:
+
In this case, when above the force limit:
 +
* A multiplier to force limit has the same effect as a reciprocal multiplier to maintenance.
 +
* The number of units that can be fielded for a fixed maintenance cost grows as the square root of the force limit.
 +
 
 +
For a navy of pure light ships, the total maintenance cost is instead
  
<math>\text{total maintenance cost} = \text{average base maintenance}\cdot\text{Maintenance increase} \cdot\text{number of units}</math>
+
<math>\text{total maintenance cost} = \text{average base maintenance}\cdot\text{number of units}\cdot\left(\text{max(force limit ratio, 1)}\right)^2</math>
  
 
In this case, when above the force limit:
 
In this case, when above the force limit:
* A multiplier to force limit has the same effect as a reciprocal multiplier to maintenance.
+
* A multiplier to force limit has the same effect as a reciprocal squared multiplier to maintenance.
* The number of units that can be fielded for a fixed maintenance cost grows as the square root of the force limit.
+
* The number of units that can be fielded for a fixed maintenance cost grows as the cube root of the force limit.
  
 
== Footnotes ==
 
== Footnotes ==
 
<references/>
 
<references/>
 
{{mechanics navbox|War}}
 
 
[[Category:Military]]
 
[[Category:Military]]
 +
{{military navbox}}

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