科研

Research is used to unlock technologies.

Research slots

Technology is unlocked by assigning a research slot to it for the required number of days.

The base number of research slots depends on the country:

• USA, democratic Germany: 4 slots, plus 2 additional possible via national focus. (Democratic Germany requires 唤醒勇虎).
• Non-democratic Germany, Italy, Japan, United Kingdom: 4 slots, plus 1 additional possible via national focus.
• France, Soviet Union, most other countries in Europe, plus Canada: 3 slots, plus 2 additional possible via national focus (in Canada's case, the last 1 requires independence).
• Other countries outside of Europe as well as Luxembourg, Bulgaria and Albania: 2 slots, plus 3 additional possible via national focus (for British subjects, the final 2 also require independence).
• New Zealand: 2 slots, plus 4 additional possible via national focus. (Requires 共赴胜利).

For most countries, unlocking the final research slot requires having a substantial number of factories (usually 50+). The Commonwealth countries must (with 共赴胜利) additionally become fully independent to maximize their available research slots.

Each research slot can store up to 30 points of Days Saved without being assigned to a specific tech. Days Saved functions as days added to research progress once a tech is chosen for the slot. See research speed.

Research time

Each technology has a base time cost. They are multiples of the standard base cost of 85 days.

Cost (days)	Techs
42	Armor Submodels
85	Artillery (II) & Upgrades (II,III,IV); Anti-Air Artillery (II,III) & Upgrades; Rocket Artillery (II) & Upgrades; Anti-Tank Artillery (II,III) & Upgrades Support Equipment; Carrier Airplanes; Electronic Mechanical Engineering; Encryption
106	Decimetric Radar (I,II); Centimetric Radar (I,II,III)
127	Infantry Weapons (I) & Upgrades (I,III); Support & Anti-Tank Weapons; Motorized Rocket Artillery; Marines (II), Mountain Infantry (II), Paratroopers (II) Support Companies (II,III,IV); Artillery (I) & Upgrades (I); Anti-Air Artillery (I); Anti-Tank Artillery (I) Shiphulls (I); Transports (I) Decryption; Experimental Rockets; Rocket Engines (II,III) Machine Tools (I,II); Equipment Conversion; Oil Processing; Rubber Processing
148	Radio, Radio Detection
170	Infantry Weapons (II,III) & Upgrade (II); Night Vision (II); Motorized & Mechanized (I,II); Marines (I,III), Mountain Infantry (I,III), Paratroopers (I,III); Special Forces Programs Support Companies (I); Artillery (III); Rocket Artillery (I); Great War Tank, Light, Medium & Heavy (I) Armor Shiphulls (II,III,IV); Transports (II,III) Airplanes Rocket Engines(I); Jet Engines Machine Tools(III); Production Line (I); Industry; Construction; Excavation
191	1st Land Doctrine; 1st Air Doctrine
212	Night Vision (I); Modern, Super Heavy & Heavy (II,III) Armor; Computing; Production Line (II)
255	Mechanized (III); Air doctrines (not 1st); Naval doctrines; Fuel Refining
382	Land doctrines (not 1st)
425	Atomic Research, Nuclear Reactor, Nuclear Bombs

Research speed

The base research cost only represents an abstract number of days the research will take. In practice, due to modifiers, research will progress by more or less than exactly one research-cost-day per day. Research speed modifiers stack additively to research speed (instead of subtractively to research cost). For example, 106 days base cost at 15% research speed bonus will take [math]\displaystyle{ \left\lceil\frac{106}{1+15\%}\right\rceil=93 }[/math] days.

Days Saved are subtracted from the modified expected number of days. Thus, Days Saved benefit from (or are penalized by) the same research speed modifiers.

The aggregate research bonus is calculated and updated every day. Thus changes in research speed (except limited-use bonuses) apply to all ongoing research.

Research speed can not fall below 10% of the default speed.

Research modifiers

Difficulty

The player can get a research speed bonus or penalty depending on the game difficulty setting as follows:

• Civilian +15% bonus
• Recruit +7% bonus
• Regular no bonus or penalty
• Veteran -15% penalty
• Elite -30% penalty

Trade law

主条目：Ideas#Trade_laws

Trade laws can also increase research speed. The more open the trade the higher the reduction as can be seen below.

Technologies that increase research speed

类型	自由贸易	专注出口	有限出口	封闭经济	经贸受限
可出口资源	80%	50%	25%	0%	25%
工厂产出	+15%	+10%	+5%	–	–
海军船坞产出	+15%	+10%	+5%	–	–
建造速度	+15%	+10%	+5%	–	–
研究速度	+10%	+5%	+1%	–	–
泄露给他国的民政情报	+40%	+20%	+10%	–	+40%
泄露给他国的海军情报	+20%	+10%	+5%	–	+40%
生活消费品工厂	–	–	–	–	5%
情报机构升级时间	–	–	–	–	+15%

Technology	Year	Research Speed
Electronic Mechanical Engineering	1936	+3%
Mechanical Computing	1936	+4%
Computing Machine	1938	+5%
Improved Computing Machine	1940	+8%
Atomic Research	1940	+4%
Advanced Computing Machine	1942	+8%

Limited-use bonuses

Limited-use bonuses are awarded by National Focus. Once available, a limited-use research bonus is activated when a Research Slot is assigned to an applicable technology. Once activated, the limited-use bonus is tied to the technology even if the slot is re-assigned. (However, Hearts of Iron IV client is known to drop limited-use bonuses on technologies not currently assigned to a research slot upon reload. Exercise caution when activating a limited-use bonus for future use.)

A limited-use bonus can alternatively or simultaneously be an ahead-of-time bonus, which reduces the ahead-of-time penalty by the stated amount.

XP for doctrines

For land/air/naval doctrines and some naval research, the corresponding XP can be used to active a one-time bonus. An XP activated bonus functions in the same way as a limited-use bonus. For doctrines, the default amount of XP required is 100 and it activates a limited-use bonus of +100%.

Equipment licensing

When licensing equipment from another country, researching that equipment gets a speed bonus of +20%.

Technology sharing

When a country is part of a research group, it gets a research speed bonus for each other country in the group that has already unlocked that technology, up to +50%. Tech sharing bonus functions in the same way as Limited-use bonus: once applied, the bonus is locked to the tech; changes in the country's tech sharing situation will only reflect in future research. Aside, subjects benefit less from technology sharing, depending on their autonomy level.

Other sources of research bonus

Various national ideas, like designers, theorist, and concerns continuously improve the research speed for applicable technologies while they are active. Design companies can additionally improve equipment being unlocked while they are active.

Ahead-of-time penalty

Most technologies (except doctrines) have a date attached to them when they become current. Researching them earlier comes at the cost of reduced research speed. Each year ahead adds +200% ahead-of-time (AOT) penalty. Ahead-of-time bonuses from National Focus reduce this penalty modifier. For research ahead of time, the in-game tool-tip displays estimated time to completion using the formula below.

With yearly AOT at 2, a technology starting to research [math]\displaystyle{ T }[/math] years before the date it becomes current, with a base research cost of [math]\displaystyle{ N }[/math] days and aggregate research bonus at [math]\displaystyle{ B }[/math]% will take [math]\displaystyle{ 365\left(T+\frac{1}{2}\right)\left(1-e^{-\frac{2N}{365}\frac{1}{1+B\%}}\right) }[/math] days to complete. This assumes the research starts with a speed higher than the minimum and finishes before the technology becomes current. It is also subject to a small approximation error (unlikely to be noticed in-game). The formula is derived by solving

[math]\displaystyle{ N=365\int_0^t \frac{1+B\%}{\text{AOT}\cdot(T-x)+1} dx }[/math] for [math]\displaystyle{ t }[/math].

If part of the research is not under penalty (ie. [math]\displaystyle{ t\gt T }[/math] from the above integral), the estimated time-to-completion is [math]\displaystyle{ 365\left(T+\frac{1+B\%}{\frac{N}{365}-\frac{1}{2}(1+B\%)\ln(2T+1)}\right) }[/math] days.

For example, at exactly one year before a tech becomes current, research speed on that tech is modified by multiplicative factor of [math]\displaystyle{ 1/3 }[/math]. As research speed is re-calculated every day, the speed penalty goes down while a technology is being researched. Half a year later, the penalty is down to [math]\displaystyle{ 1/2 }[/math]. Regular research speed modifiers apply linearly. Thus regular country-wide research bonus does not alleviate AOT penalties. If a 50% ahead-of-time bonus is active as shown in in-game tooltip, 0.5 is taken off the AOT penalty. Thus, at 1 year ahead-of-time, the research speed is modified by [math]\displaystyle{ \frac{1}{(2\cdot 1-50%)+1}=2/5 }[/math] instead of [math]\displaystyle{ 1/3 }[/math] without the bonus; similarly, at half a year ahead-of-time, the AOT penalty is reduced to [math]\displaystyle{ \frac{1}{(2\cdot 0.5-50%)+1}=2/3 }[/math] from [math]\displaystyle{ 1/2 }[/math] without bonus.

Below is a Python script to calculate the time it will take to research a technology, given its base cost, bonuses and AOT penalty.

res_perc = 0.0 time = 0 base = 170 # Base Cost bonus = 0.34 # Research Speed Bonus aot = 0.47 # Ahead-of-time penalty (not years ahead) base /= 1+bonus while res_perc<1: res_perc += 1/base/(1+aot) aot -= 2/365 if aot<0: aot = 0 time += 1 print(time) # Prints total time needed

Technologies

Technologies allow countries to unlock production of new units such as mechanized infantry, paratroopers, tanks and all kinds of airplanes; new equipment, from infantry weapons to carrier air groups and specialized armored units; as well as defensive and productive structures.

On the other hand, most technologies serve to improve the efficiency of current units. This can be achieved through a number of ways, such as improving the damage inflicted by the unit, its ability to penetrate the armor of armored units, its defensiveness and organization or simply its ability to detect enemy units.

It is possible to research improvements of already researched technologies. There could be small buttons on technology (e.g. possibility to operate from carriers for airframe). These improvements have to be researched separately.

Land

• Infantry technology: Technologies that improve infantry weapons and equipment, unlock or improve motorized and mechanized units as well as special forces (marines, mountaineers and paratroopers).
• Artillery technology: Technologies that unlock and improve all types of artillery, including anti-tank, anti-air and rocket artillery.
• Support Companies technology: Technologies that unlock and improve all types of support battalions: Engineers, Reconnaissance, Military Police, Maintenance, Field Hospital, Logistics and Signal companies.
• Armor technology: Technologies that unlock all types and models of tanks, from light to super heavy chassis, as well as their variants: tank destroyer, self-propelled artillery and self-propelled anti-air.
• Land doctrine: Unlocks one of the four land doctrine trees: mobile warfare, superior firepower, grand battleplan and mass assault.

Naval

• Naval technology: Technologies that unlocks or improve all kinds of ship units: destroyer, cruisers, battleship, carrier, submarine or improve transports for naval invasions.
• Naval doctrine: Unlocks one of the three naval doctrine trees: fleet in being, trade interdiction and base strike.

Air

• Air technology: Technologies that unlock or improve all types of airframes: light, medium or heavy, as well as their jet propulsion versions.
• Air doctrine: Unlocks one of the three air doctrine trees: strategic destruction, battlefield support and operational integrity.

Industry

• Engineering technology: Groups all technologies related to electronic engineering (computers, radios, cryptography), rockets and atomic research.
• Industry technology: Groups all technologies that improve production efficiency and volume of all factories, resources excavation and unlocks synthetic refineries.

Doctrines

All doctrines listed above serve to improve units in a specific role by providing them one or multiple bonuses once the doctrine has been researched. Some of these bonuses can be obtained through more than one doctrine, but at different depth of the doctrine tree and most bonuses are unique to a specific doctrine.

It's also necessary for all players to make a choice when researching doctrines, as opposed to all other technologies (with the exception of Industry) that can be entirely researched. Only one doctrine can be researched out of three or four options, depending on the doctrine type (land, naval or air).

It's possible to change doctrine throughout the game, but all bonuses from the old doctrine are lost, as if completely abandoned, when starting research of a different doctrine tree. There are no ahead of time penalties of doctrines.

References

科研 

海军

海军 · 海军学说

空军

空军 · 空军学说

工业

工程学 · 工业

机制 

事件与决议

事件 • 决议