Supplies are required for carrying out a wide variety of tasks performed by ships, fighters and drones. They are stored aboard these vehicles and are gradually used up as the vehicles carry out tasks which require supplies. Vehicles can and should be resupplied before supplies run out, as the consequences for running out of supplies can vary anywhere between ships being crippled or destroyed by the shortage.
Supplies are used for ship movement, firing weapons, raising shields, cloaking devices and stellar manipulation. If a ship is out of supplies, it won't be able to raise its shields, fire its weapons, use its cloaking device, perform stellar manipulation and its movement will be reduced to a meagre maximum of one sector per turn. Fighters and drones that run out of supplies are destroyed.
Each engine specifies a certain number of supplies it uses, and this amount is used with each unit of movement. Note that even bonus engine movement and the solar sail both cause supplies to be used. Total supply usage for ship movement is equal to the total distance moved times the supply usage of all the engines on the ship.
Supplies are stored in a ship's engines and in any Supply Storage components it may have. Meanwhile, planets, mines, satellites, weapons platforms and troops do not require supplies per se; they always have unlimited supplies and can't run out. Bases also have unlimited supply in the unmodded game, but they can be modded to be supply-dependent.
Researching "Supply" gives you Supply Pods and ultimately the Quantum Reactor.
To Resupply a ship, just move to a planet that has a resupply depot. If you make a full stop and depart from the planet on the following turn, you get a full resupply. However, if you just 'touch and go', leaving on the same turn you arrived, you will only get a not-quite-full resupply. Another way to resupply ships is to join depleted ships in a fleet with other ships that have supplies to share. Supplies can also be harvested from stars if the ship has the necessary components.
Note that at least as of SE4 Gold in v1.84, a fighter stack will not be resupplied at a Resupply Depot if the RD is on a moon. They get resupplied fine if the RD is not on a moon. This has been reported to MM.
Ok, I confirmed that the fighter resupply bug is inherent to unmodded SE4 Gold at least in v1.84. A fighter stack will not be resupplied at a Resupply Depot if the RD is on a moon. They get resupplied fine if the RD is not on a moon. This has been reported to MM. (This comment was placed in 2006. It does not appear to have been fixed according to the game's version history.)
Questions and answers
Q: How do I use an Emergency Resupply Pod?
___________ fighter resupply at planets and carriers
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Repairs and Retrofitting