Eldar Space Fleet
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The Eldar Space Fleet is the general term used to describe the warships that escort the massive Craftworlds as they roam the galaxy, protecting these remaining bastions of the Eldar race from outside threats. While not having that much of a presence in the main Warhammmer 40000 wargame, they are one of the main factions in the Battlefleet Gothic spin-off and its video game adaptations.
Unlike the warships of the Imperium of Mankind, which look like cathedrals in space due their Gothic ornamentation, Eldar vessels are sleek and fragile-looking, gliding silently on the spaceways thanks to their solar sails. They are also blisteringly fast, and in the right circumstances are capable of speeds that far outstrip any other ships of their size.
Eldar ships forego the armor that ships of other races use, and instead rely on their speed and Holofields to protect them, while using powerful Pulsar Lances to tear enemy ships to shreds. An Eldar ship will either try to remain undetected for as long as possible, or keep constantly on the move, as they simply aren't built to endure an extended firefight.
While they mostly deal with spaceborne threats, Eldar ships also support warhosts in their objectives, carrying these to the worlds they need to be at if a convenient Webway Gate isn't available. These ships then will conceal themselves, often at an outlying world or debris field, to await the warhost's return.
Because all Eldar ship classes are used by Craftworlders and Corsairs, Imperials have come to dread the appearance of Eldar ships, as there's equal chance that they'll either help you (only to kill you later decades down the line), or raid and plunder you (and then your direct descendants, centuries later).
Shields of the Craftworlds
Battleship
Void Stalker
The largest ship available to the Eldar, the Void Stalker embodies this ancient race's methods of war, being heavily armed, lightning fast and somehow staying as nimble as an Imperial Escort. It comes armed with mid-ranged Pulsar Lances as standard, and carries quad Launch Bays to launch Fighters and Bombers.
Battecruiser
Phoenix
The second-largest ship in the Eldar fleet, the Phoenix comes armed with front-mounted Pulsar Lances, Weapons Batteries, and a pair of Launch Bays for Fighter and Bomber support. Its weapons systems are somewhat close-ranged compared to an Imperial Battlecruiser, but in return, the Phoenix is ridiculously fast for its size, easily leaving Imperial Escorts in the dust.
Cruiser
Most Cruiser-sized Eldar ships are called "Dragonships". Rarely even sharing the same design, they do have similar armaments, and adhere to the same tactics during fleet actions. Regardless of the Dragonship type, each one is still faster than an Imperial Escort.
The most common Dragonship variants and their armaments are as follows:
Firestorm: Armed with Torpedo launchers and Pulsar Lances.
Ghost: Equipped with Lascannon batteries and Launch Bays.
Moonray: Armed with Pulsar Lances and Launch Bays.
Starfall: Equipped with Lascannon batteries and Torpedo launchers. This is the equivalent of the Prismatic for the Dragonships.
Eclipse
A dedicated Carrier-craft, the Eclipse is armed with four Launch Bays, with only a pair of short-ranged Lances to defend itself with. Because of its high speeds, it's not as vulnerable as being a Carrier implies, but usually relegated to a defensive role, providing Fighter cover to intercept Ordinance.
Light Cruiser
Smaller compared to Dragonships, Wraithships are called as such because most of their systems are formed around a wraithbone core. The crew of these ships are often psychically attuned to this material, and as a result are able to control and maneuver the ships as if it were part of their own bodies.
Due to Wraithships having the same sort of weapons configurations as the Dragonships, they also share variant names.
Firestorm: Armed with Torpedo launchers and Pulsar Lances.
Ghost: Equipped with Lascannon batteries and Launch Bays.
Moonray: Equipped with Pulsar Lances and Launch Bays.
Prismatic: Armed with Lascannon batteries and Torpedo launchers.
Escort
As with other races, Escorts come in two flavors, with the slightly larger but better-armed Frigate and the smaller but quicker Destroyers.
Aconite
Forgoing the Pulsar Lance and Torpedoes of the Hellbore, the Aconite compensates by having lots and lots of Starcannons. A pair of Aconites working in conjunction can easily put out the firepower of a Cruiser.
Hellebore
Armed with a pair of Torpedo tubes, a Pulsar Lance, and Weapons Batteries, the Hellebore Frigate has a comparatively more flexible load-out compared to its contemporary. It is used mostly as a flanker, though it can also complement Eclipses when used as a heavy Escort.
Hemlock
The designated Lance-boat, the Hemlock mounts a front-facing Pulsar Lance, and several Starcannon batteries for defense.
Nightshade
A dedicated Torpedo Destroyer, the Nightshade is armed with a pair of Torpedo launchers and Starcannons batteries.
Shadowhunter
In the videogame, this is the only Escort available to Craftworlders. To compensate, the Destroyer class was split into two variants with different weapons loadouts: one with a Shadow Lance, the other with a Lascannon battery.
In Battlefleet Gothic
Featuring fast and fragile ships that had oddly short ranges, an Eldar player has to pretty much master the art of Hit and Run. To really make the most of their ship weapons a player has to master the Eldar's unique movement mechanics.
Firstly Eldar ships have three movement speeds, with the lowest listed when a ship is moving sunward, while its fastest listed speed only available while moving abeam of a star. Secondly, Eldar had a second turn or move after all Ordinance had been used. These two combined make for a very mobile force in the right conditions, and an extremely vulnerable fleet in others, so an Eldar player needs to be mobile.
Speaking of defenses, Eldar ships... don't have a lot, actually. Holofields can defend against long-ranged snipes by Lances, but there's a hilariously long list of stuff that ignore Holofields entirely (Weapons Batteries, Bombardment Cannons, Gauss Whips...). They don't have turrets either, so good luck shooting down Ordinance!
The Eldar initially had a limited number of ships during the first release of the game, but subsequent waves mitigated that somewhat. Min-maxers will probably just bring Aconites and Hellebores anyway,but at least it has more variety now.
In Battlefleet Gothic: Armada 1 & 2
Every bit as fast, deadly, and fragile as their tabletop counterparts, the ships of the Eldar are also a bit pricier compared to anything the Imperials can field. For the sake of variety, most of the ships available to Eldar list in the tabletop game were split in-game between the Asuryani/Craftworlders and the Corsair fleets.
The Corsairs are stealthier and have access to the Void Stalker and Frigates, but even more fragile, while the Craftworlders are tougher, are limited to the Phoenix as their Capital Ship. Because of the relative short ranges of their weapons, Eldar ships have to come in close to do most of their damage, but this is leveraged somewhat by their speed and their Holofields. Glide in, unload weaponry, then get the heck out of Dodge.
In a reversal from the tabletop, Lance weapons (which can't miss) will ruin any Eldar skipper's day. Add to this a vulnerability to Critical Hits, and Eldar have to avoid taking heavy damage as much as possible.