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Afterburner
From EVEWiki
 For info on the "Afterburner" skill, see Afterburner (skill)
An Afterburner (or AB) is a mediumslot ship module that when activated increases a ship's maximum velocity.
When a properly sized Afterburner is Active, your speed is roughly doubled. While it isn't as much as a Microwarpdrive, the module doesn't increase signature radius as well. This makes it more capable of avoiding damage, if less adept at dictating the range of an engagement.
Aside from being more evasive than a MWD, an Afterburner can also keep functioning even when struck by a Warp Scrambler type Warp Jammer. In such an instance, a MWD ship would be reduced to normal speed, giving the speed advantage to the Afterburner ship. In this case, the Afterburner ship would very much dictate the range of engagement.
On the other hand, the MWD ship can simply use its superior speed to stay out of scramble range (7.5km to 9km, typically). If the MWD assailant can attack from that range, it would easily control the fight. Whether or not an Afterburner ship can counter a MWD ship depends on whether or not it can get into range in time, and on the weapons setup of the opposing ship.
Another benefit of the Afterburner is that it takes less resources to fit one. The Capacitor upkeep to run it is fairly mild, as well.
You can only have 1 Afterburner active at once. You can fit an Afterburner and a MWD on the same ship, but they cannot be active at the same time.
Contents 
Thrust Factor & Size Classes
The interactions between ship size and Afterburner size are the same as with Microwarpdrives. Afterburners have a thrust factor associated with them, a different multiple of 15 for each size class:
 1,500,000 newtons for 1MN (Frigate)
 15,000,000 newtons for 10MN (Cruiser)
 150,000,000 newtons for 100MN (Battleship)
The different classes of ship generally have a mass associated with them:
 1,000,0001,500,000+ kg for Frigates and Destroyers
 10,000,00015,000,000+ kg for Cruisers and Battlecruisers
 100,000,000150,000,000+ kg for Battleships
The Thrust Factor of the Afterburner will adjust the speed bonus of the Afterburner, depending on the mass of the ship. If the ship weighs less than the Thrust Factor, you will gain additional speed. If it weighs more, you lose speed.
Mass Gain
You must take into account that Afterburners increase the mass of the ship when active. Each class of Afterburner will give a different mass gain appropriate to the class:
 500,000 for 1MN
 5,000,000 for 10MN
 50,000,000 for 100MN
These mass gains will offset the fact that you are provided with a roughly equal amount of additional thrust (i.e. 1,500,000 instead of 1,000,000) that the lightest ship would have enjoyed. It also makes the ship turn and accelerate slower.
Overfitting
If you fit a Cruiser class Afterburner onto a Frigate, the speed increase is enhanced by the Thrust Factor/Mass ratio, giving you much more than the intended increase in speed (even after the mass gain). The reverse is also true  if you fit a module that is too small for your mass, you will not gain much of anything.
It is fairly easy to do this with the help of powergrid enhancing modules. The speed increase can be similar to a Microwarpdrive, but without the penalties. However, you will suffer from extremely reduced turn rates and slow acceleration. It is probably only worth attempting such a setup for mission running.
Deadspace Missions
Since Microwarpdrives don't work in deadspace, you are left with only Afterburners to enhance your speed.
This does not apply to Faction Warfare deadspace areas, which permit MWDs to run.
Variations
Common Statistics amongst all Afterburners
Thrust Factor  Activation Mass Penalty  Cycle Time  

1MN  1,500,000  500,000  10 sec 
10MN  15,000,000  5,000,000  10 sec 
100MN  150,000,000  50,000,000  10 sec 
Frigate
Name  Meta Level  Max Velocity Bonus  Activation Cost  Powergrid Usage  CPU Usage  

Tech I  1MN Afterburner I  n/a  112.5 %  20 Energy  10 MW  15 tf 
Limited 1MN Afterburner I  2  121.5 %  20 Energy  10 MW  15 tf  
Experimental 1MN Afterburner I  3  126 %  20 Energy  10 MW  15 tf  
Tech II  1MN Afterburner II  5  135 %  22 Energy  11 MW  15 tf 
Storyline  1MN Analog Booster Rockets  6  121.50 %  16 Energy  9 MW  13 tf 
Faction  Gallente Navy 1MN Afterburner  7  141 %  20 Energy  10 MW  17 tf 
Shadow Serpentis 1MN Afterburner  7  141 %  20 Energy  10 MW  17 tf  
Republic Fleet 1MN Afterburner  8  144 %  15 Energy  11 MW  15 tf  
Domination 1MN Afterburner  8  144 %  15 Energy  11 MW  15 tf  
Deadspace  Coreli CType 1MN Afterburner  11  150 %  15 Energy  10 MW  17 tf 
Gistii CType 1MN Afterburner  11  153 %  20 Energy  13 MW  15 tf  
Coreli BType 1MN Afterburner  12  153 %  15 Energy  10 MW  18 tf  
Gistii BType 1MN Afterburner  12  156 %  20 Energy  13 MW  15 tf  
Coreli AType 1MN Afterburner  13  156 %  15 Energy  10 MW  19 tf  
Gistii AType 1MN Afterburner  13  159 %  20 Energy  13 MW  15 tf 
Cruiser
Name  Meta Level  Max Velocity Bonus  Activation Cost  Powergrid Usage  CPU Usage  

Tech I  10MN Afterburner I  n/a  112.5 %  80 Energy  50 MW  25 tf 
Experimental 100MN Afterburner I  3  126 %  80 Energy  50 MW  25 tf  
Tech II  10MN Afterburner II  5  135 %  88 Energy  55 MW  25 tf 
Storyline  10MN Analog Booster Rockets  6  112.50 %  64 Energy  45 MW  21 tf 
Faction  Gallente Navy 10MN Afterburner  7  141 %  80 Energy  50 MW  28 tf 
Shadow Serpentis 10MN Afterburner  7  141 %  80 Energy  50 MW  28 tf  
Republic Fleet 10MN Afterburner  8  144 %  60 Energy  55 MW  25 tf  
Domination 10MN Afterburner  8  144 %  60 Energy  55 MW  25 tf  
Deadspace  Corelum CType 10MN Afterburner  11  150 %  60 Energy  50 MW  29 tf 
Gistum CType 10MN Afterburner  11  153 %  80 Energy  63 MW  25 tf  
Corelum BType 10MN Afterburner  12  153 %  60 Energy  50 MW  31 tf  
Gistum BType 10MN Afterburner  12  156 %  80 Energy  63 MW  25 tf  
Corelum AType 10MN Afterburner  13  156 %  60 Energy  50 MW  32 tf  
Gistum AType 10MN Afterburner  13  159 %  80 Energy  63 MW  25 tf 
Battleship
Name  Meta Level  Max Velocity Bonus  Activation Cost  Powergrid Usage  CPU Usage  

Tech I  100MN Afterburner I  n/a  112.5 %  320 Energy  625 MW  50 tf 
Experimental 100MN Afterburner I  3  126 %  320 Energy  625 MW  50 tf  
Tech II  100MN Afterburner II  5  135 %  325 Energy  688 MW  50 tf 
Storyline  10MN Analog Booster Rockets  6  112.50 %  256 Energy  563 MW  43 tf 
Faction  Gallente Navy 100MN Afterburner  7  141 %  320 Energy  625 MW  55 tf 
Shadow Serpentis 100MN Afterburner  7  141 %  320 Energy  625 MW  55 tf  
Republic Fleet 100MN Afterburner  8  144 %  241 Energy  688 MW  50 tf  
Domination 100MN Afterburner  8  144 %  241 Energy  688 MW  50 tf  
Officer  Brynn's Modified 100MN Afterburner  11  150 %  241 Energy  625 MW  58 tf 
Mizuro's Modified 100MN Afterburner  11  153 %  320 Energy  750 MW  50 tf  
Tuvan's Modified 100MN Afterburner  12  153 %  241 Energy  625 MW  61 tf  
Hakim's Modified 100MN Afterburner  12  156 %  320 Energy  750 MW  50 tf  
Setele's Modified 100MN Afterburner  13  156 %  241 Energy  625 MW  63 tf  
Gotan's Modified 100MN Afterburner  13  159 %  320 Energy  750 MW  50 tf  
Cormack's Modified 100MN Afterburner  14  159 %  241 Energy  625 MW  66 tf  
Tobias' Modified 100MN Afterburner  14  162 %  320 Energy  750 MW  50 tf  
Deadspace  Core CType 100MN Afterburner  11  150 %  241 Energy  625 MW  58 tf 
Gist CType 100MN Afterburner  11  153 %  320 Energy  750 MW  50 tf  
Core BType 100MN Afterburner  12  153 %  241 Energy  625 MW  61 tf  
Gist BType 100MN Afterburner  12  156 %  320 Energy  750 MW  50 tf  
Core AType 100MN Afterburner  13  156 %  241 Energy  625 MW  63 tf  
Gist AType 100MN Afterburner  13  159 %  320 Energy  750 MW  50 tf  
Core XType 100MN Afterburner  14  159 %  241 Energy  625 MW  66 tf  
Gist XType 100MN Afterburner  14  162 %  320 Energy  750 MW  50 tf 
Skills, Implants, Rigs, and Boosters
 The Afterburner skill increases the duration of the Afterburner, thereby reducing the capacitor drain. However, it will increase the time it takes to turn off and restore your mass to normal.
 The Acceleration Control skill will boost the effectiveness of a MWD or Afterburner by 5% per level.
 The Navigation skill provides 5% more base velocity per level.
 The Snake Implants (slot 16) enhance base speed (they now stack with speed modules).
 The Halo Implants (slot 16) reduce Signature Radius.
 The Slot 6 Rogue MY series of Hardwirings enhance the speed increase of Afterburners or MWDs.
 The Slot 6 Rogue CY series and Shaqil's Speed Enhancer both increase the base speed of a ship.
 The Slot 6 Rogue EY series increases the duration of the Afterburner, thereby reducing the capacitor drain. However, it will increase the time it takes to turn off and restore your mass to normal.
 The Slot 8 Rogue DY series decreases the capacitor cost of Afterburners.
 The slot 10 Skirmish Warfare Mindlink will add 50% more effectiveness to Skirmish Warfare Links, one of which provides a Gang boost to speed.
 The XInstinct series provides a Signature Radius reduction, but may reduce your base velocity as a sideeffect.
 The Auxiliary Thrusters Rig will improve base speed.
 The Polycarbon Engine Housing Rig will improve base speed and agility.
Overheat
Overheating an Afterburner will increase its velocity bonus by 50%, making it one of the most substantial boosts to receive from Overheating. Even using it in small bursts can give you a huge speed advantage over an enemy that doesn't have the Thermodynamics skill.
Related Modules
 Overdrive Injectors, which boost base speed (6.9%  12.5%) at the cost of a percentage of your Cargohold.
 Nanofiber Internal Structure modules, which also boost base speed (7.85%  9.4%), as well as agility (13.1%  15.8%) at the expense of a percenage of your ship's Structure.
 Skirmish Warfare Link  Rapid Deployment will add a speed boost to all Fleet members based on the command skills of the Gang Booster.
History
 In the very beginning, MWDs and Afterburners didn't have classes; one module fit any ship. Additionally, it was possible to activate more than one speed module.
 Build 1352 had introduced the 1MN, 10MN, and 100MN size class split, which intentionally permitted players to fit a module one size larger if they could muster up the fitting statistics. Unfortunately, this worked far too well. When Cruisers equipped two 100MN Afterburners, it granted them incredible speeds faster than even Interceptors.
 Build 2942 made it impossible to activate more than one MWD at once, defeating the dual MWD setups for good. Unfortunately, it was still possible to either utilize a MWD and an Afterburner or a pair of oversized Afterburners for still insane speeds.
 Build 3106 increased the effect of the mass increase, making ships wielding oversized speed modules much slower to accelerate and turn. Afterburners joined the MWD in not being able to be activated in conjunction with another speed module. Since proper sized Afterburners were quite weak on their own, the speed boost was changed from 30% to 100%.
 Quantum Rise would add in the effect of Warp Scrambler type Warp Jammers shutting down MWDs. This would be a huge boon to Afterburners, making Afterburner/Warp Scrambler combos a huge edge over MWD fits, provided the wielder could get into range.