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The Finer Points of Warp Speed

One of the most important stats on ships in EVE Online is one that is often overlooked in favour of a bit more tank or a little velocity. You might only have two rig slots and that second trimark just looks too tasty. What I’m here to tell you is that your fitting choice is wrong and you should listen to me because I read through the maths about five minutes ago. You also already read the title so… let’s talk warp speed.

Of course, this is in response to CCP’s recent warp speed changes which came out of nowhere just the other day. With cruisers, battlecruisers, and battleships all now enjoying improved warp speeds we’re sure to see more of a hyperspatial focus in fleets; at least for a while. Hell, my fleet was hunted by Cynabals yesterday on the way home. Turns out that dropping two supers, a HIC, and assorted tackle on 4 ships wasn’t enough for French ConneXion.


The Maths

Don’t let the numbers scare you, running through the formulae bit by bit actually works out pretty nicely when you do the maths yourself (she writes, before actually doing them). I realised during my research for this piece that what I’m writing is well-trodden ground. There’s even a chunky dev blog from 2013 by CCP Masterplan running through everything post-Rubicon and I do not intend to rehash his work.

Instead, here’s a compilation of my thoughts regarding how exactly warping works. Fact checked as much as possible and bullet pointed to stop it from being all tl;dr. EVE Uni did the teacher-style breakdown already.

Acceleration during long warps

  • Every ship covers exactly 1 AU during the acceleration part of a warp.
  • Time taken to accelerate simplifies to ln(149597870700)/warpSpeed which is roughly 25.7/warpSpeed
  • To bookmark a particular distance in metres, work out time in seconds to wait using the equation
    time = ln(distance) / warpSpeed

The first two facts are pretty simple and the derivation comes from some interesting—albeit high-school level—maths. The real deal here is point number 3. By using this formula you can pick a distance-to-target, warp, then drop a bookmark exactly on top of them after t seconds. My initial test landed me within 1km of the theoretical result and I definitely have more testing to do, but it definitely beats dropping random bookmarks to catch someone!


Deceleration

  • Instead of using warpSpeed, the calculations call for either ‘warpSpeed/3’ or ‘2’, whichever is smaller. We call this value j
  • The above means that deceleration stops getting faster over 6AU/s
  • Ships will always drop out of actual warp at either ‘100m/s’ or ‘shipBaseSpeed/2’ (whichever is smaller). This is known as ‘s’
  • The final deceleration time formula is: time = (ln((149597870700 *warpSpeed)/s)/j)

Interestingly, the deceleration formulae are much more difficult to wrap your head around. A large part of EVE Uni’s calculations involved integrating the distance function and using log rules to simplify things until we reach the above formula; one that was already complicated by the use of s and j. The key takeaway from the deceleration of a ship is that there are only two key components, warp speed between 0-6 AU/s and subwarp base speed between 0-200 m/s.

That is to say that a ship with 9999 AU/s warp speed and 9999 m/s base velocity shouldn’t slow down any faster than a 6 AU/s, 200 m/s ship. This gets a bit weird, though, since there isn’t anywhere in New Eden for such a ship to reach 10kAU of speed… In real terms it means that you can speed up your freighter by a half a second while coming of warp if you sacrifice all lows for overdrives. Don’t do this.

A slightly more useful fact is that if CCP were to double the deceleration cap to min(k/3, 4) then we could cut the deceleration of an interceptor in half! Even a small increase to a 7.5 AU/s cap would shave two seconds off scout/tackle warp times.


Cruising & Short Warps

  • Cruising (mid-warp) is very simple and time spent works out to be
    (cruiseDistance) / (149597870700 *warpSpeed)
  • The cruising distance is simply all of the space not taken up by acceleration and deceleration.
  • Most ships will only hit their full cruise speed on warps of 4 AU or greater
  • Calculations on short warps require an initial calculation of max velocity:
    vMaxAU = (distanceAU * warpSpeed * j) / (warpSpeed + j)

Remember, if you’re trying the above calculations, that the units of distance you use will work out as the units of velocity per second in your answer. To assume a 1AU warp for example will get us up to 1.5 AU/s at most in a fast ship. The same with a short 200km warp would be a crazy 300,000 m/s, albeit very briefly. This might sound like a lot compared to 1.5 AU/s, but go and work that in m/s and tell me again that warp drives are slow 😉


So what fits can we make?

Outside of the somewhat complex maths behind it, warping remains an interesting core gameplay mechanic that we all need to use all the time. The warp speed and align time of a fleet determines the effective range you can travel without your pilots dying of boredom. Having to spend 20 minutes moving a T1 battleship fleet compared to the equivalent 8 minute Jackdaws or 14 minute Machariels just adds to the pain of waiting around for a blueball and long journey home. You can easily see why we’ve been asking for warp speed changes for years now.

The new speeds are looking a little like this:
Battleships: 3 AU/s (3.5 T2)
Battlecruisers: 3.5 AU/s (4)
Cruisers: 4 AU/s (4.5)

Notable exceptions are obviously the Cynabal and Machariel at 6 AU/s and 4.5 AU/s respectively. Hyperspatial versions can even reach 10.4/7.82 AU/s before implants. The Nestor also sits at the new standard warp speed and does not retain the prior 25% bonus it had previously.

The key to actually utilising bonuses in this way is to actually focus on bringing down align time to improve total travel time. A Vedmak, for example, makes for a lovely fast response ship since it reaches a 3s align and 5 AU/s warp very easily, on par with a fast frigate fleet. The same applies to battleships where it is quite easy to turn the Praxis into a sub 6s align budget Mach-Barghest hybrid with torpedoes and 1,600 DPS. That isn’t exactly what I’d call a good fit, but being fast and surprising is the only thing that would make it work.

For the most part though, nothing has changed except for quality of life. Faster ships open up more options for fleets, but not necessarily more specific fits outside of the examples I’ve already mentioned. Take these changes in stride and spare just a moment to ask if warp speed could be more important than 5k EHP.

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