Tuesday, June 18, 2013

Why do we orbit more quicklier?

There are a number of reasons that you might be missing your targets with turrets. Using the correct turret and ammo type for the range and speed of your target is key to landing those wrecking hits. 

Optimal Range

Every turret has an optimal range statistic. This is the maximum range you can hit at without penalty (barring Tracking issues, see below). Different ammo modifies your optimal range, increasing it while doing less damage or decreasing it while doing more damage. In general, the smaller the turret, the shorter the optimal range. There are different types of each size of turrets, with different fitting requirements, range, falloff and damage.

Falloff

Your turret also has a stat called "Accuracy Falloff" which is the "buffer" for your optimal range in which you can expect to get decent hits. As you increase beyond your optimal you hit for less damage. The damage percentage decreases non-linearly:
At Optimal you hit for 100% damage
At Optimal + Falloff, you hit for 50% damage
At Optimal + 2 * Falloff you hit for 6% damage
At Optimal + 3 * Falloff, you hit for less than 0.2% damage
If you have a gun with an optimal range of 15,000 meters and an accuracy falloff of 5,000 meters, you can hit at 0-15,000 meters without penalty (again, not counting tracking issues), hit for 50% of base damage at 20,000, hit for ~21% at 22500 meters, and hit almost nothing at 30000 m. 

Transversal Velocity & Tracking

When people talk about keeping your Transversal up, they really mean Angular Velocity since that's what gun tracking ability is measured in (transversal is in m/s, angular--and gun tracking--is in rad/s). Transversal velocity is actually angular velocity multiplied by the distance from the object of reference to the rotating object, but we'll stick with the convention used in-game here. So just put Angular velocity on your overview, and if that's close to or exceeds your gun's tracking for a given target, you're gonna start whiffing. Easy.
Easier to say Transversal on vent though, I admit.

Transversal velocity is a measure of how fast two ships are moving across each other's field of view. It's always the same between two different ships, and hurts bigger guns and missiles when it's high. Thinking of a turret trying to track (rotate) to hit a moving target is an easy way to visualize it. If the target is traveling in such a way that you wouldn't have to move the turret at all, then the target has low transversal velocity. If you'd have to be moving the turret as fast as possible, that would be high transversal.

How it Works

If you were in the center of a clock (not a digital one), and a ship was sitting on the end of the minutes hand, it would be transversing 60x as fast as a ship sitting on the end of the hours hand. In EVE terms, it can be thought of as how fast something is moving across your field of vision, which mathematically can be defined as a function of its speed and approach (which form the afore referenced vector). If something were coming straight at you, it would have virtually no transversal, so even the slowest moving turret could hit it.
Imagine two stationary ships that have their turrets pointed toward each other.

A->                 <-B


The line of sight is an imaginary line that each turret follows as it targets the other ship.

A->--------------<-B


Transversal velocity describes how fast a ship is moving out of the turret's line of fire. You can see that this depends on the direction the ship moves. If B moves directly toward A, it does not leave the line of sight at all.

A->-------<-B


So his transversal velocity is zero.

On the other hand, if he moves at a 90 degree angle, all of his movement takes him out of that line of sight.
A->              
                 
               <-B

His transversal velocity equals his total velocity.
Easy enough. What if both ships are moving? In a simple case, A and B move at the same 90 degree course at the same speed.

A->              <-B


You can see that both ships remain in each others line of sight. So the transversal velocity of each ship is zero.
On the other hand, if A and B move in opposite directions, each moves out of the other's line of sight twice as fast as if only one were moving.

A->


                     
                     
                   <-B

So in this case the transversal velocity is the sum of both velocities.
In real life, the angles aren't perfect. But remember, only movement away from the line of sight affects transversal velocity. To deal with another angle, the game simply separates the ship's velocity into two parts - one in the line of sight (radial velocity) and one perpendicular to it (transverse velocity). The perpendicular components are figured for both ships. These are the gray lines in the simulation. It then adds or subtracts these perpendicular components to get the final transversal velocity.
You can display a column for the radial and transverse velocities for object on your in-game Overview, by using the right-click/settings menu.

Tracking speed

Each (non-missile) weapon has a tracking speed, and this can be further modified by skills, bonus, and weapon upgrades. Generally speaking, the higher this value, the greater the chance of hitting and more damage you will do to targets that have a high transverse velocity relative to you.
The tracking speed is specified as an angular velocity, in radians per second (rad/s). This is the maximum turning rate of a target (relative to your position) that the weapon will hit with greater than 50% base damage. If the object's angular velocity is higher than this, the weapon's damage is quickly reduced.
However, there's a complication. Each weapon has a "signature resolution", and each ship has a "signature radius". The weapon signature resolutions are consistent across all types, and only depend on the weapon size:

Weapon size Signature resolution
Small40 m
Medium125 m
Large400 m
XL1000 m

The ship signature radii vary between classes and individual types:
Ship Signature radius
Shuttle25 m
Interceptor (Crow)36 m
Frigate (Merlin)40 m
Destroyer (Thrasher)75 m
HAC (Vagabond)115 m
Cruiser (Caracal)145 m
Industrial (Bestower)210 m
Battlecruiser (Ferox)285 m
Battleship (Dominix)420 m
Dreadnought (Moros)1740 m

The ratio between the target's signature radius and the weapon's signature resolution is multiplied by the tracking speed of the weapon. Therefore, you want this ratio to be 1 or over.
For instance, shooting a frigate (radius = 40 m) with a small turret (resolution = 40 m) gives a perfect ratio of 40/40 = 1.
Shooting a BC (radius = 285 m) with a medium turret (resolution = 125 m) gives a bonus of 285/125 = 2.28 to the turret's tracking speed.
However, shooting an interceptor (radius = 36 m) with a large turret (resolution = 400 m) gives a big penalty of 36/400 = 0.09 to the tracking.
So:
(Modified tracking speed) = (base tracking speed) x (target's signature radius) / (weapon's signature resolution)
To calculate the maximum transverse velocity of a target, multiply the modified tracking speed by the range to the target:
(Max transverse velocity) = (weapon's modified tracking speed) x (target range)
For example, a 125 mm autocannon has a tracking speed of 0.395 rad/s. Let's say you're trying to shoot a frigate, so the signature ratio is 1. This means:
  • At 5 km, the maximum transverse velocity of a target is 1975 m/s.
  • At 1 km, the maximum is 395 m/s.
  • At 500 m, the maximum is 197.5 m/s.
Compare this to a 280 mm artillery cannon with a tracking speed of 0.066 rad/s:
  • At 20 km, the maximum transverse velocity of a target is 1320 m/s.
  • At 10 km, the maximum is 660 m/s.
  • At 5 km, 330 m/s.
  • At 1 km, 66 m/s.
  • At 500 m, 33 m/s.
The "maximum" transverse velocity is not really a maximum, since the falloff in hit damage is gradual:
(Damage fraction) = (0.5)^( ((Transverse velocity)/(Maximum transverse velocity) )^2 )
  • At a transverse velocity of 0% to 39% of maximum, the hit damage is 100% to 90% of the base value.
  • At 39% to 86% of maximum, the damage goes from 90% to 60%
  • At 100% of maximum, the damage is exactly 50%
  • At 182% of maximum, the damage is 10%
  • At 200% of maximum, the damage is 6%
  • At 300% of maximum, the damage is 0.2%
Now say you were trying to hit a frigate flying at 600 m/s in circles around you. Divide the 600 m/s by the modified tracking speed to find the minimum range that you want to be from the target:
  • For the autocannon, 600/0.395 = 1518 m.
  • For the artillery, 600/0.066 = 9090 m.
This allows you to find an optimum orbit range of a target that balances the falloff of damage due to range, and the falloff of damage due to tracking.
You can also use this information to avoid being hit. Say you are in a frigate (sig radius = 40 m) with a max speed of 400 m/s. You are fighting a cruiser fitted with medium Blaster weapons (tracking speed = 0.12 rad/s, sig resolution = 125 m). Assuming no bonuses:
The cruiser's modified weapon tracking speed is 0.12 x (40/125) = 0.0384
Divide your speed by the modified tracking speed: 400 / 0.0384 = 10416 m
So if you orbit at a range less than about 10000 m, the cruiser will hit you for less than 50% of max damage. At 5000 m, less that 6%, and at 3300 m, it will hit you for almost nothing. 

Related Skills

There are a number of skills related to turret damage and tracking.
  • The basic Gunnery skill boosts turret rate of fire by 2% per level.
  • Base damage is boosted by the relevant turret skill (e.g. Small Projectile Turret), and any ship skills for ships that have turret damage bonuses.
  • The Surgical Strike skill gives a 3% damage bonus to all turret types.
  • Rapid Firing reduces the delay between shots by 4% per level, thus boosting DPS.
  • Tech 2 turret specialization skills (e.g. Large Railgun Specialization) boost the damage of the relevant T2 turret types by 2% per level.
  • Sharpshooter gives a 5% boost to turret optimal range.
  • Trajectory Analysis boosts turret falloff by 5% per level, thus increase the effective range.
  • Motion Prediction gives a 5% increase per level in turret tracking speed. Some ships also have bonuses to tracking speed per level of ship skill.
~Kaphine

Hoc est proprie rapta Kaphine Goodswarm Wiki a page.
(English to Latin)

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