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Missile mechanics: Difference between revisions

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== The Basic Picture ==
== The Basic Picture ==


A missile's target is surrounded by an invisible bubble called its <span style="color:#ccffee">''Signature Radius''</span>. This is the area that weapons see when they try to lock on to the ship. Generally, the bigger the ship, the bigger the bubble. (''However, various things can extend or shrink the size of a ship's [[Signature_radius|Signature Radius]].'')  
All ships are surrounded by an invisible bubble called its ''[[signature radius]]''. This is the area that weapons see when they try to lock on to the ship. Generally, the bigger the ship, the bigger the bubble. (''However, various things can extend or shrink the size of a ship's signature radius.'')  


When a missile crosses the Signature Radius of its target, it explodes. The explosion expands in a bubble of its own. The speed at which this bubble grows is called the <span style="color:#ccffee">''Explosion Velocity''</span>, and the maximum size that the bubble will reach is called the <span style="color:#ccffee">''Explosion Radius''</span>.
When a missile crosses the signature radius of its target, it explodes. The explosion expands in a bubble of its own. The speed at which this bubble grows is called the <span style="color:#ccffee">''explosion velocity''</span>, and the maximum size that the bubble will reach is called the <span style="color:#ccffee">''explosion radius''</span>.
[[File:QSG_missile_terms.png|thumb|right|upright=0.8|A Missile Explodes|alt=drawing showing SR and ER]][[File:QSR_missile_hit.gif|A Missile Explodes|alt=animation of missile hitting ship]]
[[File:QSG_missile_terms.png|thumb|right|upright=0.8|A Missile Explodes|alt=drawing showing SR and ER]][[File:QSR_missile_hit.gif|A Missile Explodes|alt=animation of missile hitting ship]]
The missile does not so much hit the ship as explode near it. EVE uses a mathematical equation to compute the precise amount of damage that the explosion does to the ship. You can read about the details in the [[#Technical_Section|Technical Section]] of this document. The next section explains the way that missile damage is computed in general terms.
The missile does not so much hit the ship as explode near it. EVE uses a mathematical equation to compute the precise amount of damage that the explosion does to the ship. You can read about the details in the [[#Technical_Section|technical section]] of this document. The next section explains the way that missile damage is computed in general terms.


===When a Missile Explodes===
===When a Missile Explodes===
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While a missile can apply up to 100% of the Base Damage to a ship in some situations, damage is often reduced by two factors:
While a missile can apply up to 100% of the Base Damage to a ship in some situations, damage is often reduced by two factors:


*If the target ship is moving faster than the ''Explosion Velocity'' of the missile. Think of this as a fast ship being able to somewhat outrun the explosion.
*If the target ship is moving faster than the ''explosion velocity'' of the missile. Think of this as a fast ship being able to somewhat outrun the explosion.
*If the signature radius of the target ship is smaller than ''Explosion Radius'' of the missile. Think of this as a small ship flying through a large explosion and only being hit by a part of it.
*If the signature radius of the target ship is smaller than ''explosion radius'' of the missile. Think of this as a small ship flying through a large explosion and only being hit by a part of it.


In practice damage is usually reduced by the combination of these two factors.
In practice damage is usually reduced by the combination of these two factors.
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Without going into the mathematical details (''[[#Technical_Section|which are discussed below]]''), the other factors that might come into play are these:
Without going into the mathematical details (''[[#Technical_Section|which are discussed below]]''), the other factors that might come into play are these:


*If you are using missiles, you want a faster explosion (''more Explosion Velocity'') and a smaller one (''less Explosion Radius'') – in other words, a short, tight explosion is more effective than a long, loose one.
*If you are using missiles, you want a faster explosion (''more explosion velocity'') and a smaller one (''less explosion radius'') – in other words, a short, tight explosion is more effective than a long, loose one.
*If a missile reaches its target, it will always do ''some'' damage. It is the speed of the explosion that helps determine how much ... not the speed of the missile.
*If a missile reaches its target, it will always do ''some'' damage. It is the speed of the explosion that helps determine how much ... not the speed of the missile.
*Unlike with turrets, the angular velocity of the target does not matter ''for computing damage''. The missile still has to get to the target, but once it arrives, damage is computed using the target's absolute velocity.
*Unlike with turrets, the angular velocity of the target does not matter ''for computing damage''. The missile still has to get to the target, but once it arrives, damage is computed using the target's absolute velocity.
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=== An Illustration ===
=== An Illustration ===


As an illustration, here are the basic statistics for the Inferno Light Missile. These are sorted on Explosion Velocity.
As an illustration, here are the basic statistics for the Inferno Light Missile. These are sorted on explosion velocity.


{| class="wikitable sortable" style="text-align:center; text-size:90%"
{| class="wikitable sortable" style="text-align:center; text-size:90%"
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Second, you can see that the Fury missile has a larger base damage, but that the Precision missile has a faster Explosion Velocity and smaller Explosion Radius.  
Second, you can see that the Fury missile has a larger base damage, but that the Precision missile has a faster Explosion Velocity and smaller Explosion Radius.  


Explosion Radius and Velocity come into play whenever the target is small and/or fast. This means that the Fury missile will deliver its full damage against a bigger, slower ship, but is more likely to have its damage reduced against smaller, faster targets. A Precision missile will also deliver its full damage against a bigger, slower ship – though it will do less damage than the Fury because of the lower base damage – but it will also be more likely to deliver full damage to smaller, faster ships.
Explosion radius and velocity come into play whenever the target is small and/or fast. This means that the Fury missile will deliver its full damage against a bigger, slower ship, but is more likely to have its damage reduced against smaller, faster targets. A Precision missile will also deliver its full damage against a bigger, slower ship – though it will do less damage than the Fury because of the lower base damage – but it will also be more likely to deliver full damage to smaller, faster ships.


Other classes of missiles follow the same pattern. Again, the list is sorted on Explosion Velocity.
Other classes of missiles follow the same pattern. Again, the list is sorted on explosion velocity.


{| class="wikitable sortable" style="text-align:center; text-size:90%"
{| class="wikitable sortable" style="text-align:center; text-size:90%"
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|}
|}


Rockets have the smallest Base Damage (BD), but they have a very small Explosion Radius (ER) and a fairly fast Explosion Velocity (EV). So, you would expect them to do very good damage to small targets (due to their ER and EV), but relatively less damage to large ones (due to their BD). Torpedos have five times the Base Damage of Light Missiles, but they have ten times the Explosion Radius and half the Explosion Velocity. So, you would expect Torpedos to be very good against large, slow ships (due to their BD), but very poor against small, fast ships (due to their ER and EV).
Rockets have the smallest Base Damage (BD), but they have a very small explosion radius (ER) and a fairly fast explosion velocity (EV). So, you would expect them to do very good damage to small targets (due to their ER and EV), but relatively less damage to large ones (due to their BD). Torpedoes have five times the base damage of Light Missiles, but they have ten times the explosion radius and half the explosion velocity. So, you would expect Torpedoes to be very good against large, slow ships (due to their BD), but very poor against small, fast ships (due to their ER and EV).


If that all makes sense, then good ... if not, then just keep in mind that, all things being equal, EVE has balanced the damage done by missiles among themselves as well as with the damage done by projectiles, beams and other types of weapons.
If that all makes sense, then good ... if not, then just keep in mind that, all things being equal, EVE has balanced the damage done by missiles among themselves as well as with the damage done by projectiles, beams and other types of weapons.
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== How to Increase the Damage of Your Missiles ==
== How to Increase the Damage of Your Missiles ==


Skills and ship equipment can have a direct impact on missile damage. A number of implants do the same. In addition, modules such as Target Painters and Webifiers can affect the target's Signature Radius and Speed, thus making missile damage more effective.
Skills and ship equipment can have a direct impact on missile damage. A number of implants do the same. In addition, modules such as Target Painters and Webifiers can affect the target's signature radius and speed, thus making missile damage more effective.


=== Skills ===
=== Skills ===
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=== The Missile Values ===
=== The Missile Values ===


The Base Damage of a missile <b>(D)</b> can be found in the missile information under “EM damage”, “Kinetic damage”, “Thermal damage” or “Explosive damage”.  Base Shield Damage and Base Armor Damage are not relevant for this calculation.  
The base damage of a missile <b>(D)</b> can be found in the missile information under “EM damage”, “Kinetic damage”, “Thermal damage” or “Explosive damage”.  Base Shield Damage and Base Armor Damage are not relevant for this calculation.  


The Explosion Radius of a missile <b>(E)</b> represents the size of the explosion. It can be found in the missile information under “Explosion radius”.  
The explosion radius of a missile <b>(E)</b> represents the size of the explosion. It can be found in the missile information under “Explosion radius”.  


The Explosion Velocity of missile <b>(V<sub>e</sub><sub></sub>)</b> is the rate of expansion of the explosion. It can be found in the missile information under “Explosion velocity”.
The explosion velocity of missile <b>(V<sub>e</sub><sub></sub>)</b> is the rate of expansion of the explosion. It can be found in the missile information under “Explosion velocity”.


All three of these can be improved through the use of rigs and/or implants.
All three of these can be improved through the use of rigs and/or implants.
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=== Finding the Damage Reduction Factor of a Missile===
=== Finding the Damage Reduction Factor of a Missile===


The “damage reduction factor” <b>(drf)</b> of a missile is not mentioned in the game, it is however included in the [http://community.eveonline.com/community/fansites/toolkit/ data that CCP publishes], and you can easily view it in the EVEMon item browser. You can also see the value 5.5 from the above equation in the same data – it is called the Damage Reduction Sensitivity.
The “damage reduction factor” <b>(drf)</b> of a missile is not mentioned in the game, it is however included in the [http://community.eveonline.com/community/fansites/toolkit/ data that CCP publishes], and you can easily view it in the EVEMon item browser. You can also see the value 5.5 from the above equation in the same data – it is called the damage reduction sensitivity.


{| class="wikitable collapsible collapsed sortable" style="text-size:90%"  
{| class="wikitable collapsible collapsed sortable" style="text-size:90%"  
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This means that the base damage is multiplied by the smallest of either <code>1</code>, <code>S/E</code> or <code>(S/E*Ve/Vt)^(ln(drf)/ln(5.5)</code>. In the equation, then, the number 1 represents 100% of the base damage – since if either of the other values is bigger than 1, they are rejected. Thus, the damage created can be no higher than 100% of the base damage.
This means that the base damage is multiplied by the smallest of either <code>1</code>, <code>S/E</code> or <code>(S/E*Ve/Vt)^(ln(drf)/ln(5.5)</code>. In the equation, then, the number 1 represents 100% of the base damage – since if either of the other values is bigger than 1, they are rejected. Thus, the damage created can be no higher than 100% of the base damage.


When the target's Signature Radius is larger than the missile's Explosion Radius, <code>S/E</code> will be greater than 1, and that term will be rejected. If <code>S</code> is smaller than <code>E</code>, then <code>S/E</code> will be computed and compared with the third term. The smaller of these will be chosen and multiplied times the Base Damage.
When the target's signature radius is larger than the missile's explosion radius, <code>S/E</code> will be greater than 1, and that term will be rejected. If <code>S</code> is smaller than <code>E</code>, then <code>S/E</code> will be computed and compared with the third term. The smaller of these will be chosen and multiplied times the Base Damage.


Since the part of the equation that is affected by velocity ... <code>(S/E*Ve/Vt)^(ln(drf)/ln(5.5)</code> ... only matters if it is less than 1, it can be set to 1 and solved to find the point where it begins to matter.  Doing that gives <code>Vt = (S/ (1^(1/ (ln(drf)/ln(5.5)) * E)) * Ve</code>. Since <code>1^x = 1</code>, then <code>1^(1/ (ln(drf)/ln(5.5)</code> also must equal 1, and the equation reduces to <code>Vt = (S/E) * Ve</code>. This can be rewritten as  
Since the part of the equation that is affected by velocity ... <code>(S/E*Ve/Vt)^(ln(drf)/ln(5.5)</code> ... only matters if it is less than 1, it can be set to 1 and solved to find the point where it begins to matter.  Doing that gives <code>Vt = (S/ (1^(1/ (ln(drf)/ln(5.5)) * E)) * Ve</code>. Since <code>1^x = 1</code>, then <code>1^(1/ (ln(drf)/ln(5.5)</code> also must equal 1, and the equation reduces to <code>Vt = (S/E) * Ve</code>. This can be rewritten as  
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So, the Target Velocity at which the damage created begins to be reduced is equal to the Signature Radius of the target times the Minimum Velocity Factor.  
So, the target velocity at which the damage created begins to be reduced is equal to the signature radius of the target times the minimum velocity factor.  


  Vt = S * MVF
  Vt = S * MVF


This means that a Rocket will begin doing less damage when the target velocity is at 7.5 * <code>S</code>,  a Light Missile at  3.4 * <code>S</code>, and a Torpedo at 0.158 * <code>S</code>.  Thus, the same sized ship has to be going much faster to reduce damage from a Rocket than it does to reduce damage from a Torpedo.
This means that a rocket will begin doing less damage when the target velocity is at 7.5 * <code>S</code>,  a light missile at  3.4 * <code>S</code>, and a torpedo at 0.158 * <code>S</code>.  Thus, the same sized ship has to be going much faster to reduce damage from a rocket than it does to reduce damage from a torpedo.


The equations also show that there is a minimum speed that a ship needs to fly before its velocity can reduce the missile damage at all. If the ship is moving below a specific threshold, the explosion velocity and the speed of the ship do not affect the missile damage. In that case, only the Signature Radius of the target and the Explosion Radius of the missile can have an effect, and further decreases in the ship's speed will not increase the damage. However, increases the Signature Radius can, until the damage reaches 100%.
The equations also show that there is a minimum speed that a ship needs to fly before its velocity can reduce the missile damage at all. If the ship is moving below a specific threshold, the explosion velocity and the speed of the ship do not affect the missile damage. In that case, only the signature radius of the target and the explosion radius of the missile can have an effect, and further decreases in the ship's speed will not increase the damage. However, increases the signature radius can, until the damage reaches 100%.


=== Examples ===
=== Examples ===
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Required speed is therefore changed to 1051.38m/s  (''1622.5  * 0.648'')
Required speed is therefore changed to 1051.38m/s  (''1622.5  * 0.648'')
Since the speed of the Drake with a MWD (675m/s) is below the required speed (1051.38 m/s), the speed does not affect the missile damage. The damage is determined by 1, the damage is 100% of the possible damage and it is no different than the damage the ship receives without the MWD.}}
Since the speed of the Drake with a MWD (675m/s) is below the required speed (1051.38 m/s), the speed does not affect the missile damage. The damage is determined by 1, the damage is 100% of the possible damage and it is no different than the damage the ship receives without the MWD.}}
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[[Category:PvP]]
[[Category:PvE]]