Difference between revisions of "Relativity effect"

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(Added links and edited the content for spelling, grammar, and consistency.)
(big rewrite, still a bit rough, but definitely more technically accurate)
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In the real world, when two ships are flying at the same speed (regardless of direction), a projectile fired from one of them flies with the same relative speed to either of them, no matter how fast they are speeding to or away from a planet.
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In general, relativity refers to the relationship between physical quantities measured in different frames of reference.  Different relations are used depending on the desired accuracy.  Relativistic effects in [[Star Control I]] and [[Star Control II]] appear in two forms: collisions, and projectiles.
  
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[[Star Control I]] and [[Star Control II|II]] take a different approach - shots are fired with a fixed speed. For example, the [[Mycon]] [[Podship]] fires a plasmoid, which has a low speed, while a [[Druuge]] [[Mauler]] fires his cannon shot, which has a high speed. If the theory of relativity applie, the plasmoid is fired with the [[Podship]]'s starting speed plus the ship speed. Since this is not the case, many [[Mycon]] captains were forced to regrow half of their crew after being hit with their own plasmoid when the [[Podship]] is moving faster than the starting speed of the plasmoid.
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The two common relativistic relations are Newtonian Mechanics and Einstein's theory of relativity. Newtonian Mechanics uses the Galilean Transform to add velocities.  Thus a projectile's speed in the frame of reference '''b''' is simply the addition of the velocity of the source's frame '''a''' in '''b''' and the projectile's velocity in the source's frame '''a''':
  
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To try this out for yourself, grab a [[Mauler]] in Melee mode and accelerate. When you gain some serious speed (for best results, use the [[Gravity Whip]] maneuver), fire forward. You will see that the range of the cannon is very short, however, when you turn the ship around and shoot backward, you will see that the shot has a much longer range. Because of this, when an enemy is chasing you and you fire backwards at that enemy, your shots 'gain' speed, just as they would gain the speed of you and your opponent.
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u' = u + v
  
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-----X----<==--====||||<<------
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where u' is the projectile speed in frame '''b''', u is the projectile speed in '''a''', and v is the relative speed between '''a''' and '''b'''.  
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In the above diagram, if the X is a [[Pkunk]] [[Fury]], then it would be on a collision course with the projectile. If there is no planet, it will appear from the [[Pkunk]]'s point of view as if the projectile is flying with twice its normal speed toward the horrified [[Pkunk]]. Since you could say that the projectile is faster (although it's really the [[Pkunk]] [[Fury]] speeding into the projectile), it will have a longer range before it dissipates.  
 
  
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In the real world, the projectile would first decelerate (if firing forward) or accelerate (if firing backward) by the speed of the firing craft.
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This is accurate as long as none of the velocities don't get much above ten percent the speed of light.  For speeds approaching luminal speed, the Special Theory of Relativity more accurately describes the addition of velocities by using a Lorentzian Transformation. It uses the following formula to add velocities:
  
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Although it may not be real, it is fun.
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u' = (u + v) / (1 + (u * v) / c<sup>2</sup>)
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where c is the speed of light. For small u and v with respect to c, this reduces to the Galilean Transform.  For collisions, both sets of physics agree that total momentum is conserved, but differ on the definition of momentum.
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In the Star Control universe, collisions between ships and other objects appear to be not completely elastic and are governed by rules that more closely resemble Newtonian Mechanics.  Projectiles however obey a different set of rules entirely.  The velocity of a projectile is constant in the absolute frame of reference defined by the planet and the background starfield, no matter how fast the firing starship is firing. This can be verified with a Chenjesu Broodhome.  The time it takes the photon crystal shard to wrap all the way around should be the same, regardless of whether the Broodhome is stationary, is moving in the same direction as the shard, or is moving in the opposite direction of the shard. 
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For some ships, this strange bit of physics has huge implications.  A notable example of this is [[Mycon]] [[Podship]], which when moving at top speed can overtake and be damaged by its own plasmoids.  This is also responsible for the illusions of a longer range when firing backwards and a shorter range when firing forward.

Revision as of 05:32, 26 August 2005

In general, relativity refers to the relationship between physical quantities measured in different frames of reference. Different relations are used depending on the desired accuracy. Relativistic effects in Star Control I and Star Control II appear in two forms: collisions, and projectiles.

The two common relativistic relations are Newtonian Mechanics and Einstein's theory of relativity. Newtonian Mechanics uses the Galilean Transform to add velocities. Thus a projectile's speed in the frame of reference b is simply the addition of the velocity of the source's frame a in b and the projectile's velocity in the source's frame a:

u' = u + v

where u' is the projectile speed in frame b, u is the projectile speed in a, and v is the relative speed between a and b.

This is accurate as long as none of the velocities don't get much above ten percent the speed of light. For speeds approaching luminal speed, the Special Theory of Relativity more accurately describes the addition of velocities by using a Lorentzian Transformation. It uses the following formula to add velocities:

u' = (u + v) / (1 + (u * v) / c2)

where c is the speed of light. For small u and v with respect to c, this reduces to the Galilean Transform. For collisions, both sets of physics agree that total momentum is conserved, but differ on the definition of momentum.

In the Star Control universe, collisions between ships and other objects appear to be not completely elastic and are governed by rules that more closely resemble Newtonian Mechanics. Projectiles however obey a different set of rules entirely. The velocity of a projectile is constant in the absolute frame of reference defined by the planet and the background starfield, no matter how fast the firing starship is firing. This can be verified with a Chenjesu Broodhome. The time it takes the photon crystal shard to wrap all the way around should be the same, regardless of whether the Broodhome is stationary, is moving in the same direction as the shard, or is moving in the opposite direction of the shard.

For some ships, this strange bit of physics has huge implications. A notable example of this is Mycon Podship, which when moving at top speed can overtake and be damaged by its own plasmoids. This is also responsible for the illusions of a longer range when firing backwards and a shorter range when firing forward.

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