Okay, I feel silly about asking this and I feel that the answer is probably obvious, but I am wondering as a 7th level fighter if when you take the run action you are treated as if you were wearing light armor? As in if you run at 4 times your normal speed, opposed to 3 times. Same question applies to the Hellknight PrC's Hellknight Armor.
Relevant quotes from the PRD...
Run
You can run as a full-round action. If you do, you do not also get a 5-foot step. When you run, you can move up to four times your speed in a straight line (or three times your speed if you're in heavy armor). You lose any Dexterity bonus to AC unless you have the Run feat.You can run for a number of rounds equal to your Constitution score, but after that you must make a DC 10 Constitution check to continue running. You must check again each round in which you continue to run, and the DC of this check increases by 1 for each check you have made. When you fail this check, you must stop running. A character who has run to his limit must rest for 1 minute (10 rounds) before running again. During a rest period, a character can move no faster than a normal move action.
You can't run across difficult terrain or if you can't see where you're going.
A run represents a speed of about 13 miles per hour for an unencumbered human.
Armor Training (Ex): Starting at 3rd level, a fighter learns to be more maneuverable while wearing armor. Whenever he is wearing armor, he reduces the armor check penalty by 1 (to a minimum of 0) and increases the maximum Dexterity bonus allowed by his armor by 1. Every four levels thereafter (7th, 11th, and 15th), these bonuses increase by +1 each time, to a maximum –4 reduction of the armor check penalty and a +4 increase of the maximum Dexterity bonus allowed.
In addition, a fighter can also move at his normal speed while wearing medium armor. At 7th level, a fighter can move at his normal speed while wearing heavy armor.
Speed: Medium or heavy armor slows the wearer down. The number on Table: Armor and Shields is the character's speed while wearing the armor. Humans, elves, half-elves, and half-orcs have an unencumbered speed of 30 feet. They use the first column. Dwarves, gnomes, and halflings have an unencumbered speed of 20 feet. They use the second column. Remember, however, that a dwarf's land speed remains 20 feet even in medium or heavy armor or when carrying a medium or heavy load.
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2 When running in heavy armor, you move only triple your speed, not quadruple.
Like armor, a character's load affects his maximum Dexterity bonus to AC, carries a check penalty (which works like an armor check penalty), reduces the character's speed, and affects how fast the character can run, as shown on Table: Encumbrance Effects. A medium or heavy load counts as medium or heavy armor for the purpose of abilities or skills that are restricted by armor. Carrying a light load does not encumber a character.
I didn't find any relevant FAQ posts, but previous threads in this forum definitely fall in favor of the fighter only being able to run at 3x his speed.
In short:
If he is not encumbered, and he possesses the appropriate armor training class ability, a fighter in heavy armor moves at their normal base speed.
Because the Run action/speed is not referenced by the class ability, and they are still in heavy armor, they still are only able to run at x3 speed and not x4.
If they are encumbered by any amount, that encumbrance still applies to their speed as normal. (It only counts for abilities Restricted by armor, not for abilities affecting use of armor.)
Hope that helps!
I think there is an argument to be made in favor of running at 4×speed in heavy armor. A human's normal running speed is 4×30', Armor Training says that at the appropriate level you can move at your normal speed while wearing armor, thus a human 7th level Fighter can run at 4×30'. Whenever possible, I say that the rules should be interpreted in favor of the martial classes. A 7th level Wizard is casting fly and dimension door, let the Fighter run 120' to keep up with him at least.
At level 7 yes, but before that no.
At level 7 yes, but before that no.
edit: also a yes for the hellknight commander PrC
Armored Sprint (Ex): The fighter gains Run as a bonus feat. If the fighter is proficient with heavy armor, he treats heavy armor as if it were one category lighter for the purpose of determining how fast he can move while running in armor.
Since the Armored Sprint advanced armor training exists now and one requires armor training to even get it, I'd say even with armor training 2, heavy armor is still limited to x3 speed when running without the Armored Spring AAT ability.
Also, normally medium and heavy armor slows one down just the same amount. With armor training, they'd slow one down less. But the run action specifically specifies heavy armor, not slowed by armor, so armor training reducing speed penalty wouldn't help.
thanks for the answers, I was half expecting you would be able to run at normal (unencumbered) speed, but that makes a lot of sense