Check out the following videos:
"Armor Mobility" – https://www.youtube.com/watch?v=y1YEkuWYUKM
"For it to be truly effective, a knight's armor has to allow the freedom of movement to match the swiftness of a lesser-armored opponent on the battlefield." (Note: this excerpt comes from a National Geographic documentary: "Medieval Fight Book")
"Running in Armor" – https://www.youtube.com/watch?v=KNcKolKQ1F4
"Can You Move in Armor?" – https://www.youtube.com/watch?v=q-bnM5SuQkI
Now most game rules I've seen do something along the lines of the following, in the name of realism:
Unarmored: move 120'/turn
Leather armor: move 90'/turn
Metal armored: move 60'/turn
and I've even seen some games that break metal armored into:
Chain mail: move 60'/turn
Plate mail: move 30'/turn
As the videos show, there is no way in hell a fully armored man moves at one half the speed (or worse one quarter the speed) of an unarmored man. On the contrary, the evidence shows a fully armored man moves as fast, or nearly as fast, as an unarmored man in most situations.
If we want realistic encumbrance rules (and there's no point in having encumbrance at all if it's not realistic), then we need to reduce the effective encumbrance weight of armor dramatically. What I'd recommend is one of the two following options.
If we must insist on making armored characters slower than unarmored ones we could try this:
Unarmored or Leather Armor: move 120'
Chain or Plate: move 90'
This keeps things easy for dividing rates by three for combat round movement, which a lot of rules call for.
Personally though, I think even this rate is too slow for the armored man. I think the better option is to simply exclude armor worn from encumbrance calculations entirely, in the same way we typically exclude the clothing, jewelry etc. Now if you were carrying that armor, instead of wearing it, it'd just be 35-55 pounds of dead weight. But wearing it, that's another story.
So in the games I run, I intend to treat worn armor as 100% unencumbering, and will put limitations on carried items only.