Sun Setting Illusion: Explaining Constant Angular Speed

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So I was watching the Sun set the other night, and I noticed that the Sun appeared to accelerate into the horizon. If the Earth rotates at a constant angular speed, how could this be? I was thinking about swinging a ball on a string vertically, and how the ball would have different points of maximum acceleration along its path due to the different forces acting on it. But the Sun only has a single radial force that wouldn't vary thoughout its path (that is, if the Earth was taken as a stationary frame). Can anyone explain this?
 
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it must be an illusion because the sun actually slows down as it approaches the horizon due to atmospheric refraction. My guess would be that what you perceived is due to the sky being "bigger" lower down which causes people to overestimate distance from the horizon
 
I agree with Russ. It's probably the same basic mechanism that makes the moon look huge when it's on the horizon, and normal when it's high in the sky.
 
The angular diameter of the sun is 30 arcminutes ( +- seasonal things ) that is half a degree so if the sun takes about 12 hours to pass through 1800 then for half that would be 2 minutes. I mean the time it would take for the sun to pass if it "touched" the horizon till sunset.

As said above the sun "moves" slower near the horizon.
 
When the Sun is near to the horizon, it's easier to see its motion relative to the horizon. When it's high in the sky, there's no distant "static" object to compare it against, so the motion is less noticeable to the human eye.

Note that comparison against a nearby object like a tree or building doesn't work because nearby objects don't appear "stationary" (due to the parallax effect) unless you hold your head rigidly still.