A:
Dear Not an Engineer,
I assume you are talking about High Speed Detachable Quads (or six-packs, or triples if you are at Alta). The system has obviously fooled you because the chairs do, in fact, detach from the cable and are carried through the station on a seperate track. I will explain...
High-Speed Detachable lifts allow the cable to continually move at a constant speed while taking the chairs off and slowing them down for easier (and safer) loading. Thus, ski resorts increase their uphill capacity without significantly threatening the lives of the customers.
In the Park City area, almost all detachable lifts are made by a company called
Doppelmayr CTEC or by one of the two original companies which merged to form it (CTEC, Garaventa, or Doppelmayr). As I explain some of the components, you can visit their website to see more information (or to purchase your own detachable lift, if that is your desire).
Next time you ride a chairlift, look up at the grip holding the chair assembly to the cable. You will notice that it looks something like this:

(You can see a better detail of the chair assembly
here. These images all come from Doppelmayr CTEC's public site, and belong to that company. I have included them here for educational purposes only [and free advertising for them])
As the chair enters the station, each of the wheels meets a track which lifts the weight off the cable. One track pushes down the upper wheel, which opens the grip. The other tracks lift the chair away from the moving cable.
A series of rubber tires meet with the traction grip (the long black thing in the picture) and carefully slow the chair down to loading speed. At no point is the chair gliding freely (like used to happen with the old Park City Ski Area Gondola). The wheels are all precision-timed relative to the speed of the moving cable.
You can see the wheel assembly in these two pictures:

and

The pictures are actually focusing on the clutch brake assembly, which helps maintain proper chair distance. There are one or two wheels on the non-passenger side that can stop the chair momentarily to help maintain proper chair distance. Of course, if chairs ever get too close in the station, the system shuts down with a collision alarm (this is usually fixed by simply restarting the chairlift... because the chair usually realigns). Of course, "collision alarm" can sound scary, but you must remember that "too close" for the computer means 6 inches closer than usual. There are so many safety features on these chairlifts, it isn't even funny (in fact, it is annoying sometimes).
In both pictures you can see the grip assembly (similar to that pictured above) being carried along its tracks. The yellow release wheel appears on both pictures (just entering frame on the left and just under the clutch brake on the right).
Once the chair has detached from the main cable and been slowed down to a safe loading speed, more rubber wheels carry the chair around for a 180 degree turn. Then the passengers hop on (or off. The wheels then accelerate the chair forward to meet the exact speed of the main cable... and off it goes.
Did you know that Doppelmayr CTEC has developed an 8-passenger high speed detachable lift!! That is insane. Park City Mountain Resort has four high speed 6-passenger detachable lifts, but I don't know of any resorts putting up EIGHT. Man, that is like a flying sectional sofa!
Anyways, I hope my explanation of detachable lifts has been enlightening for you. I spent many a day skiing trying to figure out how those things work. I have even been up into the terminal houses and watched the works from above. They are impressive pieces of machinery... and they have changed the ski industry.
But, if you are ever at a resort riding a high speed lift made by YAN (which I don't even think is in business anymore)... um... get off. They had some serious safety issues. Otherwise, Doppelmayr CTEC makes some very good, safe lifts. You wouldn't believe how many safety features those things have! But, I think I already said that.
For more information, feel free to visit their homepage above. Or, just find time to stare up into the terminal of a high speed detachable lift sometime. It is a truly enlightening experience (but don't hold up the line).
That is All.
Horatio the Skiing Expert