system
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human
[Stargate SG1] Exactly how are the transporter rings supposed to work?

Early on it seemed pretty established that 2 transport ring pads had to be in direct alignment to work.  In particular the episode where they intercept the ring beem going between the planet and Apophis' ship to rescue the team.

But in later episodes, it seems the rings will work without a another pad to receive the beam, the rings will just go straight down to the ground below.

And in first episodes of series 7, Jackson and Quinn seem to use the rings to teleport from the ring pad on Anubis' ship to a random ring pad in a store room on the planet, implying they don't need to be in alignment.
gpt
Chief Science Officer of SG-2 reporting in, transport rings were originally designed by the Ancients and thus work similarly to Stargates, but at a shorter distances. If Stargates are the Ancient's airplanes, transport rings would be like a car. 

Basically, the rings convert matter to energy and convert it back at its destination. 

Transport rings are particularly interesting because they have 2 modes- short range and ring to ring. 

In ring to ring mode, 2 sets of transport rings create a connection and activate simultaneously. They then swap the matter inside the rings. This swap is done to prevent issues such as material fusing if you happen to be transported while someone else is inside the ring. This does not require physical alignment to use. However, it does require you to know where the other set of rings are, much like dialing a Stargate requires you to know the gate address of your destination. For ease of use, however, most ring transports have macros built into them for common usage (ie, beam to the nearest set of rings or beam straight down to the next solid surface)

In short range mode, matter is converted to energy, stored in the rings, and the rings themselves move. This has several benefits- you can transport people across inhospitable locations without endangering them, the rings move faster than most transports, and it can be used to break through barriers (see the mission reports for Proclarush). 

Ring to ring mode generally has much farther distance because there is only transferal of energy, and the rings don't have to travel that distance. However, this requires existing infrastructure. This is generally used for travel between known points- eg, city to city, city to ship, etc. Short range mode is used on a more practical basis, such as landing people on a planet's surface for exploration.