Carousel is a ritual observed in the film Logan's Run, and also in the television series.
On Last Day, instead of reporting to a sleep shop like in the book, you go to a ritual called Carousel. In this ritual, participants are flown into the air and repeatedly get shot by flames. At the beginning of the ritual, participants walk into a circle with an object that look like a lifeclock in red stage, then a voice says "Be strong, and you will be renewed," then participants put their right hand in the air and the circle starts spinning. Participants will start being shot one by one in a quick manner, it is unknown how and what renewal means and how to achieve it.
References to Carousel: "It's crazy. He could have renewed on Carousel. Now he's finished forever. Why do they run?" By Francis 7 while he and Logan chase Doyle 10.'FRANCIS : and that's my friend, Logan. We're celebrating his next in line. Carousel - Arcade - who knows? Want to come along?WOMAN (smiles, shakes her head) : Only if I make it to the top of Carousel. Thirty - and the big spin.' A conversation in an early version of the movie. 'JESSICA : I suppose. But what if you want to live?LOGAN : So? Do what everyone does. Try like hell for renewal.LOGAN : When this turns black that's it. If for any reason you want to be 31...you have the same chance as everyone else, Carousel. Another early conversation in an old script.