The Sora Hasegawa arc starts in volumes 19, and finishes here in volume 20.
Sora refuses to accept her new role as Director of the Motor club. Chihiro, the founding member of the club, gets involved (its a slow week at Whirlwind). Sora may successfully refuse her position as Director only if she wins a race against the current director, K1. Fate (or rather the universe, as Belldandy puts it) has it in store for her to take over, but she suffers from lack of self confidence again, hence her refusal. She reveals that every time throughout her life where she has become director of a club, the club quickly disbands not long afterwards. She loves the Motor Club and doesn't want to see it die. Belldandy practices on the go kart with Sora, and Sora quickly manages to overcome her problems. Eventually the race between Sora and K1 starts.
Otaki and Tamiya turn up, as check points. The race continues indoors because they are short cuts across campus. Sora drives through a Womans changing room. K1 doesn't want to follow. Urd and Skuld turns up. Urd kisses K1 on the lips, and forces him to swallow a potion (its a real proper kiss though), whilst Skuld works on the go kart. Under the control of the potion, k1 goes though the womans changing room and follows Sora outside. K1, under the influence of the drug, flies off the side of a hill and crashes in a pile of garbage. After getting up and carrying on, the kart starts to break apart, and K1 passes out.
Bell turns up, and its implied that she kisses him with a spell that neutralizes Urds potion. K1 (as well as the readers apparently? I've never seen this Belldandy 'kiss' mentioned by other fans?) hasn't got a clue about how Belldandy brought him back to normal. He quickly fixes his broken kart to a moving skateboard type motor, and goes off to catch up to Sora. he catches up, but she wins by a nose.
Having won the race, Sora decides to be the director after all, with the idea that she can delegate management tasks to other members of the club, ensuring it stays alive and active.
Otaki, Tamiya and Chihiro are found handing out flyers for the new range of go karts that are for sale. I would say these karts are Den-chan and Dai-chan's project at whatever garage they are now working for (maybe their own company?). The reason I say this is because in volume 19, Chihiro bought a pair after seeing an advert for it. So helping to sell the karts with Otaki and Tamiya suggests they are ones who made them and are selling them.
This volume sadly is the last of the thick volumes (which starts the trend in volume 15). It also sadly marks the end of the beautiful artwork. From here Fujishima tries to tweak the character designs to make them look younger and as lolicon as he can make them.
I used to think of this series as one where you could drop in during the beginning of any arc without much life changing stuff ever having happened to them to make it matter so much. This isn't the case so much any more. I would say this is well inside the 2nd era of the series- One in which K1's completely left NIT (bar having to learn German as a second language in order to graduate). Otaki and Tamiya are GONE, save for the occasional cameo like in these chapters. K1 and Bell work at Whirlwind, Chihiros garage. I love it. Its fresh and opens up ideas such like this arc, where Sora has to accept her fate as the head of the Motor Club.
TBH the only ones who haven't changed are Urd and Skuld. So naturally their mini arc at the end of the volume was a throwback to the days of the 1st era of the series. This arc also finally explained why they dont just buy another TV if they are always getting in each others hair over control of it. Its because they like to fight over petty every day things.
Overall a nice volume, and a nice long arc.