Darke, who won silver in the H3 hand cycle time-trial at Greenville in 2014, finished the 14-kilometre effort in 30:16.15, with the world title going to Italian Francesco Porcellato in a time of 27:53.94.
The Briton rode the third fastest opening lap, quicker than eventual bronze medallist Renata Kaluza of Poland but was slower on the second lap, eventually missing the podium by 19 seconds. The USA’s Alicia Dana took silver.
“I did a really good ride for me, I paced it really well, a little bit slower on the second climb," said Darke. "I felt like I was on fire because I passed loads of people, but I also knew it was a false sense of security, because the fast bikes were behind me.
“I gave it my best. I got into a really good mental state. A few weeks ago I kept going on about the hill and how it wasn’t my course. I got in a really good place for it and gave it my best but probably realistically it wasn’t my course with the climb but I did ok. I’m happy that Rio is flat!”
London 2012 Paralympic silver medallist Darke was Great Britain’s sole competitor on the third day of competition at Nottwil’s Schweizer Paraplegiker-Zentrim, on a full day of men’s and women’s hand cycle time trials.
On the previous day, Dame Sarah Storey opened Great Britain’s medal account with gold in the C5 time-trial, amid top-ten finishes for all British entrants.
Action continues on Saturday with the start of the road race events. Simon Price will ride the C2 road race with Megan Giglia in action in the C3 women’s event.
Hannah Dines will ride in the T2 class before the men’s and women’s B tandem road races in the afternoon, with Steve Bate, Adam Duggleby, Lora Turnham and Corrine Hall in action. Racing will conclude with the men’s and women’s C5-4 road races, with Dame Sarah Storey on the hunt for a second gold medal.