The 37-year-old is aiming for a start in the rowing competitions at the next Summer Olympic Games in Tokyo in 2020.
It was an inauspicious start for Wiggins, who, according to the BBC, faltered at the beginning of the race because he thought he had false started. He finished the 2000m race in 6:22.5.
The winner, Adam Neill, clocked a 5:48.2.
"Huge disappointment today! Upon hearing a call in the background, I thought the race had false started so I put my oar down," Wiggins stated on Twitter. "School boy error but hey we live & learn as my plan was 6.02. Fantastic experience racing with everyone, will come back 12 months stronger next year!"
Wiggins is around 25 kilograms lighter than the indoor record holder Mo Sbihi, but hopes to put on another 10kg to try and reach the 100kg mark. When he won the Tour de France, Wiggins was 67kg.
Wiggins, one of the subjects of a year-long investigation by UK Anti-Doping into the delivery of a suspect medical package from British Cycling to Team Sky, has been criticized for obtaining Therapeutic Use Exemptions (TUEs) for the corticosteroid triamcinolone during his cycling career. While he was not charged with any anti-doping rule violations, detractors accuse Wiggins of 'gaming the system', but the Briton asserted he had a genuine medical need for the drug.
He recently garnered the support of British Rowing chief executive Andy Parkinson, who had no problems with Wiggins competing in the Indoor Championships today. "It would be a slippery slope if we started to exclude athletes who haven't actually been found guilty of breaking any rules," he told Telegraph Sport last month.
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