Like most racers began Plowman his career in karting, where he was active from 2003 to 2005. Among other things, he won the 2003 the French Elite Championship and 2004, the Asia-Pacific Formula A Championship. In 2006, Plowman into formula racing for Prema Powerteam and launched in two racing series. While he scored fifth overall in the Italian Formula Renault, he was 23 in the Formula Renault 2.0 Eurocup. In the next season he remained in both series and worsened in the Italian Formula Renault on the seventh, and in the Formula Renault 2.0 Eurocup on the 26th place in the overall standings. In 2008 he moved to RC Motorsport in the Formula 3 Euro series and denied the first seven race weekends of the season. He never came out with a 17th place and finished at the end of the season the 31st place in the overall standings.
2009 Plowman opted for a move to North America and joined for Panther Racing in the Indy Lights. He was mostly faster than his teammate Pippa Mann and finished end of the season with two fifth places as the eleventh best results overall. In 2010 he was taken from AFS Racing / Andretti Autosport under contract. In Lexington Plowman decided his first Indy Lights race for themselves. At the end of the season he finished third in the overall standings.
Plowman, 2011, his debut in the IndyCar Series. For Sam Schmidt Motorsports, he participated in three races. His car was also mitvorbereitet AFS Racing. He finished the season in 33rd place overall.
2012 moved Plowman in endurance racing to Conquest Racing in the American Le Mans Series.
- 2003-2005: Karting
- 2006: Italian Formula Renault ( 5th place)
- 2006: Formula Renault 2.0 Eurocup ( place 23 )
- 2007: Italian Formula Renault ( 7th place)
- 2007: Formula Renault 2.0 Eurocup ( place 26)
- 2008: Formula 3 Euro Series (No. 31)
- 2009: Indy Lights (11th )
- 2010: Indy Lights ( 3rd place)
- 2011: IndyCar Series ( No. 33 )
- 2012: ALMS LMP2