Over half of the 2004 Ryder Cup team - Paul Casey, Darren Clarke, Sergio Garcia, Harrington, David Howell, Ian Poulter and Westwood - have hardly been spotted on the European Tour so far this season.
England's world number nine Paul Casey, the joint first-round leader, was still the highest placed Englishman going into the weekend after carding 73 to finish level par.
Woods was three shots off the pace at the World Golf Championships event, tied for fifth with fellow U.S. Ryder Cup star Anthony Kim, their compatriot Ryan Moore, world No. 4 Paul Casey and Hong Kong Open champion Wen-tang Lin.