 Nyorai kupfuurira kweiyi ndima - Shuman akakunda Turkey Night Grand Prix, chiitiko chikuru mumakwikwi emota duku, kanokwana kasere muna 1979, 1980, 1981, 1982, 1984, 1987, 1992 uye 1993. Akakunda Knoxville Nationals muna 1979. Akaedza ruoko rwake muChampionship Car racing muna 1980 uye akapedza ari pachinzvimbo chechi11 mumujaho wake wokutanga paOntario Motor Speedway muna April wegore iroro. Zvisinei, mwedzi mumwe gare gare akakundikana kukwanirisa nokuda kwe1980 Indianapolis 500. Muna 1981, Shuman akatsigira neUSAC mukuparadzana kwavo neCART uye Shuman akapinda mumakwikwi maviri ematope paUSACs Gold Crown Champ Car karenda, achitadza kukodzera imwe uye achipedza 15 mune imwe. Mwaka wakatevera muna 1982 Shuman akawana mugumo wake wakanakisa weChamp Car kuIllinois State Fairgrounds Racetrack nenzvimbo yechishanu uye akakwikwidza mune mamwe makwikwi maviri emadhaka. Akaita kumwe kuoneka muna 1983 nhepfenyuro yacho isati yapera. Shuman akaramba achimhanya motokari dzomumhanyi panguva yaakapinda muChamp Car uye achiri kuita zviratidzo zvenguva nenguva mumitambo mikuru yemotokari dzomumhanyi kusvikira nhasi. 