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At the Texas Motor Speedway, that trend would lead fans to Turn 1 and the Speedway Club, which bills itself as “the place where elegance and acceleration meet.”

In the three-tiered dining room overlooking the track, the chandeliers are Italian crystal, the dance floor Italian marble and the menu not exactly from the heart of Texas: grilled basil prawns, Tuscany chicken roulade and pan-seared sea bass with orzo pasta.

A giant, cantilevered window stretches from floor to ceiling, providing a close-up view of the action. Nearby is a lounge with live entertainment; another floor features a 26,000-square-foot ballroom.

The Speedway Club’s health club and spa, like the dining room, is open year-round. It provides personal trainers, aerobics and kickboxing classes, exercise equipment, saunas, hot tubs, child care services, massage therapy, manicure services and tanning beds.

The club’s initiation fee ranges from $1,500 to $37,000, depending on type of membership. Yearly membership fees also are charged, and a minimum level of spending is required on food and beverages.

Still, this rapidly expanding sport sees plenty of room for growth — and for fans of all wallet sizes.

“We were fortunate in racing that our playing fields were bigger than other sports, a mile and a half instead of 100 yards,” Mr. Wheeler says. “We can put in enough seats where we got a place for the guy who works at the plant, his boss, a place for the guy who owns the plant and a place for the people who invest in the plant.”

Eric Fisher contributed to this report.