The National Transportation Safety Board is investigating the crash. Senior air safety investigator Aaron Sauer said Sunday that a preliminary report on the crash is expected within a week, but a final report will likely take several months.
He said inspectors would examine the few remaining pieces of the plane, as well as Smith's autopsy and toxicology reports.
Smith did not make a mayday call or suggest any sign of distress before the crash, according to Sauer and Randy Ball, a good friend of Smith's.
Ball said Smith was a meticulous flier who would map every step of a flight plan beforehand.
"They practiced the day before and everything went fine," Ball said.
Smith was a longtime technology entrepreneur whose company was acquired by Tyler Technologies, a Dallas-based company that develops software for local schools and government clients, in 1998. He remained an executive at Tyler until 2006, the company said in a statement.
After retirement, Smith focused on collecting and flying vintage planes. He kept two rare Soviet MiG-17 fighter jets at the Historic Aviation Memorial Museum in Tyler, about 90 miles east of Dallas, museum president Carolyn Verver said.
Ball, who also owns a MiG-17, said he spent countless hours working on planes with Smith. Smith loved to preserve planes so others could see and appreciate them, Ball said.
"Those guys are literally using their own money to save a part of history and share that history with everybody else," he said.
Smith was also the newest member of the "Hoppers," according to the team's website. The Hoppers are a group of pilots who privately maintain and fly L-39 fighter jets at air shows and other exhibitions. The L-39 Smith flew Saturday was made by a company in the former Czechoslovakia in 1984, according to a Federal Aviation Administration registry.
"He kept it absolutely immaculate," Ball said.
Part of the Hoppers' mission is to introduce American audiences to planes produced and used by the country's former enemies, according to the website.
"It is important for people to remember and for young kids to learn, so that history does not repeat itself," the website said.
According to the HopperFlight site, Smith had been a pilot for a quarter-century and has a commercial pilot's license with an additional instrument rating certification. Details about Smith's flight history from the FAA were not immediately available Sunday.
A squadron of planes flew over the crash site Sunday in the "missing man" formation before the air show continued.
Associated Press writer Josh Funk in Omaha, Neb., contributed to this report.