The engine is a loaner from S&S Turbine Services, a Canadian firm that rebuilds J79s for repressurizing natural gas wells. The current engine has been souped up to generate 42,500 horsepower, but the one Eagle will get from S&S for the record run will top out near 50,000 horsepower.

The rules are simple. Clock the racer through a measured mile, turn around and do it again, then average the two speeds. Mr. Shadle said Eagle would need 11 miles for each run: a mile to warm up to 250 miles per hour; four miles to light off the afterburner and get up to record speed; a mile in the speed trap; and five miles to stop.

The vehicle must have at least four wheels — two of them steerable — and be back at the original start line within 60 minutes. And that’s it. “You race Formula One or Nascar, the rule books are as thick as the Bible,” Mr. Shadle said. “For this, the rule book is a half-page long.”

Image TRANSFORMED The fuselage of the Lockheed F-104 Starfighter. Credit... Landspeed

But consider the challenges. Rubber tires turn to molten licorice at anything above 350 miles per hour, so the Eagle uses custom-built, single-billet aluminum alloy wheels, grooved for traction on soft surfaces. They will not work on asphalt or concrete. The brakes are special alloy magnets that generate 4,700 brake horsepower as the magnetized drum approaches the moving aluminum wheel, slowing it gradually without ever locking up.

The big imponderable is the sound barrier. In the sky, the shock wave simply dissipates. But on land, it bounces off the ground and can flip a racer into the air. Since each car is unique, the problem has to be solved differently every time. Computer modeling is important — but only up to a point.

Mr. Noble of the Bloodhound project is well aware of the challenge. “We’ve done it once, and now we have to do it again,” he said in a telephone interview. “The forces are huge — 15 tons were pressing downward on the front of the vehicle when we set the record. You spend an enormous amount of time on the aerodynamics.”