"Bias-ply tires are constructed with ply cord that runs in a criss-cross pattern at a 45-degree angle to the bead. A radial tire has cord that runs at a 90-degree angle to the bead, allowing the tire to be more stable and to better conform to the surface," Gullett stated. The folks from Nitto tire explained further that there is a difference in the ply angle (internal construction) between the two types. In a bias-ply tire, cords are angled away from the direction of the tire to criss-cross each other. In a radial tire, the ply angle runs parallel to the radius of the tire (from the center spoke out to the rolling surface of the tire).
Mickey Thompson's Kundrick notes the most important "characteristic" of radial race tires is called "dead hook." If the radial tire is over-powered or starts to lose traction it will not recover as will a bias tire, because the radial construction doesn't absorb power. This is why radial-tire class drag racers with lots of power can really be a handful just trying to get the car to launch right. It takes a fine symphony of rpm, clutch, and throttle to get these cars to hook and leave and not bog or blow the tires off on the launch. Another distinct trait is tire growth. Due to the fact that there are steel belts running the circumference of the tire, it can't grow. Finally and in a general sense, radial drag tires are best suited for cars with automatic transmissions.
"Many Stock, Super Stock, and Comp Racers have tried to utilize the radials and in very few cases (where the clutch was adjustable enough) they have achieved a net performance improvement. Typically they have to 'give-up' elapsed time early in the run (to ensure good traction) and make up that time, plus some in the back half of the racetrack," Kundrick states. This points to the key trait of radials--reduced rolling resistance. As we all know, many years ago when radial technology first hit the highway on production cars, the critical difference between the two construction types was a better ride and increased mileage.
Gullett from Coker Tire tells us that if you buy a generic drag-racing slick, it's more than likely a bias-ply tire. The difference between a bias-ply and a radial is the tire's inner construction, as we just discussed, but it affects the way the car launches and how it handles at speed. Generally, you can run a little more air pressure in a radial tire, which reduces rolling resistance and increases stability on the top end. If you've ever raced on a bias-ply, you've felt that tire "wiggle" at the top end of the track. There's also a difference in a "drag radial" and a "radial slick."
A drag radial is a DOT-approved tire with actual tread that many Outlaw street car racers use, while the radial slick looks just like a regular slick, the only difference is the internal construction. A radial tire will, in theory, be quicker than a bias-ply tire, if you use it to its full potential. The increased air pressure capability means a quicker elapsed time due to the reduced rolling resistance. However, you must adjust your suspension accordingly to eliminate the chance of tire spin.
Radials are generally used on bracket racing cars or index racing cars, because of their consistency, but there isn't a downfall to using them on a heads-up race car or even a street/strip car. Drag radials, such as the M&H Racemaster, are generally used on street cars, as well as many Outlaw-style race teams. The main difference is the suspension setup, as it differs between the two tires.
By design, the radial slicks are more stable, but you should never have any stability issues out of a bias-ply slick if the pressures are right and you have the appropriate suspension setup. The only reason people have issues with wobble or sway on the top end is related to tire pressure, or mixing bias-ply and radial tires on the same vehicle.