A radial tire (more properly, a radial-ply tire) is a particular design of vehicular tire (in British English, tyre). In this design, the cord plies are arranged at 90 degrees to the direction of travel, or radially (from the centre of the tire).
A series of plies of cord reinforces a tire. Without this, a tire would be flexible and weak. The network of cords that gives the tire strength and shape is called the carcass. Since the 1960s, all common tires have a carcass of cords of polyester, steel, or other textile materials, inlaid with several layers of rubber.
In the past, the fabric was built up on a flat steel drum, with the cords at angles of about +60 and −60 degrees from the direction of travel, so they criss-crossed over each other. They were called cross-ply or bias ply tires. The plies were turned up around the steel wire beads and the combined tread/sidewall applied. The green (uncured) tire was loaded over a curing bladder and shaped into the mold. This shaping process caused the cords in the tire to assume an S shape from bead to bead. The angle under the tread stretched down to about 36 degrees. This was called the Crown Angle. In the sidewall region the angle was 45 degrees and in the bead it remained at 60 degrees. The low crown angle gave rigidity to support the tread and the high sidewall angle gave comfort.
By comparison, radial tires lay all of the cord plies at 90 degrees to the direction of travel (that is, across the tire from lip to lip). This design avoids having the plies rub against each other as the tire flexes, reducing the rolling friction of the tire. This allows vehicles with radial tires to achieve better fuel economy than vehicles with bias-ply tires. It also accounts for the slightly "low on air" (bulging) look that radial tire sidewalls have, especially when compared to bias-ply tires.
The first radial tire designs were patented in 1915 by Arthur W. Savage, a tire manufacturer and inventor in San Diego, CA.  Savage's patents expired in 1949. The design was further developed and commercialized by Michelin;  the first Michelin X radial tire for cars was developed in 1946 by Michelin researcher Marius Mignol, and then a radial truck tire in 1952. Because of its advantages, it has now become the standard design for essentially all automotive tires.
With only radial cords, a radial tire would not be sufficiently rigid at the contact with the ground. To add further stiffness, the entire tire is surrounded by additional belts that are oriented closer to the direction of travel, but usually at some "spiral" angle. These belts can be made of steel (hence the term steel-belted radial), Polyester, or Aramid fibers such as Twaron and Kevlar.
In this way, low radial tires separate the tire carcass into two separate systems:
- The radial cords in the sidewall allow it to act like a spring, giving flexibility and ride comfort.
- The rigid steel belts reinforce the tread region, giving high mileage and performance.
Each system can then be individually optimized for best performance.
Radial tires have different characteristics of springiness from those of bias-ply tires, and a different degree of slip while steering. Motorists were not accustomed to the feel, hence the suspension systems of cars had to be modified. Ford Motor Company engineer Jack Bajer experimented in the 1960s on a Ford Falcon, by giving it less tight steering, and adding both isolators to the drive shaft and bushings to the suspension, the latter being to absorb the thump of riding over asphalt expansion joints in a concrete roadway. Cars could now be made lighter because they would not have to make up for the deficiencies of bias-ply tires.
Radial tires have occasionally found application on bicycles, used on the 1980s Miyata touring bicycle; models 1000 and 618, and more recently in 2009 on the Maxxis Radiale. Panaracer radial tires were also standard on the Jamis Gentry model bicycle in 1985.
Interestingly, the steel wires in radial tires become magnetic with use, and as they rotate a significant alternating magnetic field is created. It is quite measurable with an EMF meter close to the wheel well when the car is moving and is a spectrum of harmonic strengths from 10 to several hundred Hertz. 
- U.S. Patent 1203910, May 21, 1915, Vehicle Tire, Inventor Arthur W. Savage
- Moran, Tim (2001-04-28). "The Radial Revolution". Invention & Technology Magazine. American Heritage Publishing. Archived from the original on 2007-12-26. Retrieved 2008-08-07.
- Sheldon Brown: Japanese cycles in the American market: http://www.sheldonbrown.com/japan.html#miyata
- Maxxis Radiale: http://www.maxxis.com/Bicycle/Road-Racing/Radiale-22c.aspx
- Michelin AG - Comparison of Bias vs Radial
- ClassicCar.com: Usage of Radial and Bias-ply Tires on Older Vehicles