Paddle tires are mainly used on off road vehicles, specifically designed for use in sand

Sand

Sand is a naturally occurring granular material composed of finely divided rock and mineral particles.The composition of sand is highly variable, depending on the local rock sources and conditions, but the most common constituent of sand in inland continental settings and non-tropical coastal...

 and mud

Mud

Mud is a mixture of water and some combination of soil, silt, and clay. Ancient mud deposits harden over geological time to form sedimentary rock such as shale or mudstone . When geological deposits of mud are formed in estuaries the resultant layers are termed bay muds...

. They consist of a smooth tire core which has a series of large rubber cups (or paddles) attached to it. The volume inside of a paddle is much larger than the void of a knobby tire, so it is unlikely to clog up with sand/mud. A street legal mud tire is a more or less normal tire, but with extra large gaps or "voids" between each tread block (called "lugs") to allow centrifugal force to "self-clean" or fling the mud out of the gap. Smaller gaps trap the mud in between the tire lugs, which turns the tire into something resembling a "slick" with no tread at all, which will have no traction in mud. A paddle tire is an even more extreme version of this, optimized for mud or sand. The paddle provides superior traction in the sand, in part, because the paddles dig into the sand and push off from the buried sand, not just the surface, and in mud, the gigantic "voids" give no place for mud to stick. They work something like a paddle wheel

Paddle wheel

A paddle wheel is a waterwheel in which a number of scoops are set around the periphery of the wheel. It has several usages.* Very low lift water pumping, such as flooding paddy fields at no more than about height above the water source....

 on a paddle-steamer. Street legal mud tires are a compromise between large voids and a smooth rolling shape for on-road use. The more "extreme" a mud tire (such as a "Super Swamper") is, the harsher and louder it is on a hard surface. A " tractor tire" on a farm tractor

Tractor

A tractor is a vehicle specifically designed to deliver a high tractive effort at slow speeds, for the purposes of hauling a trailer or machinery used in agriculture or construction...

 is a somewhat more mild version of a paddle tire, only the voids are smaller to allow for limited use on hard surfaces, and the "lugs" are angled to give lateral traction. A paddle tire is so optimized for mud that the shape is of no use on anything other than a soft surface, since the vibration and lack of control of the tire would render a vehicle almost unusable. One other way the paddle tire is a specialized-application-only is that it gives only forward/rearward traction. This means that it is used on a wheel that drives a vehicle to push it forward, but gives little "lateral" (side-to-side) traction. For that reason, the tires of the vehicle that steer it are generally more "normal" tires, since a paddle tire on a steering wheel will just slide sideways rather than pulling the vehicle with it. So many 4WD vehicles will use paddle tires only on the rear, although the front wheels are powered as well. On a 2WD or a motorbike, the rear wheel is the only drive wheel, and so putting a paddle tire on the front wheels is useless or worse, since steering performance will be negatively impacted.

Paddle tires are available for motocross

Motocross

Motocross is a form of motorcycle sport or all-terrain vehicle racing held on enclosed off road circuits. It evolved from trials, and was called scrambles, and later motocross, combining the French moto with cross-country...

 bike

Motorcycle

A motorcycle is a single-track, two-wheeled motor vehicle. Motorcycles vary considerably depending on the task for which they are designed, such as long distance travel, navigating congested urban traffic, cruising, sport and racing, or off-road conditions.Motorcycles are one of the most...

s, all-terrain vehicle

All-terrain vehicle

An all-terrain vehicle , also known as a quad, quad bike, three wheeler, or four wheeler, is defined by the American National Standards Institute as a vehicle that travels on low pressure tires, with a seat that is straddled by the operator, along with handlebars for steering control...

s, sandrail

Sandrail

A sandrail, or sand rail, or sandcar, or "rail" is a lightweight motor vehicle specifically built for traveling across a wide variety of off-road terrain. Sandrails are popularly operated on actual sand dunes, such as Glamis, Pismo and Rasor in California, St...

s, and 4 wheel drives. Because the paddles are rigid and stick up several inches, they are not suitable for use on roads or hard terrain, and are not road legal in most places.

Often on rear wheel drive quads and dirt bikes specific front sand tires are used in conjunction with rear paddle tires. These front tires are usually called "razorbacks" or simply "ribbed" front tires. The tire carcass overall is smooth with the exception of one to three longitudinal ribs around the circumference of the tire. These ribs are usually about an inch high. This design promotes flotation in the sand due to the smooth part of the tire but also, using the rib to dig into the sand, it provides extra turning force.