Larger diameter fans can move more air than smaller fans at the same speed. A high-velocity, turbulent jet of air dissipates very quickly. However, a large column of air will "travel" further than a small column due to the friction between moving air and stationary air that occurs at the periphery of the moving column.
The circumference of an air column varies directly with the diameter of the column. While the cross-sectional area varies with the square of the diameter, the large column has proportionally fewer peripheries and therefore less drag. The air column from a 3 feet (0.91 meters) diameter fan, for example, has more than six times as many frictional surfaces per volume of air moved as the air column from a 20 feet (6.1 meters) diameter fan.
As the downward air column from an HVLS fan reaches the floor, the air turns horizontally away from the column in all directions. The outgoing air is called the 'horizontal floor jet'. Since the height of the floor jet is determined by the diameter of the column of air, a larger diameter fan will naturally produce a larger column of air and therefore a higher floor jet. Smaller high-speed fans of equivalent displacement are unable to produce the same effect. The power required to drive a fan increases approximately as the cube of the average air velocity through the fan. A commercial fan moving air at 20 miles per hour (mph) requires about 64 times as much power as a similarly sized fan moving air at five mph.
The combination of air speed and fan "efficiency" means that very large, low-speed commercial fans are more efficient and effective than small, high-speed fans when the goal is to cool people or animals.