The height of the grass depends on the season, species, fertility of the soil, and whether it has been grazed/mown or not. Maximum height of some hybrid Bermuda grass or Buffalograss is about 2 inches (5 cm). Some of the tallgrasses of the American praries are about 2 meters, and tropical grasses like Cogan Grass will grow higher than two meters. Common pasture grasses like Timothy, Brome, Orchardgrass will easily grow to 1.5 meters. So the height of the grass is really a matter of taste, and the environment you are trying to simulate.