Here is a snap shot from the sky copter displaying a pattern being set up with risers. The side with risers is known as the cope of the casting/pattern.
A riser or feeder is a reservoir built into a metal-casting mold to prevent cavities due to shrinkage. Because metals are less dense as liquids than as solids (with some exceptions), castings shrink as they cool. This can leave a void, generally at the last point to solidify. Risers prevent this by providing molten metal at the point of likely shrinkage, so that the cavity forms in the riser, not the casting.
This only works if the riser cools after the rest of the casting. Chvorinov's rule states that the solidification time t of molten metal is related to the constant C (which depends on the thermal properties of the mold and the material) and the local volume (V) and surface area (A) of the material, according to the relationship
t = C \times \left (\frac{V}{A}\right)^2.
Therefore, to ensure that the casting solidifies before the riser, the ratio of the volume to the surface area of the riser should be greater than that of the casting. The riser must satisfy two requirements: it must be large enough so that it solidifies after the casting (i.e. satisfies Chvorinovs rule) and it must contain a sufficient volume of metal to supply the shrinkage contraction which occurs on cooling from the casting temperature to the completion of solidification. This latter requirement will be more important for plate like shapes; the former will be more important for chunky shapes.
Because risers exist only to ensure the integrity of the casting, they are removed after the part has cooled, and their metal scrapped. As a result, riser size, number, and placement should be carefully planned to reduce waste while filling all the shrinkage in the casting.
That last part about reducing waste always induces a chuckle or two.
Sources
Wikpedia
Bay Cast
And ME
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