  This work investigates the consequences of imposing a volume constraint on
the maximum power that can be absorbed from progressive regular incident waves
by an attenuating line absorber heaving in a travelling wave mode. Under
assumptions of linear theory an equation for the maximum absorbed power is
derived in terms of two dimensionless independent variables representing the
length and the half-swept volume of the line absorber. The equation gives the
well-known result for a point absorber wave energy converter in the limit of
zero length and it gives Budal's upper bound in the limit of zero volume. The
equation shows that the maximum power absorbed by a heaving point absorber is
limited regardless of its volume, while for a heaving line absorber whose
length tends to infinity the maximum power is proportional to its swept volume,
with no limit. Power limits arise for line absorbers of practical lengths and
volumes but they can be multiples of those achieved for point absorbers of
similar volumes. This conclusion has profound implications for the scaling and
economics of wave energy converters.
