A form of large‐amplitude elongated‐body theory appropriate for the analysis of undulatory fins attached to a rigid body of elliptical section suggests a benefit due to momentum enhancement relative to the fins on their own. This theoretical prediction is experimentally
confirmed for the first time. Theoretical momentum enhancement factors for Diodon holocanthus (2·2 and 2·7 for the median and pectoral fins, respectively) compared well to inferred thrust values determined from particle‐image velocimetry (PIV) wake measurements
(2·2–2·4 and 2·7–2·9). Caudal fin mean theoretical thrust was not significantly different from measured (PIV) values (n = 24, P > 0·05), implying no momentum enhancement. Pectoral‐fin thrust was half that of the median
and caudal fins due to high fin‐jet angles, low circulation and momentum. Average total fin thrust and fish drag were not significantly different (n = 24, P > 0·05). Vortex rings generated by the fins were elliptical, with size dependent on fin chord and stroke
amplitude. Hydrodynamic advantages (thrust enhancement at no cost to hydrodynamic efficiency, reduction of side forces minimizing energy wasting yawing motions and body drag) are probably common among rigid‐bodied organisms propelled by undulatory fins. A trade‐off between momentum
enhancement and the rate of momentum generation (thrust force) sets a practical limit to the former. For small fins whilst momentum enhancement is high, absolute thrust is low. In addition, previously suggested limitations on thrust enhancement set by reductions in propulsive force associated
with progressive reductions in fin wavelength are found to be biologically unrealistic.