# Scaling the propulsive performance of heaving and pitching foils

## TL;DR

This paper develops and validates scaling laws for the propulsive performance of oscillating rigid foils, demonstrating their dependence on Strouhal number and reduced frequency through water tunnel experiments and biological data comparison.

## Contribution

It introduces new scaling laws for thrust, power, and efficiency of oscillating foils, validated by experiments and biological data.

## Key findings

- Thrust closely follows a linear dependence on reduced frequency in low-viscous drag conditions.
- Scaling laws show excellent collapse of experimental data for thrust, power, and efficiency.
- Results are consistent with biological swimming data.

## Abstract

Scaling laws for the propulsive performance of rigid foils undergoing oscillatory heaving and pitching motions are presented. Water tunnel experiments on a nominally two-dimensional flow validate the scaling laws, with the scaled data for thrust, power, and efficiency all showing excellent collapse. The analysis indicates that the behaviour of the foils depends on both Strouhal number and reduced frequency, but for motions where the viscous drag is small the thrust closely follows a linear dependence on reduced frequency. The scaling laws are also shown to be consistent with biological data on swimming aquatic animals.