# PIV-based investigations of animal flight

## Authors

- First Online:

- Received:
- Revised:
- Accepted:

DOI: 10.1007/s00348-008-0597-y

- Cite this article as:
- Spedding, G.R. & Hedenström, A. Exp Fluids (2009) 46: 749. doi:10.1007/s00348-008-0597-y

## Abstract

An overview is presented of the principles of estimation of fluid forces exerted upon solid bodies, based upon whole-field velocity measurements such as provided by PIV. The focus will be on the range of length and velocity scales characterised by the flight of large insects, birds, bats and small unmanned air vehicles, so that while viscous terms in the Navier–Stokes equations can many times be ignored in the quantitative analysis, understanding and measuring boundary-layer flows, separation and instability will ultimately be critical to predicting and controlling the fluid motions. When properly applied, PIV methods can make accurate estimates of time-averaged and unsteady forces, although even ostensibly simple cases with uncomplicated geometries can prove challenging in detail. Most PIV-based force estimates are embedded in some analytical model of the fluid–structure interaction, and examples of these with varying degrees of complexity are given. In any event, the performance and accuracy of the PIV method in use must be well understood as part of both the overall uncertainty analysis and the initial experimental design.

### List of symbols

*A*tip-to-tip flapping amplitude (m)

*AR*aspect ratio (

*AR*=*b*/*c*)*b*wingspan (m)

*c*mean chord (m)

*C*_{L,}*C*_{D}lift and drag coefficients (

*C*_{x}=*F*_{x}/*qS*)*C*_{D,pro}profile drag coefficient of wing

*C*_{D,i}induced drag coefficient of wing

*C*_{F}laminar skin friction coefficient

*D*image displacement (pix)

*D*drag, force parallel to

*U*_{0}(N)*D*′drag per unit span (N/m)

*f*flapping frequency (/s)

*F*_{x}force component in the

*x*direction (N)**g**acceleration due to gravity (m/s

^{2})*I*impulse (kg m/s)

*l*length scale (m)

*L*lift, force normal to

*U*_{0}(N)*p*pressure (N/m

^{2})*p*_{0}freestream pressure (N/m

^{2})*q*dynamic pressure \( \left( {q = \frac{1}{2}\rho U^{2} ,\;{\text{N}}/{\text{m}}^{2} } \right) \)

*Re*Reynolds number (

*Re*_{x}based on length scale*x*)*r*_{0}vortex radius (m)

**R**general, resultant force vector (N)

*R*_{wv}wake vortex ratio

*S*control surface (m

^{2})*S*shear deformation (d

*x*/*x*, dimensionless)*S*wing planform area (

*S*=*bc*, m^{2})*St*Strouhal number (

*St*=*fA*/*U*)*t*time (s)

*T*wingbeat period (s)

**u**velocity vector field (m/s)

*u*,*v*,*w*velocity components in

*x*,*y*,*z*(m/s)*u*_{1}upstream uniform streamwise velocity (m/s)

*u*_{2}downstream,disturbed streamwise velocity (m/s)

*U*_{0}mean, undisturbed uniform streamwise velocity (m/s)

*U*mean flow speed or mean flight speed (m/s)

*V*control volume (m

^{3})*w*_{i}induced velocity (due to wing lift) (m/s)

*W*body weight (N)

**x**position vector (m)

*x*,*y*,*z*Cartesian coordinates in streamwise (flightwise), spanwise and vertical directions (m)

*α*angle of attack (deg)

*α*_{i}induced angle of attack—the decrease in

*α*caused by*w*_{i}(deg)- δ
*t* exposure time between two PIV images (typically μs)

*ϕ*velocity potential (m

^{2}/s)- Γ
circulation (m

^{2}/s)- Γ
_{0} circulation at wing centreline (m

^{2}/s)*μ*viscosity (kg/m/s)

*ν*kinematic viscosity (

*ν*=*μ*/*ρ*, m^{2}/s)*θ*momentum integral (m)

*ρ*fluid density (kg/m

^{3})- \(\varvec{\upomega}\)
vorticity vector (/s)

*ω*_{x}vorticity component in the

*x*direction (normal to the*yz*plane) (/s)

### Abbreviations

- CIV
Correlation Imaging Velocimetry

- DLE
Direct Lyapunov Exponent

- DNS
Direct Numerical Simulation

- ENOB
Effective Number of Bits

- LCS
Lagrangian Coherent Structure

- LEV
Leading Edge Vortex

- PIV
Particle Image Velocimetry