Lecture 28: Swimming & Flying

direction of biofoil motion direction of biofoil motion How to fly or swim with a biofoil 1) Lift-based propulsion direction of biofoil motion direction of average force 1) Drag-based propulsion direction of biofoil motion direction of average force

Gliding Flight q q a Fvertical lift Therefore, glide angle is minimal at maximal CL/CD. Fvertical lift q wing tip path drag q glide angle a mg Speed of descent along glide path is determined by weight

Gliding Flight Aspect ratio = span/chord High aspect ratio wings have largest lift-to-drag ratio. Span, R Chord, c High aspect ratio reduces ‘induced drag’ – a loss in efficiency due to tip effects.

Extended primaries also reduce induced drag.

Forward Flight wing tip path lift lift drag drag wing tip path downstroke wing tip path lift drag upstroke wing tip path upstroke downstroke sign of circulation does not change

Hovering Flight FV upstroke FV FH lift drag drag lift FH downstroke

Hovering Flight upstroke downstroke drag Note that sign of circulation does change drag

Thunniform swimming lateral Undulation of biofoil FL lift drag lift FT tail tip path FT FL lift

Thunniform swimming lateral Undulation of biofoil tail tip path lift Note that sign of circulation does change tail tip path lift

Penguiniform swimming FL drag lift FT tail tip path FT FL lift

But these are gross simplifications. Four basic types of fish swimming thunniform carangiform anguilliform ostracoderm But these are gross simplifications.

Energetics of Flight Pind Ptotal Two main costs associated with flight: 1) Induced Power= power required to push air downward R = wing length F = angle swept by wing U = flight speed 2) Parasite Power= power required to overcome drag on body Flight speed, U Power Pind Ptotal ‘U-shaped’ power curve Flight cost minimum at intermediate speed