Tuesday, August 9, 2011

Drag Isn't so Bad (Paleontology Myths Part 2)

One comment that I encounter relatively frequently at scientific conferences is that the limbs of aquatic marine reptiles were "paddles" (such as our friend from the LACM photographed above by yours truly). The same is sometimes suggested of the fins and flippers of living animals.  Ironically, I also regularly encounter the idea that drag is "bad" and always costly.  This is an ironic situation because a true paddle is a drag-based propulsion structure.  This came up again recently, so I thought perhaps a quick post on the subject might be a good idea.  We see both lift-based and drag-based swimming in nature today, but the roles of each are pretty different...

It turns out that most swimming vertebrates cruise using mostly lift.  It may seem odd, but the tails on fish and the flukes on dolphins are really like wings - they just aren't using lift to support weight.  Lift, after all, doesn't have to point upwards (despite the name); it's just the force you get perpendicular to the direction the fluid is going around your wing, flipper, etc.  So, during cruising, we can expect that the tail of a mosasaur or the flippers of a pliosaur probably worked at a high ratio of lift to drag.

However, there are animals today that use largely drag to swim.  Ducks, for example, do this, as do soft-shelled turtles.  Lobsters and crayfish use drag-based propulsion when they tail flick to escape from attack (for the poking of small children).  Furthermore, and perhaps most importantly, most of the animals that cruise around using lift (like sharks and ray-finned fish) also have ways of producing lots of drag for short intervals.  If lift is so good, and drag is so bad, then why are there so many draggy critters?  Well, the reality is that drag isn't so bad after all.  It's all about how you use it.

At low speeds, lift production is necessarily small for two reasons.  First, fluid force is proportional to velocity (for big, fast moving things like most vertebrates, it is proportional to the square of velocity), and therefore the lift force can only be particularly large at low speeds if the coefficient of lift is especially high.  The lift coefficient of a wing or fin has distinct limits, however, because at a very high angle of attack, stall occurs.  For a flying animal, that is particularly bad (it falls) but a swimmer will lose thrust, so it's not much better. Second, lift production does not reach its maximum value instantly. Lift production is reliant on the generation of a circulation component of flow.  It generally takes 7 to 8 chord lengths of forward travel before a wing (flapping or fixed) reaches full circulation (Chow and Huang, 1982; Graham, 1983; Dudley, 2002) and therefore full lift force potential.  This limitation is called the Wagner Effect (because it was first noted by Wagner [1925]).

Pushing off of a substrate circumvents these restrictions, and a push against the ground (or perch) can produce high accelerations immediately, starting at low (or zero) speed. As a result, pushing off of a substrate (be it solid or fluid) yields greater potential acceleration than lift production at very low speeds. This is the principle behind how most fliers take off (since they leap or run).  Pushing off of a fluid also circumvents the problems of fluid force production at low speeds, but it only works if the fluid in question is of sufficient density.  Pushing against fluid constitutes drag-based propulsion.  In colloquial terms, this is using a “paddle”.

Drag abides by many of the same rules as lift, but unlike lift forces, drag forces can be high even at near-zero velocities, especially if the fluid is dense and a broad area is used to initiate force.  This is, for example, the principle behind the extremely rapid "c-start" utilized by many fish to achieve high accelerations starting from rest (Vogel, 2003).  Unlike the lift coefficient, the drag coefficient is not subject to reduction by stall: so while the minimum drag coefficient for a streamlined foil at a low angle of attack can be quite low (producing high L/D ratios), the maximum drag coefficient at very high angles of attack can also be substantial.  Drag is also not subject to the Wagner Effect, because it does not depend on the production of circulation.

So, ultimately, for efficient cruising (either in flight or while swimming) lots of lift and very little drag tends to be preferable.  However, to get out of the gate the fastest, drag is the way to go.  Down the road, we'll look in more detail at what this might mean for the evolution of marine living in things like mosasaurs.


Chow CY and Huang MK (1982). The initial lift and drag of an impulsively started airfoil of finite thickness. Journal of Fluid Mechanics. 118: 393-409

Dudley R (2002). The Biomechanics of Insect Flight: Form, Function, Evolution. Princeton University Press

Graham JMR (1983). The lift on an aerofoil in starting flow. Journal of Fluid Mechanics 133: 413-425

Vogel S (2003). Comparative Biomechanics: Life’s Physical World. Princeton: Princeton University Press.

Wagner HA (1925). "Über die Entstehung des dynamischen Auftriebes von Tragflügeln", Zeitschrift für angewandte Mathematik und Mechanik 5: 17-35

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