How wings work

Here we describe as simply as possible how a wing works.

In the figure below, we see a cross-section through a thin airfoil and we imagine air flowing past, from left to right.

 

 

This is an example of a cambered airfoil because it has a curved shape, and it is easy to see how, if the air follows the airfoil shape, then it moves over the thick part of the airfoil and then flows downward.  The net downward acceleration is the cause of lift.  Newton's laws tell us that the reaction force to a downward acceleration, is an opposite force, upwards.  There has been a great effort over 100 years or so to find airfoil shapes that most efficiently do work on the air, accelerating the flow downwards.  A whole range of shapes exist, and they work fine — provided the flow follows the shape of the airfoil.

 

 

 

 

 

 

 

 

 

One can show that the net aerodynamic force on a wing of surface S must vary as 1/2 ρ U² S, or qS, where q is the dynamic pressure of the air moving at speed U, with density ρ.  It is convenient to define 2 components of the net force.  One is the lift, L, which acts perpendicular to the motion, U, and opposes the weight, W.  The other is a drag, D, which opposes the motion, and must be balanced by some counter force, such as thrust, T, produced by the engines.

When L = W and T = D, the plane is in equilibrium (note how we have shifted in our explanations from airfoil, to wing, to plane; there are some interesting details skipped over here. but this will do for now).

Now the appropriate normalisation of L and D are by qS, so we arrive at lift and drag coefficients, C_L and C_D.  These are dimensionless coefficients that indicate the relative magnitude of L and D compared with a reference force, qS.  (sanity check: q has units of force/unit area, S is an area, so qS has units of force.)  In general L is good (we can carry things, including ourselves) and D is bad (requires thrust, T, which comes usually from burning fuel, and we would like to do as little of that as possible).  So a commonly-used figure of merit is L/D = C_L/C_D — also dimensionless.

Much of the focus in aerodynamics is to investigate ways to maximise L/D in ways that are safe and controllable.  So that is what we do.

 

 

At the scale of small UAVs or birds, or bats, the aerodynamic performance (as measured by C_L, C_D, L/D noted in [basics]) of wings (and tails, and body parts) is strongly determined by the dynamics of the separation point.  Whether or not the flow separates, and if it does, how and whether it reattaches are famously sensitive to small variations in geometry and environmental conditions.

There are two sets of considerations here: first, how would we best design a wing to operate in these conditions, and second, can we exploit these natural flow sensitivities to exert efficient control?

Some images from early work in the Dryden tunnel show the basic idea.

The separation line at low angle of attack.

Above is a composite from 5 separate experiments, showing the mean separation line on an E387 airfoil at 4 degrees angle of attack, and Re = 30 k.  The purpose of the airfoil (recall [basics]) is to accelerate air downwards.  When the boundary-layer separates, the outer flow no longer follows the contours of the carefully-shaped airfoil, and L/D decreases.  The ability to control and modify the separation line could be very influential.

The next plot shows the flow separation over the E387 in a different way, superimposing contours of spanwise vorticity over the image.

It is quite amazing that a skilled experimentalist (this work was by John McArthur) in a good quality facility can replicate 5 completely separate experiments with essential details that are not only qualitatively but qualitatively the same.  A tip of the chapeau indeed to John, but there is a catch: these fields are time-averages.  If we wish to perform some control operations upon this flow, then any sensor will not see such a well-behaved and smooth velocity field.  It will instead see something like this:

Even at low angle of attack, the boundary layer close to the airfoil surface is quite complex and disorganised.  I like the term 'unruly'!  This is the core of the problem in understanding low Re flows.  Although, on average, events seem to be readily explicable and perhaps even controllable, in detail and in every instant, there is great variation and uncertainty.

 

At DrydenWT, we have done a lot of work on characterising low-Re flows about airfoil shapes.  It is a fabulous example of how so many things, when inspected with care, reveal so much that is new.

Our goal is flight control, and currently our teams are from USC, San Diego State University (Guus Jacobs, Bjoerne Klose perform serious computations) and Maziar Hemati (University of Minnesota, who conjures up equally serious control algorithms and strategies).

The first step is to check to see whether experiments and computations are saying the same thing.  Here is a series of flowfields (time-averaged) of the NACA 65-412 airfoil at chord Reynolds number of 20 k.  The experiments were done by Joe Tank at USC, and the computations were by Jacobs and Klose at SDSU.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

There are many amazing things here.  First, begin at α = 0°.  The NACA 65-412 is a cambered airfoil and it's design C_L is 0.4 (hence the 4 in the name) which is achieved normally (at higher Re) at α = 0°.  The problem now is that at low Re = 20 000, the flow always separates before the trailing edge, and at α = 0°, the streamlines bend upwards, guided there by the separation line.  Recalling how lift works in [basics], we see already that the lift is negative.  Not a very useful property for an airfoil,

Next look at the series α = 2,4°, where the airfoil drags along with it a slowly recirculating region (colored in yellow), which grows in size.  I often think of this as a ball and chain, as the recirculating fluid is slow and sluggish, contributing nothing towards lift, and generating only drag.  At α = 4° we have equivalent data from experiment and from computations, and qualitatively they agree quite well (but not exactly…).

The bubble in yellow grows and grows with α = 6,8°, becoming huge, about the same cross-section as the airfoil itself.  To say the dynamics are strongly affected by the separation here is not only obvious, but even an understatement.

Now, at α = 10° in experiment, something happens.  The flow magically reattaches and suddenly follows the airfoil shape.  Or not.  The final flowfield is also at α = 10°, but a little while (note vague language) later.  And later still, it could have switched back to the previous state.  The flow appears to flip between two stable states.  One of them (the attached one) is associated with unusually high lift for an airfoil at this Re, and the other with unusually poor performance.  An efficient controller might look for ways to determine the switching between states, as we can obtain a large increase in L/D (70% or more) with a small amplitude input.

This is what we are working on now, but trying to find rational rather than empirical ways to control the flow.

As a brief summary of these types of efforts, we can show two experiments, one from the wind tunnel and one from computations.

 

 

 

 

 

 

 

 

The picture above/left shows the distribution of spanwise vorticity at a number of slices through a wing.  By the solid dots, acoustic forcing is being applied through small embedded micro-speakers.  Elsewhere, the forcing is off.  It is clear that the flow response is mainly local (with some leakage past the first solid dot where unforced conditions still prevail).

The two figures below show the beginning of forcing in a computations where the base state in the forward and backward-time FTLE fields is just about to be disturbed by a synthetic momentum jet located at x/c = 0.5.

 

 

 

 

 

The key next steps will be to formulate a reduced order model that can serve as a focus for control of these complex flows, and then to find whether a systematic footprint can be found that can be implemented.

Watch for growth on the [publications] page!

 

If we were to design a plane from scratch, what would it be?  The following sequence of images shows how the search for an efficient wing might proceed, in principle.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

The top figure shows a uniform downwash distribution behind a flying wing.  One can show that in many cases this is the best it can be, the one that transports the most momentum per unit kinetic energy cost.  From the same argument the efficiency of a wing interrupted by a fuselage cannot reach such efficiencies.  Now it turns out that if you put a trailing edge flap onto the fuselage — nothing fancy, just a plate will do — then small deflections of this plate can be used to set the rear stagnation point, which in turn sets the lift.  The lift can now be trimmed to equal what would have been on the wing anyway, with no body.  Voila!  A lifting body, and a return to a flat wake downwash profile and its efficient form.

Another way to thinking about this is to inspect the wake flow and it's as if the body were never there.  Even one with a quite large profile.

Therefore, if one were building a new aircraft, from scratch, and began with this notion of wake efficiency, chances are, the new plane would look like …

 

This figure comes from J. Huyssen, with whom we have collaborated on this problem, which he has proposed and tested in a number of different forms.  Here is his drawing of a one-person sailplane, with a fuselage just big enough to contain its payload (the pilot) and a trailing edge tail.

In the background lies the question: Should we copy them?

To answer such a question we first must understand a bit about how they fly.  A long-standing collaboration with a group at Lund University in Sweden has produced a string of papers that provide quantitative answers to this type of question.  There have been numerous experiments and [publications] can be consulted for details, but let's illustrate by starting at the beginning.

Introducing our hero, Chipper, the thrush nightingale.

Here we see Chipper, sitting on a perch and perhaps looking a little nervous.  That may be because the perch is about to be removed and then flight must happen.  The vertical line supports the only bright source of light in the tunnel.  Thrush nightingales fly at night so reduced light is natural, and this one was also caught just before migration season, so he is ready to roll.

Lights, cameras, action …

These are reconstructions of the wake disturbances left behind the thrush nightingale at 3 different flight speeds.

By interrogating these datafiles, we can estimate energy and power consumption and can test the results against different predictive models.

The story gets a little involved, but the bottom line seems to be that birds act a lot like small power gliders, subject to variations due to the wings flapping (which ultimately provides the thrust).  So they work quite like our own aircraft do.  It looks like a toss-up between a propeller-driven fixed-wing plane and a flapper, at least for steady flight.

What we can see perfectly well is that birds also have extraordinary (by our standards) maneuvering abilities, gust tolerance, agility and perching ability.  So there could be reasons for bringing avian-inspiration into the design of small UAVs.

Watch this space…

 

 

 

 

 

 

 

 

 

 

Where is this research going now?  There are a number of fascinating directions we would like to explore, including:

• how can airfoil shapes be designed so the laminar separation bubble (LSB) can be manipulated easily?
• how could material properties such as flexibility and porosity affect the flight performance and stability?
• what kind of reduced order modeling can help to make a feedback control system for these complex flows?
• how can we make a wing that folds to reduce its surface area by factors of 2 or more?
• what differences in flight pattern can be seen in the quantitative wake structures?
• if novel aircraft designs are so great then what would the next steps be?
• what magnitudes of drag reduction are worth investing in?

To be continued!