Welcome to the Aerospace Digital Library's basic-knowledge content on the field of Aerodynamics. Below are links to various commonly-known areas of aerodynamics. Note that they are not mutually exclusive. Classifications of areas in aerodynamics are discussed under Introduction to Aerodynamics.

Table 1: Links to areas of aerodynamics.

Introduction to Aerodynamics	Compressible flow / gasdynamics	Viscous Flow
Low-speed steady aerodynamics / hydrodynamics	High-speed aerodynamics	Turbulence
High Angle of Attack Aerodynamics	Transonic flow	Computational Aerodynamics
Unsteady aerodynamics	High-Temperature Gas Dynamics	Flow Diagnostics
	Hypersonics	Flow Control Techniques

Rocket designers do worry about the forces generated as the rockets travel through the atmosphere, but until recently their concern has been only to reduce drag: they viewed the atmosphere as a nuisance which pulled their craft back, or even threatened to burn up the craft by friction.  A modern exception to this is the concept of "aero-braking" where a brief pass through the atmosphere of a planet is used to change the kinetic energy of the orbit of a spacecraft without changing the potential energy.

Figure 1.3: In aircraft  terms, a rocket usually flies with Lift/Drag ratio of essentially zero, but a Thrust-to-Weight ratio greater than one.

Figure 1.4: Lighter-than air craft: hot-air balloons.

3. Aerodynamics

For flight in the atmosphere, it is smart to use the forces that can be generated by moving through air to our advantage. To do so, we must understand, learn to predict, and learn to use these forces due to the motion of the air. This is the field of Aerodynamics.
 

4. And then there's the 4th way to fly..

We have not figured out Anti-Gravity yet, but when we do, it will still make sense to use aerodynamics to fly around inside the atmosphere.

The rest of this course is about Low Speed Aerodynamics. As explained in the Introduction, Low Speed Aerodynamics deals with the speed regime where nothing moves at speeds greater than about 30% of the speed of sound.  In this regime, we conveniently assume that changes in flow conditions, propagating at the speed of sound, reach everywhere "instantly",  or long before any real changes in the flowfield become noticeable.
 
 

Figure 1.6: Airliner: L/D >>1;  T/W <0.3
 
 

Figure 1.7: Glider: Lift-to-Drag Ratio of 20 (some reach 40 or even 60), but no thrust.

 In this course, we will

        • use some well-known results to get started on wing aerodynamics
        • explore several phenomena which occur in flows
        • learn how to describe these phenomena using physics and mathematics
        • develop engineering calculation methods using these descriptions
        • close the loop by using these methods to solve design problems

In aerodynamics, "lift" is the flow-generated force acting perpendicular to the "free stream" direction. "Drag" is the flow-generated force acting along the free stream direction. In airplane terms, the "free stream" is the atmosphere, so that the free stream velocity is equal and opposite to the velocity at which the airplane is moving relative to the atmosphere. Suppose an aircraft is moving at w.r.t. the ground, and the wind is w.r.t. the ground. Then to the aircraft, the free stream velocity is 

Figure 1.8 The concept of the freestream velocity

Figure 1.9 (a): Lift, Drag, Thrust and Weight force vectors acting on an airplane.

Figure 1.10: The lift, weight,  drag, thrust, drag and flight velocity  vectors
 

Note that the "lift" can be acting sideways, or even downwards, as far as we are concerned in aerodynamics. The drag is what acts along the freestream direction.

Usually, most of aerodynamic design consists of getting the most "lift" for the least "drag" -- achieving maximum (L/D). Exceptions are cases when you want to slow down quickly, and are in no danger of falling down. Here we use "spoilers" or "speed brakes", and drag parachutes.

Figure 1.11: Situations where you want high D/L..

Reading suggestion: Chapter 1 of the text.

L 
 
 

Fig. 1.12: The Planform Area S is the area enclosed by a full-scale drawing of the outline of the wings when viewed from directly above or below.

At low speeds [ < Mach 0.3 ] , the dynamic pressure is

where ris the density and the "infinity" subscript indicates that its the value in the freestream, far away from the disturbance created by the aircraft.
 

Lift

DRAG = (Dynamic Pressure) * (Reference Area) * (Drag Coefficient)

Drag 

Note: You have to be careful to check what the Reference Area is before you believe a drag coefficient value: if people want to make look small, they might use a big .

Example:

Figure 1.13: Ask about the reference area before you compare drag coefficients.

In aircraft aerodynamics, drag coefficients of the wing are often expressed using wing planform area as the reference. Sometimes you run into a situation where the "wetted area" is used as reference. Note that the wetted area of the wing, for example, is more than twice the planform area, because the upper and lower surfaces, including their curvature, are included.  The drag coefficient of the fuselage is often expressed using the cross-section area of the fuselage as reference.

Getting back to C_L:

If you increase , the "angle of attack" or (angle of "incidence") of the wing relative to [within a narrow range of angles ~ -2 degrees to , say, 12 degrees ] the lift increases, so

Putting this in terms of calculus, we can express the increase of lift coefficient, with increasing angle of attack, as

If we plot the lift coefficient on the vertical axis, and the angle of attack on the horizontal axis, the "slope" of the curve is positive, until we reach an angle of attack where the lift coefficient starts coming down quite sharply, as the wing "stalls".

 

Figure 1.14: The angle of attack, and the lift-curve slope.

The slope of the lift-curve, above, is indeed nearly constant over the "small-angle-of-attack" region from about -5 to 10 degrees for most airfoils. In other words, a plot of lift coefficient versus angle of attack is straight until one reaches near the stalling angle of attack.

The maximum slope of this line (theoretical limit for a thin airfoil at small angle of attack, meaning below about 10 degrees) is 2pa  if a   is in radians. This is a neat result. Now you can amaze your friends by calculating the approximate lift coefficient of an airfoil at a given angle of attack, simply by multiplying the degrees by p and dividing by 180 to convert to degrees, and then multiplying this by 2 times p , which is 6.28. This is the "ideal lift curve slope" predicted by "thin airfoil theory" as we will see later in this course. People can design airfoils that come fairly close to this value.

So

; witha in radians.
 
 

Example: A symmetric airfoil is one which looks exactly the same if turned upside down: i.e., it is symmetric about the chord line, which is the straight line connecting the Leading Edge and the Trailing Edge. If a symmetric airfoil is placed at an angle of attack of 0 deg., the lift coefficient is zero: the air flow characteristics over the top and bottom surfaces are exactly the same, and no net lift force is produced. Now if the lift curve slope is 2p, and the angle of attack is increased to 5 degrees (which is 5*p/180 = 0.08727 radians), the lift coefficient is 2*p*0.08727 = 0.548. At 12 degrees angle of attack, which is getting close to the stalling angle for many airfoils, the lift coefficient is 1.31...

Note: For usual airfoils, the lift coefficient is of the order of 1. i.e, values range from about 0.1 to 0.7 at cruise conditions to about 1.4 at maximum angle of attack, used at landing when you want the greatest lift at the least speed.

Special "high-lift devices" such as flaps and slats may push this value to as high as 2.5 on airplanes built for Short Takeoff and Landing (STOL). Active high-lift devices,  such as blowing high-speed jets over the surface, may enable lift coefficients as high as 4: these are used on some aircraft for landing on the decks of aircraft carriers. The associated drag penalty is also very high. Also, during sharp maneuvers, the angle of attack on some airfoils can be taken as high as 30 or 40 degrees very rapidly, and very briefly before stall occurs: the trouble is that stall does then catch up, and is pretty violent. You then have to go back far below the normal stalling angle before the lift coefficient recovers.

Airfoils versus Wings

The " = " occurs at the theoretical limit for a thin wing which extends uniformly from to [ no wingtips ]. Since it extends uniformly, it doesn't really matter where and how much of it you analyze: you might as well analyze the "section" –› an "airfoil", (of unit span). To remind ourselves that this is only for a section, we will use and as opposed to C_L and C_D for the whole wing or whole aircraft.
 

So, for a thin airfoil at small angle of attack,

Integrating,

a₀ is the value of awhich gives c_l = 0.

How can  there be an a₀ different from zero?

If you draw a line which stays equidistant from the upper and lower surface of an airfoil, that's the "mean line" of the airfoil. The straight line joining the leading edge and trailing edge of the airfoil is the "chord".

An airfoil is symmetric if the mean line coincides with the chord everywhere. Otherwise it is "cambered".
If the airfoil is cambered, some lift will occur even when the angle of attack is zero. You have to point the nose of the airfoil downwards a bit (negative angle of attack) before the lift coefficient becomes zero.

Symmetric Airfoil
 

Doesn't matter if you tilt up or down,same magnitude of force occurs:

Aspect Ratio
Aspect Ratio 
where b is the "span" of the wing (the distance from one wingtip to the other), and S is the planform area of the wing.

High Aspect Ratio is good: it gives a high L/D.  An "airfoil" has infinite aspect ratio: it is "two-dimensional", which means nothing changes along the 3rd dimension.

There are no wings of infinite aspect ratio.
 

Of course, if the wing is rectangular, untapered,

 s = bc AR = 
For an infinite wing, b , s , but faster than s, so, "infinite aspect ratio."

Infinite wings have infinite weight and require infinitely wide runways.

Also , note the structural design of an aircraft.  Compare the loads on the wing on the ground, and in flight.

 

Unfortunate Truth: (Read Anderson about Wright Brothers learning this the hard way.)

 To get high L/D, we need high aspect ratio

Why aspect ratio is important:

You know that lift is the difference between the pressure forces on the lower and upper surfaces.

 

At the tip, air rolls  around from the  high-pressure region on the bottom to the top: lift is lost. This effect is felt all along the wing. Obviously, if the tip is far away (in chord-lengths), very little change will occur to the airflow as it moves from l.e. to t.e. at inboard stations. In other words, the "spanwise load distribution" on a real wing is

The loss can be expressed in terms of an "induced angle of attack." so that

.

radians for elliptic lift distribution

Induced Drag

You pay money (in the form of fuel which runs the engines which propel the aircraft) to produce this pressure difference between the airflow on the upper and lower surfaces. Then a lot of it just leaks out because the wing is not infinite. As increases, this just gets worse. The energy in the swirling flow around the tips is just lost, left behind as "trailing vortices," or "vortex sheets." You paid to make air go round and round !! Note that inside the wing tip vortex, the velocity is high and pressure is low! The vortex pulls the wing back: even more loss.

All of this is "induced drag": drag caused only because you tried to produce lift.

At low speeds, wing drag is mostly.


Another way to look at induced drag and induced:

Normal force vector is now perpendicular to the effective freestream vector, which is the resultant of and the "downwash", W, due to the wake. This force vector can be resolved into and .
 
 

We would like all our aircraft to have L/D as high as possible. Some sail planes and gliders have L/D > 40 (very low CD). However, there are other design constraints which prevent us from getting there on other aircraft.

Transport aircraft: (L/D) 16 ~ 20

Fighters: (L/D)cruise 10 - 16

Supersonic transport: (L/D) 11

Hypersonic aircraft: (L/D) 1 [ lift is a minor problem here ]
 

Now let's look at a few designs:
 
 

1. "Voyager" High AR —> min. drag, max L/D —> max efficiency, but slow, fragile, hard to handle. High roll inertia.
 
 
 
 
 
 
 
 

2. F-22: Low AR —> poor efficiency at low speed, but v. powerful engines: T/W > 1. Performs well  in fast maneuvers, good T/D in supersonic flight.

Expensive to fly, but when F-22 is really needed,all your fuel dumps are in danger of being blownup anyway.

3. Commercial airliner: Pretty high AR. Fuel cost is very important, but so is speed and ability to fit many at each airport terminal. Can't afford
Voyager-type wings. Optimized for Mach 0.85cruise.

 

4. Helicopter rotors: Very high AR —> high  efficiency for vertical takeoff. But can't fly veryfast, for several reasons.
 

5. NASP: Lift is easy to generate at high speed: can be very small —> D_i not big issue: keepwings and body thin and slender.

 

So far, we have seen several simple results, and they are quite useful in some problems, as well as giving general guidance. (But most A.E.'s have figured these things out long ago. The problems that we must solve are more complex.)
However, we can't use these results to tell us what the shape of the airfoil should be, nor the detailed shape of the wings, or how to calculate lift when you have twisted wings, or flaps deflected, or with the fuselage present. In addition, we need to be able to calculate detailed pressure distributions over wings and airfoils in order to calculate moments.
To analyze these things, we must be able to calculate the detailed behavior of flows. To do so, we go right back to the things that we are really sure about: the laws of Physics. Then we proceed, step by step, using proven mathematical methods.

As we go through this, it is useful to remember why we do this. The author of the textbook, and (hopefully) the instructor, know the results that come out of these analyses: you get a very abbreviated run-down of those that could be explained easily. It would be possible (and such things are in fact available if one searches hard enough) to provide you with lists and tables and charts that summarize all the published results on aerodynamics, and you could search through them and find "the formula" that you need to some most simple problems. In fact, this is what is done in many industrial design departments where the workers can't be trusted to do anything more sophisticated. The trouble is that every time an unexpected problem comes up, you find that none of the formulae really "fit," and you have to use what is called the WAG method (the Wild Aerodynamic Guess). This is O.K. for hobbies, but not for billion dollar projects (or anything where someone's life, limb, and paycheck depends on it). A consistent method, whose assumptions, derivations, and limitations you understand well, lets you do a much better job and to sleep a lot better.