Copyright: NASA Lewis Research Center


FoilSim Program
   FoilSim

This simulator calculates the two dimensional flow around several basic airfoil shapes, including a flat plate and a family of airfoils.  The package includes several lessons on basic aerodynamics; the lessons are displayed by clicking on the highlighted lessons below.  Click here for assistance with the help file.

FoilSim Lessons

Airfoils

Baseball

FoilSim Operation

•	General Description

•	Airfoil Panels

•	Plotter Panels

•	Probe Panel

•	Baseball Panels

•	General Information about Aerodynamics

•	Glossary

•	Theory

•	Available Software

•	About FoilSim


About
About FoilSim

This program has been adapted for the MS-Windows environment from the UNIX version of the VuFoil program shown in the available software listing.  The original program was developed by Tom Benson.  This adaptation for MS-Windows was developed by Bruce Bream, with Tom's assistance, for the NASA Mobile Aeronautics Education Laboratory.  The software was beta tested in April 1997.

This version was compiled on: 28-Jan-98

Any suggestions, corrections, bugs, experiences (good or bad), should be sent to:

Tom Benson

NASA Lewis Research Center, MS 5-11

21000 Brookpark Road

Cleveland, OH  44135

Email: benson@lerc.nasa.gov

Tel: (216) 433-5920

or

Bruce Bream

NASA Lewis Research Center, MS 77-2

21000 Brookpark Road

Cleveland, OH  44135

Email: bruce.bream@lerc.nasa.gov

Tel: (216) 433-6532

NOTICE:

THIS SOFTWARE IS PUBLIC DOMAIN. IT MAY BE FREELY COPIED AND USED IN NON-COMMERCIAL PRODUCTS, ASSUMING PROPER CREDIT TO THE AUTHOR IS GIVEN. BUT IT SHOULD NOT BE RESOLD. IF YOU WANT TO USE THE SOFTWARE FOR COMMERCIAL PRODUCTS, CONTACT THE AUTHOR.

THIS SOFTWARE IS PROVIDED ``AS IS'' WITHOUT WARRANTY OF ANY KIND, EITHER EXPRESSED OR IMPLIED. THE ENTIRE RISK AS TO THE QUALITY AND PERFORMANCE OF THE SOFTWARE IS WITH YOU. SHOULD THE SOFTWARE PROVE DEFECTIVE, YOU ASSUME THE COST OF ALL NECESSARY SERVICING, REPAIR OR CORRECTION.


General Information
General Information about Aerodynamics

This section of the FoilSim package gives an overview of aerodynamics and explains how the simulator should and should not be used.

It is remarkable to note that humans did not learn to fly until the last century.  Despite the daily example of flight from birds and insects, humans did not unravel the mystery of flight for thousands of years.  Why do you suppose that is true?

The physics of controlled flight is a very complex problem.  It took many years to develop the underlying mathematics, the understanding of aerodynamics, the understanding of thermodynamics for engines, the understanding of materials processing for lightweight structures, and the theories of stability and control.  All of these had to be mastered before human flight was possible.

The Study of Aerodynamics

When solving a very complex problem,  the process can be simplified by breaking it up into many smaller, less difficult problems.  In order to simplify the study of aerodynamics, the aerodynamicist must decide which effects are important and must be considered and which effects can be neglected.  The following areas must be considered:

1.  Airflow is more easily analyzed when it becomes steady and constant with time.  It is difficult to describe or visualize the movement of a body through three-dimensional space where air can move in three directions.  In special circumstances, air can move in only two directions, which is much easier to describe and visualize.  But because problems in aerodynamics change quickly with time, it is even easier to analyze airflow when it becomes steady and appears to be constant with time.

2.  Air is assumed to be a single gas with uniform properties in most aerodynamic studies (even though real air is made up of many gasses).

3.  The compressibility of air can usually be ignored for low speed flight (<250 mph) because its effect is important only at flight speeds near and above the speed of sound.

4.  The viscosity (stickiness) of air can be ignored for some simple flow problems.  Viscosity causes air to stick to surfaces moving through it, resulting in a frictional drag and the heating of the air at high speeds.  The viscosity of air is hardly noticeable, but it is the source of many complex flow problems.

After determining which effects can be neglected, the flow problem can be solved by modeling it in a wind tunnel, on paper, or with a computer.

Flow Modeling Problems

There can be several possible problems involved with flow modeling, and the model limits must be considered when drawing conclusions.  Several problems are given below:

1.  The model may not accurately represent the real vehicle.

2.  There may be math errors in a mathematical model.

3.  Limitations on the model may be ignored when drawing conclusions.  For example, if compressibility is neglected, the model should not be used near the speed of sound.  Also, a two-dimensional model will not properly describe the flow over a swept, delta wing because the flow is three dimensional.

Limitations to Foil Sim Airflow Simulator

The simulator, which models the steady, two-dimensional, non-sticky, incompressible flow around several airfoil shapes, has several limitations:

1.  The simulator will not model any brief changes that could occur as flow conditions change.  It assumes that the airfoil has been at the prescribed flow conditions for a long time and that the incoming flow is steady.

2.  The simulation is two dimensional and will model only very long wings.

3.  The simulator will not properly model drag or the stall of the wing, a condition where the boundary layer separates from the wing surface, disrupts external flow, and kills lift.

4.  The simulator can be used only at low airspeeds (typically less than 250 mph).

Even though there are limitations, the mathematical model used in this simulator was developed many years ago and has been used as the basis for undergraduate airfoil theory at many universities for many years.

Analysis of Fixed Airfoil Model

The View Panel in FoilSim is a drawing of the airfoil with air flow moving past it from left to right, which is the view of a wing being tested in a wind tunnel.  Airplanes fly by moving through almost still air.  Yet when wind tunnels are used to test wings, the airplane model is fixed and the air moves past the model.

The idea of keeping the airfoil fixed and having the air flow move past the airfoil can be confusing.  Yet you experience the same thing every day.  When you stand on the corner and watch a car go by, the air around you is relatively still.  As the car moves through the air, there are aerodynamic forces present.  If you were in the car and held your hand out the window, you could feel the aerodynamic force pushing on your hand.  It feels as if the air is moving past your hand as fast as the car is moving; the forces on the car are the same whether the car drives past you or whether you are riding in the car.

The same thing is true of airplanes.  Whether the airplane moves through the air or the air is pushed past the airplane, the forces are the same.  It is usually easier, less expensive, and less dangerous to test airplanes in a wind tunnel before trying to fly them.

Airspeed vs Ground Speed

As you use the simulator, you will see that airspeed gives only the speed of the air far upstream and far downstream of the airfoil.  However, air can also speed up or slow down in the immediate vicinity of the airfoil.

It is important to distinguish between airspeed and ground speed.  The important factor in the generation of lift is the speed of the air relative to the wing (airspeed), not the speed of the wing over the ground (ground speed).  This becomes important on a windy day.

If the wind is blowing 20 mph out of the west, and an aircraft requires 100 mph of airspeed to generate enough lift to get off the ground, the aircraft must reach 120 mph across the runway to lift off if headed east with the wind (120 - 20 = 100).  But if headed west against the wind, the aircraft must reach only 80 mph ground speed (80 + 20 = 100) to lift off.  Pilots always want to head into the wind when taking off.  This explains why airplanes take off from different runways on different days.  It is also why aircraft carriers (which can travel in excess of 35 mph) turn into the wind to launch aircraft.  Just as the plane falls off the end of the flight deck, its wings are going at the speed of the wind, plus the speed of the carrier, plus the speed of the catapult, plus the speed generated by its engines.  No wonder airplanes can take off in such a short distance on an aircraft carrier!

Now that you have read the General Information about Aerodynamics, let's begin the Airfoil Lessons.


Factors That Affect Lift

We are now going to explore some of the factors that affect the lift of a wing.  We will be using the input sliders and boxes located at the lower left and will be watching the output scale marked "Lift" at the bottom on the left.  In this lesson we will be most interested in answering the question, "What changes the lift of a wing?."  If you have been playing with FoilSim, it will now be necessary to set the inputs to some initial conditions.

Click the Reset button to set the following conditions:

Airspeed   = 100 mph

Altitude   =   0 feet

Angle      =   0 degrees

Thickness  = 0.5

Camber     =   0

Area       = 1.0 sq ft

WHAT IS THE VALUE OF THE LIFT?

Increase the speed to 150.

WHAT HAPPENS TO THE LIFT?

Increase the Thickness to 0.7 and the Area to 10.

WHAT HAPPENS TO THE LIFT?

OK - let's change the Angle of attack to 10 degrees.

WHAT HAPPENS TO THE LIFT?

-->   A symmetric airfoil inclined to the incoming flow will generate lift.   <--

You don't need a curved airfoil to generate lift!!

Increase the Angle to 15 degrees.

WHAT HAPPENS TO THE LIFT?

-->   Increasing the angle of attack will increase the amount of lift.   <--

Let's decrease the Thickness to 0.05.   This will approximate a flat plate.

WHAT HAPPENS TO THE LIFT?

-->   Decreasing the thickness will decrease the amount of lift.   <--

-->   But a flat plate at angle of attack will generate a lot of lift.  <--

Let's do a little experiment with this flat plate!

Suppose we had the door to our house which is about 7 feet by 4 feet = 28 square feet.  (Set the Area = 28)  And suppose we were in a tornado which generates a wind of 150 mph.  (Set Airspeed = 150)  And suppose the door was inclined to the wind at only 10 degrees.  (Set Angle = 10)

HOW  MUCH  FORCE  IS  GENERATED  ON  THE  DOOR?

Suppose instead of a 28 square foot door we had a 4 by 8 sheet of plywood. (Area = 32)

HOW  MUCH  FORCE  IS  GENERATED  ON  THE  SHEET?

-->   Increasing the area will increase the amount of lift.   <--

Well, back to airfoils.  Let's look at an airplane problem.

Let's set the Thickness to 0.5 and the wing Area to 180 square feet (6 ft chord and 30 ft wing span).  At 150 miles per hour and 10 degrees Angle of attack, this will generate 12,640 pounds of Lift.  This will easily lift a 10,000 pound airplane off the ground.

Let's see what happens at 25,000 feet Altitude.

IS  THERE  ENOUGH LIFT  GENERATED TO  KEEP OUR PLANE FLYING?

-->   Increasing the altitude will decrease  the  lift.   <--

What can we do?

Let's increase our Airspeed to 200 mph.

IS  THERE  ENOUGH LIFT  GENERATED TO  KEEP OUR PLANE FLYING?

-->   Increasing the airspeed will increase  the  lift.   <--

Well, we've changed all the input conditions except the camber (or curvature) of the airfoil, so let's set the Camber = 0.2.

WHAT HAPPENS TO THE LIFT?

-->   Increasing the camber will increase the lift.   <--

Let's check these results at a different set of conditions.  Set Airspeed = 100, Altitude = 0, Camber = 0, then change to Camber = 0.2.

WHAT HAPPENS?

-->   Lift appears to be a very strong function of the airfoil camber.  <--

(As an engineer, when you see a result that you weren't expecting, it's a good idea to repeat the experiment!)

In this lesson we have seen the effects of various shape and flow factors on the lift of a wing.  So far, we have just taken a qualitative look.  In the next lesson we're going to be carefully comparing results to find quantitative (numerical) results.

Let's summarize what we've learned:

•	Increasing the angle of attack will increase the lift.

•	Increasing the thickness will increase the lift.

•	Increasing the area will increase the lift.

•	Increasing the altitude will decrease the lift.

•	Increasing the airspeed will increase the lift.

•	Increasing the camber will increase the lift.

•	A symmetric airfoil, or even a flat plate at angle of attack, will generate lift.

•	Lift appears to be a very strong function of the airfoil camber.

Back to the FoilSim Lessons Page

On to the Next Lesson - How Lift Changes


How Lift Changes

We are now going to explore some of the factors that affect the lift of a wing.  We will be using the input sliders and boxes located at the lower left and will be watching the output bar graph marked "Lift" at the bottom on the left.  We will also be using the Plotter Panel at the lower right.  In this lesson we will try to answer the question "How does the lift change?" based on what we learned in the last lesson.  In the next lesson we will explore a little more of "Why does the lift change?" by looking at the details of the pressure and velocity around an airfoil.  For now, let's investigate the effects of each of the input variables separately.

Let's start out by considering the effects of changing the angle of attack.  We've already learned that increasing the angle of attack will increase the lift.  Now let's see by how much.

If you have been playing with the package, it will now be necessary to set the input to some initial conditions.

Let's set the following conditions:

Airspeed  =  100 mph

Altitude  =    0 feet

Angle     =  2.0 degrees

Thickness =  0.5

Camber    =    0

Area      =  100 sq ft

This gives us a symmetrical airfoil generating 627 pounds of lift.

Now let's set up the plotter to give us some additional information.  In the lower right panel, click on the button marked "Lift vs".  Additional buttons will appear in the box and a plot will appear in the window above, with a line going from the upper right to the lower left.  (Sorry about the goofy scales on the plot - but we won't really need them in this lesson).  With the lift now at 627 pounds,

Let's first double the Angle of attack from 2 degrees to 4 degrees.

WHAT IS THE NEW VALUE OF LIFT AND HOW IS THIS RELATED TO THE OLD VALUE?

-->  Doubling the angle of attack doubles the lift.  <--

OK  -  Reset the Angle of attack to 2 degrees.

Now, cut this value in half to 1 degree.

WHAT  IS  THE  NEW  VALUE  OF LIFT AND HOW IS THIS RELATED TO THE OLD VALUE?

-->  Halving the angle of attack halves the lift.  <--

In fact, tripling the angle will triple the lift, quadrupling, quadruples ... etc.  Then:

-->  Lift is directly (linearly) proportional to angle of attack.  <--

Or mathematically:    Lift = constant  x  angle of attack

The graph shown in the Plotter View Panel shows the linear relation between lift and angle of attack.

Lift = constant  x  angle of attack

Let's let the letter "L" be the lift and "a" be the angle of attack and "C" be the unknown constant. Then:

L = C a

************  EXTRA CREDIT #1

Strictly speaking, L = C  a      (ONLY for small values of "a")

Do a little experiment where you make a big change in angle of attack.  Note the ratio of the two angles and the ratio of the two lifts.  ARE THEY THE  SAME?

******************************

Now, let's look at the variation of lift with wing area.  We know that increasing the area will increase the lift.

Our initial conditions will be:

Airspeed   = 100 mph

Altitude   =   0 feet

Angle      = 5.0 degrees

Thickness  = 0.5

Camber     =   0

Area       =  10 sq ft

This gives a lift equal to 156.6 pounds.

As before, let's double the Area to 20 square feet.

WHAT IS  THE  NEW  VALUE  OF LIFT?    HOW IS THIS RELATED TO THE OLD VALUE?

-->  Doubling the area doubles the lift.  <--

OK, set the Area back to 10 square feet.

Now, cut this value in half to 5 square feet.

WHAT  IS  THE  NEW  VALUE  OF LIFT?   HOW IS THIS RELATED TO THE OLD VALUE?

-->  Halving the area halves the lift.  <--

This relationship is identical to what we've seen with the Angle of attack!

So we can see that:

•	Lift = constant  x  wing area  <-- a linear relation

Note the constant for the wing area relation is not the same constant as the Angle of attack.

Let's let the letter "L" be the lift, and "A" be the area, and "K" be the new constant. Then:  L = K A

We can check our result by pushing the button labeled "Area" on the Plotter Control Panel below the lighted button labeled "Lift vs."

The graph shows a straight line relationship between Lift and Area.

Unlike the Angle of attack, this relationship is true for ANY increase in area.  Check it out by making a big change in Area.

OK, let's try our luck with changing the Camber (curvature) of the airfoil.  We know that increasing the camber increases the lift and that lift is very sensitive to Camber.

Our initial conditions will be:

Airspeed  = 100 mph

Altitude  =   0 feet

Angle     =   0 degrees

Thickness = 0.5

Camber    = 0.2

Area      =  10 sq ft

This gives a lift equal to 158.6 pounds.

As before, let's double the Camber to 0.4.

WHAT  IS  THE  NEW  VALUE  OF LIFT?   HOW IS THIS RELATED TO THE OLD VALUE?

-->  Doubling the camber doubles the lift.  <--

OK, set the camber back to 0.2.

Now, cut this value in half to 0.1.

WHAT  IS  THE  NEW  VALUE  OF LIFT?   HOW IS THIS RELATED TO THE OLD VALUE?

-->  Halving the camber halves the lift.  <--

Looks like our old buddy the linear relationship!

So we can see that:

• 	Lift = constant  x  camber  <-- a linear relation

Again, the constant for the camber relation is not the same constant as either Area or Angle of attack.

Let's let the letter "L" be the lift, and "c" be the camber and "K" be the new constant.  Then: L = K c

We can check our result by pushing the button labeled "Camber" on the Plotter Control Panel below the lighted button labeled "Lift vs."

The graph shows a straight line relationship between Lift and Camber.

***************  EXTRA  CREDIT  #2

Notice that we can have an airfoil generate lift, using camber, without inclining the airfoil to the incoming flow.  Angle = 0.

And we can generate lift using an angle of attack with no camber to the airfoil. Camber = 0.

***************  EXTRA  CREDIT  #3

HOW CAN YOU MAKE A CAMBERED AIRFOIL PRODUCE  NO LIFT??

This becomes very important if you wish to control the lift of your wing.  Going up in the air is easy -- but how do you kill the lift to get back down?

The answer is to combine the effects of Camber and Angle of attack.

Set the Angle of attack to the correct negative value and the wing quits lifting.

Of course, you can also take the Airspeed to 0!!

Which leads us to our next variable -- how does lift change with airspeed?

We know that increasing the airspeed increases the lift.

Our initial conditions will be the same as before:

Airspeed  = 100 mph

Altitude  =   0 feet

Angle     =   0 degrees

Thickness = 0.5

Camber    = 0.2

Area      =  10 sq ft

This gives a lift equal to 158.6 pounds.

As before, let's double the Airspeed to 200 mph.

WHAT  IS  THE  NEW  VALUE  OF LIFT?   HOW IS THIS RELATED TO THE OLD VALUE?

-->  Doubling the airspeed quadruples the lift.  <--

OK, set the airspeed back to 100 mph.

Now, cut this value in half to 50 mph.

WHAT  IS  THE  NEW  VALUE  OF LIFT?   HOW IS THIS RELATED TO THE OLD VALUE?

What's going on here?  Half of 158.6 pounds would be 79.3 pounds.

This looks like one-fourth of 158.6 pounds.

-->  Halving the airspeed cuts the lift by one-fourth.  <--

This is not a linear relationship!  In fact, this is a quadratic relationship.

•	Lift varies as the square of the airspeed.

•	Lift = constant  x  airspeed  x  airspeed  <-- a quadratic relation

•	Lift = constant  x  airspeed squared

This constant is again different from the previous constants.

Letting the letter "L" be the lift and "V" be the airspeed and "K" be the new constant,

Then:  L = K  V^2

We can check our result by pushing the button labeled "Airspeed" on the Plottter Control Panel below the lighted button labeled "Lift vs."

The graph shows a curved quadratic relationship between Lift and Airspeed.  Not a straight line!

Well, let's move along and see how the lift changes with altitude.  We know that increasing the altitude decreases the lift.

Our initial conditions will be:

Airspeed  =   100 mph

Altitude  = 1,000 feet

Angle     =     0 degrees

Thickness =   0.5

Camber    =   0.2

Area      =   100 sq ft

This gives a lift equal to 1540 pounds.

As before, let's double the Altitude to 2000 ft.

WHAT  IS  THE  NEW  VALUE  OF LIFT?   HOW IS THIS RELATED TO THE OLD VALUE?

OK, set the Altitude back to 1000 ft.

Now, cut this value in half to 500 ft.

WHAT  IS  THE  NEW  VALUE  OF LIFT?   HOW IS THIS RELATED TO THE OLD VALUE?

When in doubt ....  Cheat!

Let's look at the plot by pushing the "Altitude" button on the Plotter Control Panel below the lighted button labeled "Lift vs."

Well, that's a weirdly shaped curve!  It's not a straight line and it's not a quadratic either. It's just curved.

What's going on here?

Well, actually, we're trying to plot against the "wrong" variable.  Lift changes with altitude, but there is more to it than just the height above sea level.  The physical quantity which actually affects the lift as we change altitude is the air density.  Air density itself decreases with altitude; and it is this decrease which causes  the lift to drop.  We can use the simulator to find out how the lift changes with density, but it will take a little work.

At the lower left corner of the Airfoil View Panel you will see an output value of the air density.  As you change the altitude, this value will change. Let's do another little experiment:

Set the Altitude to 5800 ft. The Density is then 0.002 slugs/cubic ft.

Set the Airspeed to 100 mph, Angle to 5 degrees, Thickness = 0.5, Camber = 0.0.

This produces 1317 pounds of lift force.

Now let's increase the altitude while watching the density output.

We're shooting for a value of Density equal to 0.001 slugs/cu ft -- exactly half the previous value.

WHAT  IS  THE  NEW  VALUE  OF ALTITUDE?

WHAT  IS  THE  NEW  VALUE  OF LIFT?

HOW IS THIS RELATED TO THE OLD LIFT VALUE?

Looks like an Altitude of around 26,850 ft gives the desired Density  = 0.001.

The lift is then 658 pounds -- almost exactly half of the lift at 5,800 ft (Density = 0.002)

-->  Halving the density cuts the lift in half.  <--

Let's do one more check -- increase the Altitude until Density = 0.0005.

An Altitude of around 43,210 ft gives the desired Density = 0.0005.

The lift is then 329.3 pounds -- almost exactly one-fourth of the lift at 5800 ft.  (Density = 0.002)

-->  Quartering the density cuts the lift by one quarter.  <--

This is the old linear relationship again.  So we have seen that

•	Lift = constant  x  Density  <-- a linear relation

And the Density depends on the altitude in a more complicated way.

Well, that leaves only the airfoil thickness to look at.  In the previous lesson we noticed that lift increases with increasing airfoil thickness.  So let's set:

Airspeed  = 100 mph

Altitude  =   0 feet

Angle     = 5.0 degrees

Thickness = 0.5

Camber    =   0

Area      = 100 sq ft

This gives a symmetric airfoil generating 1566 pounds of lift.

If we push the "Thickness" button on the Plottter Control Panel below the "Lift vs" button, we see that the plot of lift versus thickness is not linear, but that lift increases as thickness increases.

[Our previous technique for finding linear relations by doubling and halving the input will not work here because the plot does not go through the point (0,0).  Near zero thickness (flat plate) there is still a lift value].  OK, one final check -- let's create the lift on the airfoil through Camber instead of through Angle of attack.

Change the Angle to 0 and the Camber to 0.5  This gives a curved airfoil generating 3963 pounds.

WHAT HAS HAPPENED TO THE LIFT CURVE IN THE PLOTTER WINDOW?

It's still fairly linear, BUT ...  lift now decreases with increasing thickness!

Maybe the plotter is wrong!

Let's check it by changing the value of thickness on the input panel.

HOW DOES  THE LIFT VARY WITH CHANGES IN THICKNESS?

For the curved airfoil, lift does indeed decrease with increasing thickness.  There is something much more complex going on here. If we take our curved airfoil and increase the angle of attack, watching the lift plot, we see that the variation can change from decreasing with thickness to increasing with thickness. The fact that both camber and thickness are involved together indicates that the explanation for this behavior will be found in more detailed studies of airfoil geometry.  So what have we learned in this little exercise?

1) The change of lift with thickness (airfoil geometry) is complex and will require some more study.

2) Our initial conclusion about how lift changes with thickness was correct for the conditions we were considering (symmetric airfoil), but we didn't consider enough changes in conditions!

-->  Good engineers must be thorough!

Let's summarize our results:

•	Lift = constant x angle (for small angles)

•	Lift = constant x area  (different constant)

•	Lift = constant x camber

•	Lift = constant x airspeed squared

•	Lift = constant x density  (density depends on altitude)

•	Lift depends on geometry of the airfoil  (thickness + camber)

So, there are some factors which are rather easy to figure out and some that will require more investigation.

Back to the FoilSim Lessons Page

Click here to go on the next lesson: Flow Field Details


Flow Field Details

We are now going to explore some details of the flow around an airfoil.  We will be using the input sliders and boxes located at the lower left and will be watching the Airfoil View window and the Plotter View window.  We will also be using the probe on the Plotter Control Panel to look at the flowfield.  To start, let's set some initial input conditions (you can also click the Reset button):

Airspeed  = 100 mph

Altitude  =   0 feet

Angle     =   0 degrees

Thickness = 0.5

Camber    =   0

Area      =   1 sq ft

This gives a symmetrical airfoil pointing into the wind and generating no lift.

In the Airfoil View Panel, the flow goes from left to right.  The airfoil shape is colored white.  Over the top of the airfoil, the streamlines are colored green, while under the bottom they are colored yellow.  (There is no significance to the length of these lines -- they are "chopped" just to let you know which way the flow is moving, and they move a little faster at higher speeds for a visual cue.)  The white line that hits the nose of the airfoil and leaves the back is called the "stagnation" streamline because this comes to rest at the leading and trailing edges.  While the stagnation line appears to flow through the airfoil, the front stagnation line actually splits at the airfoil leading edge, flows around the surface top and bottom, and rejoins at the trailing edge.  Streamlines have several special properties.  The velocity of the flow is always along a streamline, which means that no flow can cross a streamline.  Between any two streamlines, the amount of flow is a constant since no flow can cross the line.  Along a streamline we can use Bernoulli's equation to relate pressure and velocity.  To refresh your memory:

•  Pressure  +  0.5  x  density  x  velocity squared  =  constant    (Bernoulli's Equation)

Now, let's set up the plotter window.  Let's first push the "Speed at Surface" button on the Plotter Control Panel.  All of the additional buttons which we used before will disappear and the plot in the view window will be a curved line. On the lower axis you will note the words "Front" and "Rear" which gives the location on the airfoil.  On the vertical axis will be the value of the Speed.

The green line which appears here corresponds to the "green" upper part of the flowfield in the view window, while the yellow line corresponds to the "yellow" lower part.  For this symmetric airfoil, the velocity is the same over the top and bottom and the plots of velocity fall along the same line.  There are some interesting things to note in this plot.

1)  The velocity is zero (stagnated) at the leading and trailing edges.

2)  While the airspeed is 100 mph, the velocity over the upper surface appears to be greater than 100 mph. (Approaching 125 mph)

To verify this result, let's turn on the probe by clicking the "Activate Probe" button on the Probe Control Panel.  On the View panel, you will see a red dot connected by a white line to the top of the panel.  This gives the location, relative to the airfoil, of our probe.  You can move this probe through the flowfield by using the sliders on the Probe panel -- up/down and left/right.  As you move the slider, the probe location will change, and the speed readout will change on the probe panel.

This gives the value of the selected flow variable at the location of the probe.  By default the selection is the speed, but you can change it to measure the pressure by clicking once anywhere on readout.  Make sure, for now, that the readout says "Speed."  Move the horizontal slider as far to the left as possible.  This gives the speed far upstream.

WHAT IS THE UPSTREAM AIRSPEED?

Now move the probe horizontal slider near the center.  Do you see the probe in the Airfoil View window?

DID THE SPEED INCREASE OR DECREASE?

Slide the probe from the left part of the view window to the right using the horizontal slider.  Notice what happens to the Probe Speed readout.

WHAT HAPPENS TO SPEED?

You should see the speed initially decrease, then increase, as you move over the thickest part of the airfoil, then slowly decrease as you head to the back of the airfoil. If the slider is pushed all the way to the right, the speed should return to the freestream value of 100 mph.  This same variation in speed is seen on the plotter window.  From the leading edge, the speed increases from zero to a maximum near the thickest part of the airfoil, then decreases to near the trailing edge.  Now, let's change the angle of attack to 10 degrees, generating a little lift.

WHAT HAPPENS IN THE PLOTTER WINDOW?

The green and yellow lines now split.  The speed over the top of the airfoil is far different from that under the bottom.  The zero speed point is no longer at the very front of the airfoil, but moves downstream a short distance.  The same feature can be seen in the view window as the front stagnation line hits farther back on the airfoil.  The plotter window shows us that the speed over the top (green) is higher than that under the bottom.  The maximum speed now approaches 200 mph over the top, which you can verify using the probe.  On the upper surface, the speed accelerates from the leading edge to the maximum, then slowly decreases as you move to the rear.  On the bottom (yellow) surface, the flow stagnates near the front, then gradually speeds up toward the rear.  If we vary the airspeed on the Input Panel, we see the levels of speed change in the plotter; but the general features remain the same.  Reset the airspeed to 100 mph, then click the "Surface Pressure" button on the Plotter Control Panel.

The plotter now displays the pressure over the airfoil surfaces: green for the top and yellow for the bottom.

You should see two distinct lines.

WHICH ONE IS HIGHER?

Pressure is a force per area. Since the area of the top and bottom surfaces are the same, the forces on the top and bottom depend on the pressure.

WHICH SURFACE HAS THE HIGHER FORCE?

Since the forces are not equal, there is a net difference in force pushing up from the bottom.  This net force is the Lift of the airfoil.

If you set the Angle back to 0 on the input panel, you will notice that the green and yellow pressure lines fall exactly on each other.

--> No difference in pressure --> No Lift.

If you put in a negative value for Angle of attack, you will see the green upper surface pressure is greater than the yellow lower surface pressure.  We then have negative lift -- a net force pushing down from the upper surface.

In general, the greater the difference between the lines of the surface pressure plot, the greater the magnitude of the lift force.  And the force will be in the direction of the yellow line.  (If it's on the top, we have lift -- if it's on the bottom we have negative lift).  Once you become familiar with the surface pressure plots, you can explain most of the effects on aircraft lift which we previously encountered!  For example, set:

Airspeed  = 100 mph

Altitude  =   0 feet

Angle     =  10 degrees

Thickness = 0.5

Camber    =   0

Area      =   1 sq ft

Now change Airspeed to 250.

WHAT HAPPENS TO THE PRESSURE PLOT AND THE LIFT?

Now change the Altitude to 30,000 feet.

WHAT HAPPENS TO THE PRESSURE PLOT AND THE LIFT?

Now increase the Area to 100 square feet.

WHAT HAPPENS TO THE PRESSURE PLOT AND THE LIFT?

Kind of a trick question!!

The amount of lift equals the difference in pressure times the area. While the difference in pressure has stayed the same -- the area increased, so the lift force increases.

Now set the Thickness to 0.25.

WHAT HAPPENS TO THE PRESSURE PLOT AND THE LIFT?

Finally, set:

Airspeed  = 250 mph

Altitude  =   0 feet

Angle     =   0 degrees

Thickness = 0.5

Camber    = 0.2

Area      =  10 sq ft

WHAT HAPPENS TO THE PRESSURE PLOT?

Change the Thickness to 0.8.

WHAT HAPPENS TO THE PRESSURE PLOT AND THE LIFT?

Now for some real fun!  Set the Angle of attack = -2.

WHAT HAPPENS TO THE PRESSURE PLOT AND THE LIFT?

So what have we learned?

•	The speed and pressure change over the surface of an airfoil.

•	Where the speed is high, the pressure is low; where the speed is low, the pressure is high.

•	The lift depends on the difference between upper and lower pressure times the area of the wing.

•	The overall magnitude and the difference decreases with altitude.

•	The pressure distribution changes with the shape of the airfoil and with the angle of attack.

•	Some interesting pressure distributions are possible with the right combination of shape and angle.

You now know enough to be dangerous!

You can use this program to design and study many different airfoils.

Go on to the next lesson: The Lift Coefficient.

Return to the FoilSim Lessons Page.


The Lift Coefficient

There is a rather clever way that aerodynamicists group information about airfoils.  We have seen that lift changes linearly with area, density, camber, and small angles, and as the square of the velocity. We have also seen that lift has a complex dependence on the airfoil geometry.

The thickness and camber are geometric properties of the airfoil cross-section, the area depends on the geometric chord and the span of the wing, the airspeed and density (altitude) depend on flight conditions, and the angle of attack sort of connects the airfoil geometry to the flight conditions.

Suppose that we collect all the previous information into one equation:

•  Lift = constant  x  (geometric stuff)  x  (flight stuff)  x  area  x  angle of attack

The constant here would be a collection of all the previous constants.

We know how the flight stuff changes:

•  Lift (flight) = constant  x  density   x   velocity squared

The geometric stuff (thickness and camber) will not change when we change flight conditions -- it will still be the same shaped airfoil regardless of altitude or speed.

So let's combine the geometric stuff and the angle of attack term into a new variable called the lift coefficient -->  Cl.  The original equation then looks like:

•  Lift = constant  x  Cl  x  density  x  velocity squared  x  area

The value of Cl will depend on the geometry and the angle of attack.

The "density  x  velocity squared" part looks exactly like a term in Bernoulli's equation of how pressure changes in a tube with velocity:

•  Pressure  +  0.5  x  density  x  velocity squared  =  constant     (Bernoulli's Equation)

The term "0.5  x  density  x  velocity squared"   is called the dynamic pressure.

We can use this idea in our lift equation by re-defining the value of the constant.

•  Lift = constant  x  Cl  x  dynamic pressure  x  area

Now one last trick -- let's just include the constant in the definition of Cl.

•  Lift =  Cl  x  dynamic pressure  x   area

To summarize:

•  Lift =  Cl  x  dynamic  pressure  x  area.

•  Cl depends on geometry, angle of attack, and some constant.

•  Dynamic  pressure  =  0.5  x  density  x  velocity squared.

SO WHAT GOOD IS ALL THIS??

Well, if we know the Cl for an airfoil and we know the flight conditions (dynamic pressure) and the area, we can determine the lift of the wing. (Designs the weight of an aircraft)

•  Weight = Lift = Cl  x  dynamic pressure  x  area

Or, the reverse,  for a known Cl and dynamic pressure we can determine how big a wing (area) we need to lift the weight of an aircraft.  (Designs the size of an aircraft)

•  Area  =  Lift  /  Cl  /  dynamic pressure

Or, for a known Cl and wing size (area) and weight of the aircraft, we can determine the dynamic pressure.  This would tell us the speed to fly for a given altitude or the altitude we could attain for a given speed.  (Sets flight conditions)

•  Dynamic pressure =  Lift /  Cl  /  area

And finally, if we could measure the lift of a wing and knew the area and dynamic pressure, we could determine the Cl.

•  Cl  =  Lift  / dynamic pressure  / area

This last example seems a bit obscure -- so let's try a little experiment.

Let's set the Angle to 5 degrees, Thickness = 0.5, Camber = 0.2.

Now let's say we have a large airliner flying at 250 mph, at 25,000 ft, with a wing area of 1000 sq ft.

WHAT IS THE LIFT GENERATED?

Looks like about 88,250 pounds.

Now, what is the Cl for this wing?

•  Cl  =  Lift / Dynamic pressure / Area

•  Dynamic pressure = 0.5  x  density  x  velocity squared

Get the density from the simulator (Density = 0.00107)

WHAT VALUE OF Cl DO YOU GET?

•  Dynamic pressure = 0.5 (0.00107) (250) (250) = 33.43

•  Cl = 88250 / 33.43 / 1000 = 2.64

Now let's compare this to a radio-controlled model airplane flying at 35 mph, at 100 ft, with a 10 ft wing area.

WHAT IS THE LIFT AND THE DENSITY (NEEDED FOR DYNAMIC PRESSURE)?

•  Lift = 38.43 pounds,  Density = 0.00237

WHAT IS THE Cl FOR THIS MODEL AIRPLANE?

•  Dynamic pressure = 0.5 (0.00237) (35) (35) = 1.4516

•  Cl = 38.43 / 1.452 / 10 = 2.64

Hey, that's the same number that we got for the full sized airplane at a different altitude and speed!!!

Let's try a small wind tunnel model -- 50 mph Speed, 0 ft Altitude, 1 sq ft Wing Area.

WHAT IS THE LIFT AND THE DENSITY (NEEDED FOR DYNAMIC PRESSURE)?

•  Lift = 7.87 pounds,  Density = 0.00238

WHAT IS THE Cl FOR THIS WIND TUNNEL MODEL?

•  Dynamic pressure = 0.5 (0.00238) (50) (50) = 2.975

•  Cl = 7.87 / 2.975 / 1 = 2.64

The same number again!!  What's going on here?  We have different size objects, at different speeds, at different altitudes, and different dynamic pressures. But they all have the same Cl.

While we have been changing the size of the airplane, the speed, and the altitude, we have not changed the basic geometry of the airfoil.  For all three cases, the Angle was 5 degrees, the Thickness = 0.5, and the Camber = 0.2.

Remember that we defined the Cl to include geometry information and the angle of attack information.  So the Cl for an airfoil remains the same for all kinds of flight conditions and sizes of aircraft.

WHY IS THIS IMPORTANT?

This rather simple fact makes wind tunnel testing possible for aircraft lift.

We have seen that we can determine the Cl at wind tunnel speeds, altitudes, and sizes and get the same answer that we would get for a full size aircraft at real flight conditions.  Once we determine the Cl, we can set new flight conditions or design other sized aircraft and know what the lift will be.  The conditions which we picked for this problem contain a combination of camber, thickness, and angle of attack.  Remember in the previous lesson that it was difficult to determine how an airfoil's lift varied with this combination of variables (sometimes the lift increases with thickness; sometimes it decreases depending on the camber).  Now, if we can determine the Cl, either through wind tunnel testing or analysis, we can describe this relationship.

Return to the FoilSim Lessons Page.

Back to FoilSim Contents.


Airfoil Panels

 The Airfoil View Panel provides a schematic drawing of the airfoil problem.  This schematic displays the airfoil shape and the streamlines of flow around the airfoil.  Flow moves from left to right.  The airfoil is colored white.  The green streamlines flow over the top of the foil and the yellow pass below.  The white lines indicate the stagnation streamlines which end on the airfoil surface.

 The Airfoil Input Panel controls the shape and attitude of the airfoil displayed in Airfoil View Panel.  You can vary all the parameters which affect the lift of an airfoil using the input boxes and sliders.

•	Airspeed - Speed of the air in the simulated tunnel

•	Altitude - Height of the tunnel above mean sea level

•	Angle - Angle of attack of the airfoil

•	Thickness - Thickness of the airfoil

•	Camber - Curvature of the airfoil

•	Area - Wing Area

You can vary the display by using the sliders on the Airfoil View Panel.  Use the In and Out to zoom the size.  The position can be changed with the Left/Right and Up/Down sliders.

As the angle, thickness, or camber are varied, the geometry in the Airfoil View Panel is changed and the value of lift is computed and displayed in the output box and gauge at the bottom.  As the airspeed is increased, the lift will change.  Varying the altitude changes the local density and the lift generated by the wing.  The units for the various parameters are given to the right of the sliders.

The Lift of an airfoil can have a very wide range of values.  To obtain the value of the lift, take the number given in the output box at the left and multiply by the number to the right of the gauge.  The multiplier is always shown in powers of 10.

For a given altitude, the current Density, Pressure and Temperature are shown at the bottom of the Airfoil View Panel.

Other Topics:

•	View a General Description of FoilSim Operation.

•	Use the Plotter Control Panel to record the variation of lift, pressure, and speed around the airfoil.

•	Explore the flowfield by using the Probe Control.

•	Print and Save the data.


General Description
General Description of FoilSim Operation

FoilSim is an interactive flow simulator which determines the airflow around various shapes of airfoils.  The displays are grouped into windows or panels.  These panels provide input information for the calculation routines that produce the displays.  There are four main input panels:

•	Airfoil Input and View Panels

•	Plotter Input and View Panel

•	Probe Control

•	Baseball Panels

There are several conventions which have been used throughout the graphical user interface (GUI) to assist the user.

Airspeed:

On the Input Panels, information can be sent to the program in two ways: using the slider or the input box on the left of the slider.

To use the Slider:

1) click the mouse pointer on the arrows at the ends of the slider,

2) click the mouse pointer anywhere between the slider and the arrow, or

3) drag the slider with the mouse.

The value of the slider is shown in the input box to the left of the slider.

Using the Input Box:

To more accurately specify the input value, type the value into the input box.  Simply click in the input box, delete the original value using the "Delete" or "Backspace" key, type in the new value, and press the "Enter" or "Tab" key when finished.  The button on the slider will move corresponding to the value typed in the box.  The cursor will then move to the next input box.

Units

All the input values have dimensions or units associated with them.  You can choose to work in Metric units or English units by clicking the Units button at the bottom.  The current setting is shown on the Units button.  The units selected will appear to the right of the input slider.

Radio Buttons

On some panels there are groups of radio buttons with a small black dot indicating the chosen option.  To change your selection, click on the chosen button.

Context Sensitive Help

To access the help function, simply press the F1 key at any time.  The appropriate help page will be displayed for the window or panel where the cursor is located.

Ending the Program

Clicking the "Exit" button will end the FoilSim program.

Click here for Help on navigating this program.


Baseball Panels

If you click the "Play Ball" button at the bottom of the screen, the view panel will show a schematic drawing of the baseball flow problem.

 The Baseball View Panel displays the ball and the streamlines of flow around it as viewed from above, looking down.  Home plate is to the left and the pitcher's mound is to the right.  The flow appears to move from left to right as the ball moves through the air.  The green streamlines move around the right side of the ball as viewed by the pitcher while the yellow streamlines move to the left.  At the bottom of the panel are two buttons to set the pitcher to either a Right Hander or a Left Hander.  The Up/Down, Left/Right and Out/In sliders let you change the position and size of the baseball view.

 The Baseball Input Panel below the View Window is used to control the conditions of the pitch.  You can select the altitude of the location; this affects the air density and the amount of force that can be generated on a curveball.  Several locations are given as selection buttons below the altitude input.  The user can vary the speed of the pitch and the spin put on the ball by using the input boxes and sliders.  To move the slider, place the cursor along the slider and click the left mouse button.  The value of the slider is shown in the input box.  To more accurately specify the input value, type the value into the input box.  Simply click in the input box, delete the original value, type in the new value, and press the "Enter" or "Tab" key when finished.  The button on the slider will move corresponding to the input box value.  For the spin input, just click on the red words (Curveball, Fastball, Screwball) located below the slider and the appropriate spin will be set on the slider.

As the speed is increased, the flowing streamlines in the view window will appear to speed up.  As spin is put on the ball, the view window will show the ball's rotation and the (slight) deflection of the streamlines.  Spinning the ball creates a side force ("Magnus" effect) which causes the ball to curve in flight.  The magnitude of the side force is shown in the output box and horizontal gauge at the bottom of the input panel.  The direction is color-coded to correspond with the view window.

 The Plotter View Panel displays the pressure or speed variation around the ball.  Once again, the color of the lines corresponds to the surfaces shown in the Baseball View Panel.  Notice that the lines separate when a spin is put on the ball.  You can look for these speed differences using the airspeed probe with the Probe Control Panel.

 For the baseball problem a special plotter option has been included.  Pushing the "Ballpark" button on the Plotter Input Panel will change the plotter display to the view of a baseball infield.  Using this display, you can see the trajectory of a thrown pitch for the conditions given in the input panel.  Putting spin on the ball causes the trajectory to curve in the Plotter Window.  The trajectory is displayed as a series of dots which show the ball's position at each 0.05 seconds.  The slower the pitch, the greater the number of dots which appear.  Adding up the number of dots and multiplying by 0.05 seconds will give the time it takes to reach the plate.  You may vary the Release Point of the pitch and the Release Angle of the pitch by using the sliders in the Plotter Input Panel.

You can explore the flowfield around the ball by using the Probe Control Panel located in the Plotter Input Panel.

Ready to play!  Go to the Baseball Lessons.


Plotter Panels

The Plotter is composed of:

•  Plotter Input Panel 	Controls what to plot

•  Plotter View Panel 	Displays the plot of data

Plotter Input Panel Choices

Surface Pressure or Speed at Surface

These choices display plots of pressure or airspeed along and on the airfoil surface.  There are two lines plotted.  The green line corresponds to the values over the top surface of the airfoil, while the yellow line corresponds to the lower airfoil surface.  These lines correspond to the colors shown in the Airfoil View window.  In some cases the two plotted lines will fall on top of each other and you will see only the green line.

Lift vs

Clicking Lift vs lets you generate plots of lift as a function of the parameters listed in the radio buttons:
Airspeed	Altitude
Thickness	Angle of attack
Camber height 	Wing area

The plot is automatically rescaled and labeled as you change your selection.  You can change any of the Airfoil Input Panel parameters at the lower left, and the variation of lift with this variable will be displayed in the Plotter View Panel.

Plotter View Panel

This  is a sample plot of speed from the Front to Rear of the airfoil.  The green curve represents the speed along the upper surface of the airfoil, while the yellow curve is along the lower surface.  These are the same colors used in the Airfoil View Panel for the streamlines above and below the airfoil.  The dip shown here in the lower curve, near the front, represents the stagnation point.

Other Topics

•	Explore operation of the Baseball Panels.

•	Print and Save the data.

•	Vary the input parameters on the Airfoil Input Panel

•	Explore the flowfield by using the Probe Control


Probe Panel
Probe Control Panel

You can insert a flow probe into the airstream by clicking on the Activate Probe check box on the Probe Control Panel.  The probe appears on the Airfoil View Panel as a red dot on the end of a white stick.  The probe can be used to monitor flow conditions (speed and pressure) near the airfoil.

Using the vertical and horizontal sliders on the Probe Control Panel, you can move the probe through the flow domain streamlines around the airfoil.  The vertical slider picks a value on a streamline, while the horizontal slider moves right/left along a streamline.  Click once anywhere in the speed/pressure readout to change the probe display between speed and pressure.  The value and units of the probe variable appear on the readout.

Other Topics:

•	Vary the input parameters on the Airfoil Input Panel.

•	View variations in lift, pressure, and speed around the airfoil with the Plotter Control Panel.

•	Print and Save the data.


Theory

For further reading on classical  aerodynamics consult:

"Incompressible Flow"

Panton, R.L., Wiley, 1984.

"The Aerodynamic Design of Aircraft"

Kuchemann, D., Pergamon, 1978.

"Foundations of Aerodynamics"

Kuethe, A.M. and J.D. Schetzer, Wiley, 1965.

"Hydrodynamics"

Lamb, H., Dover, 1945.

"Theoretical Hydrodynamics"

Milne-Thomson, L.M., MacMillan, 1968.

Jump to FoilSim Contents.


Available Software

VU-DUCT version 4.1

Educational tool to design or analyze subsonic wind tunnels or ducts. Incompressible, inviscid analysis for rectangular, square, or circular cross-sections, blow down or closed loop tunnels. Contains moving probe. Multiple input and graphical output combinations. Warning flags for violations of design assumptions.

VU-TURBO version 5.1

Educational tool to design and analyze a simple turbojet engine, turbojet with afterburner, or two spool turbofan engine. Examination tool included. One dimensional Brayton cycle analysis with flight conditions, sizes, efficiencies, and materials limits specified interactively by the user. Thrust, SFC, and various diagnostic outputs presented graphically. T-s, p-v plots plus interactive plotter. Printed output and restart file.

VU-INLET version 5.0

Design/Educational tool to predict flow conditions in external and mixed compression,supersonic, rectangular inlets. Solves the inviscid 1-dimensional equations from NACA 1135 for oblique shocks, expansion fans, normal shocks, and reflected oblique shocks. Includes subsonic duct model and inlet bypass, and computes normal shock position with change in engine airflow. Computes spillage mass flow and drag, and flags unstarts.

VU-SHOCKS  version 4.1

Educational tool derived from VU-INLET which displays compressible aerodynamics for three flow problems: single compression wedge, two opposing wedges, or two wedges in series. Solves for intersecting and reflecting shock waves. Includes printed output, multiple types of graphical output and question and answer feature to lead students through interesting problems in compressible aerodynamics.

VU-FOIL  version 1.7

Educational tool to solve for 2D, inviscid, incompressible flow about airfoils. Shapes include flat plate, elliptical cross-section, and Joukowski family of airfoils.  Student can vary thickness, camber line, and angle of attack. Performs conformal mapping from flow around a circular cylinder with circulation. Includes multiple types of graphical output, flow probe, and  lessons feature.

Flow Calculators version 2.4

Small calculators to compute multiple flow problems. No graphics. Currently configured for isentropic flows, oblique shock, expansion fan, normal shock relations,Rayleigh flow, Fanno flow, and standard day atmospheric data.  Multiple combinations of input accepted. NACA 1135 in your hand.

FoilSim  version 1.0b

Educational package derived from VU-FOIL, but intended for high school students.  Computes the lift around a basic airfoils, or a spinning baseball. Students can interactively vary any of the design parameters. Output in either English or Metric units. Contains interactive lessons. Available in either Unix or PC (Windows NT, Windows 95, Windows 3.1, and Macintosh).

Coming soon ............

EngineSim

Educational package derived from VU-TURBO, but intended for high school students. Allows students to interactive design, wind tunnel test, and flight test turbojet and turbofan engines. Will be available in either Unix or PC versions.

VU-DIAMOND

Educational tool derived from VU-SHOCKS and VU-MOC which displays compressible aerodynamics for a diamond airfoil in a wind tunnel.  Intended for undergraduate study the desktop wind tunnel will include multiple types of graphical output.

VU-MOC

Interactive method of characteristics solver.  Allows students to design rocket nozzles interactively.  Intended for undergraduate study.

Visit our World Web Sites where all codes are available

For X-based Unix machines, SGI, IBM, SUN, DEC-Ultrix, HP and PC-Linux:

http://www.lerc.nasa.gov/WWW/IFMD/vusoft.html

This MS-Windows version of FoilSim and a Macintosh version are available at:

http://www.lerc.nasa.gov/WWW/K-12/aerosim

8 Jan 98


Units

The current unit system is displayed on the Units button at the bottom of the display.  Clicking the button will change the displayed units between:

Units:Metric	Units:English

Length	Meters	Feet

Velocity	Kilometers/hour	Miles/hour

(km/hr)	(mph)

Force	Newtons	Pounds

Pressure	Newtons/square meter	Pounds/square inch

(Pascal)

Density	Kilograms/cubic meter	Slugs/cubic ft

Temperature	Degrees Celsius	Degrees Fahrenheit

Jump to FoilSim Contents

Help on navigating


LF1
What is the Value of Lift?

The lift should be 0.0. - No Lift - The flow in the airfoil view window should be moving from left to right around a symmetric airfoil.  A symmetric airfoil (one whose top surface is shaped identical to the bottom surface) will generate no lift if it is pointed directly into the flow.


LF2
What Happens to the Lift?

Nothing!!  The flow goes by the airfoil faster, but a symmetric airfoil will not generate lift if it is pointed directly at the flow for any speed.


LF3
Still nothing!


LF4
Finally!   Lift is increased from nothing to 7.29 x 100 = 729 pounds.


LF5
The lift is now 1.09 x 1000 = 1090 pounds.  Lift has increased by 361 pounds.


LF6
It drops down to 948 pounds, but this is still a pretty large number.


LF7
How Much Force is Generated on the Door?

About 1780 pounds.  That's enough to lift about 10 averaged sized adults!  No wonder tornados are so bad!


LF8
How Much Force is Generated on the Sheet?

Force (Lift) is increased to 2036 pounds.  This would lift a small car!


LF9
Is There Enough Lift Generated to Keep our Plane Flying?

No!  Only 5,670 pounds of lift generated and our plane weighs 10,000 pounds.


Help
Help on Navigating This Program

Click on any of these buttons shown in the bar at the top of each page:

•	Contents will return to the starting page (Windows 3.x) or to the FoilSim Help Topics (Windows 95/NT).

•	Back will take you to the previous page.

•	Search will let you look over a list of topics in the help file.

•	Print will print the current help file topic.

•	<< and >> let you browse the pages in the help file.

•	Copy will copy the page to the clipboard.

•	Glossary will list the terms that are defined.

The keyboard buttons labeled "Page Down" and "Page Up" will scroll the text one page at a time.  For fine control, you can also use the grey scroll control bar at the right.  To make the text move down one page, place the cursor below the slider button and click the left mouse button.  To make the text move up one page, place the cursor above the slider button and click the left mouse button.

Click on any dashed underlined text for a pop-up definition.

Click on any solid underlined text to jump to another page on that topic.

To change the size of the Help and Lessons windows, drag the sides with the mouse.  Move the mouse pointer to the border until you get a two headed arrow. Hold down the left mouse button, drag the edge of the window to the desired size, and then release the mouse button.

To return the FoilSim settings and windows size to the initial values, click the Reset button at the bottom of the window.

More Information on:

How to Print and Save Data

How to change Units

General Description of FoilSim


LF10
Is There Enough Lift to Keep Our Plane Flying?

There are now 10,080 pounds of lift generated which will keep our 10,000 plane in the air.  (Actually it will start to rise even higher since the lift is greater than the weight).


LF11
What Happens to the Lift?

Lift increases from 10,080 pounds to 15,130 pounds - about a 50% increase!  The shape of the airfoil really didn't appear to change very much but this is a very big change in lift.


LF12
The lift goes from 5616 pounds to 8429 pounds - the same large increase which we saw at the 25000 foot condition. Again, the airfoil shape doesn't appear to change very much but there is a large increase in the lift.


FoilSim Lessons

The FoilSim lessons are a special utility linked to the program for educational purposes to highlight some aspect of basic airfoil theory.  Students use the FoilSim program to solve exercise problems in this Windows Help File.  To get started, read the General Information on Aerodynamics and then proceed to the lessons.  If you need help on navigating these pages click here.  Click here for a General Description of how to use the FoilSim program.

Lessons

•	Factors That Affect Lift

•	How Lift Changes

•	Flow Field Details

•	The Lift Coefficient

•	Baseball Lessons


HLC1
WHAT IS THE NEW VALUE OF LIFT AND HOW IS THIS RELATED TO THE OLD VALUE?

The new value is 1253 pounds  which is just about double the old value.


HLC2
WHAT IS THE NEW VALUE OF LIFT AND HOW IS THIS RELATED TO THE OLD VALUE?

The new value is 313.6 which is almost half the value at 2 degrees


Printing & Saving Data

There are three ways to capture and save the data from the program by clicking these buttons on the bottom of the FoilSim screen:

•  Save Data  -  Saves both images and data to your local disk.  Images of the Plotter View Panel  and Airfoil View Panel are saved into Windows bitmap images that can be edited or printed later using a Windows bitmap editor like MS-Paint.  Data used to create the Plotter View Panel plot is saved to a file that can be printed or loaded into a spreadsheet.  Data is saved in a comma separated variable (CSV) format that is recognized by most spreadsheet programs.

•  Print Data  -  Sends a printout of the current FoilSim settings, with images of the currently displayed Airfoil View Panel and Plotter View Panel, to your printer.

Obtain Help on navigating FoilSim.

Jump to FoilSim Contents


The Screwball

(Click the Play Ball button in the lower left corner if the baseball isn't already on the screen.)

Let's throw our third pitch, the Screwball.

•  HOW DOES A SCREWBALL DIFFER FROM A CURVEBALL?

To find out, watch the baseball as you move the Spin slider back to the right.  Stop a few places along the way, both to the right of Fastball and to the left of Fastball.

•  WHAT DO YOU SEE HAPPENING?

Yes, the Screwball rotates in the opposite direction of the Curveball.  To note other changes, be sure you have clicked on Surface Pressure in the Plotter Control Panel and watch the graph as you slide the Spin slider from far left to far right and then back.  Do this several times.

•  WHAT HAPPENS TO THE GREEN AND YELLOW LINES?

They change positions.  This means that the high pressure side of the ball is reversing.  Keep sliding the Spin slider back and forth and watch the Side Force bar.

•  HOW DO THE FORCE READINGS CHANGE?

They go from positive values for the Curveball to negative values for the Screwball.  This means that the Side Force being exerted is changing directions.

•  MAKE A PREDICTION ABOUT THE PATH OF THE SCREWBALL

Now click on Ballpark button on the Plotter Control Panel and view the path of your pitch to check your prediction.  Were you right?

It's time for the next lesson  -  Baseball and Altitude.

Or go back to Baseball Lessons.


Pressure and The Curveball

(Click the Play Ball button in the lower left corner if the baseball isn't already on the screen.)

We want to examine how the spin with which a baseball is thrown relates to the pressure of the air flowing around the surface of the ball.  Be sure you have chosen Speed at Surface on the Plotter Control Panel, Cleveland on the Baseball Input Panel, and Left Hander on the Airfoil View Panel.

Now we are ready to throw our second pitch.  We want to throw a Curveball, so slowly slide the Spin slider all the way to the left or click the word Curveball.

•  WHAT ARE THE CHANGES YOU SEE TAKING PLACE?

•  WHAT HAPPENED TO THE SIDE FORCE AT THE BOTTOM OF THE INPUT PANEL?

One very important but slight change you may have noted on the Plotter View Panel is that the yellow and green curves are no longer on top of each other.  You can now see that the green curve is going higher than the yellow curve.

•  DO YOU THINK THIS MIGHT SOMEHOW BE RELATED TO THE FACT THAT WE NOW HAVE A SIDE FORCE?

Our graph is showing that the air stream on the right of the ball (green) is moving faster than the air stream on the left of the ball (yellow).

•  CAN YOU THINK OF A REASON WHY THIS HAPPENS?

The reason has to do with the little bit of friction between the surface of the spinning ball and the air adjacent to it.  As the ball rotates in the same direction as the air going by it (the right side), this friction drags the air along a little faster.  On the other side (the left) the ball is rotating against the air.  The friction causes the air on the yellow side to slow down a little.

That's fine, but it still doesn't explain the side force.  To do that, you need to select the Surface Pressure button on the Plotter Input Panel.

•  WHAT HAPPENS TO THE GREEN AND YELLOW LINES?

Do you see that the color of the MAXIMUM on the Surface SPEED plot becomes the MINIMUM on the Surface PRESSURE plot?  Click back and forth between the Speed at Surface and Surface Pressure buttons and watch what happens.

•  TRY TO STATE THE RELATIONSHIP BETWEEN THE SPEED OF THE AIR AT THE SURFACE OF THE BASEBALL AND THE PRESSURE IT EXERTS.

At this point you should have derived the relationship that actually causes the ball to curve.

--->   AS THE AIR MOVES FASTER, IT EXERTS LESS PRESSURE.   <---

In the non-rotating Fastball, the air speeds up equally on both sides of the ball (remember the curves were on top of each other?).  So the reduced pressure on both sides is the same, and there is no net side force.  Therefore, the Fastball goes straight.

When the ball spins, the slower moving air on one side has more pressure than the faster moving air on the other side.  The difference in pressure "PUSHES" the ball into a curved path.  This difference in pressure creates the Side Force.

It's time for the next lesson  --  The Screwball.

Or go back to Baseball Lessons.


Play Ball

Everything that you have learned about flow around an airfoil also applies to flow around other shapes - like a baseball!

 In this little simulator you can use the input sliders and buttons to pitch at various locations (different altitudes affect lift!) and throw different pitches.  A curveball works pretty much like an airfoil to produce the curve.  But instead of changing the pressure top and bottom by angle of attack or through camber - the pressure is changed because the ball spins.  It's called the "Magnus Effect" and some of the baseball lessons will lead you through this.  If you have had enough of lessons, you can just play with the package.  If you push the "Play Ball" button at the bottom left and then the "Ballpark" button on the Plotter Control Panel, you can try to get a curve ball over the plate.  There are more variables to consider - speed of the pitch, spin on the ball, release point, and angle - but that's why they pay them the big bucks!!!

Baseball Lessons

•	Baseball Speed

•	Pressure and the Curveball

•	The Screwball

•	Baseball and Altitude

Description of how to use the Baseball Panels

Enjoy !


Baseball Speed

Let's examine how the speed at which a baseball is thrown relates to the speed of the air flowing around the surface of the ball.  To begin, choose Speed at Surface on the Plotter Control Panel and choose Cleveland on the Baseball Input Panel.

Now we need to set the conditions for our first pitch.  We want to start by throwing a FASTBALL.  This should already be set with the SPIN slider centered on Fastball and the SPIN value reading 0.  If not, click on the word Fastball.

Since we have the ability to throw some serious heat, begin moving the Speed slider slowly to the right toward 100 mph.  On the view of the ball (which is a top view), notice that the green airstream to the right of the ball and the yellow airstream to the left of the ball start moving faster as the ball speeds up.

•	WHAT OTHER CHANGES DO YOU SEE TAKING PLACE AS YOU SPEED UP?

One change that is very obvious is that the curve on the Plotter View Panel grows higher and higher as you move the Speed slider.  This shows that the ball is pitched faster.  The air at the surface of the ball moves around the ball faster relative to the air that is a little farther from the ball that is going in the same direction.

Also, a less obvious thing to note is that there is only a yellow curve in the Plotter View Panel which shows the speed of the air going around the left side of the ball.  What about the air going around the right side of the ball?  Where is the green curve for the green air?  Why only one curve?  The answer is that the green curve is there, but it is exactly under the yellow curve!  In other words, the speeds of the airstreams on both sides of the ball are identical.  This is an important point for later in our discussion.

Now move the Speed slider all the way to the left (very slowly!).  At the bottom of the Baseball Input Panel is a readout for the SIDE FORCE, a force that would act to push the baseball left or right (curve).  Write down the value when the speed is 35 mph.  Now move the Speed slider to a position near 50 mph and again record the SIDE FORCE reading.  Finally move to 100 mph and again record the SIDE FORCE on the ball.

•	HOW DO THE SIDE FORCES COMPARE?

For all speeds, the side force is zero.  The speed was identical on both sides of the ball.

•	WHAT WOULD YOU PREDICT FOR THE TRAJECTORY OF A FASTBALL WITH NO SPIN?

To verify your prediction, click on the Ballpark button on the Plotter Control Panel.

Now click back to Speed at Surface.  With the Speed slider at 100 mph, look again at the graph in the Plotter View Panel.

• 	WHERE ON THE BALL IS THE VELOCITY AROUND THE BALL THE LEAST?

• 	WHERE IS IT THE GREATEST?

• 	WHAT DO YOU CONCLUDE ABOUT THE SPEED OF AIR MOVING AROUND AN OBJECT AT THE  SURFACE?

The air moves faster the farther its path is changed.  The airstream exactly in front of the ball slows down as it approaches the ball and stagnates as it hits the front of the ball.  As it is deflected out of its path by the shape of the ball, it moves faster and faster, reaching a maximum midway around the ball at the point of its farthest deflection.  Then it starts to slow again until it reaches the rear of the ball, where it is back to its original path and back to the same speed as the rest of the nearby air.

It's time for the next Lesson  -  Pressure and the Curveball.

Or go back to Baseball Lessons.


Baseball and Altitude

(Click the Play Ball button in the lower left corner if the baseball isn't already on the screen.)

We now want to examine how the altitude at which a baseball is thrown changes our results.  Note that we have three locations to choose from.  Set up these conditions:

Altitude:  700 feet (Cleveland)

Speed:     100 mph

Spin:        0  (Fastball)

Click Speed at Surface on the Plotter Control Panel

You should remember that the yellow line and the green line in the Plotter View overlap since the air accelerates around both sides of the ball at the same rate.

Now we are ready to see what happens if we go to a higher altitude where the air is less dense.  Click on Denver which is one mile high.  Did you notice that there was no change in the graph and the SIDE FORCE remains zero?

Let's try to do the same thing except view the effects of altitude on pressure.  Click back on Cleveland and choose Surface Pressure on the Plotter Control Panel.  What happens when you click onto Denver?  Are there any changes?

Note the values for the minimum of the pressure curve.  The net result is that the pressure at the minimum drops as the altitude increases.  Since the air becomes less dense as altitude is increased, there is less air to create the side force on the ball.  Pressure is not only a function of how fast the air is moving, but is also a function of the amount of air that can create the force.  Less air means less pressure.

Since the Side Force depends on the difference in pressures, we could expect a change in Side Force with Altitude.

Verify this last idea by setting a Screwball and then clicking back and forth between the locations and watching the Side Force horizontal bar change in value.  The higher the altitude, the less dense the air, the lower the pressure, and the lower the Side Force.

Finally choose Ballpark on the Plotter Control Panel and examine the effect of your pitch trajectory as you click back and forth between locations.  You can also see the effect at other altitudes by moving the Altitude slider on the Baseball Input Panel.  Move the slider and release the mouse button to see the effect.

•	PREDICT WHAT WOULD HAPPEN TO YOUR CURVEBALL IF YOU TRIED TO THROW IT FROM THE TOP OF MOUNT EVEREST.

To check your results, click on Mt. Everest and note what happens to the trajectory of the ball.

•	WHY DO YOU THINK THIS HAPPENED?

•	COULD YOU THROW A CURVEBALL ON THE MOON?  WHY OR WHY NOT?

•	COULD YOU THROW A SCREWBALL ON THE MOON?  WHY OR WHY NOT?

•	FROM WHAT YOU HAVE LEARNED SO FAR, IF YOU WERE MANAGER FOR A MAJOR LEAGUE BASEBALL TEAM, WHERE WOULD YOU WANT YOUR BEST CURVEBALL PITCHER TO PITCH?

•	IN WHAT CITY WOULD YOU WANT TO USE YOUR BEST FASTBALL PITCHER AND PUT YOUR CURVEBALLER ON THE BENCH?

Go back to Baseball Lessons.


HLC3
WHAT IS THE NEW VALUE OF LIFT?  HOW IS THIS RELATED TO THE OLD VALUE?

Lift is now 313.2 pounds - exactly twice the previous value.


HLC4
WHAT IS THE NEW VALUE  OF LIFT?  HOW IS THIS RELATED TO THE OLD VALUE?

Lift is now 78.3 pounds - exactly half the previous value.


HLC5
WHAT IS THE NEW VALUE OF LIFT?  HOW IS THIS RELATED TO THE OLD VALUE?

Lift is now 317.1 pounds - exactly twice the previous value. (except for roundoff !)


HLC6
WHAT IS THE NEW VALUE  OF LIFT?  HOW IS THIS RELATED TO THE OLD VALUE?

Lift is now 79.3 pounds - exactly half the previous value.


HLC7
WHAT IS THE NEW VALUE  OF LIFT?  HOW IS THIS RELATED TO THE OLD VALUE?

Lift is now 634.4 pounds

WHAT ??  -  Twice the previous lift would be 317.2  - this looks like four times the previous value


HLC8
WHAT IS THE NEW VALUE  OF LIFT?  HOW IS THIS RELATED TO THE OLD VALUE?

Lift is now 39.65 pounds


HLC9
WHAT IS THE NEW VALUE OF LIFT?  HOW IS THIS RELATED TO THE OLD VALUE?

Lift has gone down (as expected!)  to 1495 pounds.  That doesn't look like any easy multiple or fraction of the original 1540 pounds.


HLC10
WHAT IS THE NEW VALUE OF LIFT?  HOW IS THIS RELATED TO THE OLD VALUE?

Lift is now 1563 pounds. It went up but this again doesn't look like a nice ratio.


Beta Testers
FoilSim Beta Testers

This computer program is the result of a team effort by many groups at the NASA Lewis Research Center. The original Unix version of the program was developed by:

•	Tom Benson - NASA

•	John Eigenauer - RMS Information Systems

•	Roger Storm - Fairview Park High School

The UNIX version was converted to the MS-Windows operating environment by:

•	Bruce Bream - NASA

This MS-Windows version was also converted for operation on a Macintosh by:

•	Darryl Palmer - Cleveland State University

The program is part of the NASA Lewis' K-12 educational project and the Mobile Aeronautics Education Laboratory (MAEL) represented by:

•	Beth Lewandowski - NASA - K-12

•	R. Lynn Bondurant - NASA - MAEL

The airfoil lessons were developed by:

•	Tom Benson - NASA

The baseball lessons were developed by:

•	Roger Storm - Fairview Park High School

•	John Eigenauer - RMS Information Systems

The program was beta tested by members of Explorer Scout Post 630:

•	Julie Dudek - NASA Advisor

•	Judy Van Zante - NRC - NASA Advisor

•	Dale Van Zante - Iowa State - Advisor

•	David Larkin - NASA Advisor

•	Amita Danak - Parma Sr. H.S.

•	Phil Jones - Home Schooled

•	Cheryl Pokrywka - Magnificat H.S.

•	Rayshaun Williams - Villa Angela St. Joseph H.S.

•	Sonal Shah - Magnificat H.S.

•	Brad Klipan - Cuyahoga Hts. H.S.

•	Damen Forte - Cleveland Hts. H.S.

Additional assistance with content of this Help file provided by:

•	Carol Galica - Thigpen & Associates

•	Ruth Petersen - RMS Information Systems


FF1
What is the Upstream Airspeed?

It should be very close to the 100 mph setting on the airspeed slider.


FF2
Which Curve is Higher?

The yellow, or bottom, surface has the higher pressure. We probably could have predicted this from Bernoulli's equation.  If the pressure plus some velocity term is a constant, then as velocity goes down, the pressure goes up.  Since the bottom surface has the lower velocity, it must have the higher pressure.


FF3
WHICH SURFACE HAS THE HIGHER FORCE?

More force is on the bottom than on the top.


FF4
WHAT HAPPENS TO THE PRESSURE PLOT AND THE LIFT?

The difference between the lines increases and the lift goes up


FF5
WHAT HAPPENS TO THE PRESSURE PLOT AND THE LIFT?

Both the magnitude and the difference between the lines decreased and the lift decreases.


FF6
WHAT HAPPENS TO THE PRESSURE PLOT AND THE LIFT?

Lift goes up, but nothing happens to the pressure!


FF7
WHAT HAPPENS TO THE PRESSURE PLOT AND THE LIFT?

The lift goes down a little and you can see the pressure distribution (the shape of the pressure plot) change.


FF8
WHAT HAPPENS TO THE PRESSURE PLOT?

Well, this starts to get subtle.  The airfoil generates lift (about 990 pounds) and the plot shows a difference in the lines with the yellow on top - as expected.

But, the distribution of pressure, the shape of the plot is different than before.  The big differences in the lines now occurs toward the center and back of the airfoil, before, the big differences occurred at the front.


FF9
WHAT HAPPENS TO THE PRESSURE PLOT AND THE LIFT?

Lift goes down, and the pressure plot is modified.  The differences between the lines appears to become smaller, while the magnitude decreases slightly.  These changes in the pressure plot are very small as is the change in lift.


FF10
WHAT HAPPENS TO THE PRESSURE PLOT AND THE LIFT?

The lift goes down, but the pressure plot ....

The lines cross!  The front part of the airfoil is producing negative lift while the middle and back are producing positive lift.  The total lift on the airfoil ends up being the sum of these conflicting forces.  You could eventually find an angle of attack where the conflicting forces cancel each other and there is no lift.


Glossary

A

aerodynamicist

aerodynamics

airfoil

airspeed

altitude

angle

angle of attack

area

C

camber

chord

compressibility

E

equation

F

force

friction

G

geometry

L

lift

P

pressure

S

span

stagnation

stall

streamlines

T

thermodynamics

thickness

trajectory

turbulence

V

velocity

W

wind tunnel

wing


aerodynamicist

A person who studies aerodyamics.


aerodynamics

The science that deals with the motion of air and other gaseous fluids and the forces acting on objects as a result of the relative motion between the air and the object..


airfoil

A streamlined surface designed in such a way that air flowing around it produces useful motion.  The cross section of an airplane wing is an airfoil.


airspeed

How fast the wing moves through the air, or how fast the air is moving past the wing. Depending on the system of units we are using, it is measured in miles per hour, feet per second, or kilometers per hour.


altitude

The height above sea level at which our wing is flying. It is measured in feet or meters. This becomes important for wings because the conditions of the air (temperature, pressure, and density) change as we go higher. This will effect the amount of lift that a wing generates.


angle

See Angle of Attack


angle of attack

How the airfoil is inclined relative to the air coming towards it.  It is measured in degrees.  At zero degrees, the front of the airfoil is pointed directly into the stream.  At 90 degrees it is pointed straight up. The angle of attack in this simulation is limited since it does not simulate stall characteristics.


area

The wing area in square feet or square meters when the wing is viewed from above. It is equal to the chord length times the wing span for our simple straight wing. The simulation only shows the side view (cross-section) of the airfoil.


camber

A measure of the curvature of the airfoil. The mean camber line is an imaginary line which lies halfway between the upper surface and lower surface of the airfoil and intersects the chord line at the leading and trailing edges. But between the leading and trailing edge the camber line can curve above or below the chord line. The camber value specified here gives the highest value above or below the chord line divided by the chord length.


chord

This doesn't appear in the input list but is an important definition in airfoil geometry. The chord length is the distance from the leading edge to the trailing edge of the airfoil.  The chord line is a straight line connecting the leading and trailing edges of an airfoil.


compressibility

A measure of how easily a gas can be forced into a smaller volume.  As planes fly close to and above the speed of sound, the air near the wing is compressed.  For this situation, compressibility has to be included in the simulation.


equation

A statement that relates two quantities, usually with an equals sign (=).  (examples: A=6,  A+B = C)


force

A push or pull exerted on an object usually measured in pounds or Newtons.


friction

The resistance to relative motion between two surfaces in contact


geometry

1) the physical shape and dimensions of an object, 2) the branch of mathematics that deals with the relations and measurements of lines, angles, surfaces and solids.


lift

A force generated by a wing which acts perpendicular (90 degrees) to the incoming flow.  Lift allows an airplane to climb and fly.


pressure

The force exerted over a unit area (e.g., k-pascals, pounds per square inch).


span

The distance from one wing tip to the other.


stagnation

The point on an airfoil that separates the upper and lower streamlines.  These are depicted by a single white line between the yellow and green streamlines.


stall

The condition in which an airfoil has stopped producing lift.  The most direct cause is an excessively high angle of attack.  For most airfoils this occurs in the 15-20 degree range.


streamlines

A line depicting the flow path of a particle of air.


thermodynamics

The science concerned with the conversion of heat to energy.


thickness

The maximum difference between the upper and lower airfoil surfaces divided by the chord length.


trajectory

The curve described by a projectile in flight


turbulence

Irregular motion of air; uneven currents of air.


velocity

The rate of motion in a particular direction; the combination of airspeed and direction.


wind tunnel

A facility where an airstream is forced across an airfoil or other objects to study aerodynamics.


wing

A three dimensional object that moves through the air and can generate lift. In this simulator we will study a simple straight wing whose leading edge and trailing edge are parallel. When viewed from above, this wing will look like a rectangle and when viewed from the side, we will see a cross-section which can be either a flat plate, or an airfoil shape. The cross-section will be displayed on the airfoil view panel.