AEROCFD ROCKET: INSTRUCTIONS BACK
The V-2 rocket is used to illustrate the step-by-step procedure necessary to perform a typical analysis using AeroCFD. Initially, the user specifies the analysis units and flight conditions on the main page of the program. The following steps are required on the main screen to perform an analysis using AeroCFD. Please read the definitions section for explanation of each variables meaning.

1) For the Analysis Units data entry specify whether the required units are inches-pounds-seconds (IPS), feet-pounds-seconds (FPS), or meters-newtons-seconds (MNS) by using the pull-down menu control. Depending on the selection, the resulting units are inches, feet or meters for linear dimensions, pounds or Newtons for force and seconds for the basic units of time. Select IPS for this example.

2) In the Analysis Data section specify the Rocket Flight Speed as either IN/SEC, FT/SEC, M/SEC or MACH number using the pull-down menu. Select MACH for this example and for Rocket Flight Speed insert 0.25 Mach.

3) In the Analysis Data section specify the Rocket AOA (angle of attack) in degrees by inserting the data entry. Insert 1.0 degree AOA for this example.

4) In the Analysis Data section specify the Rocket Flight Altitude using the pull-down menu. Select SEA LEVEL for this example.

5) In the Analysis Data section specify whether the fluid is COMPRESSIBLE or INCOMPRESSIBLE using the pull-down menu. The INCOMPRESSIBLE selection allows AeroCFD to perform a 3-D potential flow analysis. The COMPRESSIBLE flow selection allows AeroCFD to apply a linearized compressibility correction (using the Prandtl-Glauret rule) to the 3-D potential flow results. The Prandtl-Glauret rule is reasonably accurate for 0.3 < M < 0.8. However, for M > 0.8 the accuracy of the Prandtl-Glauret rule diminishes rapidly. Select COMPRESSIBLE for this example.

6) In the Analysis Data section specify the Mesh Size of the computational flow field in the axial (X) and transverse (Y) directions using the pull-down menu. The size of the computational flow field can range from 10 X 10 elements to 100 X 100 elements. More elements yield more accuracy but add to the total computational time for a solution. Insert 50 for this example.

7) In the Analysis Data section specify the Element Aspect Ratio as 1:1, 2:1, 3:1, or 4:1. Increasing the element aspect ratio is useful to cluster the mesh around the body tube and to get better plot resolution in regions where the flow velocity and pressure are changing rapidly. Clustering elements in regions where the flow is changing rapidly is especially important for accurate line-contour plots and filled-contour plots. Select 1 for this example. Note: "mesh" refers to a grouping of grids.

8) In the Analysis Data section specify the Grid # on Circumference as either 8, 10 or 12. The default of 8 panel control points on the circumference is fine for most analyses. But, more panels control points on the circumference will yield better accuracy. Select 8 for this example.

9) The user must dimension the body tube to be able to perform a CFD solution. "Click" the first icon at the top of the main screen to bring up the Body Tube Geometry screen. Prior to specifying body tube geometry, clicking anywhere else on the main screen will cause AeroCFD to display error messages in the status bar at the bottom of the screen. These messages indicate what AeroCFD needs to proceed to the next step of the analysis.

Note: CX refers to the drag force coefficient in the axial direction of the airframe and CY (CN) refers to the lift force coefficient perpendicular to the axial direction of the airframe. CD refers to the drag force coefficient in the flow direction and CL refers to the lift force coefficient perpendicular to the flow direction.

Please click the first (Body Tube Geometry), second (Fin Geometry), third (Flow Visualization) and forth (Force Distribution) icons in the toolbar. Please click SHOW RESULTS / SHOW ANALYSIS button to view either the CFD Results or the Analysis Data sections. The "X" command button on the AeroCFD toolbar hides or shows the Analysis Data and CFD Results sections.

Main AeroCFD screen - Analysis Input


Main AeroCFD screen - CFD Results

BODY TUBE GEOMETRY
To generate a "Standard" body tube perform the following sequence of operations.

10) On the main AeroCFD screen "click" the first icon on the toolbar to bring up the Body Tube Geometry screen. In the Body Tube Geometry section select the Standard Tube Geometry option button. Selecting the Free-Form Tube Geometry will display the Free-Form Body Tube Geometry screen. However, these V-2 rocket instructions will use the "Standard" method to create the body tube for this illustration. "Click" the subdued Free-Form icon for instructions to see what the Free-Form Body Tube Geometry screen looks like . To use the Free-Form Body Tube Geometry screen, simply select the number of points describing the body tube using the up-down control. Then "drag" each point into position on the screen. Better point resolution is possible by resizing the window to fit the entire computer screen by clicking the RESIZE command.

11) In the FREE-FORM AND STANDARD GEOMETRY DATA section specify the nose cone shape as CONICAL, ELLIPTICAL, PARABOLIC, SEARS-HAACK, or TANGENT OGIVE. The SEARS-HAACK nose cone has an up-down control that applies a power-series shape modification. When the Shape index is equal to 2 a SEARS-HAACK nose cone is defined and for other values of Shape index a power series shape is defined. Select TANGENT OGIVE for this example.

12) For Nose Cone Length insert 208.5 inches.

13) For Nose Cone Diameter insert 65.0 inches.

14) For Body Tube Length insert 185.0 inches.

15) In the FREE-FORM AND STANDARD GEOMETRY DATA section specify the Transition shape as either CONICAL, ELLIPTICAL, PARABOLIC, or TANGENT OGIVE. The aft end of the V-2 is defined by a Tangent Ogive shape. Select Tangent Ogive for the Transition Shape.

16) For Transition Diameter insert 40.9 inches.

17) For Transition Length insert 142.9 inches.
The Base Tube Length may be ignored for this example.

18) "Click" back to the main AeroCFD screen by "clicking" the fifth icon on the toolbar.
Please remember that you need to "click" back using the Return icon. Clicking the [X] box will kill the results and delete the modifications.

Note: To generate a Free-Form body tube shape click "Free-Form Tube Geometry" to enable the Free-Form command button. Click on the Free-Form command button to proceed to the Free-Form Geometry screen.

Please click the fifth (Return) icon in the toolbar to return to the main screen.

Body Tube Geometry Screen

FIN AND LAUNCH LUG GEOMETRY
To define the fins of the V-2 rocket perform the following sequence of operations.

19) On the main AeroCFD screen "click" the second icon on the toolbar to bring up the Fin and Launch Lug Geometry screen.

20) In the Fin Quantity and Type section select the total number of fins as 3, 4, 5, 6, 7, or 8. Alternatively, any number of fins may be specified by simply inserting the desired number of fins. Insert 3 fins for this example.

21) In the Fin Quantity and Type section select the option button corresponding to either Main Fins or the Canard Fins. The Main Fins are the lowest most set of fins on the rocket and the Canard Fins are the upper most set of fins on the rocket. For this example select the Main Fins option button.

22) In the Fin Planform Shapes section select the option button corresponding to either Triangle, Rectangle, Tapered, or Elliptical fin planforms. For this example select the Tapered planform fin shape.

23) In Airfoils Sections select the option button corresponding to either Square, Round, Streamlined, or D'Wedge cross-sectional fin shape. The fin cross-sectional shape determines the drag and lift characteristics that are computed in the 2-D vortex panel analysis for the fins. An average span of the fin is used in the 2-D vortex panel fin analysis. For complex fin designs the user must enter values that approximate the root chord, fin tip chord, span length and fin thickness of the actual fins. For this example select the Streamlined airfoil section.

24) In the Surface Finish section select the option button corresponding to either None (unpainted), Good (painted), or Excellent (waxed) for the surface finish of the entire model rocket. This selection determines whether the flow on the rocket body and fins are either laminar or turbulent when determining the drag coefficients. Whether the flow is laminar or turbulent flow is determined by the Reynolds number (Rn) which of course is based on the flow velocity (V), dynamic viscosity and characteristic length (L). For a body tube the characteristic length is the total rocket length, and for fins the characteristic length is always the average fin chord. As for all aerodynamic coefficients (Cd, CL, etc.) the reference area (S) is either the cross-sectional area immediately behind the nose cone or the maximum cross-sectional area of the body tube. The selection for finish quality applies to fins and body tube and launch lug. For this example select Good (painted) for the surface finish.

25) Finally, insert all the remaining fin dimensions and launch lug dimensions into each data entry area on the screen. The relative location of each dimension is indicated when each fin planform type is selected using the option buttons. For defining multiple launch lugs the total length of all the launch lugs on the body tube should be inserted for Total Length in the Launch Lug(s) section. In addition, for non-circular launch lugs compute the equivalent inside and outside circular diameter of the launch lug. Then, insert the launch lug's equivalent outside diameter into the Outside Diameter data field and the equivalent inside diameter into the Inside Diameter data field. The total length of the body tube determines if the flow over the lug is laminar or turbulent when computing drag coefficients. For this example insert 393.5" for the distance from the nose cone tip to the leading edge of the fin root. Insert 449.96" for the distance from the nose cone tip to the leading edge of the fin tip. Insert 102.6" for the tip chord of the fin, insert 37.65" for the semi-span of the fin. insert 142.9" for the root chord of the fin. Insert 3.75" for average fin thickness. Insert 0.0" for the Total Length of the launch lug. Insert 0.0" for the Outside Diameter of the launch lug. Insert 0.0" for the Inside Diameter of the launch lug. Note: most model rockets have launch lugs, but the V-2 rocket does not.

26) "Click" back to the main AeroCFD screen by "clicking" the fifth icon on the toolbar.
Please remember that you need to "click" back using the Return icon. Clicking the [X] box will kill the results and delete the modifications.

27) When the body tube geometry and fin geometry are complete the user may "click" SOLVE to perform a CFD analysis, "click" MESH to see the resulting flow field grid, "click" LOOP to perform a CFD Loop Analysis with or without the fins or "click" STOP to stop the solution or proceed with a solution.

Please click the second (XML File Fin Geometry and Fin Placement), forth icon (Fin AeroDynamics) and fifth (Return) icons in the toolbar.

Fin Geometry Screen

FREE-FIELD FLOW VISUALIZATION
Flow visualization is easy using AeroCFD. To plot the free-field flow in AeroCFD perform the following sequence of operations after the flow is SOLVE'd.

28) On the main AeroCFD screen "click" the third icon on the toolbar to bring up the Flow Visualization screen.

29) To plot velocity filled-contour plots or velocity line-contour plots in the Plot Velocity section "click" either the Field-Filled or Field-Lines command buttons. Plots will occur automatically.

30) Adjust the number of levels displayed in the contour plots by using the up-down control to set the number of color levels from a minimum of 3 to a maximum of 256.

31) To plot pressure filled-contour plots or pressure line-contour plots in the Plot Pressure section "click" either the Filled-Field or Field-Lines command buttons. All plots will occur automatically and be displayed in real-time. Plot dynamic pressure, static pressure or pressure coefficient (Cp) by selecting one of the option buttons listed in the Plot Pressure section. Please see the definitions section for more information about dynamic pressure, static pressure and pressure coefficient (Cp).

32) Adjust the number of levels displayed in the contour plots by using the up-down control to set the number of color levels from a minimum of 3 to a maximum of 256.

33) "Click" back to the main AeroCFD screen by "clicking" the third icon on the toolbar.
Please remember that you need to "click" back using the Return icon. Clicking the [X] box will kill the results and delete the modifications.

Please click the third (Return) icon in the toolbar or click SHOW PROFILES to view the velocity profile toolbar. The "X" command button on the AeroCFD toolbar hides or shows the Contour Plot and Profiles sections.

Flow Visualization Screen


Flow Visualization Screen - [X] Button Clicked Showing Levels Display

AIRFRAME SURFACE FLOW FIELD VISUALIZATION
Flow visualization on the surface of the airframe is easy using AeroCFD. To plot the airframe flow field in AeroCFD perform the following sequence of operations after the flow is SOLVE'd and the Flow Visualization screen is displayed.

34) To plot airframe velocity filled-contour plots in the Plot Velocity section "click" the Airframe-Filled command button. The Plot will occur automatically.

35) Adjust the number of levels displayed in the contour plot by using the up-down control to set the number of color levels from a minimum of 3 to a maximum of 256.

36) To plot airframe pressure filled-contour plots in the Plot Pressure section "click" the Airframe-Filled command button. The plot will occur automatically. Plot dynamic pressure, static pressure or pressure coefficient (Cp) by selecting one of the option buttons listed in the Plot Pressure section. Please see the definitions section for more information about dynamic pressure, static pressure and pressure coefficient (Cp).

37) Adjust the number of levels displayed in the contour plots by using the up-down control to set the number of color levels from a minimum of 3 to a maximum of 256.

38) View the profile plots by clicking the SHOW PROFILES command button.

39) Plots may be interrupted or stopped by "clicking" the STOP command button.

AIRFRAME POINT-PROPERTY DISPLAY
40) Display control point velocity or pressure and X,Y,Z panel control point coordinates for each three-dimensional source panel on the surface of the airframe. After the Airframe-Filled command button has plotted either velocity or pressure on the surface of the airframe, the Airframe Values section appears. The Airframe Values section makes available the up/down command button that allows the user to display control point values for velocity, dynamic pressure, static pressure and pressure coefficient (Cp). Control point coordinates are displayed in the status bar at the lower-left part of the screen. As the up/down command button is clicked a red dot on the surface of the airframe moves from point-to-point in real-time displaying either velocity or pressure depending on whether the airframe plot was generated in the Plot Velocity or the Plot Pressure sections. But, the user must first plot the airframe filled-contours, either velocity or pressure to expose this utility and make the Airframe Values section visible. This X,Y,Z coordinates on the airframe use a right handed coordinate system. The X-axis is down the axis of the rocket from the tip of the nose cone, the Y-axis is up and the Z-axis points out from the surface of the screen. A small coordinate system located on the lower left of the screen makes the coordinate system clear. For added clarity a sketch in the figure below shows a cross-sectional view of the airframe and the resulting Y-Z axis that appears when looking at the rocket from the front. Panel control point 109 represents one of 12 control points on the surface of the airframe at this particular cross-sectional location. In this representation the number of panel control points on the circumference of the airframe was increased to 12 points. The V-2 example used 8 panel control points on the circumference but 10 panel control points on the circumference could have been selected in step 8.

Please click the third (Return) icon in the toolbar or click SHOW PROFILES to view the velocity profile toolbar. The "X" command button on the AeroCFD toolbar hides or shows the Contour Plot and Profiles sections.

Airframe Surface Flow Field - Dynamic Pressure Filled-Contour Plot


Airframe Point Property Display

VELOCITY AND PRESSURE PROFILES PLOT
41) View the profile plots by clicking the SHOW PROFILES command button.

42) Plots may be interrupted or stopped by "clicking" the STOP command button.

43) Velocity and pressure variation from the surface of the model in the vertical direction is displayed on the Profiles - Velocity and Pressure section. The slider bar determines the location of the pressure profile plot along the axis of the model. The zero axial location is defined at the tip of the nose cone.

44) "Click" back to the main AeroCFD screen by "clicking" the third icon on the toolbar.
Please remember that you need to "click" back using the Return icon. Clicking the [X] box will kill the results and delete the modifications.

NOTE: The vertical velocity or pressure profile at each X-Location from the flow inlet to the end of the rocket is being plotted each time the slider bar is moved. By definition, the tip of the nose cone is the origin (X = 0, Y = 0) and the flow inlet (left most part of the flow field) has a negative X-Location. Depending on the number of grids selected in the X and Y directions, AeroCFD needs to proportion the grid spacing along the airframe to put the proper number of grids on the airframe for each mesh size selected. The physical locations of the vertical profiles are located at panel control points and not the intersections of the grid lines. For this reason, properties are not displayed at the tip of the nose cone where X =0 and Y =0, but a half panel width away for the first profile section.

Please click the third (Return) icon in the toolbar or SHOW CONTOURS to view the contour plot toolbar. The "X" command button on the AeroCFD toolbar hides or shows the Contour Plot and Profiles sections.

Profiles Screen

ROCKET FORCE DISTRIBUTION
A complete list of all the aerodynamic coefficients, forces and moments can be viewed by clicking the forth icon on the AeroCFD main screen toolbar. The data on the Rocket Force Distribution screen includes the aerodynamic data presented on the main page of the analysis and much more.

45) After reviewing the Rocket Force Distribution screen "Click" back to the main AeroCFD screen by "clicking" the forth icon on the toolbar.
Please remember that you need to "click" back using the Return icon. Clicking the [X] box will kill the results and delete the modifications.

Please click the third (Cross-Flow Cp Distribution) and forth (Return) icons in the toolbar.

Results Summary Screen

XML FILE FIN GEOMETRY AND FIN PLACEMENT
This screen presents the XML File Fin Geometry and Fin Placement screen. XML fin data for a two stage rocket is displayed below after being imported from the XML data file. Perform the following sequence of operations to import fin data from an XML file. These steps are not part of the V-2 rocket instructions. However, if Free-Form fins are desired the user may import them from an XML file. AeroCFD then determines the average fin chord, etc. and inserts that information into the analysis.

1) On the Fin Geometry screen "click" the second icon on the toolbar to bring up the XML File Fin Geometry and Fin Placement screen.

2) In the XML File Fin Geometry and Fin Placement screen, "Click" the left icon in the toolbar to import XML custom or XML standard fins.

3) Using the option buttons, select the fin-set that needs to be re-positioned.

4) Pull the slider-bar to position each fin set.

5) Units may be modified using the Fin Units pull-down menu. These units are reflected on this screen and on the Fin Geometry screen.

6) "Click" back to Fin Geometry screen by "clicking" the fifth icon on the toolbar. Then "click" back to the main AeroCFD screen.
Please remember that you need to "click" back using the Return icon. Clicking the [X] box will kill the results and delete the modifications.

Note: This screen does not represent the V-2 rocket example. It is being provided for illustration and description.

Please click the fifth (Return) icon in the toolbar.

XML File Fin Geometry And Placement Screen

CFD LOOP ANALYSIS AND PLOTS
To perform a CFD Looping Analysis perform the following sequence of operations. These steps are not part of the V-2 rocket instructions but are directly applicable.

1) On the main AeroCFD screen "click" the LOOP icon to bring up the CFD Looping Analysis and Plots screen.

2) In the CFD Loop Analysis section select either AOA or Velocity to perform a Loop Analysis of the plot variables as a function of AOA or Velocity. For this example select the AOA option button.

3) In the CFD Loop Analysis Data section insert the total number of CFD Loops. Insert 21 CFD loops for this example.

4) In the CFD Loop Analysis Data section insert the Initial AOA (DEGREES). This is the starting AOA performed by the Looping Analysis. Insert 0.05 degrees for this example.

5) In the CFD Loop Analysis Data section insert the AOA Increment (DEGREES). This is the amount the AOA is incremented for each iteration of the CFD Loop Analysis. Insert 0.5475 degrees for this example.

6) Perform the CFD Looping Analysis by "clicking" the plot icon in the CFD Looping Analysis section. The loop counter is displayed to the right of the plot icon. The counter indicates the progress of the CFD Looping Analysis. Finally, to the right of the loop counter a Stop watch is provided to allow the analysis to be interrupted or terminated.

7) "Click" back to main AeroCFD screen by "clicking" the ninth icon on the toolbar.
Please remember that you need to "click" back using the Return icon. Clicking the [X] box will kill the results and delete the modifications.

NOTE: The Barrowman results may be plotted verses the Looping Analysis results by clicking the second icon from the right. The Barrowman results are plotted for standard body tube shapes and are not plotted for Free-Form body tube shapes. Also, the Barrowman results are not plotted for Velocity Loop Analyses. Finally, a variety of options are provided at the toolbar, such as Send formatted data to printer, Print screen, Save data to disk, Increase Y-Axis scale, Reset Y-Axis, and Plot Barrowman results.

CFD LOOPING ANALYSIS RESULTS DISCUSSION
The results plotted along with the CD and CN plots illustrated below is an extension of the analysis presented on the AeroCFD Description page. Please note the excellent agreement between the modified Sutton data for drag (CD) and normal force coefficient (CN) over the range between 0 to 12 degrees angle of attack. Because the Sutton data is in the form of CD and CL a simple transformation of the data puts the results into the form of CD and CN (CY). The following two equations are solved simultaneously to determine CN (CY) in terms of CD and CL. (1) CD = CY * sin(AOA) + CX * cos(AOA) and (2) CL = CY * cos(AOA) - CX * sin(AOA) . The equation for CN (CY) is: CN = [ CL + CD * tan (AOA) ] / [ cos(AOA) + sin (AOA) * tan (AOA) ] and is plotted along with the AeroCFD results and the Barrowman equation results. The Modified Sutton data for drag (CD) do not require a transformation and are shown plotted directly with the AeroCFD results.

AeroCFD normal force coefficient (CN) results exactly match modified Sutton V-2 CN data up to approximately 5 degrees angle of attack and then begin to depart from the modified V-2 data. The departure between the AeroCFD results for CN and the modified Sutton V-2 CN data beyond 5 degrees is expected because AeroCFD does not model separation effects as the gradients in the flow field become large and viscous effects predominate. AeroCFD drag coefficient (CD) data track the modified Sutton CD results over the entire range from 0.0 degrees to 12 degrees angle of attack. Also note the Barrowman equation normal force coefficient (CN) predictions depart from the AeroCFD and Modified Sutton results over the entire range of the analysis. Therefore, this analysis indicates the Barrowman CN results are not accurate at small AOA (0 to 5 degrees) for boat tail shapes.

CD VERSES AOA LOOPING ANALYSIS
Please click the ninth (Return) icon in the toolbar or click the CN option button to view the CN plot.

CD verses AOA Loop Analysis Display. Modified Sutton CD verses AOA plotted With AeroCFD Results

CN VERSES AOA LOOPING ANALYSIS
Please click the ninth (Return) icon in the toolbar or click the XCp option button to view the XCp plot.

CN verses AOA Loop Analysis Display. Modified Sutton CN verses AOA plotted With AeroCFD Results

AVERAGE CD (DRAG) LOOPING ANALYSIS
This screen shot illustrates that AeroCFD will compute average CD over a range of velocity. Click the Velocity option button and define the total Number of Loops to be performed by AeroCFD. Then, specify the constant angle of attack (Initial AOA), Initial Rocket Flight Velocity (Normally from 1 to 5 ft/sec), and finally the Rocket Velocity Increment that will provide the desired upper limit on flight velocity. After the analysis is complete the Average CD over the velocity range specified is displayed as illustrated below. Use this value for drag coefficient (CD) in any flight simulation computer program.


XCp VERSES AOA LOOPING ANALYSIS
Please click the ninth (Return) icon in the toolbar.

XCp verses AOA Loop Analysis Display

CROSS-FLOW DISTRIBUTION
The Cross-Flow pressure Cp Distribution screen displays the pressure distribution on the airframe at AOA. AeroCFD results are plotted verses the potential flow equation of Cp verses angular location on the body tube. For comparison with classical cross-flow results, the AOA on the main screen of the analysis must be set to 90 degrees for the results plotted here to agree with the potential flow equation. For cross-flow comparisons, select a station well back from the tip of the nose cone but before the base of the rocket. These steps are not part of the V-2 rocket instructions.

Please click the fifth (Return) icon in the toolbar (AOA = 90 degrees on main screen).

Cross-Flow Cp Distribution Screen

FREE-FORM BODY TUBE GEOMETRY
To use this screen perform the following sequence of operations. These steps are not part of the V-2 rocket instructions.

1) On the Body Tube Geometry screen click the Free-Form Tube Geometry icon to bring up the free-form editor.

2) Select the total number of points that will describe the body tube using the Points defining body up-down control. Select up to 20 points that will define the body tube shape.

3) For better accuracy "click" the Resize icon to maximize the plot area image. This will allow AeroCFD to use all available pixels on your computer screen for more accuracy.

4) Using the cursor, drag each point into place one after the other. Position each point by referencing the X-Location, Y-Location and Y-Diameter values as they are updated as you move the cursor.

5) "Click" back to the Body Tube Geometry screen by "clicking" the eighth icon on the toolbar or the large Return icon. Then "click" back to the main AeroCFD screen.
Please remember that you need to "click" back using the Return icon. Clicking the [X] box will kill the results and delete the modifications.

Note: This screen does not represent the V-2 rocket example. It is being provided for illustration and description. However, it is part of a separate V-2 analysis that used a Free-Form body tube instead of the Standard body tube geometry.

Please click the eighth (Return) icon in the toolbar to return to the Body Tube Geometry screen.

V-2 Free-Form Geometry (Alternate Method For generating Airframe Shape)

AERODYNAMIC DEFINITIONS SECTION
1) Mach Number (Mn) = V / C, is the ratio of flow velocity (V) at a point in the flow to the speed of sound (C) at that same point in the flow.
2) Reynolds Number (Rn) = V L / v, is the ratio of dynamic forces (Velocity * Length) to friction forces (Kinematic viscosity) at a point in the flow.
3) Drag Coefficients (CD) = D / q S, is the drag force (D) in the flow direction divided by the dynamic pressure (q) and the reference area (S).
4) Lift Coefficient (CL) = L / q S, is the lift force (L) perpendicular to the flow direction divided by the dynamic pressure (q) and the reference area (S)
5) Drag Coefficients (CX) = X / q S, is the drag force (X) in the axial direction of the rocket divided by the dynamic pressure (q) and the reference area (S).
6) Lift Coefficient (CY) = Y / q S, is the lift force (Y) perpendicular to the axial direction of the rocket divided by the dynamic pressure (q) and the reference area (S).
7) Normal Force Coefficient (CN) = N / q S, is the normal force (N) perpendicular to the axis of the rocket divided by the dynamic pressure (q) and the reference area (S).
8) Pitch Moment Coefficient (CM) = M / q S L, is the pitch moment (M) acting around the tip of the nose cone divided by the dynamic pressure (q), reference area (S) and the reference length (L). A negative pitch moment (CM) indicates that a positive angle of attack will cause a restoring moment (M) tending to return the rocket to equilibrium flight. Having a negative CM when AOA is "positive" is a "good" thing. It means the rocket is stable! In other words the rocket will try to return to its stable equilibrium position (zero degrees AOA) when a disturbance, like a gust of wind, acts on the rocket.
9) Rocket Cp location (Xcp) = XCp/L, is the non-dimensional location of the center of pressure. XCp/L is computed by dividing the dimensional location of the center of pressure (XCp) by the reference length (L) of the rocket, normally the total rocket length. Center of pressure is the location or point where the resultant of all distributed aerodynamic loads effectively act on the body. Center of pressure can also be computed from: XCp = - M / N, where the M acts around the tip of the nose cone.
10) Rocket Base Drag Coefficient (Cd_Base) is the contribution to pressure drag caused by the action of the insulating boundary layer "jet-pump" on the surface of the rocket that tends to "pump" air away from the base of the rocket causing the static pressure at the base of the rocket to be reduced. Cd_base = 0.029 / SQRT(Cfb) * (Dbase / Dbody)^3 . Where Cfb is the total forebody drag coefficient that does not include base drag effects. This relationship is valid for subsonic and supersonic flow. Cd_Base ranges from 0.025 to 0.20 for most rockets. Note: For turbulent boundary layer flow the forebody drag coefficient (Cfb) can be estimated to be a function of Mach number, Reynolds number and body shape.
11) Dynamic Pressure (q) = 1/2 * Air Density * V^2.
12) CD, CL, CX and CY are related by the equations: CD = CY * sin(AOA) + CX * COS(AOA) and CL = CY * COS(AOA) - CX * SIN(AOA).
13) Static Pressure = Total Pressure - Dynamic Pressure. Can be understood to be the pressure between streamlines in the flow.
14) Total Pressure = Pressure that would exist in a flow if the flow were slowed isentropically to zero velocity. Also called stagnation pressure for subsonic flow.
15) Dynamic Pressure = 1/2 * Air Density * V^2.
16) Pressure Coefficient (Cp) = (P - PINF) / q. Definition of pressure coefficient. Where P is the pressure anywhere in the flow, PINF is the freestream pressure and q is the dynamic pressure.
17) Derivative of Normal Force Coefficient (CNa) is the slope of CN verses angle of attack . Specifically, CNa = (CN1 - CN2) / (AOA1 - AOA2).

NOTE: For more discussion on these topics please read Fluid Dynamic Drag, by S.F. Hoerner. This is an excellent book and is easy to understand.


 

AeroCFD® 2D-WING Bonus Feature Addition, Instructions BACK

AeroCFD includes a new program called 2D-WING™ for the aerodynamic analysis of two-dimensional (2-D) and finite aspect ratio (AR) airfoil sections. 2D-WING uses vortex lift panels to compute CD, CL and Cm,c/4 for airfoil sections using NACA four digit airfoils, streamlined, flat plate, double wedge (D'Wedge) and imported custom shapes for a wide range of 2-D and finite AR airfoils. Several NACA five-digit airfoils from Appendix III in the book Theory of Wing Sections allow the user to rapidly specify complex imported shapes. Other useful input variables include wing Reynolds number (Re) and angle of attack in degrees. Also, 2D-WING produces filled color contour plots and line color contour plots for pressure coefficient (Cp) and U/U0 where the number of contour levels can be specified from 3 to 256 levels. In addition, the following standard plots are produced, Cp verses chord length and U/U0 verses chord length for the upper and lower airfoil surfaces. Also, CL verses AOA, CD verses AOA, CD verses CL, CL/CD verses AOA and Cm verses AOA are quickly plotted. Finally, the total number of 2-D vortex panels that define the upper and lower surfaces of an airfoil can be specified as 100, 200 or 300.

AeroCFD 2D-WING uses 2D vortex lift panels to determine drag coefficient (CD), lift coefficient (CL) and moment coefficient (Cm,c/4) of airfoil sections. Airfoil section shapes are specified using the NACA four digit series, Streamlined, Flat Plate, D'Wedge and Imported shape options. The following steps outline the basic procedure used to operate AeroCFD 2D-WING.

Step 1. The specification of Streamlined, Flat Plate and D'Wedge airfoil section shapes requires the specification of fin thickness in terms of maximum thickness in percent chord (Tmax/Chord X 100). Maximum fin thickness in percent chord for all airfoil types is specified by using the third data entry box on the first line, NACA Four-Digit series airfoil description. The first two data entry boxes for Streamlined, Flat Plate and D'Wedge airfoil section shapes are disabled. However, for the NACA Four-Digit series, the first two data entry boxes are enabled, where the first data entry box refers to maximum camber in percent chord and the second data entry box refers to position of the maximum camber in tenths of a chord from the leading edge (LE). The following definitions are needed to define camber and camber location for NACA airfoils. First, the mean camber line is the locus of points halfway between the upper and lower surfaces of the airfoil as measured perpendicular to the mean camber line. Then, the chord line is a straight line that connects the leading and trailing edges of the airfoil and is simply referred to as the chord of the airfoil and is usually defined using the symbol, c. Using these definitions the camber is the maximum perpendicular distance between the mean camber line and the chord line of the airfoil. Camber location is simply located as a percentage of the chord length from the leading edge of the airfoil.

The complete specification of four-digit NACA airfoils and standard airfoils are summarized below for the first line, NACA Four-Digit series airfoil description. Where the first two spaces are disabled for Streamlined, Flat Plate, and D'Wedge airfoil section shapes but are required for NACA four-Digit airfoils.
[Max camber in percent chord], [Position of max camber in 1/10th chord], [Max thickness in percent chord].

Step 2. The Reynolds number (Re = rUc/m) of the fin is defined on the second line of input data. Reynolds number is defined as the ratio of the inertial forces represented by the density of the medium (r), free stream velocity (U), and fin dimension (c) to the friction forces in the boundary layer represented by the viscosity of the medium (m). Reynolds number is automatically inserted if entering from AeroCFD Rocket but is an input if entering from the AeroCFD 2D-WING command buttons. The following Reynolds number calculator is useful for computing Reynolds number for AeroCFD 2D-WING (Note: This off-site calculator has not been checked for accuracy). For more information and theory about Reynolds number please visit the Wikipedia on-line encyclopedia.

Step 3. Fin angle of attack (a) is defined relative to the chord line for all section shapes on the third line of input data.

Step 4. Fin aspect ratio (AR = Span/Chord) is defined on the fourth line of input data. Aspect ratio must be non-zero and Checked to be included in the computation of CD, CL and Cm,c/4. The Aspect ratio input allows an "approximate solution" of end effects and 3D wings.

Step 5. Select one of five fin section shapes using the Airfoil Shapes pull-down menu. Streamlined, NACA four-digit, Flat Plate and D'Wedge section shapes are directly drawn after selection. In addition, arbitrary fin section shapes may be defined using the Import X-Y command. Many NACA Five-Digit section shapes are included in NACA_AIRFOILS.zip (located in the AeroCFD directory) and are drawn by using the Import X-Y command after unzipping the file.

Import File format for each station (X) and ordinate (Y) given in percent of airfoil chord (LE is the Leading Edge): [Upper Surface X-location from LE], [Upper Surface Y-location from Chord Line], [Lower Surface X-location from LE], [Lower Surface Y-location from Chord Line] for each station from the LE to TE.

Step 6. Perform a 2D Vortex Panel aerodynamics analysis by clicking the SOLVE command button and follow the instructions displayed in the lower left status bar. Instructions displayed in the Status bar will state when a valid solution is achieved and when it is permissible to click the various plot command buttons.

Step 7. Display results using the following commands in the Plots pull-down menu: Cp verses X, U/U0 verses X, CL verses AOA, CD verses AOA, CD verses CL, CL/CD verses AOA, Cm verses AOA, U/U0 Contours (Filled and Line) and finally Cp Contours (Filled and Line). Where AOA refers to angle of attack in degrees, Cp = (P - PINF) / q = 1 - (U/U0)^2 is the pressure coefficient and U0 refers to the free stream velocity. Please note the results obtained by modifying data in AeroCFD 2D-WING are not reflected back into the AeroCFD Rocket analysis except for the number of panels that define the airfoil section. However, fin shapes used on the Fin and Launch Lug Geometry screen may be analyzed and the results plotted in AeroCFD 2D-WING. Reference: THEORY OF WING SECTIONS, by Abbott and Doenhoff.


Figure 1, Fin Vortex Panel Method Analysis Screen, U/U0 Filled Contours and U/U0 verses X.



Figure 2, Fin Vortex Panel Method Analysis Screen, Cp (pressure coefficient) Line Contours and Cp verses X.


(1) NACA 0012 AIRFOIL VALIDATION
     
Figure 3, NACA 0012 CL verses AOA and CD verses CL.


(2) NACA 63-212 AIRFOIL VALIDATION
     
Figure 4, NACA 63-212 CL verses AOA and CD verses CL.

NOTES:
1) Reference: THEORY OF WING SECTIONS, by Abbott and Doenhoff.
2) AeroCFD 2D-WING results (red dots) generated using the Save Results As command under File. The Results were plotted using Excel (or any spreadsheet program) and compared to THEORY OF WING SECTIONS data for the NACA 0012 and NACA 63-212 wing sections.
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