AeroDRAG & Flight Simulation Instruction Manual Purchase OuR (High Speed) Rocket Example What is AeroDRAG & Flight Simulation AeroDRAG & Flight Simulation is a computer program that allows the rocketeer to quickly and easily perform rocket drag (Cd) and flight simulations using the power of Microsoft Windows. AeroDRAG & Flight Simulation interactively predicts subsonic, transonic and supersonic rocket drag to Mach 20 using the Newtonian surface inclination method for nose-body and fin combinations. AeroDRAG & Flight Simulation also performs flight simulations of rockets in vertical flight. For flight simulations the basic equations of rocket motion are repeatedly integrated to determine rocket velocity, altitude and acceleration using a finite difference procedure. In this latest version of AeroDRAG & Flight Simulation, the Cd can vary with rocket velocity and air density varies with altitude. The ability to model the variation of Cd with velocity (Mn) is important for accurate high speed and high altitude rocket predictions. Many other Flight Simulation programs assume Cd is constant, possibly causing serious flight prediction errors. Please note that AeroDRAG & Flight Simulation is not a CAD program used to painstakingly define rocket model geometry. Instead, it is a tool that rapidly determines the performance of small and large scale rockets in seconds by the definition of basic shapes and environmental considerations.

OPERATING INSTRUCTIONS
The main source of error in the prediction of velocity and altitude of high speed, high altitude rockets is that most commonly used and moderately priced flight simulation programs do not allow Cd to vary with Mach number. Instead, many flight simulations fix Cd at launch or use Cd = 0.75, a common value based on the Alpha model rocket experiments conducted over 40 years ago. Some flight simulations make allowances for the user to plug other values of Cd in place of 0.75 without much explanation. For low speed model rockets Cd is fairly constant over a wide range of velocity as long as the flow is turbulent. But, what Cd is correct for a particular rocket, even a model rocket, and when does turbulence and the variance of Cd with Mach number become important for accurate flight predictions? These questions are what AeroDRAG and Flight Simulation is designed to answer for most commonly flown model rocket and high power rockets. A secondary, but still important source of error for the prediction of velocity and altitude of rockets is the accurate representation of thrust-time information. AeroDRAG & Flight Simulation allows the use of either average-thrust (Favg) and burn time (Tburn) data OR user generated thrust-time curves. Very accurate flight predictions for model and high power rockets have been obtained by the use of average-thrust (Favg) and burn time (Tburn) data where the thrust is considered constant over the entire burn-time of the motor. The thrust-time profiles for most model rocket motors are relatively flat with small burn-times, making the use of this option very accurate. In addition, this option can more easily be based on the latest and most easily obtained manufacturer rocket motor data by knowing only the total impulse (Itotal) and motor burn-time (Tburn). Because, Itotal = Favg * Tburn, the average-thrust is computed to be, Favg = Itotal / Tburn. Then, the user can be sure his thrust-time data is based on the latest manufacturer information and not obsolete information. Finally, the user has the option to generate his own thrust-time profile in the Thrust-Curve Free-Form editor or to manually create the thrust-time profile by simply using any text editor, including NotePad.

A. ROCKET DRAG (CD VERSES MACH NUMBER) DETERMINATION
The OuR Project rocket was fired in 1996 to an altitude of 94,000 feet. This design is used to illustrate the step-by-step procedure necessary to perform a typical drag and flight simulation analysis using AeroDRAG & Flight Simulation. Please reference the July 1997 issue of High Power Rocketry magazine for project details and experimental data collected on this flight.

AIRFRAME DATA ENTRY
The main screen consists of a single, large window with a toolbar of pull-down buttons across the top. Each button opens a sub-window for the insertion of measurements taken from the airframe,
launch lugs and fins of a typical rocket. The rocketeer simply starts at the left of the toolbar and works across filling in the measurements requested by the program. Starting with the airframe, a sub-window will request information about body diameter, nose cone shape (ogive, cone, hemisphere and parabolic), nose cone length, body tube length, finish quality (none good-painted, excellent)-polished and base shape (blunt or boat tail). The user will be prompted to add the nose cone length, and boat tail diameter if the rocket is so equipped. For rockets with increasing or decreasing transitions after the nose cone but before the end the rocket, the user simply specifies the base diameter as the transition diameter in the boat tail section. The rocket information is automatically entered onto the main screen during the data input session. The following inputs are required on the Airframe Parameters input screen by first clicking Airframe in the tool bar.

1) For Body Diameter enter 10.5 inches. This is the reference area (i.e. diameter) used to compute Cd and is the diameter just behind the nose cone.
2) For Nose Cone Shape use the pull-down menu and select, Cone.
3) Because nose cone length is required for defining a conical nozzle, please enter 52.5 inches for Nose Cone Length.
4) For Body Tube Length enter 175.5 inches. This is the entire length of the airframe not including the nose cone.
5) For Finish Quality enter Good, indicating a painted surface. However, None indicates a non-painted surface and Excellent indicates a polished surface.
6) Enter the Base Shape as Blunt. Because the Blunt Base Shape was selected, the Boat Tail Diameter is not required and is not enabled for data entry in this example. However, the optional Boat Tail selection models a transitional airframe shape normally used for drag reduction where the boat tail diameter is normally smaller than the airframe. The Boat Tail transition may also be used to model an airframe having an increasing or decreasing transition to a larger or smaller body size. For airframes with transitions, use the smallest diameter at the end of the airframe and use the Boat Tail option.
7) Leave the Motor Off option button selected. The Motor Off condition allows the computation of Cd without the jet-effect of the rocket motor and the Motor On condition allows the computation of Cd with the jet-effect of the rocket motor.
8) Click the CLOSE button to return to the main drag analysis screen.

8) OPTIONAL: AeroDRAG & Flight Simulation can estimate the drag effects of an in-line ramjet. The nose can incorporate an Open Nose Inlet for ramjet operation or simply a Blunt Nose for the condition where a ramjet inlet is blocked or simply for a blunt nose rocket. First, select whether to insert or remove the ramjet by selecting either the Insert Ramjet Duct or the Remove Ramjet Duct option button in the Select Ramjet section. Then, determine if the nose is an inlet to a ramjet or simply a blunt nose rocket by selecting either Open Duct or Blocked Duct in the Open/Closed Duct section. Finally, for an Open Duct ramjet select whether the duct inlet-edges are round or sharp by selecting either the Sharp Inlet Edge or Round Inlet Edge option buttons in the Inlet Edge section. The other inputs for Ramjet Duct Inlet Diameter, Inlet Cone Base Diameter, Cone Half-Angle, and Mass Flow Rate Ratio (M_out / M_in) are self-explanatory but are further illustrated in the Help section in the program. The Mass Flow Rate Ratio (M_out / M_in) is required to determine ramjet additive drag for subsonic and supersonic flow. Additive drag is caused by the loss of momentum of a stream tube of fluid passing through the ducted portion of the vehicle.

LAUNCH LUGS DATA ENTRY
For the launch lugs, the user inserts total launch lug length, inside lug diameter and outside lug diameter. A solid T-lug can be modeled by inserting 0.0 for the inside diameter and then inserting an outside diameter of a circular section having the same cross-sectional area as the solid launch lug. Multiply the launch lug length by the number of launch lugs.The following inputs are required on the Launch Lug Parameters input screen by first clicking Launch Lugs in the tool bar.

1) For total launch lug length enter Length as .75 inches. The length is the total length of all the launch lugs attached to the airframe.
2) For launch lug Outside Diameter enter 1.323 inches. This diameter is the equivalent OD of the rectangular frontal area of the T-lug.
3) For launch lug Inside Diameter enter 0.0 inches. Because a T-lug is solid the launch lug has no inside diameter.
4) Click the CLOSE button to return to the main drag analysis screen.

FINS DATA ENTRY
The fin pop-down menu has provision for up to 3 sets of fins. Required fin measurements include the fin sweep angle, total number of fin sets (1, 2, and 3), number of fins in each fin set (1, 2, 3, 4, 5, 6, 7, 8), fin edge shape (square, rounded, streamlined and double wedge), fin thickness, fin root chord, fin span and fin planform shape (triangle, rectangle, tapered and elliptical). The user will be prompted to include the fin tip chord for tapered fin planform shapes. Optionally, there are selections to include the drag effects of a single set of either Ring-Fins or Tube-Fins used for rocket stability. Data is automatically entered on the main screen during the data input session. Help is provided in the form of Help screens that display program nomenclature on various diagrams and step-by-step procedures are provided to operate the program. When all required measurements have been input into the program, drag coefficient (Cd) is determined as a function of Mach number (Mn) and velocity by dragging the velocity slider-bar control. Finally, Cd verses Mn is plotted by clicking the PLOT command button. The following inputs are required on the Standard Fins input screen by first clicking Fins then Standard Fins in the tool bar.

1) For Fin Sweep Angle enter 10 degrees by using the pull-down menu to select from a range of values.
2) Define the total number of fin sets by using the pull-down menu to select 1 Fin-Set.
3) Define the number of fins per fin-set by using the pull-down menu to select 3 Fins per fin-set.
4) For Fin Edge Shape use the pull-down menu to select the D'Wedge or supersonic double-wedge shape to approximate the shape used in this design.
5) For Fin thickness enter 0.375 inches as the fin average thickness.
6) For Fin Root Chord enter 20.0 inches.
7) For Fin Span enter 15.0 inches.
8) For Fin Planform Shape use the pull-down menu to select the Tapered fin.
9) Fin Tip Chord is is indicated as "required". Enter 15.0 inches for the Fin Tip Chord.
10) Click the CLOSE button to return to the main drag analysis screen.

GENERATE CD VERSES MACH NUMBER DATA
On the main Drag screen click the PLOT command button to generate the drag coefficient data necessary to perform a flight simulation analysis. Pulling the velocity slider-bar is not enough to generate the data required for a flight simulation. The status bar at the bottom of the main screen will say, "Cd verses Mn plot complete. Proceed to Flight Simulation" when all the necessary data has been entered and when the PLOT button has been clicked. At this point proceed to the Flight Performance Analysis screen by clicking Flight Simulation on the toolbar. For multiple stage rockets save the drag coefficient data for each stage configuration by clicking, Save As. Also, on the main Drag screen, Open the Cd vs Mn data file and then in the Flight Simulation screen, Insert the Cd vs Mn data for each stage of the rocket. Alternatively, manually enter the Cd by simply typing the Cd to the left of the Insert command button for each stage.

B) FLIGHT SIMULATION
For flight predictions of velocity, altitude and acceleration, AeroDRAG & Flight Simulation solves the basic equations of rocket motion using a finite difference procedure. Prior to performing a flight simulation the Cd verses Mn curve must be created by clicking the PLOT command button on the main Drag screen. This new release allows Cd to vary with Mach number for high speed and high altitude flight predictions. Once all data is entered, the user simply clicks the SOLVE command to calculate ballistic coefficient [lb/ft^2], Burnout Altitude [ft], Burnout Velocity [ft/sec], Maximum Acceleration [G's], Average Stage Cd(Mn), Coasting Ballistic Coefficient [lb/ft^2], Burnout to Max Altitude Distance [ft], Velocity at Coast Time [ft/sec], Altitude at Coast Time [ft], Max Altitude Time Delay [sec], Time to Max Altitude [sec] and Maximum Altitude [ft]. After a flight analysis is performed the user may compute maximum altitude optimal mass and maximum coast time optimal mass for his rocket with a few clicks of the mouse.

THRUST-CURVE DEFINITION
In the Flight Performance Analysis screen the user must display one of two methods of Thrust-Time data generation. By default, a pull-down menu of 290 motors are displayed where average thrust, burn time and propellant weight are listed for each rocket motor. The user can directly use the displayed values of average thrust, burn time and propellant weight or insert other values. The default list of 290 motors is obtained by clicking Input Thrust Curves on the toolbar and then clicking Pull-Down Motor List. In addition, for the pull-down menu of 290 motors the user can edit those values by clicking Generate Thrust Curves and then clicking Rocket Motor List Editor. While in the Rocket Motor Editor the user can Add Motor data, Update Motor data and review the other motors in the list.

For the OuR Rocket example presented here the Thrust-Time curve data may be defined by the Free-Form method or by the Manual Entry method. The Thrust-Curve Generation screen is displayed by clicking Generate Thrust Curves on the top toolbar and then clicking Free-Form Thrust Curve. Using the Free-Form editor the Thrust-Time curve is generated by dragging up to 20 points into position using the cursor.  Generate a Thrust-Time curve by toggling between the The Free-Form and Manual Entry options by clicking the Display Free-Form or manual input fields button on the side toolbar of the Manual Entry and Free-Form Thrust Curve Generation screen.

OPTION 1: Free-Form Thrust-Curve Method
1) Establish the maximum burn-time scale along the horizontal time-axis by inserting the maximum plot scale of 14.5 sec into the box labeled, Max Burn-Time (X).
2) Establish the maximum thrust scale along the vertical thrust-axis by inserting the maximum plot scale of 6,000 pounds into the box labeled, Max Thrust (Y).
3) Click the Up/Down control until 9 points are displayed on the plot.
4) Using the cursor, slowly drag each thrust-time point into place on the plot.
5) In the toolbar select the icon labeled Save Thrust-Time Curve (floppy icon) to save the thrust-time data as an .FVT file (FVT stands for Force Verses Time).
6) Perform these operations for each rocket motor required in the analysis for each stage and save using different file names.
7) Click the Quit Thrust-Curve Generation option on the toolbar to return to the Flight screen.

OPTION 2: Manual Thrust-Curve Method
1) Establish the maximum burn-time scale along the horizontal time-axis by inserting the maximum plot scale of 14.5 sec into the box labeled, Max Burn-Time (X).
2) Establish the maximum thrust scale along the vertical thrust-axis by inserting the maximum plot scale of 6,000 pounds into the box labeled, Max Thrust (Y).
3) Click the Up/Down control until 9 points are displayed on the plot.
4) Insert thrust and time data describing the Thrust-Time curve into each data box.
5) In the toolbar select the icon labeled Save Thrust-Time Curve (floppy icon) to save the thrust-time data as an .FVT file (FVT stands for Force Verses Time).
6) Perform these operations for each rocket motor required in the analysis for each stage and save using different file names.
7) Click the Quit Thrust-Curve Generation option on the toolbar to return to the Flight screen.

Back in the Flight Performance Analysis Screen perform the following:
8) Click Atmosphere to display the Atmospheric Conditions and 2-D Flight options screen. This screen defines the launch site temperature and elevation and whether the rocket is Ground-Launched or Air-Launched. Also, this screen specifies the initial orientation of the launch as either vertical as for a V-2 rocket or horizontal as for the SS1 space plane when air-launched. In addition, by specifying a Flight Path Angle other than 90 degrees this screen allows AeroDRAG to perform a 2-Dimensional Flight Analysis. Otherwise, if the Flight Path Angle is 90 degrees a standard 1-Dimensional Flight Analysis is performed. For the OUR Rocket analysis insert 80 degrees F as the launch site temperature and 3,393 feet for the launch site elevation.  In addition, click Ground-Launched and make sure the Flight Path Angle is set to 90 degrees from the horizontal. Please see the SS1 and V-2 examples for further explanation of the Atmospheric Conditions and 2-D Flight options screen.
9) Import the thrust-time data by clicking the Import Thrust vs Time command button and selecting the previously saved thrust-curve .FVT file.
10) For Propellant Weight enter 284.5 lbs.
11) For Number of Motors enter 1.
12) For Total Weight with Motors enter 660.0 lbs.
13) For Reference Diameter enter 10.5 inches. The reference diameter should be the same as the Body Diameter previously defined.
14) For the estimated Coast Time enter 151 seconds. If the value of Coast Time input here is less than the actual Coast Time to apogee from last stage burnout, the program will display,
Increase Tc, to indicate a larger value of Coast Time needs to be input instead.
15) In the Cd Selection section click the Cd vs. Mn Curve option button. Then, click Insert next to the Drag Coefficient [Cd] input box. If the Cd vs. Mn has been plotted on the main Drag screen the message, Stage-1 Cd verses Mn has been inserted successfully, will be displayed in the status bar at the bottom.
16) Click SOLVE, to perform a flight simulation analysis. If the solution is successful the message, Flight Solution Complete, will appear in the status bar. However, if the Cd verses Mn range is insufficient to cover the Mach number range of the analysis the message, WARNING, Increase S1 Mn on main screen, indicating the Maximum Mach number on the main Drag screen should be increased for the Cd vs. Mn Curve option. Also, in general the
Cd may be inserted manually or the Slider-Bar or Cd vs. Mn Curve option button selected for Cd to be specified for any flight analysis. By default, the Cd Slider-Bar or manual entry method of Cd entry appears.

FLIGHT SIMULATION ANALYSIS
After clicking SOLVE the following data is computed: Ballistic Coefficient [lb/ft^2], Burnout Altitude [ft], Burnout Velocity [ft/sec], Maximum Acceleration [G's], Average Stage Cd(Mn), Coasting Ballistic Coefficient [lb/ft^2], Burnout to Max Altitude Distance [ft], Velocity at Coast Time [ft/sec], Altitude at Coast Time [ft], Max Altitude Time Delay [sec], Time to Max Altitude [sec] and Maximum Altitude [ft]. After a flight analysis is performed the user may compute maximum altitude optimal mass and maximum coast time optimal mass for the rocket with a few clicks of the mouse. For optimal mass prediction, the calculus equations presented in TR-10 allow AeroDRAG & Flight Simulation to determine optimal mass faster than any other flight simulation program. Rapid computation of optimal mass is now a practical tool. Finally, in the toolbar click Plot Results (or click the plot) to display the Velocity verses Time, Altitude verses Time, Mn verses time, Theta verses time (q, degrees) and Acceleration verses Time (G's, Gx's and Gz's) curves describing the thrusting (red) phase and coasting (blue) phase of flight.

IMPORTANT NEW FEATURE: AeroDRAG & Flight Simulation automatically computes the average Cd over a range of Mach number for rockets having up to 3 stages. When the Cd vs. Mn Curve is selected, the flight simulation averages Cd over the actual velocity (Mn) range for each stage. For example, Cd for the first stage is averaged from 0.0 to V1Max, Cd for the second stage is averaged from V1Max to V2Max and Cd for the third stage is averaged from V2Max to Vfinal (t =Tc). The average Cd for each stage computed by AeroDRAG & Flight Simulation may be entered into other flight simulation programs for more accurate predictions of velocity, altitude and acceleration.

 STAGE-1 Ballistic Coefficient [lb/ft^2] 2,751.46 Burnout Altitude [ft] 20,365.67 Burnout Velocity [ft/sec]/[M] 2,710.14 (M 2.7) Maximum Acceleration [G's] 6.85 Average Cd F(Mn) .40445 COASTING Ballistic Coefficient [lb/ft^2] 1,677.31 Burnout to Max Altitude Distance [ft] 77,986.07 Velocity at Coast Time [ft/sec]/[M] -1,628.6 (M 1.48) Altitude at Coast Time [ft] -6.62 Max Altitude Time Delay [sec] 67.85 Time to Max Altitude [sec] 82.35 Maximum Altitude [ft] 98,351.7

 Results Time to Apogee [sec] Error Apogee Altitude [ft] Error OuR Rocket Flight Measurement 80 - 94,000 - AeroDRAG & Flight Simulation, Cd = Fn(Mn,Rn) 82.35 +2.9% 98,352 +4.6% Rogers Aeroscience ORBIT V4.5 (1997) 84.24 +5.3% 105,132 +11.8%

MULTI-STAGE ANALYSIS USING CD THAT VARIES WITH MACH NUMBER
Specifying a constant drag coefficient (Cd) for each stage of a multi-stage rocket is very simple. First, in the Flight routine specify the number of stages in the Stage Selection region by clicking one of the three option buttons. Then, in the Cd Selection region select the Slider-Bar Value option button and click Insert to use the Cd from the main AeroDrag screen for each stage of the rocket. Alternately, the Cd may be entered manually into the Drag Coefficient [Cd] data entry box for each stage of the rocket. Finally, perform a Flight analysis once the motors, stage weights, reference diameters and coast time are specified by clicking SOLVE. Note: the reference diameter for each stage of the rocket should be the diameter at the base of the nose cone and should be the same for each stage of the rocket. However, variable reference diameter input was provided to accommodate the case where the Cd for each stage of the rocket is determined from the maximum diameter of each stage.

For a multi-stage rocket the procedure to specify Cd as a function of Mach number for each stage is a little more involved. The first step is the creation of the drag files that describe the geometry and therefore drag of each stage of the rocket. For a two stage rocket the first drag file is saved from the main AeroDrag screen using the Save As command. The first drag file includes the booster and its fins and the sustainer and its fins. The illustration labeled Stage-1 describes the first stage of the rocket. The second stage drag file is also created from the main AeroDrag screen using the Save As command. The second stage drag file includes the sustainer and its fins. The illustration labeled Stage-2 describes the second stage of the rocket.

After the two drag files for a two stage rocket have been defined, display the first stage drag file on the main AeroDrag screen using the Open command. Immediately click PLOT and proceed directly to the Flight routine. In the Flight routine specify the number of stages in the Stage Selection region by clicking one of the three option buttons. Then, in the Cd Selection region select the Cd vs. Mn Curve option button and click Insert to input the Cd verses Mach number curve generated on the Main AeroDrag screen for the first stage of the rocket. Go back to the main AeroDRAG screen and display the second stage drag file using the Open command and click PLOT and proceed directly to the Flight routine. Click Insert to input the Cd verses Mach number curve generated on the Main AeroDrag screen for the second stage of the rocket. Finally, perform the Flight analysis once the motors, stage weights, reference diameters and coast time are specified by clicking SOLVE. Note: the reference diameter for each stage of the rocket should be the diameter at the base of the nose cone.

 Stage-1 Stage-2

MAIN SCREEN DRAG ANALYSIS SCREEN, GO BACK

AIRFRAME SCREEN, GO BACK

LAUNCH LUGS SCREEN, GO BACK

STANDARD FINS SCREEN, GO BACK

FLIGHT SIMULATION ANALYSIS SCREEN, GO BACK

FLIGHT SIMULATION ANALYSIS PLOTS, ALTITUDE VERSES TIME, GO BACK

FLIGHT SIMULATION ANALYSIS PLOTS, ALTITUDE VERSES TIME, GO BACK

ROCKET MOTOR EDITOR SCREEN, GO BACK

FREE-FORM THRUST-CURVE GENERATION SCREEN, GO BACK

OPTIMAL MASS AND OPTIMAL COAST TIME ANALYSIS SCREEN, GO BACK
For optimal mass prediction, the calculus equations presented in TR-10 allow AeroDRAG & Flight Simulation to determine optimal mass faster than any other flight simulation program. The Optimal Mass analysis displays Maximum Coast Time (sec) when computing Maximum Altitude Optimal Mass and displays Maximum Altitude when computing Maximum Coast-Time Optimal Mass. Before performing an optimal mass analysis be sure to perform a flight simulation on the Flight Performance Analysis screen.

1) Perform Flight Simulation Analysis.
2) During the flight simulation make sure the Cd is inserted manually or the Slider-Bar or Cd vs. Mn Curve option button is selected and the Pull-Down Motor List is chosen.
3) Start by clicking the Increase Initial Mass command button and click until the red instructions above the plots say to click the Increase Final Mass command button.
4) The Maximum Altitude Optimal mass in pounds and grams is displayed in the Optimal Mass Simulation section. Also, the Maximum Altitude and the associated Maximum Coast Time is displayed in the upper plot to the right.
5) The Maximum Coast Time Optimal mass in pounds and grams is displayed in the Optimal Mass Simulation section. Also, the Maximum Coast Time and the associated Maximum Altitude is displayed in the lower plot to the right.

 Maximum Altitude Optimal Mass (lb) Maximum Altitude (ft) Maximum CoastTime (sec) Maximum CoastTime Optimal Mass (lb) Maximum CoastTime (sec) Maximum Altitude (ft) AeroDRAG & Flight Simulation 2.300 2742.86 8.503 3.780 9.448 2443.27 Popular Flight Simulation Program 2.257 2892.87 NA NA NA NA

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