AeroDRAG & Flight Simulation ($35.00) New! An Aerodynamic Drag & Flight Simulation Computer Program for Microsoft Windows By AeroRocket | Buy On-Line | Add To Cart | For Instructions Please Click Below AeroDRAG & Flight Simulation Instruction Manual OuR (High Speed) Rocket Example

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.

AERODRAG HISTORY
Very early during his participation in model rocketry John Cipolla recognized the need to develop a methodology for the accurate estimation of rocket drag coefficient (Cd) for accurate model rocket altitude and velocity prediction. Before the availability of personal computers, empirical and graphical data from the book, "Fluid Dynamic Drag" by Dr. S. F. Hoerner was used to compute zero-lift model rocket drag. Having to compute zero-lift drag for each and every model rocket configuration was a tedious and time-consuming process. However, empirical methods proved to be inadequate and experience in the aerospace industry provided the theory to develop a new methodology for predicting model rocket drag. The best single source for the theory used in his early work for estimating subsonic rocket drag is contained in report TR-11, Aerodynamic Drag of Model Rockets by Estes Industries. For several years, MathCAD, a mathematical-equation spreadsheet program, was used to solve the equations described in TR-11 to estimate rocket drag. The components of rocket drag computed by those early MathCAD analyses included the nose and body friction drag, base drag, fin surface drag, fin interference drag, and launch lug drag. MathCAD computed the major drag components and summed the results for zero-lift drag as a function of velocity and Mach Number. He used those MathCAD drag analyses extensively until 1994 when he developed a series of C++ computer programs for the Macintosh called DRAG. In 1996 the C++ DRAG computer program was converted to Visual Basic 3 and then converted to Visual Basic 6 in 1999 to utilize the Windows Graphical User Interface (GUI). The program's name was changed to AeroDRAG when the capability to estimate transonic and hypersonic rocket drag was included in November 1999. In the future new innovations will include air-start rocket motors and other exotic configurations.

NOTE: AeroDRAG & Flight Simulation is a completely revised version of the previous AeroDRAG, version 5.1. Many data input problems have been corrected and the new flight simulation routine make AeroDRAG & Flight Simulation a totally new computer program. Please contact John Cipolla at aerocfd@aerorocket.com to upgrade to AeroDRAG & Flight Simulation if you are a previous purchaser. Please provide name, address, date of purchase and email.


BASIC PROCEDURE
Unique AeroDRAG & Flight Simulation features include a velocity slider bar control that constantly displays velocity and automatically updates all drag components in real-time as a function of Mach number and velocity. Graphical output is automatically scaled regardless of maximum Mach number requested by the user or magnitude of drag coefficient computed within the program. Presently, AeroDRAG includes the ability to model 3 sets of fins having up to 8 fins per set. In addition, cone, ogive, parabolic and hemispherical nose shapes are incorporated as well as blunt and boat tail base shapes. Fin shapes include rectangular, triangular, swept-tapered and elliptical planforms that can have squared, rounded, streamlined and double wedge cross-sections. Launch lugs may also be included in a typical drag coefficient analysis.

The drag analysis program 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 type (i.e. ogive, parabola, etc), body tube length, finish quality and base shape. 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 transition 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 into the main Drag screen during the data input session. For the launch lugs, the user inserts total 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. The fin pop-down menu has provision for up to 3 sets of fins. Required fin measurements include the total number of fin sets, number of fins in each fin set, fin edge shape, fin thickness, fin root chord, fin span and fin planform shape. The user will be prompted to include the fin tip chord for tapered fins. Again, data is automatically entered onto the main Drag 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.

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 needs 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. 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.


FLIGHT SIMULATION THEORY
The basic equation of rocket motion during thrusting and coasting is obtained from Newton's First Law of Motion, SF = ma. Where, SF is the summation of all external forces applied to the rocket, m is the mass of the rocket and a is the acceleration of the rocket. Acceleration is also expressed as dV/dt or the rate of change of velocity with respect to time. The forces acting on a rocket during the thrusting phase of flight are its weight (W), thrust (T), and aerodynamic drag ( D = Cd * 1/2 * r * V^2 * A). Where Cd is the drag coefficient, r is the air density, V is the velocity and A is the reference area of the rocket, typically the section just behind the nose cone. However, during the coasting phase of flight the forces acting on the rocket are its weight (W) and aerodynamic drag ( D = Cd * 1/2 * r * V^2 * A) and T (Thrust) = 0 because the rocket motor is no longer operational.

THRUSTING PHASE OF FLIGHT
For vertical flight, Newton's equation of motion for the thrusting phase becomes: m * dV/dt = T - Cd * 1/2 * r * V^2 * A - W. The following equation is derived for the term, dV/Dt, Notice that m = W/g in the equation of motion. The acceleration term, dV/dt determines the added (+/-) increment of velocity at the end of each time step (Dt) during the flight integration process where dV = dV/dt * dt is the incremental velocity.


Velocity (V) and altitude (H) at the (n+1)'th time level are determined from the following equations knowing the velocity and altitude at the previous or n'th time level. Typically, the initial thrusting boundary conditions are V(1) = 0.0 ft/sec and H(1) = 0.0 feet at t = 0 seconds. The equations of motion are integrated by performing the analysis at a time step, Dt. These equations can be integrated using a variety of techniques including the Euler method or ordinary time stepping.


Rocket acceleration (G's) is estimated using the following equation. Where, V is the rocket velocity, Dt is the time increment and g is the local acceleration of gravity.


COASTING PHASE OF FLIGHT
For vertical flight, Newton's equation of motion for the coasting phase becomes: m * dV/dt = - Cd * 1/2 * r * V^2 * A - W. The following equation is derived for the term, dV/Dt, Notice that m = W/g in the equation of motion. The acceleration term, dV/dt determines the added (+/-) increment of velocity at the end of each time step (Dt) during the flight integration process where dV = dV/dt * dt is the incremental velocity.


Velocity (V) and altitude (H) at the (n+1)'th time level are determined from the following equations knowing the velocity and altitude at the previous or n'th time level. Typically, the initial coasting boundary conditions are V(1) = VbMax ft/sec and H(1) = HbMax feet at t = 0 seconds. The equations of motion are integrated by performing the analysis at a time step, Dt. These equations can be integrated using a variety of techniques including the Euler method or ordinary time stepping.


Rocket acceleration (G's) is estimated using the following equation. Where, V is the rocket velocity, Dt is the time increment and g is the local acceleration of gravity.


In Summation, If you are like many entering hobbyists who can't afford a great deal without cutting into your flying budget, AeroDRAG & Flight Simulation is a very cost-effective, viable alternative to the other higher priced computer programs on the market.

PROGRAM REVISIONS
AeroDRAG 7.1.0 Fix (05/10/2007)
Fixed run time error resulting in program termination that occurred when forgetting to insert a value for Max Thrust (Y) or Max Burn-Time (X) in the Thrust-Curve Manual Input and Display screen. Run Time error also occurred when highlighting these values and back spacing to insert a value.

AeroDRAG 7.0.0 NEW Features (05/14/2005)
1) Model 2-dimensional flight path of rockets that fly in the proximity of the gravitational field of the Earth. Accurate solutions to 500 km.
3) Launch rockets either vertically (V-2) or horizontally (SS1) by selecting the Vertical or Horizontal Take-off options.
2) New plot screen options include, flight path angle (q) verses time, axial acceleration verses time (G), vertical acceleration verses time (Gy), horizontal acceleration verses time (Gx). Also output on the plot screen are altitude at impact/coast time, Mach number at impact/coast time, velocity at impact/coast time, range at impact/coast time, time from lift-off to impact, apogee altitude and 2-dimensional residual accuracy.
4) Perform roll maneuvers for 2-dimensional flight by specifying the final flight path angle at insertion, time from lift-off to roll initiation and time from lift-off to flight path angle insertion. A linear variation of roll angle verses time is assumed during the programmed roll maneuver.
5) Include lift to drag ratio (L/D) of rockets with oversized fins, like the V-2 rocket in performance determination.
6) Greatly improved speed of point response in the Free-Form Thrust-Curve screen (increased by a factor of 10).

AeroDRAG 6.2.3 NEW Features (03/28/2005)
1) In addition to plotting Altitude, Velocity and Acceleration in G's verses time this version includes an option button to plot Mach number verses time.
2) Improved the Cd verses Mach number and air density (r) verses Mach number interpolation routines for smoother plots of Altitude, Velocity, Acceleration and Mach number verses time.

AeroDRAG 6.2.2 Revisions and Fixes (03/26/2005)
1) A sign error of the drag component (D) in the descent acceleration equation (dV/dT) caused the program to compute incorrect velocity (V), altitude (H) and total acceleration (G) during the downward trajectory of the rocket. This error condition does not affect the predictions for velocity, altitude and acceleration for boosting or coasting during ascent (that is, while the rocket is going up). 
2) Fixed a slight error (<1% for altitude and velocity) in the atmospheric model that determines air density as a function of altitude.
3) Modified the velocity plot screen to "fully" display positive velocity during ascent and negative velocity during the downward trajectory of the rocket.
4) Added the ability to specify whether a rocket is ground-launched or air-launched in the Atmospheric Properties screen.

AeroDRAG 6.2.1 Fixes (03/10/2005)
1) A Cd determination error occurred when Opening design files if the number of fins equaled 1,2,5 or 7 for fin-set 1, fin-set 2 or fin-set 3. The correct number of fins per fin set appeared correct on the main drag screen and on the Fin Data Entry screen, but the values were incorrect internally. A work around for this problem in the previous version is simply to refresh the number of fins per fin-set in the Fin Data Entry screen.

AeroDRAG 6.2.0 Features
1) Added the option to specify 1 and 2 fins per fin-set for 1 to 8 fins per fin-set. This modification allows AeroDRAG to model the aerodynamic drag effects of aircraft type configurations having two wings, two horizontal stabilizers and one vertical rudder, for example.

AeroDRAG 6.1.0 Features
1) Added the option to save flight data to a CSV file for generating plots within Excel or reviewing by NotePad. Flight time, velocity and acceleration are output for each stage and during the coasting phase of flight.
2) Added the option to specify 5 and 7 fins per fin-set for 3 to 8 fins per fin-set.

| BACK TO TOP | BACK TO INSTRUCTIONS |

For more information about AeroDRAG & Flight Simulation please contact AeroRocket at john@aerorocket.com.

| MAIN PAGE | PRODUCTS | CONSULTING | MISSION | RESUME | Buy On-Line | Add To Cart |