AeroDRAG & Flight
Simulation An Aerodynamic Drag & Flight Simulation Computer Program for Microsoft Windows By AeroRocket AeroDRAG & Flight Simulation Instruction Manual OuR (High Speed) Rocket Example | MAIN PAGE | SOFTWARE LIST | AEROTESTING | MISSION | RESUME | Copyright © 1999-2015 John Cipolla/AeroRocket |
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 & Flight Simulation Main Screen, OuR Rocket Cd Analysis For more information about AeroDRAG & Flight Simulation please contact John Cipolla. |
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.
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For more information
about AeroDRAG
& Flight Simulation please contact John Cipolla.
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