Rasp XP

Rocket Altitude Simulation Program for Windows

Rasp XP is a Windows program that simulates the flight of a rocket in one dimension (one degree-of-freedom).

Outline

1.      Origin

2.      Physics

3.      Data Flow

4.      Databases

5.      DigiTrak

6.      Software modules

1.      Origin of wRASP

The original RASP was a BASIC program written by Harry Stine in 1979 and published in his Handbook of Model Rocketry.

DOS RASP was converted to the C programming language by Mark Storin in 1989. New features were added by Kent Hoult in 1990 and Mark Johnson in 1990-94.

wRASP is an adaptation of that venerable RASP program for DOS that runs with a typical Windows graphical user interface (GUI). It was first made available to Compuserve’s Sport Rocketry forum in 1995.

Rasp XP is a new incarnation of wRASP, which has not has an update since 1998. Rasp XP is rebuilt to run on any Windows system from Windows 95 up. Refinements have been made to file handling, data handling, and calculations. Further improvements will see the use of XML as the preferred data format, additionally output formats, multiple degrees of freedom in analyses, and user interface improvements.

Wrasp 2.0 and Rasp XP 3.0 and up includes Larry Curcio's DigiTrak, and is based on his version 5.4. v2.0 also includes the NAR tracking algorithms, also originally available in BASIC.

2.      Physics

Simulation programs typically define the level of sophistication of the program in “degrees of freedom” (DOF). These define how the airframe behaves in 3 dimensional space. The maximum degrees of freedom is six, three for movement (x,y,z) and three for rotation (roll,pitch,yaw). A full simulation is usually referred to as a “Six-DOF”.

The simulation engine in wRASP is “raspsubs.c”, derived directly from the main program in DOS RASP’s “rasp.c”. This engine has always been altitude only (specified as “x”), so they are both One-DOFs.

The simulation engine solves the differential equations for velocity and position by resolving the force summation on the rocket. The method is basic numerical methods for integrating acceleration and velocity:

                        a = åF/m        (from F=ma)

              ⌠

v = │a dt = a Δt + v₀

              ⌡

         ⌠

x = │v dt = v Δt + x₀

              ⌡

            where: F = force in newtons

                                    m = mass in kilograms

                                    a = acceleration in meters/second²

                                    v = velocity in meters/second

                                    x = distance in meters

                                    dt = differential time in seconds

                                    Δt = delta time in seconds = 0.001 second

The time step () was originally 0.1 second but was later changed to one millisecond (0.001 second). There are provisions for changing it but they are currently not implemented.

The simulation continually calculates these values and monitors for these events:

            When altitude (x) reaches the top of the launch rod

            Motor burn-out

            Apogee

            Motor delays

            Ground impact

The force summation is the guts of these calculations:

            åF = (th - drag)

            where: th = thrust in Newtons

                                    drag = drag force in Newtons

The thrust is determined by the motor(s)’s thrust-time curve and the time into the burn. The drag is based on:

            drag = c v²      (a form of ½ ρ v²)

            where: drag = drag force in Newtons (kg m/sec²)

c = drag form factor

v = velocity in meters/sec

The drag form factor is defined as:

            c = ½ r  π  C_D  d² / 4

            where: c = drag form factor in kilograms/meter

                                    r = atmospheric constant in kilograms/meter³

                                    C_D = coefficient of drag

                                    d = maximum body tube diameter in meters

The atmospheric constant is a function of the air density (ρ). The original RASP program used a constant value of:

r = 1.205 kg/m³

Rasp XP also allows the use of an atmospheric model to calculate the air density (ρ) at a specific altitude above mean sea level:

r = ρ 32.1725 / 2.204623 / 0.028317

where: ρ = air density in slugs/feet³

                        rest = the constants to convert to kilograms/meter³

Acceleration is then calculated:

     a = (thrust - drag)/m – G         (upward motion)

     a = drag/m – G                    (downward motion)

            where: a = acceleration in meters/second²

th = thrust in Newtons

                                    drag = drag force in Newtons

                                    m = mass in kilograms

                                    G = acceleration of gravity in meters/second²

Mass varies with motor burn and staging. It is assumed that 100% of the propellant weight specified in the motor data file is consumed from the beginning to the end of the motor burn time. This can be done two ways:

            m = total motor mass – (burn time)/(total burn time)*(propellant mass)

            m = motor mass – (expended impulse)/(total impulse)*(propellant mass)

Rasp XP uses the first method – linear reduction of mass during the burn. The second is probably more accurate – this may be added as an option in the future.

3.      Data Flow

4.      Databases

rasp.eng – motor data

; semi-colon in the first column followed by text is a comment and is not processed.

Type  diameter  length  delays  propellant_wt  total_wt  mfg  notes

time1 thrust1

time2 thrust2

...

timeN thrustN

Internally, prior to wRASP v1.61, each motor was stored in blocks of 64 values – a maximum of 32 time/thrust pairs were allowed.

From v1.61 and later, motor data values were stored in a “pool” of 16384 double precision values. There is no maximum for an individual motor.

rocket.dat – rocket kit database

mfg name [; alias#1] [; alias#2]...

weight length diameter max_alt

catalog#, motor list (catalog date) price

Useful if the data is complete. Many manufacturers do not include a typical rocket empty weight.

vendor.dat – manufacturer data

abbreviation full_name [; abbrev alias#1][...]

The rocket database is only used to browse the kit list. The vendor list is used to identify the manufacturer of a motor or kit.

5.      DigiTrak (by Larry Curcio)

Special Features:           optimal mass calculation

                                          C_D backtracking (time or altitude based)

DOS DigiTrak used a separate program, AIRSTART, to combine the thrust curves of multiple motors. Rasp XP does this automatically and outputs the result in airstrt1.out for stage 1, airstrt2.out for stage 2, and airstrt3.out for stage 3.

See the “help” file for additional DigiTrak information and tips on backtracking. Larry’s original discussions from his DigiTrak version are included there.

Newton’s method of slope (first derivative) is used to adjust the C_D while backtracking. The C_D is not allowed to go below 0.015.

6.      Software Modules

7.      Resources

The latest versions and source will appear here:

http://www.aresinstitute.org

General rocketry calculations:

http://www.execpc.com/~culp/rockets/rckt_eqn.html

http://www.execpc.com/~culp/space/space.html