# The following is from the Sky Dark team web site and it is published with authorisation from its author so that it can be translated in other languages.

## Adding New Engine

**Note: **The below tip is irrelevant for the later versions. Starting from the release 1.1.9 custom engine data can be loaded through **Edit/Preferences/Options/User-defined trust curves**.

It is possible to add a custom engine data file to Open Rocket, though it is not a straightforward procedure. Some advises can be found on the Open Rocket forum. One of the ways to do it is with a help of WinZip software. You have to open the .jar file through WinZip or something similar. Then go to datafiles\thrustcurves\ folder. There you'll see files representing motors available in OR. There are two different types .eng and .rsp. For some motors there may be a couple of different files in different format. Both can be viewed in a text editor. .eng format is easier to work with and I usually use it if I want a custom made thrust curve. Elsewhere on http://www.thrustcurve.org/motorstats.shtml there is a description of both formats, but basically it's just a list of time-thrust values with some additional information in the first row, such as a motor weight, delay etc. Alternately I suggest you just compare what OR shows and context of the corresponding file.

Here are the steps again:

- Start WinZip and open the Open Rocket .jar file (for example OpenRocket-1.1.0.jar). All thrust curves can be found in datafiles/thrustcurves folder.
- Using menu Action-Add or Add button on the WinZip tool bar add a new .eng file to the thrustcurves folder.

## Simulating Boosted Darts

A boosted dart rocket is a vehicle consisting of a rocket booster and an un-powered upper stage called " a dart". The dart separates from the booster due to a difference in drag and coasts to the apogee.

Here are several examples of boosted darts:

- Loki Dart
- Hopi Dart
- RRS 50 boosted dart project (large pdf download!)
- Loki model project

Excellent NARAM -31's report by Spaceman Spiff Team provides very useful theoretical inside and experimental data related to the boosted dart type model rockets.

OpenRocket can be used to simulate this type of rockets. The trick is to represent the dart as a powered sustainer using a motor with an insignificantly small impulse. A "dummy dart motor" file is attached at the bottom of this page. After adding it to the Open Rocket *thrustcurves* folder as described above, the dummy motor appears in the motor list under TheSkyDart name (see the screen-shot below).

The manufacture can be changed to any name by editing the .eng file in a text editor.

**;;Dummy A size motor with 0 thrust.A0T 13 45 0-2-4-6-8-10-20-40-60-80-100 0.0001 0.0001 TheSkyDart 0.01 0.00010.1 0.00010.2 0.00010.3 0.00010.4 0.00010.5 0.00010.6 0.00010.7 0.00010.8 0.00010.9 0.00011.0 0.0;**

The motor provides several delay options, but again they can be easily modified to any desired value.

The sustainer motor ignition should be specified as "*First burnout of previous stage*".

## Dynamic Stability Characteristics

This section is added to reflect upon the six-part series of articles in Apogee's news letter, Peak of Flight. These are:

Issue #192 - (09/11/07) Basics Of Flight Analysis - Moment Of Inertia

Issue #193 - (09/25/07) Basics Of Flight Analysis – Corrective Moment Coefficient

Issue #195 - (10/23/07) Basics Of Flight Analysis - Damping Moment Coefficient

Issue #196 - (11/06/07) Basics Of Flight Analysis - Radial Moment of Inertia and the Natural Frequency

Issue #197 - (11/20/07) Basics Of Flight Analysis - Damping Ratio

Issue #198 - (12/04/07) Basics Of Flight Analysis - Optimizing For Altitude

The formulae presented in the articles can be found in 'Advanced Topics In Model Rocketry' by Mandell, Caporaso, and Bengen. The book is quite rare thus quite expensive. However, the basis if the Dynamic Stability section of the book was published as a series of articles in Volume 1 of Model Rocketry magazine (in 1968; #10 and #11 and in 1969; #1, #2, #3 and corrections in #4).

There are several parameters important to a rocket dynamic stability characteristics. The above literature provides the relevant formulae and suggest some design criteria to be adhered to to get required performance of a model. These characteristics are:

- IL = Longitudinal Moment of Inertia
- C1 = Corrective Moment Coefficient
- C2 = Damping Moment Coefficient
- IR = Radial Moment of Inertia (not analysed here)
- ωn = Natural Frequency
- z = Damping Ratio

Of the above list only the Longitudinal Moment of Inertia is explicitly calculated in OR and it is available for plotting and exporting. The rest is not available in the current release of the tool. However, with some additional Excel processing it is still possible to get these parameters.

### Corrective Moment Coefficient

To compute C1 the following formula is to be used:

C1= (V^2)*Aref*Cna*(Z-W)*p/2 **(1)**

Where:

p- density of air, approx 1.24 kg/m^3

V- velocity of the rocket (Total velocity of rocket in OR), m/sec

Aref - reference area, m^2

Cna - normal force coefficient

Z- CP of the rocket , m

W - CG of the rocket, m

In (1) velocity V, reference area Aref, centre of pressure Z and CG of the rocket W can be directly obtained from OR.

There are two ways to obtain the Normal Force coefficient Cna. It can be calculated as follows:

Cna= Cn/alfa **(2)**

Where:

Cn - Normal force coefficient as it is calculated by OR (name is confusing, but it is a slightly different parameter).

alfa - Angle of attack, rad

In (2) both Cn and alfa can be obtained from OR. It has to be noted that (3) is a valid approximation for small angles of attack.

Alternatively a value of Cna corresponding to a particular angle of attack is available on the Stability tab of Analyze/Component Analysis menu. The required value is the Cna column row Total (3.47 on the picture below)

Note that the total Cna depends upon Angle of Attack and speed (Mach number). The Angle of Attack should be set to 0deg, but the Mach number can be set to any value between Vmax and 0 (I need to do some more characterisation here)

### Natural Frequency

Once C1 coefficient is calculated the Natural Frequency ωn can be calculated as follows:

ωn =sqrt(C1/IL) **(3)**

Where:

ωn - natural frequency, rad/sec

C1 - corrective moment coefficient

IL - Longitudinal Moment of Inertia, kg*m^2

### Damping Moment Coefficient

The Damping Moment Coefficient is calculated using the following formula:

C2=C2r + C2a **(4)**

Where:

C2- Damping Moment Coefficient

C2r – Propulsive Damping Moment Coefficient

C2a – Aerodynamic Damping Moment Coefficient

Propulsive C2r is calculated using the following formula:

C2r = m_dot * (Ln-W)^2 **(5)**

Where:

m_dot – mass expulsion rate, kg/sec

Ln – Distance to the nozzle throat from the tip of the nose cone, m

W - CG of the rocket from the nose cone tip, m

m_dot component can be approximately calculated as follows:

m_dot = propellant mass/burn time [kg/sec] **(6) **

The Aerodynamic Dumping Moment Coefficient C2r is calculated as follows:

C2r = (V*Aref*p/2)* SUM(Cnai*(Zi-W)^2) **(7)**

Where:

p- density of air, approx 1.24 kg/m^3

V- velocity of the rocket (Total velocity of rocket in OR), m/sec

Aref - reference area, m^2

Cnai - normal force coefficient of the individual components

Zi- Distance from the nose cone tip to CP of the component , m

W - CG of the rocket, m

V and Aref are available in OR export, however Cnai and Zi are not exported and have to be extracted manually. They can be found in menu Analyze/Component Analysis, tab Stability (see the example picture under formula (2) above). There Cnai for each element is provided in the column CAN, and column CP provides Zi. Note that (7) requires CP to be in meters.

### Damping Ratio

Finally, the Dumping Ratio is calculated as follows:

DR = C2/(2*SQRT(C1*IL)) **(8)**

Where:

C2 - Damping Moment Coefficient (4)

C1 - Corrective Moment Coefficient (2) (see Calculation of Natural Frequency in OpenRocket)

IL - Longitudinal Moment of Inertia, kg*m^2 (available in OR export)