Parameters to Cover All Types of Engineering Data
Engineering data can come in many forms, including constants, multi-dimensional tables, derivatives, equations and rates of change. In some cases, resultant variables can be combinations of the above and all need to be managed and evaluated at each analysis step.
When writing code, routines need to be written to calculate each of these variables and the summation equations for each resultant parameter must also be included. If new contributions are added, they too need to be evaluated and added to the totals.
Values and derivatives can vary from constant (simple) values through to multi-dimensional tables or equations. J2 Aircraft Dynamics has written a very efficient interpolation routine for all tables that has been tested to allow a complete aircraft model to run real time, or offline at a frequency of 1000Hz. This efficiency ensures that even the most complicated of models can run on any simulator through the j2 Pilot SDK.
Tables are added to the model using the graphical interface by selecting the independent variables from a list of the parameters on the model. This avoids common mistakes, such as mixing aircraft projects or using variable names that are not on the model. Values can be typed or whole tables copied and pasted into place. Data can even be transposed as it is being pasted.
When dealing with equations, j2 Builder has an integrated Expression Builder. This allows any variable on the model to be included in an expression. Via a simple graphical interface, formulas may be added that are specific to the chosen aircraft – this can also include conditional and logical statements.
If variable names are changed, the expressions and table names are automatically updated, thus minimising errors and avoiding the need to change every area where a variable has been referenced.
This is the simplest form of parameter available. It is a constant value for any case or condition.
These are used for fixed locations and reference information.
Even when constant values are used in expressions, it is worth adding in a constant value so that it can be referenced and commented for use by other engineers.
Up to 3-Dimensional look up tables can be used. These can represent anything from aerodynamics to propulsion information.
Data can be copied and pasted into the tables and then reviewed using the integrated charting.
Values outside of the tables can be extrapolated, held, or dropped to zero.
Derivatives represent the gradient of a curve at a given point. This can be used to provide damping factors such as the change in the rolling moment due to roll rate or the stiffness of the undercarriage.
When specifying a derivative, the user will enter the denominator from any of the available parameters on the aircraft from a simple drop down list.
Simple Derivatives are constant throughout.
Derivative Lookup Table
In some cases, the derivative is not constant and changes due to the aircraft’s status. To accommodate this, a Derivative Lookup Table is used. Here the user still specifies the denominator and can also add up to 3 other parameters that define how the derivative varies up to a 3-D table.
Expressions enable the user to define their own equations.
j2 Builder provides a built in graphical expression builder. The user can select any of the available parameters on the model and combine them with mathematical operations and functions to create any type of expression desired.
Conditional expressions can be created to account for changes in aircraft configuration or flight condition too.
In some instances it may be easier to specify a derivative in terms of an expression.
Derivative Expressions can be set up easily, by defining the derivative denominator and then creating the expressions using the built in expression builder.
A Time dependent variable is a rate of change, or a variable that changes with time (e.g. Fuel Flow). This is similar to a derivative but with the denominator pre-defined as time.
A Time Dependent value has an initial value that in itself can be a Simple Value, Lookup Table, or Expression. Multiple contributions to the rate of change can then be added which can be any combination of Simple, Lookup Table, and Expression.
When dealing with complex values, multiple contributions can be added using any of the Parameter Types. When the analysis runs, all contribution values are automatically summated.