Custom expressions

Write custom mathematical expressions to compute new variables during simulation, then plot or export them alongside built-in flight data.

OpenRocket is not limited to its built-in simulation variables. Since version 12.09, you can define custom expressions — mathematical formulas that are evaluated at every simulation time step and treated exactly like native variables for plotting and CSV export.

Overview

Custom expressions are stored in your .ork rocket document. To manage them, go to Analyze → Custom expressions. The Custom Expressions window lists all expressions defined for the current document.

Initially the list is empty. Use the New expression button in the lower right to open the Expression Builder. You can also import expressions from another .ork file.

Building an expression

The Expression Builder requires four fields before you can save an expression:

Field	Rules
Name	Any string not previously used as an expression name
Symbol	A short locale-independent identifier: no numbers, whitespace, or special characters (brackets, operators, etc.)
Units	Any string; leave blank for dimensionless quantities. If you enter a standard SI unit exactly, OpenRocket will offer unit conversion when plotting or exporting.
Expression	A valid mathematical expression using variable symbols, operators, and numbers

Each field has an adjacent indicator that turns from red to green when the value is valid. You cannot save the expression until all indicators are green.

Supported SI units for automatic conversion

If your expression’s Units field contains one of these exactly, OpenRocket will automatically offer unit conversion:

m m^2 m/s kg kg m^2 kg m^3 N Ns s Pa V A J W kg m/s Hz K

Inserting variables and operators

Click Insert Variable to open a searchable list of all available simulation variables and their symbols. Selecting a variable inserts its symbol at the current cursor position in the expression box.

Click Insert Operator to open a similar list of all available mathematical operators and functions. This is especially useful for operators whose symbols cannot be typed on a standard keyboard.

Nesting custom expressions

You can use the symbol of one custom expression inside another. This allows you to build up complex calculations incrementally.

Nested expressions are calculated in list order. If expression B depends on expression A, then A must appear above B in the Custom Expressions list. Use the blue up/down arrow buttons to reorder expressions.

Available variables

The full list of available variables is accessible from the Insert Variable dialog. The variables correspond to the built-in FlightDataType values used throughout OpenRocket’s simulation engine. Key variables and their symbols include:

Time and position

Symbol	Variable
t	Time
h	Altitude
ha	Altitude above sea level
Vz	Vertical velocity
Vt	Total velocity
Az	Vertical acceleration
At	Total acceleration
Px	Position East of launch
Py	Position North of launch
Pl	Lateral distance

Mass and inertia

Symbol	Variable
m	Total mass
mp	Motor mass
Il	Longitudinal moment of inertia
Ir	Rotational moment of inertia
g	Gravity

Stability

Symbol	Variable
Cp	CP location
Cg	CG location
S	Stability margin (calibers)

Thrust and drag

Symbol	Variable
Ft	Thrust force
Twr	Thrust-to-weight ratio
Fd	Drag force
Cd	Drag coefficient
Cdf	Friction drag coefficient
Cdp	Pressure drag coefficient
Cdb	Base drag coefficient

Characteristic numbers

Symbol	Variable
M	Mach number
R	Reynolds number

Index expressions

Custom expressions are evaluated at each time step, but sometimes you need a value from an earlier point in the flight. Index expressions use square bracket syntax to specify a time in seconds:

m / m[0]

This gives the ratio of the current mass to the launch mass (mass at time 0).

m - m[t-1]

This gives the change in mass over the last one second.

The value inside the brackets can be any valid sub-expression. Interpolation is used to return the exact value at the specified time, independent of the simulation’s actual time steps. If you specify a time less than 0 or greater than the current time t, it is clamped to 0 or t respectively. You cannot reference data that has not yet been calculated.

You cannot nest another index or range expression inside square brackets.

Range expressions

Some operators work on a range of values rather than a single point. These range operators are identified in the Insert Operator dialog by the [:] placeholder already filled in for one or more parameters.

Range expressions use a start:end syntax inside square brackets:

mean(At[t-0.5:t])

This calculates the moving mean of total acceleration (At) over the last 0.5 seconds — a simple model of a low-pass filtered accelerometer output.

The bounds can be any valid expression. If you omit the upper bound, it defaults to t; if you omit the lower bound, it defaults to 0:

mean(At[t-0.5:])

Practical example: filtered accelerometer voltage

Many accelerometers clip above a maximum acceleration and return an analog voltage. This expression models a sensor that clips at 10 g and returns 0.2 V per g:

0.2 * uclip( mean(At[t-.5:]), 10 )

• uclip(x, max) clips x to a maximum value of max
• mean(At[t-.5:]) computes the mean of total acceleration over the last 0.5 s
• The outer 0.2 * converts from acceleration (m/s²) to a voltage-like output

Range data is generated by interpolation over the specified range with a fixed time step equal to the default simulation time step. This makes it straightforward to use integration functions like trapz([:]) (trapezoidal integration) or tnear([:], x) (find the time when a variable is nearest a target value).

Example expressions

Launch mass fraction

The ratio of current rocket mass to launch mass:

m / m[0]

Symbol: mf
Units: (dimensionless, leave blank)

Net force

Thrust minus drag gives the net axial force:

Ft - Fd

Symbol: Fn
Units: N

Drag-to-thrust ratio

How much drag relative to available thrust:

Fd / Ft

Symbol: DtT
Units: (dimensionless)

Stability margin in body diameters

Convert the standard caliber stability margin to a fraction of body length (assuming reference length is the body diameter):

(Cg - Cp) / h

Note: Replace h with the appropriate reference length symbol for your design.

Troubleshooting

If an expression produces no data after running a simulation:

1. Verify all indicator lights in the Expression Builder are green before saving
2. Check the error log at Help → Debug log; look for entries under the USER category
3. Verify that nested expressions are in the correct calculation order

OpenRocket validates expressions as you type, but some errors only become apparent at runtime (for example, dividing by a variable that is zero during part of the flight). An invalid runtime expression produces no data for that time step but does not crash the simulation.

Custom expressions are interpreted during the simulation and are slower than built-in variables. A few simple expressions have negligible overhead, but range expressions in particular can noticeably increase simulation time. If performance is a concern, consider implementing your calculation as a simulation extension instead.