# Formulas

The formula syntax below can be used to add calculated variables when loading data:

- In the upload screen in Njord Player or Njord Analytics
- In Njord Analytics, modify already uploaded data by selecting the uploaded data segment (
*Data*section), and select*Process* - In Njord Analytics, configure one or more formulas to be applied every time data is uploaded to a certain boat. Set this up under
*Boat*-*Settings*-*Process*

## Examples

Formula | Description |
---|---|

`Heading - COG` | Difference between `Heading` and `COG` |

`DELTAPERSEC(UNWRAP(Heading))` | Rate of turn in degrees per second |

`DELTAPERSEC(BoatSpeed) * 60` | Acceleration in knots per minute |

`BoatSpeed / -(FILTER(DELTASEC(BoatSpeed, 10), DELTASEC(BoatSpeed, 10) < 0) / 10)` | When decelerating, how many seconds to zero knots at current 10 second deceleration average |

`INTERPOLATED(SERIES("2022-10-01T08:00+02:00", 10, "2022-10-01T11:00+02:00", 14))` | This could be `TWS` rising from 10 kts at 8 am to 14 kts at 11 am, for example |

## Operators

Operator | Description | Notes |
---|---|---|

`+` | Addition | |

`-` | Subtraction | |

`*` | Multiplication | |

`/` | Division | |

`<` | Less than | To be used with `FILTER()` |

`<=` | Less than equal | To be used with `FILTER()` |

`>` | Greater than | To be used with `FILTER()` |

`>=` | Greater than equal | To be used with `FILTER()` |

`==` | Equals | To be used with `FILTER()` |

`!=` | Not equals | To be used with `FILTER()` |

`&` | Logical and | To be used with `FILTER()` |

`\|` | Logical or | To be used with `FILTER()` |

`!` | Negate | To be used with `FILTER()` |

## Functions

Function | Description |
---|---|

`ABS(value)` | Absolute of value / remove sign |

`MIN(value1, value2)` | Minimum of two values |

`MAX(value1, value2)` | Maximum of two values |

`MOD(a, n)` | Modulo operation |

`SIN(value)` | Sine of `value` (which is expected to be in degrees) |

`COS(value)` | Cosine of `value` (which is expected to be in degrees) |

`ARCTAN2(x, y)` | Element-wise arc tangent (in degrees) of `x` /`y` choosing the quadrant correctly. |

`FILTERPORT(value)` | Retains the value only on port tack (`AWA` between -170 and -10) |

`FILTERSTBD(value)` | Retains the value only on starboard tack (`AWA` between 10 and 170) |

`COALESCE(value1, value2)` | Choose `value1` if it's not empty, else `value2` |

`SELECTPORTSTBD(valuePort, valueStbd)` | Select `valuePort` when sailing on port tack, `valueStbd` on starboard tack |

`UNWRAP(value)` | Removes wrap at 0/360 degrees, instead expands value below 0 or above 360 as needed for safe calculations |

`SHIFT(value, rows)` | Shifts value (series) by given number of rows |

`SHIFTSEC(value, seconds)` | Shifts value (series) by given number of seconds |

`DELTASEC(value, seconds)` | Delta of value compared to `second` seconds ago |

`DELTAPERSEC(value)` | Delta of value compared to previous datapoint, divided by number of seconds since last datapoint |

`ROLLINGMEAN(value, seconds)` | Rolling mean over `second` seconds |

`ROLLINGSUM(value, seconds)` | Rolling sum over `second` seconds |

`FILTER(value, mask)` | Filters value using the given mask, returning empty value where the mask is false |

`INTERPOLATED(value)` | Fill blanks between values by linear interpolation |

`INTERPOLATEDBEARING(value)` | Fill blanks between values by linear interpolation, correctly handling 0/360 degree wrap around |

`SERIES(time1, value1, time2, value2, ...)` | Produces a data series with the given values at the given times. Write times in ISO 8601 format with quotes, like `"2022-10-01T10:00+02:00"` . Use with `INTERPOLATED()` . |

`TWA(awa, aws, sog)` | Calculates true wind angle from apparent wind and SOG/boat speed |

`TWS(awa, aws, sog)` | Calculates true wind speed from apparent wind and SOG/boat speed |

`AWA(twa, tws, sog)` | Calculates apparent wind angle from true wind and SOG/boat speed |

`AWS(twa, tws, sog)` | Calculates apparent wind speed from true wind and SOG/boat speed |

Note: all function names are case insensitive and may be written in lower case too.