We are back from our summer break! Now it's time to start the second half of the year, and we have big plans. Today's update is a bit shorter; over the last two weeks, we could only complete a few features. Nevertheless, we now have custom stairs for the ground equipment, and we have made many bug fixes and enhancements to the PFD. Our primary focus is currently on our custom FMS, and in our last status update, you were able to get a behind-the-scenes look. Today, we also want to give you an insight into our VNAV calculations.
We added a generic method to interpolate data points from an N-dimensional table, which is useful for any performance data, including VNAV, landing calculations, autopilot, engine thrust rating, or anything based on performance table data.
It's easy to perform calculations on 2-dimensional data (x/y), where on a table, x (row) and y (column) are the parameters you have. The "cell" or intersection between the x-axis and y-axis is the value you look for based on those two parameters.
Now, if we add another parameter, the table becomes a 3-dimensional table, where the point you look for is on the z-axis on the x/y surface.
If we add another parameter, it will be for the 4th dimension, and so on. Humans should not imagine how the visualization should be; we just can't, but mathematically it is possible.
Performance data parameters mostly do not depend on a single input parameter. For example, to determine "how much fuel needs to be burned," several factors are involved, such as the aircraft weight, altitude, speed, air temperature, flap configuration, etc.
We could have a 2D table for "aircraft weight" (on the x-axis) vs. "altitude" (on the y-axis), and the intersection is fuel burn. If the fuel burn also depends on air temperature, then there would be multiple tables for that weight-altitude table, like tables for ISA+10C, ISA+20C, and so on.
For VNAV, the climb phase alone will need an 8-dimensional table. The dimensions/parameters are:
To calculate the VNAV climb profile, we need to know "how much fuel will be burned if we are climbing from FL-A to FL-B, how long it will take, and how much distance will be traveled."
The code needs to answer that, even if there are no data points for that condition available, hence the need for interpolation based on the closest data we have, an N-dimensional interpolation.
The next step is to fill these tables with data. Once this is done, we can show you the results. You can look forward to it!
For now, enjoy the new E-Jets version!