Sorry, couldn’t help myself with the pun in the title 
You probably guessed it by now, but my fall down the rabbit hole of aircraft performance continued last week and, sadly, there isn’t really an end in sight. But I suspected as much in devlog 2024-44 already.
Back to payload/range
As discussed last week, when I realised that my new take-off performance approximations didn’t quite cut it, I started to read up on the underlying principles. As such, I also took another look at my payload/range formulas that I was actually fairly happy with until recently.
Here’s a shot from my performance editor for the A380:
If you look at the right-most takeoff weight curve (red line), it’s a near perfect fit with the line from Airbus’ manual.
Here’s the corresponding shot for the 747-8:
Again, close to perfect. BUT Boeing (to their credit!) provide lines for other takeoff weights as well, and as you can see, the shorter the flight distance, the less accurate the approximation gets.
Perfection, again
Initially, I disregarded this imprecision as I deemed it irrelevant for low ranges…those aren’t within the primary operational envelope of the type anyway, so why bother? But as I looked further into it, I got a feeling that the opposite is likely true: I bother with this aircraft performance madness because I want the types in AS to behave in a way that’s coherent with reality. A long-distance type like the 747-8 should become less efficient on shorter flights, not the opposite, as my current approximation suggests.
Also, due to classic selection bias, I deemed my formulas to be better than they actually were because I didn’t really test them on a wider range of types yet. Here’s an example chart for the 767-300:
Not too shabby, but one can clearly see how the slope of the weight line doesn’t match the reference, even for MTOW.
Here’s the CRJ700:
Also, not bad, but you can see how the fit is only good for a single point on the chart…which makes sense as that’s essentially the point the approximation is based upon. On a side-note here: The line for the ER-version actually looks pretty good, despite the parameters being based on the regular version. Something I was hoping to get out of the new formulas as a “side effect”. More on that below.
Going deeper
The above imprecisions sort of make sense: My current approximation is based on the average fuel consumption at a given range, taking into account (the weight of) reserves. As this range is within the ideal operational envelope of the type, the average is pretty good because the additional fuel consumption from takeoff and climb doesn’t have as much of an impact as it would at lower distances. Consequently, the value becomes “better” as the range decreases.
With what I’ve learned over the past few weeks, I hope I can come up with something that models this better, based on a handful of new key properties of a given aircraft:
- engine thrust
- a (probably static) fuel efficiency factor of the engines
- a rough estimate of drag/lift coefficients
- typical operating speeds and altitudes
The idea is to compute the actual flight phases (takeoff, climb, cruise, etc.) based on a simplified performance model that uses the above parameters (and likely others) as input and then adjust the values until we get a reasonable good fit for the reference data we have available. This is easier said than done, as pretty much all of these parameters are anything but static and vary wildly based on the actual operating conditions. They are also strongly interrelated…a thrusted relationship, so to be speak (sorry).
Anyway, if this turns out the way I hope it will, the artefacts should become less pronounced. As a bonus, such a more generic model should also work better with different variants of the same type. Think different weight and engine options.
Complexity explosion
Speaking of engines…as the performance model becomes more nuanced, it also becomes a lot more tricky to decide which versions of a given type to actually add to AS. Let’s take the A320neo family as an example:
With the existing model, we opted to add more or less arbitrarily selected “light”, “medium” and “heavy” variants. This gives us the current 11 variants spanning from the A319neo to the A321LR (excluding the A321XLR).
For a new performance model, I count 8 different variants based on engines (master series only, no subtle engine variations) for the A321neo alone (including the A321XLR). When taking into account common weight variants as well, I get 53. Again, just for the A321 line…no A319 or A320 yet.
So there is a discussion to be had about what we should include and what shouldn’t make the cut. Or whether all of this implies a second attempt at adding a “build to order” feature to AS…
But let’s not get ahead of ourselves…I need to get these formulas to work, first.