# Is there a reason why the vertical lines of some airplane envelope graphs are not parallel?

I am working on a project to develop an easy solution for mass and balance generation for my aviation club. (First example below)

I checked the Graph of a PA-44-180 from the POH and wondered why piper chose to make the vertical lines non-parallel. (The lines diverge towards the top as shown in the second example below).

Is there any good reason to present the graph in such a way? Is there simply a mistake in the linear graph, or in the way I want to project it? Thanks in advance.

vs

• In my logic, piper decided to make the graph diverge towards the top, so that a pilot will be able to more precisely plot the actual calculated CG in the area, where more precision is required... that is my guess. Commented Sep 28, 2023 at 9:37
• Not sure about that, since in the end the only thing that really matters is whether or not you cross the outer lines. What happens in between is not so important.. Commented Sep 28, 2023 at 9:47
• In my opinion, some older figures had an additional axis below, which was lost (maybe no more needed), but they keep the shape for consistency of older figures. (Possibly some GC-measure near wheels: more weight, more leverage, more deformation). Commented Sep 28, 2023 at 13:00
• To continue on @GiacomoCatenazzi, the missing horizontal axis seems to be torque moment around the datum. By presenting it this way one can presumably more easily add contributions of additional weight, and retrieve the new location of the cog Commented Sep 28, 2023 at 13:24
• Related, but not a duplicate: aviation.stackexchange.com/q/98806/7532 That question refers to the limitations themselves; this question is about how those limitations are presented. So not a dupe.
– Ralph J
Commented Sep 28, 2023 at 14:04

This kind of presentation is called a weight vs. moment 'fan chart'. Although the labeled and drawn x-axis is in CG position, it is really calculated in terms of moment (inch-lb). The reference datum is the location at the center of the chart with a vertical line.

Adding a mass at a location (relative to the datum) will cause a horizontal change -- independent of where you are vertically on the chart. For example, filling a forward fuel tank from empty to full -- will always cause the same change in moment relative to a datum. It will also cause the same vertical change. So, you can compute this change once and then 'move it around' in terms of a sequence of changes. This will tell you how the CG moves throughout a mission.

Any CG change will have an associated 'change vector'. We can add these vectors head-to-tail to get the history of a CG during a load.

Notice in this example how the gear up / gear down lines are exactly the same horizontal width? This is because raising and lowering the gear will always cause equal and opposite changes in moment. The gear change vector stays the same.

Imagine if we extended the gear when the aircraft was at 30,000 lb (in this scenario). We can quickly graphically compute the change in CG - to every point from there on down (ignoring that the gear would be separated from the airplane and other problems would occur if you put them down at that speed).

• Very nice. Someone please offer a bonus to reward this answer. Commented Sep 29, 2023 at 1:49
• Would the change vectors work the same way on the graph the OP generated? Is there anything about the fanned-out vertical (ish) lines that makes the vectors work, that wouldn't work if those lines weren't drawn fanned out? As I read it, the fan itself is the central question, if it's essential, or just nice-to-have (and if the latter, why is it nice to have?)
– Ralph J
Commented Sep 29, 2023 at 3:49
• If the OP plotted their chart in terms of Weight vs. Moment -- and then overlaid lines of constant CG, they would get a fan chart. The fan is a bit of an illusion -- it is a consequence of doing the calculations. Alternatively, if you were to plot constant moment lines on the OP's chart, it would form an upside-down fan. Unfortunately, that isn't useful the way the traditional fan chart is. Commented Sep 29, 2023 at 4:45
• Thanks @quietflyer Commented Sep 29, 2023 at 4:46