Weight Balance chart design mystery aka "attractive waist" ;-)

[itlee]

This document explains everything about how and why..
https://www.smartcockpit.com/docs/Center_Of_Gravity_Limitations.pdf

That's an amazing deck, and it totally explains everything about how and why except...

the Piper charts we have attached in this thread, which are still a little odd to me. If we TL;DR through all the big pile of interesting info in the deck, the key to the rationale behind the "attractive waist" presentation seems to be slide C-10, that the advantage in doing the plot with weight vs moment as axes is that then you can do vector/graphical addition of components in any order. This is as opposed to if the plot were with weight vs cg axes, where if you did components in different orders you would have path vectors with differing lengths. Thing is, the Piper plots don't have a grid marked in units of moment, so you would have to either draw one on yourself, or do the explicit math to get several weight/CG value points one particular order, and then for whatever reason shuffle the vectors around to find an arrangement you like better.

Something I found confusing in the deck is that the plots in slides 1-10 are explicitly labelled as weight vs moment, then 18-55 are labelled as weight vs. %MAC, but are clearly the same methodology as before (weight vs moment) since the values are indicated at the top of the plot with iso-%MAC lines wasp-waisting down towards the bottom, and then 57-61 are weight vs %MAC except now these are straight lines down as one would expect if you were plotting weight vs cg (as is the way it is shown in my Arrow III POH).

 

[DJ Spathis]

That's an amazing deck, and it totally explains everything about how and why except...

the Piper charts we have attached in this thread, which are still a little odd to me. If we TL;DR through all the big pile of interesting info in the deck, the key to the rationale behind the "attractive waist" presentation seems to be slide C-10, that the advantage in doing the plot with weight vs moment as axes is that then you can do vector/graphical addition of components in any order. This is as opposed to if the plot were with weight vs cg axes, where if you did components in different orders you would have path vectors with differing lengths. Thing is, the Piper plots don't have a grid marked in units of moment, so you would have to either draw one on yourself, or do the explicit math to get several weight/CG value points one particular order, and then for whatever reason shuffle the vectors around to find an arrangement you like better.

Something I found confusing in the deck is that the plots in slides 1-10 are explicitly labelled as weight vs moment, then 18-55 are labelled as weight vs. %MAC, but are clearly the same methodology as before (weight vs moment) since the values are indicated at the top of the plot with iso-%MAC lines wasp-waisting down towards the bottom, and then 57-61 are weight vs %MAC except now these are straight lines down as one would expect if you were plotting weight vs cg (as is the way it is shown in my Arrow III POH).

I agree on that amazing deck. @sanjiv, thanks for the reference.

As to the how and why, I have a thought that might explain the evolution of the diagram from wasp waist to straight. Early on it seems that the diagram was modeled as wasp waist after the more sophisticated commercial version, but without the %MAC references that are not common in our planes. Later on, someone noticed that the existing diagram could just as easily be represented with straight sides. I'm willing to entertain simpler explanations (ala Occum's razor).

DJ

 

[visualexport]

@sanjiv that pdf is pure GOLD...

 

[visualexport]

so far... so good