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enter image description here
(fireair.co.uk)

Why is a weight and balance graph lozenge-shaped? I have tried to find the answer but it seems to be really hard to find. Why is it not a square?

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  • $\begingroup$ What aircraft is it for? $\endgroup$ – Terry Mar 21 '18 at 23:37
  • $\begingroup$ @Terry - OP didn't add the image, I found a random one that matched OP's description and added it. $\endgroup$ – ymb1 Mar 21 '18 at 23:38
  • $\begingroup$ @757toga That's a valid explanation I believe, and you see that cutout (or whatever it s/b called) on numbers of aircraft types. The question is a bit ambiguous though. I interpreted it as asking why the c.g. location lines are at an angle rather than straight up since showing them as 90 degrees vertical would make it rectangular save for the cutout. Perhaps the OP will see this and elucidate. $\endgroup$ – Terry Mar 22 '18 at 0:02
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    $\begingroup$ That's also an interesting question: is the horizontal spreading of the cog lines meaningful (perhaps indicating more accurate numbers at the wide end?), or is it just for effect. $\endgroup$ – StarWeaver Mar 22 '18 at 0:22
  • $\begingroup$ The chart, from my point of view, needs to be drawn at an angle beginning at about 1950 lbs or else the distance measurements from the datum could not be illustrated unless the entire chart was redesigned. As far as the chart being drawn more narrow at the bottom and wider (visually) at the top, is probably better readability. Just my opinion. $\endgroup$ – 757toga Mar 22 '18 at 0:29
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In a strict mathematical sense the graph should be extended into a complete right triangle, not a rectangle. However there are practical limits on how far forward you can fill the compartments so the graph can be cut off at 83 inches in this case. The top is clipped because increasing weight above that point reduces performance and safety margins below design intent and angers bureaucrats.

The reason for a right triangle is because the acceptable location of the center of mass is more critical at increased gross weight. When the plane is very low weight the center of mass can be very far forward and not overwhelm the tail down force and leverage. At high gross weights the tail needs more leverage to counter the nose down moment, so the forward limit of the center of mass must be brought back closer to the center of lift. There is no angle on the aft limit side of the chart because moving the center of mass behind the center of lift, at any loading, will make stall and spin recovery impractical or impossible on a traditional wing and tail layout.

The slight radial flair in the particular chart pictured is simply styling.

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"The slight radial flair in the particular chart pictured is simply styling" is not quite accurate. This type of graph is the OEM's choice; many are in standard Cartesian coordinates. The reason for this style is for the purposes of loading in various manners. Regardless of the Gross takeoff weight, the fuel burn will be the same. If you create one fuel burn curve, this type of chart allows you to slide that curve to a new gross weight, and you will immediately see if the CG will go out of the allowable area. On a Cartesian chart, you have to plot every point and connect the dots instead of just sliding the whole curve. This is very useful on swept wing aircraft that have multiple tanks that are expended in a specific order. 707 has 7 tanks; a good example.

There has been discussion of moment and downforce capability of the horizontal stabilizer. Most of this is good, but you need to take that one step further. There are also structural limits at certain points of the airframe that cannot be exceeded. Too much downforce from the HorStab could exceed those limits. Conversely, a CG too far forward could exceed bending moment allowances forward of the wing root.

To build a chart, check out Vector charts in T.O. 01-1B-50 (2005), available online.

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  • $\begingroup$ Welcome to aviation.stackexchange.com! $\endgroup$ – rclocher3 May 21 at 22:22

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