Forward CofG in a B738 and Fuel penalty?

[saddest aviator]

Does anybody know where I can find out the information concerning fuel burn penalty for flying with a forward c of g on a 737 8Any guidance would be appreciated

[Mad (Flt) Scientist]

On other aircraft I've seen a 1% for 5% cg shift number quoted as a rule-of-thumb.
To get a better idea for a specific type:
The cg effect is basically a pseudo-weight effect, caused by increased trim dat the tail at more forward cg's, which causes the wing to have to lift more, so the aircraft appears (as far as the wing is concerned) to be heavier.
If you work out the tail arm - distance from the tailplane to the nominal cg - then for every foot you shift the weight forward, the download at the tail increases by 1ft/tail arm in ft times the aircraft weight. So for every foot you shift the cg forward, the aircraft appears to get heavier by that amount.
So, grab a three view, or the equivalent data, and find:
The nominal tail arm (if its not given specifically, measure from the nominal cg (or the 1/4 chord position on the centreline, failing all else) to the tail 1/4 chord similarly. Call that LT.
The MAC.
Now pick a weight somewhere in the middle of the operational range, and look up the fuel flow from some perf charts.
For the same weight, calculate:
delta weight = weight * 0.10 * MAC / LT
Crudely, that's the increased download for a 10% cg shift
Add that to your first weight, and look up the fuel flows for the new weight.
Take the percentage increase in fuel flow, and that (crudely) is the effect of a 10% cg shift. Factor up or down as required.
very rough calc:
A 738 is about 130ft long, and 113ft span, with an AR of about 9.5, which implies a MAC of about 15ft. Since the wing is roughly halfway along the fuselage, call LT about 65ft. That makes MAC/LT about 0.23. So for a 10% cg shift, the aircraft has an apparent weight increase of about 2.3%. Sorry, don't have any fuel flow data for the aircraft.

edit: of course, that just gives you the penalty per cg shift - you still need to know what the OEM assumed in generating the baseline data to apply the factor onto. OEMs being OEMs, it's probably about 2/3 towards the back of the cg range, to make the numbers look as good as reasonable....

[XPMorten]

Thanks for that Mad_ :)
Found some Airbus data. Note that the general rules don't apply
for the A32x family due to a "complex interaction of aerodynamic effects".
Any idea what that means? Has it got something to do with the inverted
airfoil on the stabilizer?
http://www.xplanefreeware.net/morten/DOCS/CG1.png
http://www.xplanefreeware.net/morten/DOCS/CG2.png
Cheers,
M

[Mad (Flt) Scientist]

Shouldn't have anything to do with the shape of the airfoil on the tail. The efficiency of the tail airfoil in producing the download shouldn't overcome the effect on the increased download on apparent weight.

One factor could be if your tail is already almost unloaded at your nominal cg position. In which case it might be that moving the cg aft required an UPLOAD on the tail, which although it unloads the wing, the tail is less efficient than the wing, so the over aircraft lifting efficiency drops? But I didn't think the A320s had less static margin than the 330/340s, and they show a (reduced) effect, so that seems a bit unlikely.

Perhaps as the cg moves aft the FBW system becomes more active in pitch and the increased control activity creates drag which offsets the gain in trim drag? Again, it sounds a bit of a wild theory.