Longitudinal CG

[CHARLES DEBOER]

I was asked a question by my grandson about the longitudinal CG.  IF THE FUEL TANK ON THE XL IS IN ONE WING AND FILLED WITH FIVE GALLONS OF GASOLINE, WONT THAT THROW THE BALANCE OFF?  How do I explain to him how that works?  Could someone help me give him a short answer?

Not being a GA pilot the only thing I could come up with was that the extra weight (30 lb.) on that side was still close to the CG and could be off set by a slight adjustment in the aileron.  Does that sound right?

[Vince Carucci]

I may have part of the answer. There is a torque generated by the prop. By placing the tank in the left wing, it is in a position that it may help offset that force.

[Nical]

Excuse me but don't you mean lateral cg?  Longitudinal would be nose to tail, lateral would be wingtip to wingtip.
       Anyway, the tank offset would counter engine torque, but  effective trim would be both fuel quantity and airspeed related. Centering up the fuel load  and countering torque with a slight vertical stab offset and/or rudder trim tab would be the classic solutions...........

[CHARLES DEBOER]

countering torque with a slight vertical stab offset and/or rudder trim tab would be the classic solutions...........
Yes, lateral cg.  Thank-you.  
I am confused about your statement on the vert. stab. offset and rudder trim for adjusting lateral motion.  I think of those adjustments as yaw control.

[Vince Carucci]

Charles, 

There are  a few forces that require yaw correct, especially during the take-off roll on prop driven aircraft. The 2 links below do a great job explaining them. I suspect that might be what Nical is referring to. Perhaps he can elaborate. But that is separate from CG. 

Any how, all this is academic for me. Except for gluing some wood together, I don't have anything close to a flyable plane.  I welcome the opinion of experienced flyers about changing flight dynamics with fuel consumption and about roll-out yaw on the LE.

Vince

See the following:

http://cfi-wiki.net/w/Turning_Tendencies
http://members.localnet.com/~docsteve/av_files/P-factor.htm

[Nical]

Indeed, the fact is that the problem is actually  an unbalanced airplane. But as Mr. Deboer pointed out, close to centerline.
   Seems logical not to misalign the structure but to simply put in a bit of correctional aileron.  Do any current LE/LX pilots have some input here? Do you even notice the  weight offset??
       The concerns here may be in fact unnecessary.
         Regards,
            Nical.     LX E-20

[leshoman]

My wind tank on the yellow eagle i do not notice a differance full to tempty. I have tried moving my body, by loosing seat belts as far to the side as possible but did not notice very much difference, I believe on these machines unless air was very calm, pilot had lots of experience to notice minor changes, and was really trying to find them,  no one would ever notice an actual difference in real world flying.  Wing tanks are not that far from center line.

[stevejahr]

Not that it matters or is significant, but this is a basic weight and balance problem...

Calculate the rolling moment of the offset full fuel tank, using:
    Centerline of wing to centerline of tank: 7" or 0.58' (derived from similar Hi-Max wing plan - it is probably a couple inches further out)
    Fuel tank capacity: 5 gallons --> gives a fuel weight of 31.5 lbs

The overall moment of the fuel from centerline is a smidge over 18 foot-lbs (compare to torquing a bolt to 20 ft-lbs).  This is the rolling moment the aircraft sees.

Calculate the lateral CG shift using:
    Plane weight: 254 lbs (FAR-103 legal ;-) )
    Wingspan: 23.5'

Using a wingtip as the zero reference point, the overall moment of a LE is 2984.5 ft-lbs.
Using a wingtip as the zero reference point, the full full tank moment is 590.6 ft-lbs.
Total full fuel plan moment 3575 ft-lbs
Lateral CG shift: 2.3"

Framing this problem another way:

You and your grandsone know the wing on the fuel tank side must generate extra lift to compensate for the weight of the fuel.  We had a centerline moment for the fuel of 18 ft-lbs, and the center of the wing lift area is 5.9 ft so the extra lift moment is a smidge over 3 lbs.  If the tank-side wing area is 53 square ft we increase wing loading by 0.058 lbs/sq ft. or about 2%.  Note that we added 15 lbs of load to that wing to carry the fuel load so the extra 3 lbs of uneven loading is definitely a secondary effect.

If I remember exactly how to calculate this stuff and have my math correct 

Give the grandson a cookie for being that sharp to pick up on that.  Give him a box of cookies if he can follow the math/reasoning here to figure it out exactly.

[CHARLES DEBOER]

the wing on the fuel tank side must generate extra lift to compensate for the weight of the fuel.  We had a centerline moment for the fuel of 18 ft-lbs, and the center of the wing lift area is 5.9 ft so the extra lift moment is a smidge over 3 lbs.  If the tank-side wing area is 53 square ft we increase wing loading by 0.058 lbs/sq ft. or about 2%.  Note that we added 15 lbs of load to that wing to carry the fuel load so the extra 3 lbs of uneven loading is definitely a secondary effect.

I am always amazed by the talent that exists on this web site.  Thank-you.  My hope is that when I show him your full reply that it will increase his interest in math and engineering.  He has gotten interested in my project.