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CG location when fuel is burned

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CG location when fuel is burned

Old 06-16-2012, 06:20 AM
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ytell
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Default CG location when fuel is burned

I'm a little confused on this one,
If the fuel tank is located exactly on CG, there will be no change in CG position throughout the flight.
But if you calculate CG position relative to a datum (say leading adge) you will calculate a different CG location when the tank is full or empty.
How can this contradiction be explained?

Yoav
Old 06-16-2012, 06:56 AM
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edsplane
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Default RE: CG location when fuel is burned

There is no contradiction. What you say is absolutely true. It is customary to calculate the CG location with the tank empty, I think because you want the plane to be stable when you are ready to land. The fuel tank is normally forward of the CG, so when it is full, the plane will be even more stable.

In a pattern plane, you don't want any variation in performance, depending on how full the tank is, so if the tank is located on the CG, you eliminate this variable.

The key factor that many people miss, is that the pitch stability of an airplane depends on the CG location, in relation to the plane's Neutral Point(NP). Just putting the CG at 25% of the Mean Aerodynamic Chord(MAC) only does half the job. Where is the CG relative to the NP?

The Neutral Point location depends on tail location, tail efficiency and some other factors. It can be very different from one plane to the next. I suggest that you find this out and locate the CG accordingly. There's more information on this at www.rcaeronauts.com . Good luck.
Old 06-16-2012, 07:08 AM
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ytell
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Default RE: CG location when fuel is burned

But still, if the tank is located exactly on CG, I'm expecting CG position not to change when fuel is consumed. However, if you calculate CG position with a datume line you will find it changed from full to empty. so waht's going on?
Old 06-16-2012, 08:56 AM
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jgg215
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Default RE: CG location when fuel is burned

What you are doing with an arbittrary datum point is calcuating moments around that point. When you pick the LE of the wing clearly there will be a moment arond that point. when the tank is empty. If the tank is then filled the moment dropping the tail would increase by the added weight times the distance to the tank CG..
There is only one point where there will be no moment with an empty tank and that is the empty weight CG. Both intuitively and mathmatically if you fill a tank placed at the empty weight CG and calculate the adjusted moment it will not changeas the moment arm of the tank is zero.
John
Old 06-16-2012, 09:31 AM
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ytell
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Default RE: CG location when fuel is burned

Sorry for being slow on this...

1. If CG is calculated about empty CG, than the arm is always zero and fuel amount has no affect.

2. If CG is calculated about LE, then the moment of fuel tank is the product of the arm (constant) times the weight of the fuel (changing). As a result, the CG will change as fuel is consumed. Am I missing something?
Old 06-16-2012, 10:03 AM
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Top_Gunn
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Default RE: CG location when fuel is burned


ORIGINAL: ytell

Sorry for being slow on this...

1. If CG is calculated about empty CG, than the arm is always zero and fuel amount has no affect.

2. If CG is calculated about LE, then the moment of fuel tank is the product of the arm (constant) times the weight of the fuel (changing). As a result, the CG will change as fuel is consumed. Am I missing something?
By "calculate" the CG, I assume you mean determine where the CG is supposed to be. If so, that calculation has nothing to do with whether the tank is full or empty. When you determine whether the CG is where it's supposed to be, you normally do it with the tank empty because the tank is usually in front of where the CG is supposed to be. But if the tank is on the CG (i.e. on the point where the CG is supposed to be), it doesn't matter whether the tank is full or empty when you check to make sure the CG is where you wanted it.

So there is no contradiction. If the tank is on the CG, no change in CG when it empties.
Old 06-16-2012, 11:13 AM
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jgg215
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Default RE: CG location when fuel is burned

OK, lets try this again.

We know the distance from the LE is the same to the CG of the empty model(ACEWT) and Full fuel tank(FUELWT)

So the moment at the leading edge of the wing(LE) is:

[email protected] = dist * ACEWT + dist * FUELWT = dist*( ACEWT + FUELWT)

Then the distance of this calculated moment is: New Dist to CG from Leading edge = dist * (ACEWT + FUELWT) / New total weight
Since the total weight is ACEWT + FUELWT
These weights are the same and cancel out leaving the distance to the CG from the LEexactly the same.

John

Old 06-16-2012, 04:31 PM
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fledermaus
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Default RE: CG location when fuel is burned

Perhaps the problem here is the assumption that the CG is a fixed point during flight. It isn't, not in models, not in full-scale.

The "optimal CG" is determined by the centre of lift (among other things) and this is the point modelers usually are trying to get their planes to balance at. We do this when the tank is empty. Thus, at take-off, our "actual CG" will be somewhat forward of the "optimal CG". As fuel is consumed, the plane will balance further aft, but it will never reach a point where the "actual CG" is behind the "optimal CG".

This is good, since having the "actual CG" too far aft leads to pitch instability.

The changing point of balance is one reason models and full-scale planes have trim adjustments.
Old 06-16-2012, 05:12 PM
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Default RE: CG location when fuel is burned

The contradiction is explained because you are taking moments about a different point than that where the airplane balances. (Not CG please, that is an entirely different concept). If you take your moments about the balance point, then it does not matter how much or little fuel is in the tank, the total moment is still zero. The airplanes weight will change, but not the balance position.
Evan, WB #12.
Old 06-17-2012, 06:56 AM
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edsplane
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Default RE: CG location when fuel is burned

Hey Guys, Let's try this a different way; forget the moment arms for now.

The balance point for the airplane is, by definition, where the CG is located. If you put the CG of the fuel tank at the CG of the plane, there will not be any imbalance of the plane, no matter what the fuel level is in the tank. If the CG of the fuel tank is forward of the plane's CG(with Tank empty), then any fuel in the tank will tend to make the plane more stable in Pitch(nose up & down). You can eyeball the tank CG at about half the length of the tank.That's why the pattern guys put the tank CG right on the Plane CG. And, that's why we never put the tank CG aft of the plane's CG.

Now, back to the Moment question. If you take the sum of the moments about the plane's CG(with fuel tank empty), the sum of all moments is zero, thus the balance point. If the tank CG is not at the tank-empty plane's CG, then any fuel that's put into the tank, will cause an imbalance about the Plane's CG and the sum of the moments will not be zero. In other words, the plane's CG has now been moved.

If the plane's CG is moved forward, the plane becomes more stable in pitch and will be less aerobatic, but safer. If the tank is behind the Plane's CG, the more fuel that's added will make the plane less stable and less safe. If the tank is located behind the plane CG far enough, then the plane will be unstable in pitch. There's more on this at www.rcaeronauts.com.
Hope this helps.


Old 06-17-2012, 08:35 AM
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ytell
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Default RE: CG location when fuel is burned

John,

These two weights are not the same. the second is lesser than the first becuase fuel has been consumed so FUELWT-1 is grater than FUELWT-2 and so you can't conclude that "dist" remain unchanged

All, the point that is still unclear to me is why the datum calculation of CG does not show that CG remain unchanged even though fuel tank (full and then empty) is installed exactly on AC empty weight CG?

Thnaks,

yoav
Old 06-17-2012, 09:12 AM
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jgg215
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Default RE: CG location when fuel is burned

It doesn't matter how much fuel is consumed as long as the tank is on the CG. The total weight is still the empty weight plus whatever fuel is onboard. I fail to understand why you think "dist" would change.

I showed you mathematically why the CG does not change. Others have shown logically why the CG does not change.

I suggest you go away and do some testing with your model to demonstrate to yourself that the CG does not change.
Old 06-17-2012, 09:53 AM
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ytell
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Default RE: CG location when fuel is burned

John,

I perfectly understand that CG will not change if tank is on CG. What I fail to understand is how to show this using datum calculation.

If you take moments about (say LE) then you have:

Chnage-of-moment = (moment_flight_start)-(moment_flight_end) = dist_to_LE*(weight_full_tank - weight_empty_tank)


Since the expression in the last parenthesis is greater than zero, I find that CG has changed

Yoav

Old 06-17-2012, 09:58 AM
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da Rock
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Default RE: CG location when fuel is burned

In theory, practice and theory are the same. In practice, they often are not.

ytell,
If a fuel tank is located where the plane balances (fingers under the wing etc) it's weight has no moment with which to affect that balance. That's logical, right? No matter how much things weigh that are stacked directly on a balance point, those weights don't tip the balanced object.

So look closely at the formulas you think give a fuel tank located at the balance point some influence to do so. You've seen 'practice' at work. Apparently your 'theory' doesn't work correctly if is says otherwise.
Old 06-17-2012, 10:01 AM
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jgg215
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Default RE: CG location when fuel is burned

No, you are saying the moment around the wing LE has changed which is true. That is not the same thing as the CG changing. Go back and look at the original equation I sent you. The CG is actually where the moment is zero. This location (dist) did not change.
Your basic fallacy is when you equate a change in the moment at the LE to a chage in CG location. This is just not true.
Old 06-17-2012, 10:11 AM
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da Rock
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Default RE: CG location when fuel is burned


ORIGINAL: ytell
Chnage-of-moment = (moment_flight_start)-(moment_flight_end) = dist_to_LE*(weight_full_tank - weight_empty_tank)


Since the expression in the last parenthesis is greater than zero, I find that CG has changed

Yoav


The expression does not describe the balance of the airplane. It is extremely limited and only describes the effect the weight of the tank has on the moment of the tank relative to an arbitrary point. I assume you're using it to describe why you think it would have an effect.

Would you care to show us an example of a computation you use to establish the location of a CG?
Old 06-17-2012, 10:34 AM
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da Rock
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Default RE: CG location when fuel is burned

BTW, if you're trying to understand the usual method of "CG computation" for a Cessna or such, that method actually does not compute the balance point of the airplane at all. It seeks only a value to compare to a range of acceptable values. The range itself is established based on where the CG would be with no fuel/payload/etc to permissable maximums for those.

The moment arm that results from this calculation must be within the moment arm limits for the center of gravity that are dictated by the manufacturer. You are not figuring the CG of the airplane at all. And the numbers you come up with aren't even the moments the weights you use would have on the "perfect balance point" modelers would want if that airplane were their model. Those moments would be both positive and negative as the weights would be both fore and aft that modeler's perfect balance point.
Old 06-17-2012, 10:53 AM
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ytell
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Default RE: CG location when fuel is burned

Da_rock,

Even though there may be thousands of acting moments that determine CG (the entire AC) only one is changing from start to finish of the flight and that is fuel tank.
Therefore it is (i think) justified to neglect all but this moment in calculating a change in CG position.

John,
you wrote:

"Then the distance of this calculated moment is: New Dist to CG from Leading edge = dist * (ACEWT + FUELWT) / New total weight"

and then:

"Since the total weight is ACEWT + FUELWT "

But I say this is not true. We need to compare beginning of flight to end of flight (fuel consumed) and therefore, total weight does not equal the same "ACEWT + FUELWT" because FUELWT has changed and that is why dist has change too
Old 06-17-2012, 11:21 AM
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jgg215
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Default RE: CG location when fuel is burned

At any given time the aircraft zero fuel weight plus the current weight of the fuel on board is the gross weight of the aircraft. Since YOU stipulated that the fuel tank is on the CG, everything i said is correct.

You need to go away and research this on your own since you wont listen to anone.

I'm done
Old 06-17-2012, 12:04 PM
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Default RE: CG location when fuel is burned

Wow this is getting WAY over complicated. Not sure what airplane we are talking about but if the tank in on the CG then I am going to assume it is an aerobatic airplane. That being said, adjust the position of equipment so the airplane balances according to directions. Test fly the airplane and determine if you want to shift forward, aft or leave it alone. The test is simple, do a 45 degree upline and roll inverted. Watch what the airplane wants to do. If it climbs hands off then you want to move more forward. If it pulls to the canopy badly then move it aft.

Don't spend too much time with these calculations intended for full scale aircraft. They usually end up confusing the issue. So far this thread indicates just that. Most of this type of aircraft have very light wing loadings and can get away with a rather aft CG. I wouldn't say that this leads to instability per say but will make the elevator more sensitive. It's summer time, pack up your airplane and go have fun, after all that's what this is all supposed to be about right?
Old 06-17-2012, 05:21 PM
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Default RE: CG location when fuel is burned

ORIGINAL: ytell

Da_rock,

Even though there may be thousands of acting moments that determine CG (the entire AC) only one is changing from start to finish of the flight and that is fuel tank.
Therefore it is (i think) justified to neglect all but this moment in calculating a change in CG position.
ytell,
You cannot calculate the change of a CG position by working out one moment. Unfortunately, nobody can neglect all but one moment computation and come up with a CG location anymore than they can compare the moments of two different weights to discover the change in a CG location.

Having worked for a couple of different airlines in computer applications with experience developing Weights & Balance and Flight Planning among other things, what is involved with CG computations really is familiar to me.

You seem to be missing quite a lot of the things people are trying to tell you about your interpretation of the problem.

Do you have an example of the computations you are trying to understand? ...one that includes all the algebra you accept as adequate to predict a CG location?

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