In-flight calculation for Centre of Gravity

[hudla84]

Hi, my theme of Bachelor thesis is Weigh and Balance. And I want to mention that is possible to calculate the CG during the flight. But I cant find any datas or information about that. I tried to "google" a lot of combination of words like weigh and balance, inflight balance. I watched out many websites, but I was unsuccesful.

I know only basics. There is combination of grossweigh, fuel consuption, altitude and angle of attack. Uff, my kowledge wreks now!

Would you be so nice and help me with that. Will appreciate any information. Thanks Michal. :confused:

Nice day from Czech Republic for you!

[Loose rivets]

Hello hudla84.

Well, the first thing to find out is wether modern Flight Management Systems already do this. If they do, you will be re-inventing the wheel. I'm sure there will be several people on here that will let you know about the most modern or so-called "state of the art" systems.

But for now, let us just look at a very simple aircraft, as the concepts are fairly straight-forward.

Imagine an aircraft in the cruise. Imagine that it is right in the middle of it's C of G range and the control trims are exactly in the middle of their normal range. If the fuel or load changed, it would be necessary to alter the trim to maintain level flight without putting pressure on the main controls. The amount that the crew would alter the trim tabs is very precise, BUT, the indications of such a movement would be less than perfect in older aircraft, so it would be difficult to get this information back to a simple display. This is where modern electronics come in.

Precise position data can now be sent from any moving part in digital form. Data from trim tabs for example, sent to a computer, would allow all sorts of calculations to be made.

Let's see what others have to say.

[Mad (Flt) Scientist]

Depends what you mean by calculation of CG.

If you mean continuously calculating an assumed CG based on zero fuel weight data and fuelk tabnk quantities (or on landing gear loads at startup, say, and then subtracting fuel burn) then I'm sure there are FMSs doing variants of those.

But those aren't really calculating CG - they are estimating it. There's always going to be some margin of error due to the inherent inaccuracy of the input data - especially fuel quantities within tanks.

The alternative is to calculate CG based on aerodynamic behaviour - that's a LOT harder. The problem is that unless you have near-perfect knowledge of the aircraft aerodynamic characteristics then you'll end up needing to know the cg in order to work out the CG - the equations of trim end up cancelling each other out. The only way to break the cuircle is to measure a load directly - like tailplane strain gauging would - but that brings its own problems. If you just go for a "compare the stab-to-trim to prediction" method your accuracy won't be much better than the predictive FMS style system.

[Bellerophon]

Concorde used to display a CG position throughout flight.

This calculation was done by a CG computer (of which there were actually three) which monitored fuel tank quantities and distribution, and, based on initial zero fuel weight and CG entries, displayed the CG position.

Although this was accepted as being reasonably accurate, Mad (Flt) Scientist is quite correct to say that this was really just an estimate of the CG position, rather than a measurement or calculation of it.

One of the more demanding abnormal procedures for the F/E was to alter/monitor the aircraft CG position, by means of fuel transfer, following a triple CG computer failure, particularly during the deceleration and descent from supercruise to subsonic flight.

This usually involved many muttered comments about the parentage of the avionic engineers responsible for maintaining said computers, coupled with not quite so muttered comments about the inabilty of his pilots to fly at exactly the speeds he wanted, when he wanted!

However, despite these shortcomings, and despite having to use various charts and graphs, when later viewed on the FDR or simulator trace, the movement of the CG always seemed to have gone better than when the CG computers were available!

In reality, as Loose rivets suggests, provided the aircraft Mach number was known accurately, the position of the elevons, as displayed on the control position indicator, was considered at least as good an indicator of CG position as the CG computer derived position!

[Swanie]

is it really worth doing?? correct me if i'm wrong i'm only in single props, but you work out a zero fuel weight on the ground, and a take-off weight with the fuel you intend on carrying, join the dots and presto, you've got a graph of whats happening with the COG through out the flight, right up to the point where you would run out of fuel

[john_tullamarine]

.. join the dots and presto ..

careful ...

(a) graph needs to be IU by weight, not CG by weight

(b) fuel arm needs to be constant with fuel quantity.

[smith]

On your google search you could try typing in "weight and balance" or else "mass and balance". I know English is not your mother tongue but this might help.

[Mad (Flt) Scientist]

.. join the dots and presto ..

careful ...


also, what are you going to do when the 10lbs each of salted peanuts and mini-pretzels has been consumed by the occupants of the cabin? Or the pax move about? or the fuel doesn't transfer as expected?

[galaxy flyer]

Mad Scientist:

In our products, consumption of salted food items and the associated drinks will inevitably be deposited in the aft plumbed lavs, thus resulting in a more aft CofG. Fuel efficiency should be the outcome!! Unfortunately, the food and drink are dearer than jet fuel, not a good trade-off.

GF

[Swanie]

"also, what are you going to do when the 10lbs each of salted peanuts and mini-pretzels has been consumed by the occupants of the cabin? Or the pax move about? or the fuel doesn't transfer as expected?"

hey i said i only flew single piston props props
not alot of peanut eating a seat changing goes on;)

depends on what loading system you use as to what you plot against weight.... doesn't it?
besides aren't the big commercial jets loaded and balanced by someone other than the captain...does it actually get re-calculated in flight

[john_tullamarine]

.. depends on what loading system you use as to what you plot against weight.... doesn't it?

It does depend ..

(a) weight by CG .. you only plot end points, not lines

(b) weight by moment (or IU) .. you can plot both .. provided for the line the loading arm which relates to the line is constant.. which gives a straight line

[wobble2plank]

I once wrote a program that calculated the inflight C of G of a large helicopter that was drawn from the C of G shift graph produced by the manufacturer. (Early 90's) As discussed here the C of G was purely an estimation as the graphs were produced by calculating the C of G shift during the consumption of fuel and from what tank.
As stated above this is an estimation. In flight in a large airliner I can see thousands of other variables creeping in. Distribution of passengers, use of potable water, use of inflight catering, movement of personnel throughout the flight and the position of the Captain's wallet ;) . Therefore even an aerodynamic calculation would be a 'snapshot' of the weight distribution of the aircraft at that time.
Good luck!

(Forgot to add, on the Airbus the load sheet calculates our MACZFW and MACTOW for take-off. This is then entered into the FMS (MACZFW) on the INIT page and the MACTOW is then dialled onto the pitch trim wheel. Once done it is left well alone in flight)

[nosignificantweather]

Slightly off topic of the original question, but can someone provide some typical weight and balance and performance figures for a Cessna 152 with 2 persons on board and full fuel based on a one hour flight?

Beside fuel usage, what other factors cause centre of gravity to change during flight?

What method has been used to identify the centre of gravity limits for say the Cessna 152 at the certification stage. What I mean is where do the forward and aft limits come from and how do these relate to weight?

Back to the original poster's question - is there any value in doing calculations in flight in the context of SEP's and does it actually happen on commercial flights?

NSW

[ft]

Hello hudla, excellent choice of thesis subject if you ask me! ;)

What you want to get your hands on is a Weight & Balance manual. It will tell you what you need to know for the aircraft type it applies to. I wish I could supply you with one, but I'm not sure I'm able to. Try google and if you can't find one, get back to me and I'll see what I can do. I noticed a while ago that EADS have the POH for their TBM 700 Socata available online, including the weight and balance information. Perhaps that could be useful?

The first thing you have to consider is fuel burn. In a WBM, you will find the center of gravity of the fuel for various amounts of fuel (in the various tanks, if applicable). If you know the take-off weight (TOW) and center of gravity you will be able to calculate the center of gravity as the fuel burns off from these figures.

The other thing you have to consider are in-flight movements. That's the gear and flaps retracting, F/As and trolleys moving around, passengers and crew visiting the lavs and so on. You can never contain the case where all passengers pile up in one end of the cabin, so you have to assume reasonable worst-case scenarios for forward and aft in-flight movements.

The way this is usually handled in real life is through curtailing the center of gravity envelope. Curtailing the CoG envelope means moving the forward and aft limit of the take-off envelope in sufficiently to contain the aforementioned worst-case scenario for in-flight movements. That way you know that if you are OK (within the curtailed envelope) on take-off, you'll be OK in flight.

You can curtail the envelope for fuel burn as well, but as the fuel is located around the expected CoG for most aircraft, fuel burn tends to bring the CoG in towards the middle of the CoG envelope. Thus, if you are fine at zero fuel weight (ZFW, no fuel on board) you'll be fine when fueled. If you have e g a stabilizer tank, you might need to consider the effect of burning that fuel.
For flight testing, when we want to know the exact CoG for all phases of the flight and when we will often want the aircraft to be at the forward or aft extremes of the weight envelope, a fuel burn vector (a slight misnomer IMO) will be calculated to make sure that we are never actually outside of the envelope. This will be done both for extended and retracted gear, and for all the possible/expected in flight movements (although there typically aren't any during flight testing - you can simply tell people to stay put).

You might want to visit the Society of Allied Weight Engineers, www.sawe.org, and browse through the papers available. You will probably find lots of good source material in there.

If you have any further questions, ask away.

Regard,
/Fred

[hudla84]

Thank you all for very usefull information. I actually dont want to write "precise" principle of balancing each type of acft. I would like to mention only general principle.
I want to focus on FMS measuring. I am going to try use the data, you ve given me. Try to google and finally I will post here my conclusion and ask you for the opinion.
Best regards, Michal :D

[enicalyth]

Company "A" does a [I]Getting to Grips With[I] document on Weight and Balance. Rather lightweight (groan). It doesn't do peanuts but manages to do "movement" of potable water with a straight face. Cue the usual jokes.

BTW I think is weight (force) and not mass in this instance. No doubt Virgin Galactic calculate COI in the vast heavens and Lord Knows maybe COM too.

[Milt]

In the 1950s we TPs had to grapple with CGs moving around.

The following from memoirs.

Weapons release trials from the Valiant created a challenge. Keeping the centre of gravity (cg) within limits was an onerous task during normal flight, requiring frequent use of a special purpose slide rule. Fuel usage from three fuselage tanks and four wing tanks was juggled to keep within limits. Weapon releases from the load points along the weapons bay considerably complicated the cg position management. I would often spend several hours planning fuel usage for the release trials. Electronic calculators and computers had not yet become available. Pondering the problem one day I reasoned that I should be able to accomplish the weight and balance solution electrically. I considered various approaches to the problem before settling for a relatively simple solution.

My plan was to use a centre reading micro-ammeter scaled to show the centre of gravity (cg) range of the Valiant. I represented each fuel cell and each loading point with a module made up of a battery cell and two potentiometers. One potentiometer was scaled from zero to the maximum load possible at the location represented. The second potentiometer was used to adjust the effectiveness on the total cg position for weight at that load point. Polarity was arranged to swing the meter left or right appropriate to the direction of movement of the cg. All modules were linked in series, together with a module for setting the cg position for an empty aircraft.

I found to my delight that the electrical solution was within 5% of any solution produced by the slide rule or mathematically. This accuracy was more than adequate. It was not long before I was carrying my magic box on to the aircraft where it was used extensively to quickly determine the feasibility of variations to trial plans in flight. The box saved me an enormous amount of time during pre-flight planning.

The Vulcan and Victor each had automatic fuel flow control to keep the cg within bounds. Nevertheless we were required to test weapon releases for cg position at the limits before we could issue a release for squadron operations. My cg calculating machine proved to be very popular.

[john_tullamarine]

.. well done, sir .... I trust that you put all manner of esoteric symbols on the box to confuse the uninitiated ?

[enicalyth]

Got to be the best pun!