Inaccuracy due to CG computation method

The balance chart used to determine the aircraft CG position can be :

− graphical

− tabulated

− computerized

In each case the computation is based on

− a sum of weights = DOW + Payload Weight +Fuel Weight

− a sum of index = DOI + Payload ∆Index +Fuel ∆Index Each weight of the sum is rounded to the closest unit value.

Each index and ∆index of the sum may be rounded to :

− the closest index unit in the case of paper systems (graphical or tabulated)

− the closest decimal (tenth or hundredth) in the case of computerized systems.

The weight sum is then considered to be precise and no inaccuracy is taken into account.

Depending of the rounding system of the index and on the method to determine the index value for each weight value, an index inaccuracy has to be taken into account.

Note1 : the computerized systems rounded to the tenth or hundredth, are considered usually to be precise enough not to take into account any inaccuracy.

Note2 : some computerized systems may be based directly on each item H-arm value and not on the item ∆index, in this case the computation is usually much more precise (without pre-computation) and no inaccuracy is considered.

The index inaccuracy is first determined analyzing the balance chart as a number of index units.

The value of the inaccuracy in term of moment depends on the index formula chosen.

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On the tabulated balance chart the ∆index value for each item loaded is read in an index table.

There are two methods to define index tables :

− Tables with constant step in index

− Tables with constant step in weight.

a) Tables with constant step in index

Those tables are usually used for passengers and cargo ∆index for fuel ∆index tables with constant step in weight are used.

CARGO n CARGO n

Building this type of table consists of determining the transition weights for which there is a step between one index value and the other.

In the above example :

− For weight between 0 and 203 kg the ∆index value varies between 0 and 0.49…

− For weight between 204 and 611 kg the ∆index value varies between 0.5 and 1.49…

− …

Note : The same examples apply for passenger ∆index table except that the weight is replaced by the number of passengers.

In those tables the user selects the ∆index corresponding to the weight or passenger number range he is considering.

For each weight range the ∆index range is 1 index value.

So selecting the rounded figure the user generates an maximum inaccuracy of ±0.5 index unit in each table.

The inaccuracy due to one table is independent from the inaccuracies due to the other tables so :

table

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b) Tables with constant step in index

Those tables are usually used for fuel ∆index or for all ∆index tables in the balance chart.

DENSITY (kg/l)

In those tables the user selects the ∆index corresponding to the weight or passenger number he is considering. For a weight value not presented in the table different solutions are available :

− interpolation allowed : the user finds the ∆index by interpolating between the 2 closest ∆index values. Ex: for weight of 6500 kg the ∆index is –3.

In this case the maximum inaccuracy value is reached for the maximum range of

∆index between two weights and the inaccuracy value equals half the ∆index range. Ex: in the above table the maximum ∆index range is between 7000 kg and 8000 kg and corresponds to a maximum inaccuracy in index of ±1.5 index units.

− interpolation is not recommended by the operator procedure, the user always retains the value corresponding to the lowest (highest) weight. Ex: for weight of 6500 kg the ∆index is –2 (–4).

In this case the maximum inaccuracy value is reached for the maximum range of

∆index between two weights and the inaccuracy value equals the ∆index range.

Ex: in the above table the maximum ∆index range is between 7000 kg and 8000 kg and corresponds to a maximum inaccuracy in index of ±3 index units.

The inaccuracy due to one table is independent from the inaccuracies due to the other tables so :

table

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On the graphical balance chart the ∆index value for each item loaded is read on a diagram.

On this diagram the ∆index is drawn manually on each line for each item loaded.

The manual drawing generates an inaccuracy due to the drawing precision as illustrated below : the blue line being the ideal drawing and the red line a manual drawing.

The inaccuracy due to this manual input is highly dependant on the index scale readability on the balance chart and the index scale is linked to the choice of index formula C constant.

AIRBUS standard constants are determined in order to have a major step in index length drawn on the chart between 1 and 1.5 cm, each major step is divided into 10 minor steps so one minor step length is between 1 and 1.5 mm. Then the cargo weight steps and passenger number steps on the diagram are determined so that between two oblique lines on the scale there is no more than 5mm to ensure sufficient accuracy when interpolating.

Following these design rules it is assumed that on each scale the maximum inaccuracy is of 0.5 index unit.

The inaccuracy due to one scale is independent from the inaccuracies due to the other scales so :

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3.5.3. example on A330 graphical balance chart

On this balance chart the final CG is determined

− entering the Dry Operating Index in the initial scale.

− determining ∆index for each cargo compartment (5 scales)

− determining ∆index for each cabin section (3 scales)

− determining the fuel ∆index in the fuel index table (inaccuracy depends on the weight step in the table, and on the procedure interpolation/no interpolation) in this example inaccuracy = 2 index units.

− entering the fuel index in the fuel scale

Each inaccuracy scale is independent from the other ones.

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3.6. Item movements during flight impacting the