The weight and balance calculations

Same five-part form as GEN-H Procedures. Every procedure here ends in a number that goes on a form and stays there, so the checks matter more than usual.

Write every sign explicitly, including the positive ones (GEN-C Concepts §2).

Procedure 1 — Find the aircraft's weight and balance information (S11, S12, S13)

Before any calculation. These three are Locate elements and they are the foundation of everything below.

1. The type certificate data sheet gives the datum, the CG range, and maximum weights. Read the datum definition literally — "88 in forward of the wing leading edge" means measure it, not assume it.
2. The aircraft's weight and balance record gives the current empty weight and empty weight CG, and the date they were established.
3. The equipment list gives what is installed and its arm.
4. The placards give the operating limitations the pilot works to.

Check — say the datum out loud, as a physical location on the aircraft. If you cannot point at it, you cannot measure an arm from it.

Failure — using a datum from a different model in the same family. They differ, and every arm inherits the error.

Procedure 2 — Compute a moment (S9)

Method — moment = weight × arm. Carry the sign of the arm.

Given — a 40 lb radio at an arm of −15 in. Method — 40 × (−15) = −600 in-lb.

Check — a negative arm must produce a negative moment. If your moment column has no negative entries and your arm column does, you have dropped a sign.

Moment index (K4). Moments are large numbers, and large numbers breed arithmetic errors. So many aircraft use a moment index: the moment divided by a reduction factor, such as 100 or 1,000. A record column headed "Moment (lb-in/1,000)" is an index. FAA-H-8083-1B Ch. 2, Manufacturer-Furnished Information, and Ch. 5, Moment Indexes.

Given — the same radio, in a record that uses a reduction factor of 1,000. Method — −600 ÷ 1,000 = −0.6.

Check — every moment in one calculation uses the same reduction factor. Adding a raw moment to an index is an error of a hundred or a thousand times. To get a CG back from indexes, multiply the total index by the reduction factor before dividing by total weight.

Procedure 3 — Compute empty weight and empty weight CG (S8, with S10)

Given — scale readings: nose 340 lb at arm 32.0 in; left main 830 lb at 96.0 in; right main 828 lb at 96.0 in. Tare on the nose scale: 4 lb.

Method

1. Subtract tare from the scale it sits on, not from the total: nose becomes 336 lb.
2. Total weight = 336 + 830 + 828 = 1,994 lb.
3. Total moment = (336 × 32.0) + (830 × 96.0) + (828 × 96.0) = 10,752 + 79,680 + 79,488 = 169,920 in-lb.
4. Empty weight CG = 169,920 ÷ 1,994 = 85.2 in.

Check — the CG must fall between the most forward and the most aft arm used. Here between 32.0 and 96.0. A CG outside that range is arithmetically impossible and means a moment is wrong.

Failure — subtracting tare from the total weight instead of from its own scale position. The weight comes out right and the CG comes out wrong, because the tare's arm was never removed.

Procedure 4 — Perform a weight and balance calculation (S2)

Method

1. Start from empty weight and empty weight moment from the record.
2. Add each item: weight, arm, moment, in a column. Fuel, oil, occupants, baggage, equipment.
3. Total the weights. Total the moments.
4. CG = total moment ÷ total weight.
5. Compare against the CG range for that total weight — the range often narrows as weight increases.
6. Compare total weight against maximum.

Check — two independent checks, and use both. One: the CG must lie between the smallest and largest arm in the table. Two: re-total the moment column by a different route — sum the fuel and occupants separately and add to the empty moment. If the two totals disagree, one of them is an arithmetic error and you have found it before it reached the form.

Failure — checking weight against maximum and forgetting the CG range varies with weight. An aircraft can be inside the CG range for its empty weight and outside it when loaded.

Procedure 5 — Weight shift (S3, S15)

Given — a 2,000 lb aircraft with CG at 85.0 in. Fifty pounds of baggage moved forward by 60 in.

Method — CG change = (weight moved × distance moved) ÷ total weight = (50 × 60) ÷ 2,000 = 1.5 in. Moving forward, so the new CG is 85.0 − 1.5 = 83.5 in.

Check — total weight does not change when you shift weight, so if your new total weight differs from the old one you have used the addition formula instead of the shift formula. And the CG moves in the direction the weight moved, always.

Failure — moving weight aft and computing a forward CG shift. The formula gives a magnitude; you supply the direction, and it is the direction the weight went.

Procedure 6 — Ballast (S3, K9)

Given — a 2,000 lb aircraft with CG at 85.0 in. The forward limit is 84.0 in. Ballast can be carried at arm 40.0 in.

Method — weight to add = total weight × (new CG − old CG) ÷ (ballast arm − new CG) = 2,000 × (84.0 − 85.0) ÷ (40.0 − 84.0) = 2,000 × (−1.0) ÷ (−44.0) = 45.5 lb.

Check — recompute forward. New weight 2,045.5 lb; new moment (2,000 × 85.0) + (45.5 × 40.0) = 170,000 + 1,820 = 171,820; new CG = 171,820 ÷ 2,045.5 = 84.0 in. It lands on the limit, which is what was asked.

Failure — a negative answer taken at face value. Two negatives in the formula give a positive weight; a negative result means the ballast arm is on the wrong side of the target CG and ballast there would move the CG the wrong way.

Ballast is a last resort and it must be secured, placarded and permanent where the installation requires it. Loose ballast is loose weight at an unknown arm.

Procedure 7 — Compute forward and aft loaded CG limits (S6, S16)

Method — from the TCDS, take the CG range at the relevant weight. Older aircraft may have no TCDS. Aircraft certificated before January 1, 1958 were issued Aircraft Specifications under the Civil Air Regulations (FAA-H-8083-1B Ch. 2, FAA-Furnished Weight and Balance Information), and specifications remain in effect for them (FAA-H-8083-30B Ch. 2, Aircraft Specifications). The ACS also names aircraft listings, a third document of this kind; the handbook indexes them but does not describe them. Take the CG range from whichever of the three the FAA holds for that aircraft. Interpolate where the range is given as a graph or at discrete weights (GEN-B Procedures Procedure 6).

Check — the range narrows or shifts with weight on most aircraft. A CG range you have taken as constant across the weight envelope is probably being read at one weight only.

Procedure 8 — Check scales for calibration (S4)

1. Confirm the scales are within their calibration period, with records.
2. Confirm they are level, on a firm surface, and zeroed with nothing on them.
3. Check with a known weight where one is available.
4. Record the scale identification with the weighing.

Check — zero them again after the weighing. If they no longer read zero, the weighing is invalid — and you will only know if you check.

Procedure 9 — Record a weight and balance change (S7, S14, S17)

The output of this unit is a record, not a number.

1. Compute the new empty weight and empty weight CG after the change.
2. Revise the equipment list: add what was installed with its weight and arm, remove what was taken out.
3. Make the maintenance record entry under § 43.9 (GEN-I Procedures Procedure 6).
4. Amend the weight and balance record, dated and signed.
5. Check whether any placard changes as a result (S13).

Check — the new empty weight should differ from the old by exactly the net weight installed. If it does not, either the arithmetic is wrong or you have accounted for something twice.

Failure — computing the new numbers correctly and never amending the equipment list. The aircraft then has a weight and balance record that does not match what is installed, and nobody finds out until the next weighing.

The checks, collected

License

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