Weight and Balance Basics for Canadian Pilots

Two checks, not one

Weight and balance is two separate limits, and a load can pass one and fail the other.

TC AIM RAC 3.4.3 defines balance as "the location of the CG along the longitudinal axis of the aircraft." The forward and aft limits "are the maximum CG positions at which the longitudinal stability requirements can be met," and outside them the aircraft's "handling is either unsatisfactory or has not been investigated."

In the figure, load the seats, the baggage and the fuel. Adding weight behind the CG moves the dot up and to the right; burning fuel moves it down and forward, not straight down. A load under the maximum weight can still be outside the envelope. The envelope is an illustrative trainer, not any real aeroplane's chart.

The rule, word for word

The CARs do not set weight or CG numbers. They make the flight manual's limits law. TC AIM RAC 3.4.3 then spells out what that means for weight and balance.

The words you need

• Datum: the reference point the manufacturer measures every distance from.
• Arm: the distance from the datum to where a weight acts. In this page's examples it is in inches, positive aft of the datum.
• Moment: weight × arm, here in lb-in.
• CG: total moment ÷ total weight.
• Empty weight: the airframe, the power plant, fixed ballast, unusable fuel, the maximum amount of normal operating fluids such as oil, and all installed equipment (TC AIM RAC 3.4.1(g)). Usable fuel, the people and the baggage are added on top.
• Maximum take-off weight: the maximum take-off weight "as authorized by the aircraft's state of registry or as provided for in the aircraft type certificate" (TC AIM RAC 3.4.1(j)).

The aeroplane's empty weight and empty CG are recorded in its journey log, and any change to them must be entered "at the latest, before the next flight" (CARs 605.94(1) and Schedule I, item 2). The owner also keeps an empty weight and balance report (CARs 605.92(1)(c)). That is where your calculation starts.

Working it out

Write one line for each item, multiply weight by arm, then add the columns. The stations are the figure's trainer: maximum take-off weight 2,300 lb, aft CG limit 47.3 in., forward limit 38.4 in. at this weight.

CG = 98,060 ÷ 2,290 = 42.8 in. The weight is 10 lb under the maximum, and the CG is inside the limits.

Now check the landing. Burn 20 US gal (120 lb) at the fuel arm of 48.0 in.: the weight falls to 2,170 lb and the moment to 98,060 − 5,760 = 92,300 lb-in. The CG becomes 92,300 ÷ 2,170 = 42.5 in. It moved forward, because the fuel sat behind the CG. TC AIM RAC 3.4.3 warns that "in many aircraft, there is significant CG movement as fuel is being consumed." Check both ends of the flight.

Mind the fuel units. TC AIM RAC 3.4.2 notes that fuel "is supplied in pounds, kilograms, litres or gallons," and that a wrong conversion could be hazardous. Use the weight per unit your flight manual gives.

Weighing the load

TC AIM RAC 3.4.2 is blunt about light aeroplanes: "with many four- and six-seat aircraft, it is not possible to fill all the seats, use the maximum baggage allowance, fill all the fuel tanks and still remain within the approved weight and CG limitations." Something has to give, usually fuel or baggage.

• Weigh, don't guess. "If it is possible that the aircraft is operating close to its MTOW, the baggage must be weighed," and "if the aircraft is suspected to be operating anywhere close to its maximum weight, passengers must be weighed" (TC AIM RAC 3.4.2).
• Use actual weights in small aeroplanes. For a passenger seating capacity of less than five, actual weights give the greatest accuracy, and standard or segmented weights are not recommended (TC AIM RAC 3.4.7, note).
• People come dressed. A passenger's weight "must include personal clothing and carry-on baggage allowances" (TC AIM RAC 3.4.2).
• Check the baggage floor. Do not exceed its weight per unit area limit, and secure the load so it cannot move or block an exit (TC AIM RAC 3.4.2).

Forward CG and aft CG

Within the limits, where the CG sits still changes how the aeroplane flies (From the Ground Up, Theory of Flight, stability):

• Forward CG: more stable in pitch, heavier on the elevator, and a little faster to stall, because the tail has to push down harder. Near the forward limit you can run out of elevator to flare.
• Aft CG: less stable in pitch and light on the controls. Past the aft limit the aeroplane can become unstable, and stall and spin recovery can be hard or impossible.

TC AIM RAC 3.4.2 adds that the effects stack up with other things that cut performance, such as contaminated runways, icing, turbulence and high temperatures.

Where candidates lose marks

• Under the maximum weight is not enough. The CG has to be inside the limits too (TC AIM RAC 3.4.3).
• The CG moves in flight. Fuel burned from tanks behind the CG moves it forward; from tanks ahead of the CG, aft. Check take-off and landing.
• CG is total moment ÷ total weight, not the average of the arms.
• Out of limits is not a judgment call. "The aircraft must not be flown outside these limits" (TC AIM RAC 3.4.3), and the airworthiness certificate "is nullified" if you do.
• Fuel by volume is not fuel by weight. Convert litres or gallons to pounds or kilograms with your manual's figure.

Practice

Original questions in the style of the Transport Canada written exams. Tap an answer to see why it is right or wrong.

1. Question 1 of 4

   An aeroplane weighs 1,600 lb empty at an arm of 40.0 in. You add a 300 lb pilot at 36.0 in. and 150 lb of fuel at 48.0 in. Where is the centre of gravity?

   139.4 in.240.0 in.340.7 in.441.3 in.

   Tap an answer to check it.

2. Question 2 of 4

   Your loaded aeroplane is 60 lb under its maximum take-off weight, but the CG is behind the aft limit in the flight manual. Which is correct?

   1The flight is legal if the pilot is the only person on board.2The flight may not be made until the load is changed to bring the CG within limits.3The flight is legal, because the aeroplane is under its maximum take-off weight.4The flight is legal if full nose-down trim holds the attitude.

   Tap an answer to check it.

3. Question 3 of 4

   In your aeroplane the fuel tanks are behind the loaded centre of gravity. What happens to the CG as the fuel burns off in flight?

   1It stays where it is, because only the weight changes.2It moves forward.3It moves aft until half the fuel is gone, then forward.4It moves aft.

   Tap an answer to check it.

4. Question 4 of 4

   You are loading a four-seat aeroplane that will be close to its maximum take-off weight. According to TC AIM RAC 3.4, which passenger weights should you use?

   1Transport Canada's segmented passenger weights.2Transport Canada's standard passenger weights.3Each passenger's actual weight, including clothing and carry-on baggage.4Each passenger's stated weight, with nothing added.

   Tap an answer to check it.

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