Weight and balance

Every flight has two questions to answer before you start the engine: is the airplane too heavy, and is the weight in the right place? Here's how to answer both.

Why it matters

The airplane was certificated to fly safely within a weight limit and a center of gravity (CG) range. Outside either one, you're a test pilot.

Too heavy

• Higher takeoff speed and a longer takeoff roll
• Slower, shallower climb and a lower service ceiling
• Higher stall speed and higher approach and landing speeds
• Longer landing roll and more load on the structure, especially in turbulence

CG too far forward

• The tail has to push down harder to hold the nose up, so the wing carries more load and the stall speed goes up.
• You may run out of elevator to rotate on takeoff or to flare on landing.
• Cruise is a little slower because of the extra tail-down force.

CG too far aft

• The airplane gets less stable in pitch and the controls get lighter, so it's easy to over-control.
• Stall and spin recovery get harder. Far enough aft, recovery may not be possible.

The terms

Datum

The reference point the manufacturer picked for measuring everything. It's often the firewall, the wing's leading edge, or a point ahead of the nose. The POH tells you where it is.

Arm (or station)

The distance in inches from the datum to an item. Behind the datum is positive, ahead of it is negative. Seats, fuel tanks, and baggage areas each have a fixed arm listed in the POH.

Moment

Weight times arm, in pound-inches. It's how much that item tries to rotate the airplane around the datum. Many POHs divide moments by 100 or 1,000 to keep the numbers small. That's called a moment index.

Center of gravity (CG)

The point where the airplane would balance. You find it by dividing the total moment by the total weight, and it comes out as an arm in inches from the datum.

CG envelope

The allowed range of CG at each weight, usually drawn as a graph in the POH. The forward limit often moves aft as the airplane gets heavier.

Basic empty weight

The airplane with its installed equipment, unusable fuel, and full engine oil. It comes from the airplane's own weight and balance record, and it changes whenever equipment is added or removed. Some older POHs use licensed empty weight instead, which leaves out the oil, so the oil has to be added as its own line.

Useful load

Maximum weight minus basic empty weight. It's everything you can add: people, bags, and usable fuel.

Walkthrough

You're taking two passengers and a bag on a one-hour flight with 40 gallons of fuel. Is it legal?

1. Start with the airplane's empty weight and moment

   Take these from the airplane's current weight and balance record, not the sample page in the POH. Here it's 1,650 lb at an arm of 39.0 in, for a moment of 64,350 lb-in.

2. Weigh everything you're adding

   Use real weights for people and bags. Fuel weighs 6 lb per gallon for 100LL, so 40 gallons is 240 lb.

3. Multiply each weight by its arm

   Takeoff loading

   Item	Weight (lb)	Arm (in)	Moment (lb-in)
   Basic empty weight	1,650	39.0	64,350
   Pilot	180	37.0	6,660
   Front passenger	160	37.0	5,920
   Rear passenger	150	73.0	10,950
   Baggage	40	95.0	3,800
   Fuel, 40 gal	240	48.0	11,520
   Total	2,420		103,200

4. Check the weight

   2,420 lb is under the 2,550 lb maximum, with 130 lb to spare.

5. Find the CG

   103,200 ÷ 2,420 = 42.6 in aft of the datum.

6. Check the CG against the envelope

   At 2,420 lb the forward limit works out to about 39.7 in, and the aft limit is 47.3 in. 42.6 is between them.

   Takeoff: 2,420 lb at 42.6 in. Within limits.

7. Do it again for landing

   The fuel you burn changes both the weight and the CG. An hour at 8 gallons per hour plus taxi and climb is about 24 gallons, or 144 lb. Take that weight and its moment back out:

   Landing

   Item	Weight (lb)	Arm (in)	Moment (lb-in)
   Takeoff total	2,420	42.6	103,200
   Fuel burned, 24 gal	−144	48.0	−6,912
   Landing total	2,276	42.3	96,288

   96,288 ÷ 2,276 = 42.3 in. The CG moved forward, because the fuel sits aft of the CG. In an airplane whose tanks are ahead of the CG, it moves aft instead, so always check where you'll land as well as where you'll take off.

   Landing: 2,276 lb at 42.3 in. Within limits.

The example airplane's envelope. The filled dot is takeoff, the open dot is landing, and the dashed line is the CG moving as fuel burns.

Moving weight around

If the CG is out of limits, you can often fix it by moving something instead of leaving it behind. You don't have to redo the whole table:

Say you move the 40 lb bag from the baggage area (95.0 in) to the empty rear seat (73.0 in). That's 22 inches forward:

40 × 22 ÷ 2,420 = 0.36 in forward, so the takeoff CG goes from 42.6 to about 42.3 in. The total weight doesn't change.

To add or remove weight, add or subtract its moment and its weight, then divide again, the same way you did for the fuel burn.

Doing it for real

• Use the empty weight and moment from that tail number's current weight and balance record. Two airplanes of the same model can differ by a lot.
• Use the arms, limits, and envelope from that airplane's POH, Section 6.
• Use real weights for people and bags, including headsets, flight bags, and anything in the seat pockets.
• Check both takeoff and landing, and check the per-seat and baggage limits as well as the totals.
• If the POH gives a loading graph or moment index, it's the same math in a different form. Learn the table first and the graph will make sense.

Sources

• FAA-H-8083-1B, Aircraft Weight and Balance Handbook
• FAA-H-8083-25C, Pilot's Handbook of Aeronautical Knowledge, Chapter 10, Weight and Balance