14.1 Weight-and-Balance Principles

ACS PA.I.F.K2e (weight and balance) and PA.I.F.S1 (compute it, then decide if you are inside the envelope) rest on the same four definitions the FAA-H-8083-1 Aircraft Weight and Balance Handbook and PHAK Chapter 10 use on every sample problem. The Private Pilot Airplane knowledge test does not ask you to jack a trainer onto scales. It asks what a datum is, whether 40 gallons of avgas weigh 40 pounds, what still sits in empty weight after you drain the tanks, and whether useful load includes fuel.

Datum, arm, moment, CG

The datum is an imaginary vertical plane chosen by the manufacturer. Every horizontal distance used for balance is measured from that plane. Some trainers put the datum at or ahead of the spinner so every listed arm is a positive number. Others put it at the firewall or a wing leading-edge station, so a battery or a nose-baggage item can have a negative arm.

The arm (also called the moment arm) is the horizontal distance from the datum to the item’s center of gravity, in inches. A station is just a named location along the fuselage, usually written as its arm.

Moment is the item’s tendency to rotate the airplane about the datum:

Moment = weight × arm

Units are pound-inches (lb-in). A 170-pound pilot at station 37.0 produces a moment of 6,290 lb-in. An item forward of the datum has a negative arm and therefore a negative moment — you still add it algebraically.

The airplane’s center of gravity (CG) is the point at which it would balance if suspended. Computationally it is the weighted average of every arm:

CG = total moment ÷ total weight

That one division is the entire computational engine. Get the pounds and the inches honest, add them without dropping a line, and the CG falls out in inches from the datum. Compare that inch figure — and the total weight — with the AFM/POH envelope. Both must be inside.

Empty weight, BEW, and the oil question

Empty weight in the handbook sense is the airframe, engines, and permanently installed equipment, plus the fluids that never leave: unusable fuel and, depending on the certification paperwork, some amount of oil.

Standard empty weight is that standard airplane as the factory delivered it: unusable fuel, full operating fluids, and full oil.

Basic empty weight (BEW) is standard empty weight plus optional equipment that was later installed — a second nav radio, a fancy interior, an autopilot. The BEW and its empty-weight CG on this airplane’s current weight-and-balance record are the numbers you start every loading problem from. Do not use the sample-problem empty weight printed in a generic textbook if the aircraft’s equipment list has changed.

Licensed empty weight is the older term still printed on some pre-Part-23 records. It usually includes unusable fuel and only undrainable oil, not a full sump. On those airplanes, full oil is a separate loading line. On a modern BEW airplane, full oil is already inside BEW and you do not add it again. Read the record in front of you. The knowledge-test tell is the phrase “includes full oil” versus “undrainable oil only.”

Unusable fuel stays in empty weight because you cannot send it to the engine. Usable fuel is the only fuel that belongs on the loading table.

Useful load, payload, and the three operating weights

Useful load is what you may still add after empty weight:

Useful load = maximum takeoff weight − BEW

(Some POHs quote useful load from maximum ramp weight, because that is the heaviest the airplane may sit on its tires. The difference is the few pounds of start, taxi, and runup fuel.) Useful load is occupants, baggage, cargo, drainable oil if it is not already in BEW, and usable fuel.

Payload is the part of useful load that is not fuel: people, bags, and cargo. Payload = useful load − usable fuel. A full-fuel departure therefore has a smaller leftover payload than a ferry with tanks at tabs.

The airplane then changes weight three times before it is parked again.

• Ramp (taxi) weight is the airplane as it sits on the ramp, ready to start — people, bags, and all the fuel in the tanks, including the gallon or two you will burn before takeoff. It must not exceed maximum ramp weight.
• Takeoff weight is ramp weight minus the fuel used for start, taxi, and runup. It must not exceed maximum takeoff weight.
• Landing weight is takeoff weight minus the fuel burned in flight (plus anything you picked up, which a PAR trainer will not). It must not exceed maximum landing weight, which is often a few tens of pounds below maximum takeoff on light airplanes and much lower on heavier types.

Maximum zero-fuel weight, when published, is the maximum weight with no usable fuel. It protects the wing-attach structure from a fuselage that is too heavy relative to fuel in the wings. Many light trainers do not publish one; do not invent it.

Standard weights — convert before you multiply

PHAK’s loading standards that the knowledge test actually uses:

• Aviation gasoline (avgas): 6 lb/gal
• Oil: 7.5 lb/gal (a U.S. gallon is four quarts, so 8 quarts of oil are 2 gallons × 7.5 = 15 lb)

Use actual occupant weights when you have them. Sample problems sometimes state 170 lb per adult; that is a problem-given standard, not a regulation that replaces a 220-pound passenger.

The trap is putting 40 in the weight column because the tanks hold 40 gallons. Forty gallons of avgas weigh 240 lb. Forty gallons of oil would weigh 300 lb. Water, if you ever see it, is about 8.35 lb/gal. Convert, then multiply by the arm.

Why the FAA cares

Weight and CG are not paperwork for the dispatcher. Weight sets performance. A heavier airplane stalls faster (stall speed rises with the square root of weight), needs more runway to take off and to land, climbs worse, and has a lower service ceiling. Those numbers are the Chapter 13 charts — and every one of them assumes you are at the weight you claimed.

CG sets whether you can still control the airplane that is producing that performance. A CG outside the envelope can make the elevator unable to rotate for takeoff, unable to flare for landing, or unable to pitch the nose down in a stall. Section 14.3 is that story. Here, remember that a legal-looking total weight with an illegal CG is still an illegal airplane.

Moment indexes are a chart convenience

Moments in the tens of thousands of pound-inches make ugly graphs. Manufacturers divide every moment by a reduction factor — usually 100 or 1,000 — and call the result a moment index. The loading graph then plots pounds against index, and the CG envelope is drawn in index-versus-weight (or CG-inches-versus-weight).

The algebra does not change. If you divided by 1,000,

CG = (total index × 1,000) ÷ total weight

Use the same factor on every line. Mixing a ÷100 empty-weight index with a raw pound-inch baggage moment will invent a CG that is not on this planet. The index is not a different kind of physics. It is smaller handwriting.

Scenario: Jordan’s 40-gallon line

Jordan’s BEW is 1,500 lb at 39.0 inches. Useful load at a 2,550-lb maximum takeoff weight is 1,050 lb. He writes “fuel 40” in the weight column, adds himself and a bag, and the total still looks under 2,550. The 40 was gallons. The tanks actually added 240 lb, and he is now 200 lb heavier than the sheet claims — plus every moment on the fuel line is a factor of six too small, so the CG is fiction. Convert at 6 lb/gal, then multiply by the fuel arm. That is the whole first skill.