The Flight DeckLESSON 06 · WEIGHT & BALANCE
A weight and balance calculation checks whether total weight and center of gravity remain within the airplane’s approved limits. Each load’s position matters because weight multiplied by arm produces a moment.
THE MATHEMATICS OF BALANCE
Imagine pushing a door near its hinge, then near its handle. The same force has a larger turning effect with a longer perpendicular lever arm. For aircraft loading, we multiply each weight by its signed horizontal distance from a common reference.
A manufacturer-selected reference plane: the zero from which arms are measured. It may be ahead of the airplane or at another specified location. It is not automatically the nose, the CG, or a physical support.
The signed horizontal distance from the datum to an item’s CG. In the convention used here, aft is positive and forward is negative. Always use the aircraft’s published datum, stations, and units.
Weight multiplied by arm. With pounds and inches, moment is in pound-inches (lb·in), not pounds or inches alone.
CG is a weighted average of the load positions. It moves toward added weight, away from removed weight, and in the direction a load is shifted. With positive weights, it lies between the occupied stations.
FAA PHAK Chapter 10: weight-and-balance terms and computational method.
THE AIRCRAFT CALCULATION
An aircraft calculation includes its current empty weight and moment, then occupants, baggage, usable fuel, and any other items required by its approved method. Don’t double-count oil or unusable fuel already included in its empty-weight definition.
| Item | Weight (lb) | Arm (in) | Moment (lb·in) |
|---|---|---|---|
| Empty airplane | 1,400 | 40 | 56,000 |
| Front occupants | 340 | 37 | 12,580 |
| Baggage | 60 | 95 | 5,700 |
| Usable fuel | 200 | 48 | 9,600 |
| Total | 2,000 | CG: 41.94 | 83,880 |
83,880 lb·in ÷ 2,000 lb = 41.94 in aft of datum
For a real flight, plot the weight and CG against the aircraft-specific envelope, whose boundaries can vary with weight. Check applicable ramp, takeoff, and landing weights, compartment and seat limits, and required fuel reserves. A CG number alone cannot establish an acceptable loading.
A load forward of the datum can have a negative arm and moment. Keep that sign when adding. Changing the datum changes numerical arms and moments but not the airplane’s physical balance.
Some POHs divide moments by 100 or 1,000 to simplify tables. Restore the stated scale when calculating CG, or use the matching published graph. Never mix raw moments with indexed moments.
FAA PHAK Chapter 10, computational, graph, and table methods.
MOVE IT, ADD IT, REMOVE IT
When a load moves inside the airplane, total weight stays the same. Only the moment changes. For a signed movement, positive is aft in this lesson:
In the example above, moving the 60 lb bag from 95 in to 45 in changes moment by 60 × (45 − 95) = −3,000 lb·in. CG moves −3,000 ÷ 2,000 = −1.50 in, from 41.94 to 40.44 in. Moving the bag forward moves CG forward.
At 2,000 lb total weight, with a 50 in forward move available: shifted weight = (2,000 × 2) ÷ 50 = 80 lb. This is an arithmetic example; the destination must permit and safely restrain that load, and the new loading must be checked against the full envelope.
Adding or removing weight changes the denominator too. Recompute both total weight and total moment. The unchanged-total-weight shift formula does not apply directly to fuel burn.
WEIGHT CHANGES THE LIFT REQUIREMENT
In steady, level flight, the airplane’s net upward aerodynamic force balances weight. At the same airspeed, density, and configuration, a heavier airplane generally needs a higher lift coefficient and AOA. The wing reaches its critical AOA at a higher airspeed. Added weight does not itself increase the wing’s critical AOA.
For a simplified comparison at the same configuration, load factor, and maximum lift coefficient:
If stall speed is 50 kt at 2,000 lb, the estimate at 2,400 lb is 50 × √1.2 = 54.8 kt. That is a 20% weight increase but about a 9.5% stall-speed increase. These are invented values, not permission to exceed a maximum weight.
Higher weight generally increases takeoff and landing distances, reduces climb performance, and increases induced drag at a given speed. AOA is not automatically higher in every phase or at every speed; the comparison conditions matter. Use published performance charts.
In the simplified positive-maneuver model, the stall boundary intersects the limit load factor at VA ≈ VS√nlimit. Less weight lowers stall speed, so the intersection moves to a lower speed. At the same airspeed, a given lift force produces a larger load factor when divided by a smaller weight.
At the same airspeed and configuration in level flight, a lighter airplane needs less lift. It therefore flies at a lower AOA, farther from critical AOA. That extra AOA margin allows a larger increase in lift before the wing stalls—but the lighter airplane also reaches its load-factor limit with less lift. This is why maneuvering speed decreases with weight. Use the aircraft’s published speeds for its current weight.
VA is not a guarantee that the airplane will “safely stall before it breaks” in turbulence. Repeated or reversing large inputs, inputs in multiple axes, and gust loads can exceed design assumptions. Follow the POH/AFM’s turbulence guidance and operating limitations.
FAA PHAK Chapter 5: load factors, stall speeds, maneuvering speed, and rough air.
CONNECT IT TO STABILITY
The seesaw locates the mass balance point. In flight, the airplane has no support underneath it: aerodynamic forces and moments determine its response. As in the Stability lesson, pitch moments are evaluated about CG.
Generally increases static pitch stability for a fixed configuration. In a conventional airplane it often increases required tail downforce, so the wing must provide weight plus that downward tail force.
This can increase stall speed, trim drag, and control forces. Beyond the forward limit, there may be insufficient nose-up control for rotation or flare.
Generally reduces static pitch stability and may reduce required tail downforce and trim drag. Aft CG within the approved range is not automatically unstable.
Beyond approved limits, controllability and stall/spin recovery can deteriorate severely. A particular flat or “tail-first” spin is not guaranteed.
In the simple controls-fixed model, the whole-airplane neutral point marks neutral static longitudinal stability. CG forward of it gives positive static margin; moving CG toward it reduces that margin. Do not substitute the wing’s aerodynamic center for the neutral point, or treat the neutral point as an approved aft CG limit.
You can be under the maximum weight and still outside the CG envelope. You can also have an acceptable CG and be overweight. Check both.
EXPLORE THE LEVER
Start with equal loads. Then choose “Lighter, farther out.” Watch the weights, arms, and moments together. Move the support under CG to find the balance point.
Aft / increasing arm → · The beam is kept level so arms stay horizontal. The arrow shows which end would initially tip down; it does not predict a tilt angle.
| Load | Weight (lb) | Arm (in) | Moment (lb·in) |
|---|---|---|---|
| A | 100 | 40 | 4,000 |
| B | 100 | 160 | 16,000 |
| Total | 200 | — | 20,000 |
CG = 20,000 ÷ 200 = 100.00 in
Moment about support = 20,000 − (200 × 100) = 0 lb·in.
Balanced: the support is under CG.
Teaching model: two point loads, rigid weightless beam, vertical gravity, one support. The beam’s own weight is excluded. Values are fictional; this is not an aircraft loading calculator.
The table uses the datum at zero. The tipping calculation uses the support at P. For each load, the arm from the support is (item arm − P). Adding those moments gives total datum moment − total weight × P.
When P = CG, the moments of the weights about the support cancel. The sum of the weights’ moments about the datum can still be positive. Moving the support changes the tipping tendency, not the load positions or their CG.
WATCH THE FLIGHT PROGRESS
Burning fuel removes weight at the tank’s arm. CG moves away from the weight being removed. Compare tanks forward of, at, and aft of the nonfuel CG below.
Fixed nonfuel load: 1,800 lb, moment 74,280 lb·in, CG 41.27 in. These totals combine the empty airplane, front occupants, and baggage from the fictional loading example in Learn, leaving out its 200 lb of usable fuel. The selected tank then adds fuel to this fixed load.
CG = (83,880 − 0 × 48) ÷ (2,000 − 0) = 41.94 in
No fuel burned yet. This aft tank will move CG forward as fuel is consumed.
Displayed numbers are rounded; calculations retain full precision. One tank, constant tank arm, no fuel transfer; all fuel amounts are weights in pounds. The zero-fuel endpoint explains the mathematics, not a flight plan. No aircraft limits or reserve requirements are represented.
For example, burning 100 lb at arm 48 removes 4,800 lb·in: the new CG is 79,080 ÷ 1,900 = 41.62 in. It moves forward from 41.94 in. With fuel ahead of CG, the direction reverses.
Check loading throughout flight, including relevant fuel-transfer or tank-sequencing stages. Takeoff and landing checks alone may miss an intermediate extreme in a more complex fuel system. Use the approved fuel-management and weight-and-balance information.
CHECK YOUR UNDERSTANDING
They are equal: each is 4,000 lb·in from the same datum. Weight and arm both matter.
No. The weights’ moments about the support cancel. Total datum moment divided by total weight gives CG; those datum moments need not sum to zero.
50 × (−40) ÷ 2,000 = −1 in. CG moves 1 in forward; total weight is unchanged.
Aft, away from the removed weight. Recalculate both total moment and total weight.
No. Applicable maneuvering speed generally decreases with weight. Use the published speeds; it is not unlimited protection against gusts or control inputs.
No. Check weight limits, loading and restraint limits, fuel, performance, and other operating requirements. CG is one part of the loading decision.
SUMMARY
Weight and arm determine moment; total moment divided by total weight locates CG. Moving loads or burning fuel changes that balance. Check both total weight and CG against the aircraft’s approved limits.
PRACTICE
Review six flashcards, then answer five questions.
Enable JavaScript for flashcards and the knowledge check. The lesson and scenario remain available without it.
Based on the supplied Weight, Balance, & Aerodynamic Loading outline, with clarified assumptions and original teaching examples.
Terminology, loading calculations, weight shifting, addition/removal, and CG effects.
Weight and load distribution, stall speed, load factor, maneuvering speed, and stability.
Moments about CG, neutral point, and static margin; also discussed in our Stability lesson.
Use the specific aircraft’s current weight-and-balance records and approved POH/AFM for flight planning. These labs explain relationships; they do not assess an actual airplane’s loading.