Project
Aircraft Weight and Balance CG Envelope Loading Project
Aerospace engineering project for preparing an aircraft weight-and-balance loading package with station moments, percent MAC, fuel-burn CG movement, envelope checks, corrective loading and release evidence.
This project builds an aircraft weight-and-balance loading package. The goal is to decide whether a proposed loading condition can be released for flight after mass, arm, moment, center of gravity, percent mean aerodynamic chord, fuel-burn movement and envelope limits are traced.
The calculation is simple enough to fit on one page, but the engineering risk is not trivial. A wrong loading record can reduce static margin, consume elevator authority, change stall behavior, invalidate takeoff and landing performance, overload structure, or make a flight-control release apply to the wrong aircraft state.
Project Objective
Prepare a loading review for a small transport aircraft. The final deliverable should answer:
- What is the zero-fuel mass and center of gravity?
- What is the takeoff mass and center of gravity?
- What is the expected landing center of gravity after fuel burn?
- Do all reviewed points sit inside the approved CG envelope?
- If a point fails, what loading change or restriction corrects it?
- Which evidence must be attached before dispatch or test release?
The deliverable is a traceable engineering note: loading table, source data, moment arithmetic, envelope plot or table, accepted loading instruction, restrictions and final release statement.
Baseline Scenario
Use the following simplified aircraft and loading data.
| Item | Value |
|---|---|
| Datum | aircraft nose reference |
| Mean aerodynamic chord, \bar{c} | 1.80\ \text{m} |
| Leading edge of MAC, x_{LEMAC} | 3.95\ \text{m} aft of datum |
| Maximum takeoff mass | 4500\ \text{kg} |
| Maximum zero-fuel mass for this review | 4000\ \text{kg} |
| Takeoff fuel | 520\ \text{kg} |
| Landing fuel after mission burn | 160\ \text{kg} |
| Fuel station arm | 4.85\ \text{m} |
Approved envelope points for this simplified exercise are:
| Mass | Forward CG limit | Aft CG limit |
|---|---|---|
| 3500\ \text{kg} | 15\%\ \bar{c} | 37\%\ \bar{c} |
| 4000\ \text{kg} | 18\%\ \bar{c} | 36\%\ \bar{c} |
| 4500\ \text{kg} | 22.5\%\ \bar{c} | 35\%\ \bar{c} |
Real aircraft work must use approved weight-and-balance manuals, equipment lists, weighing records, loading schedules, fuel-density rules, baggage limits, seat maps, operational procedures and regulatory requirements. This page is an engineering training project, not an airworthiness approval.
Step 1: Define the Release Boundary
The review boundary should state exactly what is being released:
One loading condition for the stated aircraft configuration, seat layout, baggage distribution, takeoff fuel, landing fuel estimate and approved CG envelope.
The result must not be reused after a cabin reconfiguration, equipment change, baggage relocation, fuel policy change, passenger substitution, maintenance alteration, store fit, icing condition, test instrumentation change or updated flight-control release. Weight and balance is configuration-controlled data.
The package should include:
- current basic empty mass and arm;
- payload item masses, station arms and source records;
- fuel quantity basis and fuel arm;
- zero-fuel, takeoff and landing CG points;
- envelope limits and interpolation method;
- corrective loading action if a point is outside limits;
- sensitivity checks for mass and placement uncertainty;
- final operational restriction or release.
Step 2: Build the Moment Table
Use station moment:
where m_i is item mass and x_i is station arm measured from the datum.
| Item | Mass | Arm | Moment |
|---|---|---|---|
| Basic empty aircraft | 3250\ \text{kg} | 4.20\ \text{m} | 13650\ \text{kg m} |
| Crew | 170\ \text{kg} | 3.20\ \text{m} | 544\ \text{kg m} |
| Forward baggage | 60\ \text{kg} | 2.30\ \text{m} | 138\ \text{kg m} |
| Passenger row 1 | 240\ \text{kg} | 4.70\ \text{m} | 1128\ \text{kg m} |
| Passenger row 2 | 180\ \text{kg} | 5.80\ \text{m} | 1044\ \text{kg m} |
| Aft baggage | 80\ \text{kg} | 6.60\ \text{m} | 528\ \text{kg m} |
Zero-fuel totals:
Engineering Comment
A moment table is only as good as the input state. The reviewer should check whether the basic empty mass includes installed equipment, whether baggage was weighed or estimated, whether passengers were assigned to the correct stations and whether any temporary instrumentation or cargo is missing.
Step 3: Compute Zero-Fuel CG and Percent MAC
The center-of-gravity station is:
For the zero-fuel condition:
Convert to percent mean aerodynamic chord:
Engineering Comment
Percent MAC is a nondimensional way to compare the loading point with aerodynamic and flight-dynamics limits. It does not replace the arm-based loading table. Both are useful because maintenance, loading and weighing records often use arms, while stability and control discussions often use percent MAC.
Step 4: Compute Takeoff CG
Add takeoff fuel:
Takeoff mass:
Takeoff moment:
Takeoff CG:
Percent MAC:
Engineering Comment
Fuel is aft of the zero-fuel CG in this scenario, so adding fuel moves the CG aft. That may look helpful for a forward-CG problem, but the approved forward limit also moves aft at higher mass. The envelope must be checked at the actual mass, not at a convenient reference point.
Step 5: Compute Landing CG After Fuel Burn
Landing fuel is:
Landing fuel moment:
Landing mass:
Landing moment:
Landing CG:
Percent MAC:
The fuel-burn CG movement from takeoff to landing is:
Engineering Comment
Fuel burn moves the CG forward because the burned fuel was aft of the aircraft CG. A loading point that passes at takeoff can therefore fail later in flight or at landing if the forward limit is tight. Weight-and-balance review should check the mission-relevant sequence, not only a single point.
Step 6: Interpolate the CG Envelope
Use linear interpolation between tabulated mass points. Between 4000\ \text{kg} and 4500\ \text{kg}, the forward limit changes from 18\%\ \bar{c} to 22.5\%\ \bar{c}:
The aft limit over the same range changes from 36\%\ \bar{c} to 35\%\ \bar{c}:
For the zero-fuel mass of 3980\ \text{kg}, interpolate between 3500\ \text{kg} and 4000\ \text{kg}:
For the takeoff point:
For the landing point:
Envelope check:
| Condition | Mass | Actual CG | Forward limit | Aft limit | Decision |
|---|---|---|---|---|---|
| Zero fuel | 3980\ \text{kg} | 18.3\%\ \bar{c} | 17.9\%\ \bar{c} | 36.0\%\ \bar{c} | Pass, small forward margin |
| Takeoff | 4500\ \text{kg} | 22.0\%\ \bar{c} | 22.5\%\ \bar{c} | 35.0\%\ \bar{c} | Fail forward limit |
| Landing | 4140\ \text{kg} | 19.5\%\ \bar{c} | 19.3\%\ \bar{c} | 35.7\%\ \bar{c} | Pass, small forward margin |
Engineering Comment
The original loading is not releasable because the takeoff CG is 0.5 percentage points ahead of the forward limit. The zero-fuel and landing points also have thin forward margins. Accepting the flight because two of three points pass would be poor engineering judgment.
Step 7: Correct the Loading Condition
One corrective option is to move 40\ \text{kg} of baggage from the forward baggage station to the aft baggage station.
Moment change:
The mass is unchanged, but the moment increases. Corrected zero-fuel moment:
Corrected takeoff moment:
Corrected landing moment:
Corrected CG positions:
| Condition | Mass | Corrected moment | Corrected CG station | Corrected CG |
|---|---|---|---|---|
| Zero fuel | 3980\ \text{kg} | 17204\ \text{kg m} | 4.323\ \text{m} | 20.7\%\ \bar{c} |
| Takeoff | 4500\ \text{kg} | 19726\ \text{kg m} | 4.384\ \text{m} | 24.1\%\ \bar{c} |
| Landing | 4140\ \text{kg} | 17980\ \text{kg m} | 4.343\ \text{m} | 21.8\%\ \bar{c} |
Corrected envelope check:
| Condition | Corrected CG | Forward margin | Aft margin | Decision |
|---|---|---|---|---|
| Zero fuel | 20.7\%\ \bar{c} | +2.8 points | +15.3 points | Pass |
| Takeoff | 24.1\%\ \bar{c} | +1.6 points | +10.9 points | Pass |
| Landing | 21.8\%\ \bar{c} | +2.5 points | +13.9 points | Pass |
Engineering Comment
The correction solves the forward-CG issue without exceeding mass limits. It must still be operationally possible: aft baggage volume, floor loading, restraint, access, emergency equipment clearance and baggage identification all need confirmation. A mathematically valid move is not an acceptable loading instruction unless it can be executed and verified.
Step 8: Check Sensitivity and Uncertainty
For a small mass relocation, the CG shift can be estimated by:
For the corrective baggage move:
In percent MAC:
This matches the takeoff shift from 21.4\%\ \bar{c} to 24.1\%\ \bar{c}.
Now check a passenger-seat uncertainty. If 20\ \text{kg} effectively moves from row 1 to row 2:
The corrected takeoff forward margin is about 1.6 points, so this passenger-seat uncertainty does not consume the forward margin. It does, however, move the aircraft aft. The reviewer should also check whether the aft envelope remains acceptable for a more aft passenger and baggage distribution.
Engineering Comment
Sensitivity calculations are not decorative. They tell the reviewer which records must be controlled. In this example, the correction is large enough to overcome the original forward-CG failure, but the release still depends on accurate baggage placement and no unrecorded payload.
Step 9: Prepare the Loading Release Matrix
| Check | Evidence | Result | Release action |
|---|---|---|---|
| Basic empty aircraft state | current weighing or equipment-list revision | required | attach source record |
| Seat and baggage assignment | manifest and loading instruction | original failed | revise loading |
| Zero-fuel mass | moment table | 3980\ \text{kg} | below 4000\ \text{kg} limit |
| Takeoff mass | fuel plus zero-fuel mass | 4500\ \text{kg} | at maximum takeoff mass |
| Original takeoff CG | envelope table | 22.0\%\ \bar{c} | reject original loading |
| Corrected takeoff CG | revised moment table | 24.1\%\ \bar{c} | pass |
| Landing CG after fuel burn | revised mission fuel state | 21.8\%\ \bar{c} | pass |
| Sensitivity screen | seat and baggage movement checks | acceptable | keep load control |
| Operational execution | aft baggage volume and restraint | must be confirmed | no release without physical check |
Failure Modes
Common failure modes include:
- using an old basic empty weight after equipment changes;
- mixing pounds and kilograms or inches and meters in the same worksheet;
- using total payload mass without station arms;
- checking takeoff CG but not zero-fuel or landing CG;
- assuming fuel burn has no CG effect;
- interpolating the envelope incorrectly;
- applying a loading instruction that cannot physically be executed;
- failing to update the flight-control, performance or structural review after a mass-state change;
- accepting a spreadsheet output without traceable source records.
The arithmetic errors are often easy to catch. The harder failures are configuration-control failures: the calculation is correct for an aircraft state that is not the aircraft being released.
Evidence Required for Acceptance
A defensible loading package should include:
| Evidence | Why it matters |
|---|---|
| approved weight-and-balance manual or envelope data | defines valid limits |
| current basic empty mass and arm | anchors every calculation |
| equipment and configuration record | prevents stale mass properties |
| passenger and cargo manifest | defines payload masses |
| station-arm source | prevents invented arms |
| fuel quantity and density basis | defines mission fuel mass |
| corrected baggage loading instruction | makes the fix executable |
| physical load verification | confirms bags and cargo are where the calculation says they are |
| final zero-fuel, takeoff and landing CG report | preserves the release basis |
| open restriction list | prevents reuse outside the reviewed state |
Final Decision
The engineering decision is:
Reject the original loading because the takeoff CG is forward of the approved envelope. Release the flight only after moving 40\ \text{kg} from the forward baggage station to the aft baggage station, verifying restraint and volume limits, preserving the corrected moment table and confirming zero-fuel, takeoff and landing CG points remain inside the approved envelope.
The main lesson is that weight and balance is not bookkeeping after the real engineering is done. It is an input to flight dynamics, control authority, stall margin, performance, structural loads and operational release. A loading package should therefore be reviewed with the same discipline as any other flight-critical engineering calculation.