Aircraft Weight and Balance Calculator with CG Envelope

The manual weight–arm method follows FAA-H-8083-1B (2016), Chapter 2 and Chapters 5–6. For every station, $M_i=W_i a_i$; sum weight and moment, then calculate $x_{CG}=\sum M_i/\sum W_i$. Signed arms share one datum. The worksheet includes basic empty weight, active payload stations and takeoff usable fuel.

Zero fuel excludes usable fuel but retains everything already included in the aircraft's basic empty record. At burned-fuel fraction $s$, $F(s)=F_{TO}-s B$, $W(s)=W_{ZF}+F(s)$ and $M(s)=M_{ZF}+F(s)a_f$. Thus $x(s)=M(s)/W(s)$. Takeoff is $s=0$; landing is $s=1$.

The envelope algorithm is derived here: validate a simple ordered polygon, then use a ray-crossing test with boundary inclusion. To test the continuous burn path, substitute $x(W)=a_f+(M_{ZF}-a_f W_{ZF})/W$ into each polygon edge equation. Multiplication by positive $W$ gives a quadratic. Split the planned weight interval at all real edge-line roots, then test those points and one midpoint in every resulting interval. Membership cannot change between roots. The 81 plotted points are for display; they do not determine the track assessment. Polygon computations are normalized by axis spans; the boundary tolerance is $10^{-9}$ of normalized coordinates.

Takeoff and landing must satisfy the polygon and their separate maximum weights. The optional maximum zero-fuel weight is checked separately. A zero-fuel point outside the flight envelope is reported informationally, since it need not be an actual flight condition.

• All defaults are illustrative, invented loading data, not an aircraft preset. Replace them with your current aircraft record and approved POH/AFM.
• One longitudinal datum, fixed payload and one constant effective usable-fuel arm. Combining tanks is valid only if their effective arm remains constant throughout the assumed burn.
• Up to six payload stations and three to ten polygon vertices. Group items only when they share an arm. Do not omit a POH envelope corner to fit the vertex limit.
• Fuel inputs are weights after start/taxi consumption, not volumes. Determine volume-to-weight conversion from applicable approved fuel data.
• Basic empty weight already contains the oil, unusable fuel and equipment specified by its weighing record; prevent double counting.
• The burn-progress control is a fuel fraction, not a time or a fuel-flow model.
• Pounds are the conventional aviation weight entries. Using mass units in the moment ratio gives the same CG because gravity cancels; worksheet moments are full moments in lb·in, not POH moment indexes.

AVIATION — Calculation support only; not flight authorization. Verify every entry and result against the current aircraft-specific weight-and-balance record, approved POH/AFM, placards and operating limitations. The pilot in command is responsible for loading and flight planning.

This implements the FAA-H-8083-1B (2016) calculation method, not a determination of regulatory compliance. Check the approved documents and rules in force for the operation. No aircraft database or preset is supplied.

The polygon must be a simple CG-arm-versus-weight envelope for the correct configuration/category, with straight edges. Do not enter a moment-index envelope, percent-MAC coordinates, disjoint envelopes or curved boundaries. Boundary inclusion is a mathematical convention and supplies no safety margin.

Variable fuel arms, tank switching/transfer, payload movement, lateral balance, helicopter lateral limits, compartment/seat/floor limits, minimum fuel, reserves, aircraft performance and aerodynamic stability are outside this model. Aircraft requiring those checks need the appropriate approved method. A zero-fuel point inside the polygon does not certify a maximum zero-fuel weight unless that limit has been entered and enabled.

Input/result fields use the viewer's metric/US conversions. Table weight and arm headings follow the displayed units (lb/in or kg/mm); the moment columns retain full, unscaled moments in lb·in in either display system. The two original drawings retain explicitly labelled inch/pound coordinates.