Csdrhrt

I'm writing a weight and balance calculator for a charter operation.

Every aircraft I've ever flight planned for has all the tanks on the same moment arm, so I don't know how you calculate the W&B for an aircraft that has swept wings. Do they have one tank on each wing whose moment changes as it drains, or do they have multiple tanks? And if they have multiple tanks, so you have to calculate for 'drain the forward tanks first' and 'drain the rearward tanks first' and plot both of those on envelope?

In supplement to @Dave's answer and as he said depending on the airplane, the complexity of calculating the c.g. can vary greatly. The manufacturer of every large aircraft I've programmed weight & balance for has had tables for each tank. In Boeing's case for the 747-400, each table line is a tank volume in gallons and the tank c.g. at that volume in inches. For example, and using JSON notation since the OP is JavaScript fluent:

{"vol":3200,"ba":1453.7},
{"vol":3250,"ba":1454.8},
{"vol":3300,"ba":1456.0},
{"vol":3350,"ba":1457.2},
{"vol":3400,"ba":1458.4},
{"vol":3450,"ba":1459.7},

"vol" is the fuel volume in the tank in gallons

"ba" is the balance arm at that volume in inches

Since fuel is loaded by weight, one has to use the fuel density to convert to volume.

Typically, at least for large aircraft, you have to satisfy the c.g. envelope for:

1. zero fuel weight


2. ramp weight after fueling


3. takeoff weight


4. landing weight

Also there has to be provision for carrying ballast fuel if that is necessary.

You will need to consult the POH for the airframe in question and see what it says in regards to fuel burn from tanks at different moment arms. Ultimately you will need to program in the variable factor of fuel burn. It sounds like the program will have more inputs than just the weight of the passengers, fuel, and cargo. The end user will also need to input their planed fuel burn schedule and the order of the tanks they intended to burn off of. Once you have all this info you can compute inflight CG at different times. What you are going to end up with is a piecewise system that describes your WB at various points in the flight.

One of the contributors here @Terry built a WB app for some 747 variants that he used when he flew. You can find it here, it might be worth reaching out to him if he does not add an answer here.

Most twin engine jets have one very long tank in each wing for each engine and often a center tank that feeds both. The fuel shifts forward as fuel is consumed from the wings (dihedral plus sweep), and aft as fuel is consumed from the center tank, if installed (always before the wings, so if there is a center tank the C of G moves aft until the tank is dry and forward as the wings are consumed). The manufacturer's weights engineering group will determine the overall fuel load's center of gravity moment for different fuel volumes and plot the results on a chart as a curve.

When you do the load sheets on a swept wing airplane the fuel moment/mass curve will be integrated into the chart data so that an accurate fuel moment/mass value is applied to the C of G calculation for takeoff. Also, some form of the fuel curve will be overlaid onto the C of G limits chart to confirm that the C of G shift will stay in limits as fuel is burned during the flight. This is especially important for jets with center fuel tanks, because you may be able to load it with a marginally aft G of G, such that the aircraft is technically in C of G limits at takeoff with a full fuel load, but as the center tank is burned off the C of G could move past the aft limit temporarily until some of the wing fuel is burned off. The result is the C of G with center tank at zero will determine the aft limit for freight/pax.