Solving for weight in aircraft center of gravity calculations

[Bohn507]

Wondering if you have time for a (hopefully) quick math question:

To put it simply, the equation is as follows:

(xA + zB) / (x + z) = y

Where all values except x are pre-determined, and x needs to be changed so the left equation equals y.

y represents the center of gravity for a given aircraft configuration. the denominator on the left equation represents the total weight of the aircraft, and the numerator represents what's known as the total moment (totalMoment (simplified) = (pilotWeight * pilotArm) + (passengerWeight * passengerArm) + ...) (Arm = inches aft of datum).

The math involved is for an aircraft weight and balance application I'm creating for the iPhone. If a given configuration exceeds center of gravity limits, then the application will give suggestions for removing weight for each of the positions aft of the datum (i.e. remove xx weight from front, remove xx weight from baggage, remove xx weight in fuel, etc.). There are variables to represent each of the four seats, baggage, fuel, and oil, along with their respective "arms".

The formula for center of gravity in this scenario is: CG = totalMoment/totalWeight

Thanks,
Eric

 

[Mark44]

Wondering if you have time for a (hopefully) quick math question:

To put it simply, the equation is as follows:

(xA + zB) / (x + z) = y

Where all values except x are pre-determined, and x needs to be changed so the left equation equals y.

There is no "left equation." You mean the left side of the equation. It's possible to solve for x so that the left side equals the right side. I think this is what you want to do, but I'm not sure.

(Ax + Bz) / (x + z) = y
==> Ax + Bz = xy + zy
==> Ax - xy = zy - Bz
Now factor x from the two terms on the left, and divide both sides by the other factor.

y represents the center of gravity for a given aircraft configuration. the denominator on the left equation represents the total weight of the aircraft, and the numerator represents what's known as the total moment (totalMoment (simplified) = (pilotWeight * pilotArm) + (passengerWeight * passengerArm) + ...) (Arm = inches aft of datum).

The math involved is for an aircraft weight and balance application I'm creating for the iPhone. If a given configuration exceeds center of gravity limits, then the application will give suggestions for removing weight for each of the positions aft of the datum (i.e. remove xx weight from front, remove xx weight from baggage, remove xx weight in fuel, etc.). There are variables to represent each of the four seats, baggage, fuel, and oil, along with their respective "arms".

The formula for center of gravity in this scenario is: CG = totalMoment/totalWeight

Thanks,
Eric

 

[Bohn507]

My bad...brain fart. I got it. Thanks