Aircraft weight and balance related math - help needed

AI Thread Summary
The discussion revolves around solving a mathematical equation related to aircraft weight and balance for an iPhone application. The equation, (xA + zB) / (x + z) = y, is intended to determine the center of gravity (CG) for various aircraft configurations. The numerator represents the total moment, calculated from the weights and arms of the pilot, passengers, and cargo, while the denominator indicates the total weight. Participants clarify the equation's structure and provide guidance on isolating x to ensure the left side equals y. The application aims to suggest weight removal options if the CG exceeds limits, enhancing safety and balance in aircraft operations.
Bohn507
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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
 
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Bohn507 said:
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.


Bohn507 said:
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
 
My bad...brain fart. I got it. Thanks
 
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