Aircraft weight and balance related math - help needed

In summary, the conversation discussed an equation for finding the center of gravity in an aircraft configuration, where x needs to be changed to equal y. The equation also involves pre-determined values and a total weight and moment. The conversation also mentioned an application being created for the iPhone that uses this equation to give weight removal suggestions if the aircraft exceeds center of gravity limits. The formula for center of gravity is CG = totalMoment/totalWeight.
  • #1
Bohn507
4
0
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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  • #2
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
 
  • #3
My bad...brain fart. I got it. Thanks
 

FAQ: Aircraft weight and balance related math - help needed

What is aircraft weight and balance?

Aircraft weight and balance is the process of calculating and managing the weight and distribution of an aircraft to ensure it is within safe limits for flight. This includes calculating the total weight of the aircraft, as well as the location of the center of gravity.

Why is weight and balance important for aircraft?

Weight and balance is crucial for aircraft because it directly affects its performance and stability during flight. An improperly balanced aircraft can lead to difficulties controlling the aircraft, and an aircraft that is too heavy can exceed its weight limits and compromise safety.

How is an aircraft's weight and balance calculated?

An aircraft's weight and balance is calculated using a specific mathematical formula that takes into account the weight of all components on the aircraft, as well as their location and the center of gravity. This information is typically found in the aircraft's weight and balance manual.

What is the center of gravity and why is it important?

The center of gravity is the point on an aircraft where its weight is evenly distributed. It is important because it affects the aircraft's stability and maneuverability. If the center of gravity is too far forward or backward, the aircraft may not be able to maintain stable flight.

What are the consequences of not properly managing an aircraft's weight and balance?

Not properly managing an aircraft's weight and balance can have serious consequences, including difficulty controlling the aircraft, reduced performance and maneuverability, and potential structural damage. In extreme cases, it can lead to a loss of control and a crash.

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