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Lets say a plane had 2 engines located 9m ahead of its rear wheels. Give each engine a mass of 7.5 tonnes. A force of 147150N will act 9m ahead of the rear wheels. lets say the aircraft was 133 tonnes in total.

My question is if you were trying to determine the position of the centre of mass of the aircraft would 133 tonnes act through the centre of mass or would 133 tonnes subtract the weight of the 2 engines act through the centre of mass? So what would be the equlibrium equations when resolving vertically and taking moments?

I have made up some numbers for the distance between the front and rear wheels and the overall length of the aircraft in my diagram. I have indicated an guess for the mass centre using a cross.

enter image description here

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    $\begingroup$ You have three things present: The two engines and the airframe without the engines. Each one has its own mass and its own COG. Put together, they all have a new mass and new COG. If you have the COG of the whole, you can back-calculate the COG of the airframe when the engines are removed. Of course, if you have the COG and mass of each engine and the airframe, you can calculate the mass and COG of the whole. $\endgroup$
    – DKNguyen
    Feb 21, 2022 at 23:31
  • $\begingroup$ please tag as homework $\endgroup$
    – Pete W
    Feb 22, 2022 at 1:19

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We could not figure out the COG of the plane with or without knowing the COG of the engines. We would either need the exact geometry and location and weight of all its parts, the wings and their COG the landing gear.. etc., or suspend the plane from an adjustable hook and move the attachment of the hook to the plane till it hangs in balance. (they actually do this for small airplanes).

But let's say we know the COG of the plane is at $X_1$ and let's call the distance to COG of the plane after removing the engines $X_2$.

Then we can try to see where the COG of the plane with engines removed will be.

$$W_{plane- no engines}=133-15=118tons$$

Taking moment about the rear wheels,

$$118*X_2 +15*9=133*X_1$$

$$X_2=\frac{133X_1-15*9}{118}$$

If the plane's mass was distributed evenly along its length like a rod this would cause the COG to move forward.

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