# Weight Shift/Change Calculation...Help!

#### Zero1Niner

##### Well-Known Member
OK. Having the toughest time with one particular type of weight shift problem, and I just cant wrap my mind around this for the life of me. Its been a while since I've practiced up on my algebra skills, so I am hoping someone can dumb this down for me somehow.

I am working in the Gleim Flight/Ground Instructor book, and they suggest a formula that they say is 'a single, universal, uncomlicated formula' that can be used to answer all weight shift or change questions, and that they provide this formula instead of the FAA formula found in the PHAK. The explanation as it appears in the 2008 version of the Gleim book (page 130) is as follows:

The formula is: NEW CG = Original Moment +- New Moment / Original Weight +- New Weight

In the Gleim, they give this example problem and break it down in detail, but I am just not following.

EXAMPLE QUESTION:
What is the maximum weight that could be added at Station 130 without exceeding the aft CG limit?
Total Weight 2,900lbs
CG Location Station 115.0
Aft CG Limit Station 116.0

I follow the formula for this portion:

116.0 = 2,900(115.0) + 130.0 (X) / 2,900 + X

I get lost on this next line

2,900 (116.0) + 116.0(X) = 2,900(115.0) + 130.0(X)

Where does the 2,900(116.0) on the left side come from all of the sudden?

Then, the next line down in the explanation it shows:

336,400 + 116X = 335,500 + 130X

336,400 – 333,500 = 130X – 116X

Then here, the 335,500 switches from the left side to the right side, and the 116X switches from the left side to the right side.

2,900 = 14X

207.1 = X

#### upup89

##### Well-Known Member
EXAMPLE QUESTION:
What is the maximum weight that could be added at Station 130 without exceeding the aft CG limit?
Total Weight 2,900lbs
CG Location Station 115.0
Aft CG Limit Station 116.0

I follow the formula for this portion:

116.0 = 2,900(115.0) + 130.0 (X) / 2,900 + X

I get lost on this next line

2,900 (116.0) + 116.0(X) = 2,900(115.0) + 130.0(X)

Where does the 2,900(116.0) on the left side come from all of the sudden?

Then, the next line down in the explanation it shows:

336,400 + 116X = 335,500 + 130X

336,400 – 333,500 = 130X – 116X

Then here, the 335,500 switches from the left side to the right side, and the 116X switches from the left side to the right side.

2,900 = 14X

207.1 = X

Are you sure that 2900(116) should be there. I mean did that come from a book? If you are adding a certain amount then there is no way possible that your airplane is going to weigh 2900 lbs at station 116

#### LineUpAndWait

##### Well-Known Member
I'm no algebra expert, but try this easier way instead:

Weight Lost or Gained/New Total Weight = Change in CG/Distance between Original CG and Point of Weight Removed or Added

X/2900+X = 1/15

Cross multiply (I think we used to call it), meaning multiply the numerator on one side of the equals sign by the denominator on the other (X*15 then 2900+X*1)

15X = 2900+X

You don't want the X on both sides of the equation so subtract from both sides, right?

14X = 2900

X = 207.143

Hope that helps, hope I'm right!

#### Zero1Niner

##### Well-Known Member
Are you sure that 2900(116) should be there. I mean did that come from a book? If you are adding a certain amount then there is no way possible that your airplane is going to weigh 2900 lbs at station 116
I know, right? Just went back and double checked the book to make sure I copied it correctly, and that is exactly how they have it in the book.

#### Zero1Niner

##### Well-Known Member
I'm no algebra expert, but try this easier way instead:

Weight Lost or Gained/New Total Weight = Change in CG/Distance between Original CG and Point of Weight Removed or Added

X/2900+X = 1/15

Cross multiply (I think we used to call it), meaning multiply the numerator on one side of the equals sign by the denominator on the other (X*15 then 2900+X*1)

15X = 2900+X

You don't want the X on both sides of the equation so subtract from both sides, right?

14X = 2900

X = 207.143

Hope that helps, hope I'm right!
That is the FAA formula given in the PHAK (and you are correct!). I can get that formula to work no problem, but I was really curious about this Gleim version.

#### LineUpAndWait

##### Well-Known Member
'a single, universal, uncomlicated formula'

Seems like an oxymoron doesn't it!

Anyway, the trick seems to be in the magical cross multiplication. If you take their formula and cross multiply you get their "2,900 (116.0) + 116.0(X) = 2,900(115.0) + 130.0(X)".
Remember you are multiplying 116 times the 2900 plus 116 times the plus X, right?

#### tgrayson

##### New Member
I follow the formula for this portion:

116.0 = 2,900(115.0) + 130.0 (X) / 2,900 + X

I get lost on this next line

2,900 (116.0) + 116.0(X) = 2,900(115.0) + 130.0(X)
First, you've mistyped the first equation. It should read:

116.0 = (2,900(115.0) + 130.0 (X) )/ (2,900 + X)

The next step multiplies both sides by (2900 + X), which gives

116.0 (2900 + X) = 2900(115.0) + 130X,

which is equivalent to

2900(116) + 116X = 2900(115) + 130X

#### Zero1Niner

##### Well-Known Member
First, you've mistyped the first equation. It should read:

116.0 = (2,900(115.0) + 130.0 (X) )/ (2,900 + X)

The next step multiplies both sides by (2900 + X), which gives

116.0 (2900 + X) = 2900(115.0) + 130X,

which is equivalent to

2900(116) + 116X = 2900(115) + 130X
I checked the book, and I did not mistype. The way I posted is exactly the way its in the book.

But you are right. Thanks.

#### Zero1Niner

##### Well-Known Member
OK. Here is a detailed explanation of the conclusion I have come to based on some help from Gleim, as well as a few other resources. You need to be pretty up on your basic algebra skills to make this formula work, but it certainly does work.

The first step is to get rid of the fraction, which is done by multiplying everything by the common denominator (or only denominator in this case) of ‘2,900 + X’. Multiplying the right side by '2,900 + X' clears the denominator on the right. Then on the left side, you multiple the number by 2900, and also multiply the number by ‘X’, the left side then becomes 116 x 2900 [or 2900(116) or 116(2900)..same thing], and 116 x X [or 116(X)], which would result in 116(2900) + 116(X).

Then, to get the variables on the same side, apply the principle of ‘opposites*’ which allows us to subtract 116.0(X) from both the left and the right side, and also add 333,500 [2,900 x 115] to both sides, and end up with
336,400 – 333,500 = 130X – 116X

From there, on the left side, you basically subtract 333,500 from 336,400 and get 2,900.

On the right side, you subtract 116X from 130X and get 14X

Then just divide 2,900 by 14, and you solve for X with 207.142

Schwuuuu...I need a nap.

*Principle of Opposites definition

When solving equations in algebra, doing the opposite operation is usually required. One way to keep your equation balanced is to move things around by doing the opposite because you have to undo operations that have been done to the variable. The opposite of an operation is one way to move things around in an equation.

#### tgrayson

##### New Member
You need to be pretty up on your basic algebra skills to make this formula work, but it certainly does work.
The Gleim formula is the best way to do the way shift, in my opinion, because it makes it clear what you're doing and is much more flexible. The other formula is too much rote memorization.

However, those with limited math backgrounds may find the Gleim formula a bit intimidating, particularly when it comes to solving for X. The latter task strikes me as having little real-world value.

#### Maurus

##### The Great Gazoo
I'm no algebra expert, but try this easier way instead:

Weight Lost or Gained/New Total Weight = Change in CG/Distance between Original CG and Point of Weight Removed or Added

X/2900+X = 1/15

Cross multiply (I think we used to call it), meaning multiply the numerator on one side of the equals sign by the denominator on the other (X*15 then 2900+X*1)

15X = 2900+X

You don't want the X on both sides of the equation so subtract from both sides, right?

14X = 2900

X = 207.143

Hope that helps, hope I'm right!
This formula doesn't always work depending on the weight problem. The Gliem formula always works as all it is is an extension from the original Moment/Weight=CG

• frankgh
R

#### Roger, Roger

##### Guest
I like the

(weight added, subtracted, or shifted)/(new total weight)=(distance CG moves)/(distance from CG of addition/subtraction, or distance of weight movement)

w/W=d/D in shorthand

formula because it can be run on an E-6B. Too many years of NIFA here. Also, this is my first post after lurking for about 4 months, lol.