W & B? Moving CG

MDeitch1976

MDeitch1976

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MattCanFly
Hello Everyone,

Now that I have moved from the 2 an Piper Sport to the Cessna 172, W&B is going to matter more with taking people and baggage along.

My question is if you are out of CG for example a forward CG, and you want to move the CG to a known CG. Also, you know what station you are going to use. Is there an equation for determining the weight of an object that would have to be placed at a station for the new CG? I am not talking about moving any of the existing weight.
 
bartmc said:
Just cheat and use WnB pro in the iTunes Store.
Click to expand...

:yeahthat:

Jesse's app makes it easy to play with the weights at the various arms to find out the right solution for the situation you describe.

But on a 172 with the forward seats filled, full fuel, and a bit of baggage in the baggage area, it's hard to envision you being out of the envelope forward.

Care to post some numbers so we can work the problem together?
 
This question actually arose when I had written a weight down of 2202 instead of 2002 as my gross. I had a CG of 79.5 On the Cessna 172M Envelope I was off. I was actually in the utility category when I realized my mistake.

My question is, if I decided I wanted to shift the CG from 79, to 85. And I was going to place some extra weight at station 95. Could the weight to be placed there be determined to move the CG to 85. In the FAA weight and balance, I did see an equation for adjusting an empty weight CG with a ballast. I think this was more for an A&P recalculating and adjusting. However, I wondered if there is similar equation or not possible?
 
It's just algebra

Moment current = Weight current *CG current

Moment desired = (Weight current+Weight added)*CG desired
= Weight current *CG current + Weight added * Arm added
Solve for Weight Added

Weight current*CG desired + Weight added *CG desired = Weight current*CG current + Weight added * Arm added

Weight added *CG desired - Weight added * Arm added = Weight current*CG current - Weight current*CG desired

Weight added *(CG desired - Arm added) = Weight current* (CG current - CG desired)

Weight added = Weight current* (CG current - CG desired) / (CG desired - Arm added)
 
Capt. Geoffrey Thorpe said:
It's just algebra

Moment current = Weight current *CG current

Moment desired = (Weight current+Weight added)*CG desired
= Weight current *CG current + Weight added * Arm added
Solve for Weight Added

Weight current*CG desired + Weight added *CG desired = Weight current*CG current + Weight added * Arm added

Weight added *CG desired - Weight added * Arm added = Weight current*CG current - Weight current*CG desired

Weight added *(CG desired - Arm added) = Weight current* (CG current - CG desired)

Weight added = Weight current* (CG current - CG desired) / (CG desired - Arm added)
Click to expand...


Thank you
 
In addition to that formula, you can also use the King method. It's kind of cool because you neither have to memorize the formula nor derive it again algebraically.

The technique is to pretend your datum is where you want the CG to be. This makes the desired CG zero and the desired moment zero (in reference to the pretend datum). You then restate ALL the arms in terms of the new datum, and recalculate their moments. You then know the additional weight must create exactly enough moment to balance that out and equal zero when they are added. Once you know the moment, you can solve for the unknown with the standard Wt * Arm = Mom formula.

Example:

Code: 
The following aircraft has a forward CG limit of 44 inches:

            Weight      Arm    Moment
 Aircraft      1500     40.0   60,000
 Pilot          200     30.0    6,000
 ------------------------------------
 Loaded A/C    1700     38.82  66,000

Say there is a bag compartment at 120" where we can add a sandbag.

The King method requires us to subtract 44 from each arm and create a new table:

             Weight      Arm   Moment
 Aircraft      1500     -4.0   -6,000
 Pilot          200    -14.0   -2,800
 Sandbag          ?     76.0        ?
 ------------------------------------
 Loaded A/C       ?        0        0

We can fill in the moment for the sandbag for 8,800, and divide it by the arm, 76, to find its weight, and complete the table. 

             Weight      Arm   Moment
 Aircraft      1500     -4.0   -6,000
 Pilot          200    -14.0   -2,800
 Sandbag        115.8   76.0    8,800
 ------------------------------------
 Loaded A/C    1815.8      0        0
 
Last edited:
dmspilot said:
In addition to that formula, you can also use the King method. It's kind of cool because you neither have to memorize the formula nor derive it again algebraically.

The technique is to pretend your datum is where you want the CG to be. This makes the desired CG zero and the desired moment zero (in reference to the pretend datum). You then restate ALL the arms in terms of the new datum, and recalculate their moments. You then know the additional weight must create exactly enough moment to balance that out and equal zero when they are added. Once you know the moment, you can solve for the unknown with the standard Wt * Arm = Mom formula.

Example:

Code: 
The following aircraft has a forward CG limit of 44 inches:

            Weight      Arm    Moment
 Aircraft      1500     40.0   60,000
 Pilot          200     30.0    6,000
 ------------------------------------
 Loaded A/C    1700     38.82  66,000

Say there is a bag compartment at 120" where we can add a sandbag.

The King method requires us to subtract 44 from each arm and create a new table:

             Weight      Arm   Moment
 Aircraft      1500     -4.0   -6,000
 Pilot          200    -14.0   -2,800
 Sandbag          ?     76.0        ?
 ------------------------------------
 Loaded A/C       ?        0        0

We can fill in the moment for the sandbag for 8,800, and divide it by the arm, 76, to find its weight, and complete the table. 

             Weight      Arm   Moment
 Aircraft      1500     -4.0   -6,000
 Pilot          200    -14.0   -2,800
 Sandbag        115.8   76.0    8,800
 ------------------------------------
 Loaded A/C    1815.8      0        0
Click to expand...


I like that method
 
Isn't that a question on the Commercial Pilot written exam?
 
Remember, Grasshopper:
A nose heavy plane flies poorly.
A tail heavy plane flies once.
 
I think the question about rearranging the load has been answered.
But the title to the thread made me think about airplanes where the cg moves as you fly along burning fuel.
I've seen situations where one took off with a slightly forward CG and landed with a way aft CG. (should have took off with a way forward CG)
Most airplanes with fuel in the wings don't suffer this too much, but those with fuel in the nose do. The Chief, with aux tank, can take off with slightly forward CG, then shift to way aft CG, and land with forward CG. All due to fuel burned and transferred.
 
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