CG aft of datum. How do I figure this out?

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JasonM

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I'm trying to figure out all this weight and balance stuff, when this question came up on sportys practice test.

I thought I understood how to figure these things out, but this one has me confused.

Can someone please explain how to solve this. I know the answer and still cant figure out how to make sense of it. No charts or diagrams to help on the practice test for this question. I am lost on this one..

The Question: "Spelling is exactly as on the practice test. Word for word"

The CG if located how far aft of the datum? GIVEN: Aircraft empty weight 1,495.0 lbs., CG 101.4 in., Moment 151, 593.0 in./lbs.; Pilot and passengers 380.0 lbs., 64.0 in.; Fuel (30 Gal usable, no reserve), 96.0 in.

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I hid the correct answer given if you don't want to have it spoil the fun. Just remove the 5's and 6's. Answer: CG 59645.5061
 
JasonM said:
I'm trying to figure out all this weight and balance stuff, when this question came up on sportys practice test.

I thought I understood how to figure these things out, but this one has me confused.

Can someone please explain how to solve this. I know the answer and still cant figure out how to make sense of it. No charts or diagrams to help on the practice test for this question. I am lost on this one..

The Question: "Spelling is exactly as on the practice test. Word for word"

The CG if located how far aft of the datum? GIVEN: Aircraft empty weight 1,495.0 lbs., CG 101.4 in., Moment 151, 593.0 in./lbs.; Pilot and passengers 380.0 lbs., 64.0 in.; Fuel (30 Gal usable, no reserve), 96.0 in.

........
........
........

I hid the correct answer given if you don't want to have it spoil the fun. Just remove the 5's and 6's. Answer: CG 59645.5061
Click to expand...

(151593+(380*64)+(30*6*96))/((1495+380+(30*6))

Weight * Arm = Moment

You know the Moment for the empty aircraft

Calculate the moments for the pilot and the fuel and add to the empty aircraft and divide by the total weight to get the CG.
 
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Convert everything to moment. Add all the moments. Divide by gross weight.

Gasoline weighs 6 lb/gal.

If there is more than one passenger (it's plural), this is a weird aircraft that has them all side by side.
 
Let's see.... (plugs in following to my W&B App)

Aircraft (Empty) 1495# @ 101.4 inches
Pilot/Pax: 380# @ 64 inches
Fuel: 180# @ 96 inches

151,593 + 24,320 + 17,280 = 193,193 in/lbs

Total weight = 2055 lbs

193,193 in/lbs / 2055 lbs = 94.01 Inches

Answer: CG is 94.01 inches

Tossing in the moment number, 151,593 in/lbs is acting as a distraction at first. But it's helpful since it already has the moment calculated for the aircraft.
 
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MAKG1 said:
If there is more than one passenger (it's plural), this is a weird aircraft that has them all side by side.
Click to expand...

ROFL! I just saw that!

He must be the SMART pilot! Doesn't have the fly the plane, doesn't have to remove the chocks or open the hangar door.

(a variant of who's the smarter cowboy story)
 
gosh.. Thank you guys. That seems so dang simple now. I was looking at the first part as it giving me:

>> empty weight 1,495.0 lbs.
>> CG 101.4 in.
>> Moment 151
>> 593.0 in./lbs

I was having a hard time understanding what I was looking at. 151593.0 in/lbs. didn't resolve in my mind. I was making this out to be a lot harder than it was. I'm glad I asked, you guys really helped me out. :)
 
Nope, they're just giving you the moment for each section in the problem which is just the weight multiplied by the CG, that's how the 151,593 number came about. If they give you everything you need like they did in that problem, it's just addition, division and multiplication. If you wanted to find the CG and all they gave you was the empty weight and the moment you would just take the 151,593 and divide it by the empty weight, 1,495 to get a CG of 101.4 :)
 
ok, I got another one wrong..:dunno: :mad2:

Here it is. Can someone show me how I am supposed to do this one please? I don't really know exactly what I did for this one since I didn't have the arm for the empty plane weight, but I came up with the 81.7 figure. How do I get the Arm for the planes empty weight? or does that matter. What am I missing?

(Refer to figures 33 and 34.) Calculate the weight and balance and determine if the CG and the weight of the airplane are within limits.
Front seat occupants 350 lb
Rear seat occupants 325 lb
Baggage 27 lb
Fuel 35 gal

Your answer:
B: CG 81.7, out of limits forward.

The correct answer was:
A: CG 83.4, within limits.
 
Never-mind.. I just entered in all that data not using the arm and only the weight and moment and got the correct number. I guess if moment data is present I should just use moment and not worry about figuring out the ARM stuff.
 
If you have an electronic E6-B calculator, it can help with these problems.
 
AggieMike88 said:
If you have an electronic E6-B calculator, it can help with these problems.
Click to expand...

That wasn't my experience. They help a lot for wind calculations, but W&B is just arithmetic, and any old calculator (including the one that is included in the test) works fine.

As I said earlier, convert everything to moments. If they come as moments, so much the better. Add all the moments and divide by gross weight to get CG.
 
Kevin H. said:
Or just download an app for that :) And yeah, I got 83.4 as well. Just use the ARM.
Click to expand...

Yeah, there is a certain Angell around here somewhere that wrote a real Pro of a W&B app for iPhone and Android.
 
I do have sportys new E6B, and that is what I used. I was again obviously confused.. Since this makes the most sense to me, i'm going to just use the ARM is arm data is present and use MOMENT if moment data is present. the whole converting everything one way or the other; I cant grasp good enough..
 
JasonM said:
I do have sportys new E6B, and that is what I used. I was again obviously confused.. Since this makes the most sense to me, i'm going to just use the ARM is arm data is present and use MOMENT if moment data is present. the whole converting everything one way or the other; I cant grasp good enough..
Click to expand...

I know this may sound like I'm trying to complicate it when all you want is a simple understanding, but it may help you if you just remember the actual differences between all these terms. It helps to visualize the loading problem as a seesaw, or any simple lever. The datum is the pivot point, or fulcrum. The aircraft empty CG is not the fulcrum- it's just another load on an arm, exerting force at the datum.
This is a good picture of this idea...

http://www.free-online-private-pilot-ground-school.com/images/balance.gif

"Datum" is just a reference point to take measurements from. Why the datum is where it is doesn't really matter- just think of it as the point on which all these loads have to balance. Remember: it is not the empty CG, although it's usually close to it.
"Arm" is the distance from the datum to the load. "Station" is pretty much the same as "arm"; it can be expressed as the distance from the datum to the load, but it might be called "A", "B", etc on a diagram. "Moment" is the leverage exerted at the fulcrum by the weight of the load on that arm (expressed in foot-pounds). Knowing this, it's really not a big deal to convert weight and arm to moment. Weight times arm equals moment, that's all you need to know about that. Any calculator will speed that up, but it's still just grade-school arithmetic.
And as others have pointed out, all you need to do is add up all the moments (however you get them), add up all the weights, and divide the total moment by the total weight to find the CG. The number you get is the arm of the CG itself- its distance from the datum. In other words, you should never be adding up arms... they are only considered individually, when you're trying to find the moment for a particular load.
Sometimes there are issues with decimal places, depending on how they word the sample problem, but it's usually easy enough to just look at the resulting number and deduce how many inches it really is. Negative or positive values, though, are important, because they refer to an arm that is forward or aft of the datum.
 
What is the best method to solve this?

WBDatum.jpg



BTW.. Beaky, thanks for that description. I'm a little tired to make sense of it today. I'll read it again in the morning. :)
 
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JasonM said:
Maybe you could explain that process in relation to that image a bit for me. Not all of us paid attention the full time back in school math class.:dunno:
Click to expand...

Distance(arm or CG) * weight = moment

Moment / Weight = distance (arm, or CG)

The total moment is the sum of the moments.

The total arm (or CG) is the sum of the moments divided by the total weight.

So, for the picture presented, the moment on each side of the fulcrum has to be equal to get it to balance.

(55lb * 43") + (x lb * y") = 92lb * 327 inches.

Then
x*y = (92*327)-(55*43) = 27719

Pick a value for x or y and solve for the other:

x = 27719/y or y = 27719/x

For any particular value of x or any particular value for y there is a corresponding y or x that will work.

Or, if you prefer to put it in a more aircraft like order:

CG" = [(55lb * 43") + (x lb * y") + (92lb * -327")] / (55 + x + 92)

CG = sum of the moments / total weight

In the above equations you can use either the weight times the arm (as written) or just plug in the moment (which is equal to the weight times the arm) if you have it .
 
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