Center of gravity PLEASE HELP!

[pilatus96]

The brother is doing a school project and he needs to know the formula for finding the center of gravity on an airplane and what all of the variables stand for. We have looked on the Internet, but have not been able to figure it out. Any help is greatly appreciated. Thanks in advance.

 

[tonycondon]

uh, weight times arm equals moment. total moment divided by total weight equals CG?

 

[Metro752]

do a cessna 172

 

[mpflies2]

Ok. The center of gravity can be thought of as if you were to hang the airplane by a string attached to the center of gravity, it would be balanced at that point.

To start you need to know that the Arm is a given distance behind the standard datum plane. The standard datum plane for an aircraft will never change as far as I know. The manufacturer decides where the standard datum plane is. Some put it right on the tip of the prop spinner, some at a given distance in front of the spinner, and some maybe behind it. Regardless, you just need to know that the arm is a distance measured in inches behind the standard datum plane.

So lets work a weight and balance for a piper warrior.

The manufacturer provides the following arms.

Basic Empty Weight = 85.9
Pilot and front passenger = 80.5
Fuel = 95
Rear Passengers = 118.1
Baggage Compartment = 142.8

Next one has to multiply the weight of each item times the arm to find the moment.

So..... sidenote......lets say we have 25 gallons of fuel and fuel weighs 6 pounds for gallon (AVGAS)

25 gallons X 6 lbs per gallone =

Weight Arm Moment
Basic Empty Weight = 1500 lbs X 85.9 = 128850
Pilot and Front Pass = 360 lbs X 80.5 = 28980
Fuel = 150 lbs X 95 = 14250
Rear Passengers = 160 lbs X 118.1 = 18896
Baggage = 20 lbs X 142.8 = 2856


Next step is to add up all the weights to get the Gross Weight, and add up the all the moments to get the total Moment

Gross Weight = 2190 Total Mom= 193832

The max gross weight for the airplane is 2325, so we know we are within tolerances at 2190 lbs.

Now the center of gravity is figured out by dividing the total moment by the gross weight of the aircraft.

An easy way to remember this is by saying your mom is overweight! haha

CG = MOM CG= 193832
-------- so ----------
Weight 2190



so... CG = 88.51


This means your CG is 88.51 inches behind the standard datum plane

The manufactur has also provided in the pilots operating handbook a CG envelope.

To see if your CG is in the envelope you need to know the CG and the weight of the gross weight.


The forward limit is 83" aft the datum
The aft limit is 93" aft the datum.

Thus 88.51 is within the allowable CG envelope and the weight is acceptable as well.

However, once you reach approx. 2000 lbs (looking in the POH) I can tell that the forward CG limit starts to move aft as the weight increases.

But I'm looking at the book and can tell you that with this weight and that CG, the airplane is within limits.


A few other terms worth knowing....

Standard empty weight = weight of a standard airplane including unusable fuel, full operating fluids and full oil
Basic empty weight = standard empty weight plus optional equipment
Payload= Weight of occupants, cargo, and baggage


Now you must consider when you are actually flying, the above weight and balance for was with the given amount of fuel.

When you burn fuel while flying the CG and weight will change. This can be easily figured out as well. For example, if an airplane burns 10 gallons per hour and you plan on flying for 2 hours, then you can anticipate that you will burn 20 gallons, or 120 pounds of fuel....you would then subtract this from your gross weight, then multiply the 120 by the arm for fuel....which is 95...which will give you a moment of 11400.....

The reason you subtract is because you are burning the fuel thus losing the weight. So the new gross would be 2070, and the new moment after subtracting 11400 from the earlier figured total moment would be 182432

So we divide 182432/2070 and we get 88.13, so our CG has moved up


Now as a student you can take this information and correlate it to other situations. Perhaps you are flying a shorts skyvan with a cargo area full of skydivers. You can figure out all of there weights, subtract the weight and moment and then figure your new CG after they jumped out.

Hope this helps.

Good luck with the assignment!


Marc

 

[mpflies2]

i am a bit confused...you have 3000 plus hours, and didn't know that? Not busting your balls, just wondering...maybe I read the question wrong?

Oh well either way

 

[siucavflight]

The brother is doing a school project and he needs to know the formula for finding the center of gravity on an airplane and what all of the variables stand for. We have looked on the Internet, but have not been able to figure it out. Any help is greatly appreciated. Thanks in advance.

\
with all of your experience I think that you should know the answer to your own question.

 

[Amish RakeFight]

He's asked this question elsewhere and got chewed just the same.

http://forums.flightinfo.com/showthread.php?t=79105

Anyway... hope you understand how to calculate a CG now.

http://forums.flightinfo.com/showthread.php?t=79105




.

 

[mpflies2]

He's asked this question elsewhere and got chewed just the same.

http://forums.flightinfo.com/showthread.php?t=79105

Anyway... hope you understand how to calculate a CG now.






.

haha, and i spent so much time writing that explanation...oh well

 

[siucavflight]

haha, and i spent so much time writing that explanation...oh well

But it was well written, so nice job!

 

[mpflies2]

haha thanks man