# How To Calculate Arm Of Baggage Compartment, Fuel, and Seats

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#### HomeBuilt101

##### Well-Known Member
Can someone please give me the math or a spreadsheet to use for calculating the arms of fuel, people, and bags???

So I have the three airplane wheels on digital scales and the airplane is drained down to unusable fuel and oil and I can read the digits on each scale...great...

I then add 10 gallons of fuel and read the three scale digits again...add 10 more gallons...repeat.

Same with people...measure a guys weight and have him sit in the front seat and read three scale digits...then move him into the back seat...repeat.

Same-o with the baggage compartment...place a 50 pound object in the baggage compartment and read the three scales...easy-squeezy...

That part was easy...now the math...not so much.

Geez...I remember doing this crap way back in college however the Google has not been helpful...it keeps giving me the easy stuff like loading 50 pound weight in a known arm baggage area...dang that stupid teeter-totter and the W X A = M...and change in weight and change in moment = new CG minus old CG...or something like that...

I sure do wish I could copy off of someones homework...pretty girls were always useful for that...Any help please?!?!?

#### TFF

##### Well-Known Member
Weight x Arm= Moment of course but to find the CG, Arm has to be measured from the Datum so numbers are relative to that point. To get a new CG like adding fuel to tanks, you do the WxA=M of fuel then you add the weight of fuel to the empty weight and you add the Fuel moment to the empty moment. Divide the total moment by the total weight will equal the new CG. You can do that with anything anywhere as long as you know the weight and arm. You can also look up AC43-13. There are examples there too.

#### cblink.007

##### Well-Known Member
Can someone please give me the math or a spreadsheet to use for calculating the arms of fuel, people, and bags???

So I have the three airplane wheels on digital scales and the airplane is drained down to unusable fuel and oil and I can read the digits on each scale...great...

I then add 10 gallons of fuel and read the three scale digits again...add 10 more gallons...repeat.

Same with people...measure a guys weight and have him sit in the front seat and read three scale digits...then move him into the back seat...repeat.

Same-o with the baggage compartment...place a 50 pound object in the baggage compartment and read the three scales...easy-squeezy...

That part was easy...now the math...not so much.

Geez...I remember doing this crap way back in college however the Google has not been helpful...it keeps giving me the easy stuff like loading 50 pound weight in a known arm baggage area...dang that stupid teeter-totter and the W X A = M...and change in weight and change in moment = new CG minus old CG...or something like that...

I sure do wish I could copy off of someones homework...pretty girls were always useful for that...Any help please?!?!?
Just like @TFF s response. Weight x Arm = Moment. CG = Total Moment x Total Weight.

Good references to get on FAAs website:

1. Pilots Handbook of Aeronautical Knowledge
2. AC 43.13-1B
3. FAA-H-8083-1 (Weight & Balance Handbook)

Total cost of above pubs: \$0.00

This math is easy peazy...once you do it, you do not forget. I am about 100% sure you can search "aircraft weight & balance" into the searchbar on YouTube and see the whole thing in action.

Shout out if you have questions!

#### Turd Ferguson

##### Well-Known Member
Is it a homebuilt airplane?

#### HomeBuilt101

##### Well-Known Member
Thanks...yes it is a homebuilt airplane.

I was able to make a spreadsheet that I could plug and chug...it was the bit about differences in moment divided by difference in weight that I forgot from 35 years ago...sometimes the brain dont work as good as it once did...

#### Toobuilder

##### Well-Known Member
HBA Supporter
Log Member
This is a Velocity, right? The arms for the datum, seats, fuel, and baggage should be right in your logbooks. Or at least on the web somewhere. No need to figure this out from scratch.

Hell, if nothing else, give Marc Z a call.

#### wsimpso1

##### Super Moderator
Staff member
Log Member
Set a datum for the airplane. Every distance aft of the datum is positive, every distance forward is negative, and we will call those x's or arms. W is weight of item or the whole thing. Moment is product of weight and arm, so...

Sum(Wi*xi) = Total Moment
Sum(Wi)= Total Weight
CG = xbar = Sum(Wi*xi)/Sum(Wi)

If you want to know the CG with some item or items removed, Take the total moment and subtract the moment (W*x) of the items removed, do the same with the weight and then compute the new CG by dividing the new Moment by the new weight.

If you want to know the CG with some item or items added, Take the total moment and add the moment (W*x) of the added items, do the same with the weight and then compute the new CG by dividing the new Moment by the new weight.

If you have the weight and know the CG of any part (or of the whole thing), just multiply the weight by the arm.

Play with it in Excel with some things like weights of whole even numbers of pounds and arms in whole even numbers of inches, and you will get it, then do the certified airplane you have info for...

Billski

#### cblink.007

##### Well-Known Member
Sum(Wi*xi) = Total Moment
Sum(Wi)= Total Weight
CG = xbar = Sum(Wi*xi)/Sum(Wi)
I might only be an XP & FTE, but you had me a little confused for a split second...then came to the conclusion these are excel formulae for the OP!

Carry on!!

#### Toobuilder

##### Well-Known Member
HBA Supporter
Log Member
He's looking for the arm of various compartments for a well known kit airplane... There is zero math required.

#### HomeBuilt101

##### Well-Known Member
>Sum(Wi*xi) = Total Moment
Sum(Wi)= Total Weight
CG = xbar = Sum(Wi*xi)/Sum(Wi)

Oh yeah...Blah...Blah...Blah says the Peanuts cartoon teacher. That is all I heard the whole time during my California public school education...

So sometimes the "as built" airplane might not be exactly like the airplane that is advertised by the manufacturer so someone who is as anal as I am wants to make double sure. Mine was off by .75 inches...and as we all know every...ah...well never mind...

Anyway...I am here to tell ya...This doing things right the first time...and going the extra mile bit... really sucks...

So since I FORGOT EVERYTHING I LEARNED thirty five years ago in college when I studied all of this crap (we did not have these new fangled things called "computers" back then because we were real men and our teachers smoked cigarettes in class and we had real books with real paper in them...they diddnt need a charger err nuth'n...we had lead pencils and survived...and we had to walk uphill to school both ways...in the snow in Daytona Beach FL ...you young whipper snappers and your fancy new...Zzzz...Zzzz...drool...

Anyway...since nobody on the forum gave me their homework to copy I came up with this Excel spread sheet...

To use it just measure how far back the nose wheel axle and main wheel axles are from the tip of the nose (datum) and go get you some digital scales and find some guy and have him stand on the scale...then put the airplane on three digital scales (I rented three from a guy in the EAA for 50 bucks) and record the nose wheel weight and both main gear weights...then put that same guy in the pilot seat then record the three new digital scale readings...then...Take my handy dandy spreadsheet (attached but batteries not included) and plug in the number you just came up with into the fields highlighted in green and it will spit out the data you need in blue...

So there...you scronny little E6B...take that...you little spinning wheel piece of...Zzzz...Zzzz...drool...

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#### rollerball

##### Member
I made a very detailed spreadsheet for an AX3 ultralight that works out where the CG is for various fuel and passenger loads and tells you if it's outside the max limits. I'll have another look at it and see if it's suitable for any 3-axis aircraft. I think it should be. Will take a day or so as I've got quite a bit on right now but it might help if no-one comes up with anything else.

Here's the link if you want to play with it.

#### PagoBay

##### Well-Known Member
@HomeBuilt101 -- There are lots of spreadsheets for CG calculation on the Internet. Here is one:

No mention in your case of the fore and aft CG limits. Trust you have those as well?

See the Blue Box on the above spreadsheet. MIN and MAX Limits are clearly shown on Rollerball's trike spreadsheet.

#### Mad MAC

##### Well-Known Member
I have seen plenty of professional pilots and engineers stuff up weight and balance checks. Don't forget record the aircraft's configuration (for a homebuilt a pic of the cockpit such that one can see the insturment panel and any removable items: axe, fire extinguisher, ELT etc would be fine). That way if you ever have to figure out just what was in or not in the last weight and balance you can.

I once encountered a B737 there they had left the empty food carts on board at weighing & as part of the operational weight calculations added in the weight of full food carts in, it meant they had over estimated their weight by a couple of hundred kilos for the last couple of years (it was weight crtical for the routes it flew).

#### Pilot-34

##### Well-Known Member
Easy enough.
“ Don’t you hate it when someone says that“
Do you know where the datum point is on your plane ?
You simply measure from there to the center of the load or area you are interested in.

It’s generally in the front area of the airplane sometimes it’s even located in a point in space ahead of the airplane.
But if you have the arm of moment of any part of the airplane you can simply measure forward from that position to find your datum and then take all of your other measurements from that spot.

#### Toobuilder

##### Well-Known Member
HBA Supporter
Log Member
I guess I'm missing something here... The "arm" of any component is the location of the object's CG from the datum. In the case of a seated human, the belly button is the generally accepted approximation of CG. So all you need is a tape measure from the datum location to the belly button . No spreadsheet needed.

I get that you can also back out the location with a moment change (as you are attempting to do) but doing so introduces at least two opportunities for compounding error. If you can physically locate the arm location on the structure, that should always be the "go to" method.

#### cblink.007

##### Well-Known Member
Anyway...since nobody on the forum gave me their homework to copy
@wsimpso1 and I did. Don't go accusing us of not "giving you our homework to copy". Doesn't work that way in this craft...it is absolutely incumbent of you to verify everything you see. After all, your life depends on it!

Just take a look at what you see in the texts provided. Your spreadsheet is a good start. Just remember to have your bird all empty (with the exception of engine oil) for a basic weight, and be able to differentiate between that basic weight, your zero fuel weight, takeoff gross weight and such. Give me a few hours as I am on my mobile device, and once I get on my desktop I'll will send you a copy of the W/B spreadsheet for my project that you can customize to yours...complete with graphs. Or, you can google search and find one for your particular aircraft if you want an ideal baseline.

#### Toobuilder

##### Well-Known Member
HBA Supporter
Log Member
W&B spreadsheets are easy to develop and abundant to find. BUT Even the best spreadsheet is of NO HELP if you do not know the raw engineering data such as the Fuselage Station of the components you are attempting to "locate". And if the arm is suspected to be off by .75 inch as the OP suggests, then the location of the reaction points (wheels) is also highly suspect.

Frankly people, a spreadsheet is just about the last thing the OP needs right now. What he needs is a plumb bob, bubble level, and a tape measure.

Remember: Garbage in, garbage out. Baseline the aircraft, THEN start plugging in numbers to the spreadsheet.

#### cblink.007

##### Well-Known Member
W&B spreadsheets are easy to develop and abundant to find. BUT Even the best spreadsheet is of NO HELP if you do not know the raw engineering data such as the Fuselage Station of the components you are attempting to "locate". And if the arm is suspected to be off by .75 inch as the OP suggests, then the location of the reaction points (wheels) is also highly suspect.

Frankly people, a spreadsheet is just about the last thing the OP needs right now. What he needs is a plumb bob, bubble level, and a tape measure.

Remember: Garbage in, garbage out. Baseline the aircraft, THEN start plugging in numbers to the spreadsheet.
Amen!!

#### HomeBuilt101

##### Well-Known Member
>Frankly people, a spreadsheet is just about the last thing the OP needs right now. What he needs is a plumb bob, bubble level, and a tape measure.

Amen...preach it on down my brother...bring on the drill with the hole saw...

Two of the locations I need to find would require a hole to be drilled through the floor of the fuselage to be able to drop down the plumb bob (or I would need to plumb bob up from the floor to the airplane in then inboard to the interior and then measure back up a non level floor..way too much work when you already have the airplane up on digital scales...and you have a computer...

Oh...not to mention the shape of the fuel tanks are triangular and they have a bunch of curvy sidewalls and a landing gear well shaped like a lolly-pop right in the middle so there is no way to "calculate" anything about the fuel tank.

So for my application the most accurate way to find the arm of certain parts would be to use highly accurate digital scales and people and objects of known weights and put them in the appropriate spots, record the weight delta and moment delta and do the math. The part that I forgot from decades ago was the bit about the mathy stuff and I was soo busy I had hoped that I could borry someones spreadsheet and plug and chug.

When I sat down at a blank spreadsheet and thought about it it all started coming back to me...like a whiz Wheel bad dream...So I tapped away at a couple of keys and batta-bing---batta-boom...

On my airplane the CG first moves dramatically forward as the fuel is added end then it gets to the most forward point when the tanks are 60 percent full and then the CG starts to march aft again as the tanks keep getting filled up. The only way to find out Fo-Sho was the digital scales and the digital math...

>I once encountered a B737 there they had left the empty food carts on board at weighing & as part of the operational weight calculations

I had the opposite happen once...almost took out the runway lights at the far end of RWY 26R at LFPG. It seems that the load master forgot to add in the weight of the cargo pallets and tie downs...oh and the liquid in the containers...yup...we discovered that little ditty when "V1 ROTATE" came and went (a long time ago) and the nose was right up at the max pitch limit that prevents a tail strike and we were there just doing a long wheelie down the runway and finally we had enough of that crap as we were rapidly approaching the departure end of the runway and the "Set ERP" was not doing the trick so we fire walled those T levers...I betcha that there was a lot of smoke and noise coming from the engines on that takeoff...burned up 13K of a 13.5 K runway in the middle of the night in Paris.

Oh yeah...those days wont come back...I hope...

#### cblink.007

##### Well-Known Member
>Two of the locations I need to find would require a hole to be drilled through the floor of the fuselage to be able to drop down the plumb bob (or I would need to plumb bob up from the floor to the airplane in then inboard to the interior and then measure back up a non level floor..way too much work when you already have the airplane up on digital scales...and you have a computer...
So a few days ago, you were wanting everyones homework regarding weight and balance, because you were apparently unable to find it in a simple google search. Now, you have an airframe that is not bespoke, where in that case, you can find all the STA/WL/BL dimentioning you need (direct from its manufacturer), yet you are wanting to blindly drill through the airframe with a hole saw, potentially compromising the structural integrity, just for the sake of getting the exact station line for an area with a plumb bob?

Please tell me I have misunderstood your intent. In fact, I am praying I have!

There are self-leveling laser plumb bobs for this kind of thing, and available at your local hardware store (Bosch is the best). I have one for my projects here. I even have a rig for it that can be set up where you can plot out reference datums, as well as the appropriate Station/Butt/Water Lines. All measurements are indexed on the rig also in the event you need to shoot a point from above the aircraft. Very inexpensive and effective as long as it is built and kept square.