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

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#### Dana

##### Super Moderator
Staff member
OK… if I understand correctly, the OP is confused not by how to do a basic W&B, how to experimentally determine the arm for various loads, not involving measuring tapes and plumb bobs, etc., but instead with scales during the weighing process. The math involved is at best junior high level. Please forgive me if some of this is elementary.

We’ll assume you know the primary datum and the arms for each of the wheels, where the plane is sitting on the scales. You start with the plane empty. Empty weight is, of course, the sum of the weights given by the three scales. The empty moment is the sum of the three moments, which is the weight on that scale multiplied by the corresponding arm. The empty CG is the empty weight divided by the empty moment.

Empty weight: EW = W1 + W2 + W3
Empty moment: EM = (W1 * arm1) + (W2 * arm2) + (W3 * arm3)
Empty CG = EM / EW

To determine the arm for any fuel, pilot/passenger, or baggage, weigh the airplane with that fuel, person, or baggage. Calculate the new moment as described above. Subtract the empty moment from the new moment to get the moment of whatever you added. Divide that by the weight of what you added, and you have the arm for that addition.

Loaded weight: LW = LW1 + LW2 + LW3
Added weight: AW = LW – EW (cross check this against the known added weight)
Loaded moment: LM = (LW1 * arm1) + (LW2 * arm2) + (LW3 * arm3)
Arm of added weight = (LM – EM) / AW
Loaded CG = LM / LW

Of course, for subsequent additions, base it on the last loaded weight, unless you removed that weight (back to empty) before adding the new load.

#### HomeBuilt101

##### Well-Known Member
Dana,

THANKS so much!!! This is exactly what I needed the other day as I was pressed for time because I had the scales rented and the airplane was up on them and I was trying to remember all of this stuff so as to be able to record the weights and make the calculations and do the fuel tank pours. Appreciate all of your help!!!

#### Toobuilder

##### Well-Known Member
HBA Supporter
Log Member
I think that you are missing the point that you need to establish a datum and the position of the reaction points (relative to the datum) FIRST. The best scales in the world and a spreadsheet from a supercomputer will not help you if you do not know the location of the reaction points. And that takes physical measurement.

If you do not trust the engineering data or the build of your Velocity, then you have to establish that yourself. And yes, even weird shaped compartments can be measured to a high degree of accuracy WRT C/G.

#### Marc Zeitlin

##### Exalted Grand Poobah
I think that you are missing the point that you need to establish a datum and the position of the reaction points (relative to the datum) FIRST. The best scales in the world and a spreadsheet from a supercomputer will not help you if you do not know the location of the reaction points. And that takes physical measurement.
This is all completely true, but it can be decoupled from the actual weight measurements. The OP can take all the WEIGHT measurements they want in various configurations and just list the weights on each of the three scales in a table, for each configuration measured. Then, after they've gone and verified the datum and axle locations, they can put in the #'s for the reaction point (axle) FS's and spit out the results for the loading arms. Those measurements don't have to be done prior to the weighing - they just need to be done prior to getting accurate results.

#### BoKu

##### Pundit
HBA Supporter
It looks like we're pretty much done here, but the algebra trick for finding the pilot CG location using only one extra weighing at the tailwheel (assuming, of course, you know the pilot weight) is demonstrated in the HP-18 assembly instructions. See step 4B:

You can use this trick to find the CG location of irregular solids of known mass.

The trick of assuming that the pilot CG falls exactly at their navel is surprisingly good for middle percentile adults. However, near the edges of the anthropometric envelope for height and leg/torso ratio it can be off by far enough to make a difference for light airplanes with short CG ranges.

#### Pilot-34

##### Well-Known Member
Never expect to get an answer to the question you’re asking here instead expect The answer to the question they want to talk about

#### Pilot-34

##### Well-Known Member
Locating your own personal center of gravity is actually quite easy.
Sitting in the position that you were interested in simply balance on a railing ,your center of gravity will be directly above the railing.

#### BJC

##### Well-Known Member
HBA Supporter
Can someone please give me the math or a spreadsheet to use for calculating the arms of fuel, people, and bags???
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.
Documents for self-education referenced:
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)
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)
Never expect to get an answer to the question you’re asking here instead expect The answer to the question they want to talk about
It is common to get an answer or three, followed by a new / revised question and discussion thereof. It is not common to do someone else’s homework for them, although people are willimg to share their previous, personal work, such as spread sheets.

BJC

#### Toobuilder

##### Well-Known Member
HBA Supporter
Log Member
Never expect to get an answer to the question you’re asking here instead expect The answer to the question they want to talk about
I guess I could have gone with my correct and much easier answer to the OP:.

"No"

But then people might misconstrue the directness and honesty with being an A hole, and I just couldn't have that.

...my reputation as a nice guy would be ruined!

#### Pilot-34

##### Well-Known Member
But if there was a scale somewhere he could drive on that would indicate his center of gravity IT would do his homework for him.........

#### HomeBuilt101

##### Well-Known Member
Wow...I guess the word "homework" has conjured up some agitation...yikes...sorry my bad.

Dear Collective please forgive me for the inappropriate and bad memory inducing choice of words...I will never do it again...

I bet I am not the first person who has been completely overwhelmed and pressed for time with a major airplane project and just wanted a little help...

For clarity...I was NOT...REPEAT NOT...ACTUALLY asking anyone to do my "dwelling-place work" for me...I just wanted to "borrow" a spreadsheet in a time of need...when scales were rented...and I needed to get the job done...

Regardless that person (me) did indeed sit down and construct a spreadsheet from scratch therefore doing that "thing that shall not be mentioned" myself...without anyone's help (not even my mommy) ...all by myself...and I shared it with the community so that in the future a person (not me) will run into the same question and come to this site and find a spreadsheet that will help them out and they will be thankful that a person (me) uploaded it.

And yes I am ALWAYS GRATEFUL for the answers to questions that I did not ask because all learning is good learning and you all are good teachers...but please do not assign any homework...

Drats I just did it again...I must be an A-hole...

#### Toobuilder

##### Well-Known Member
HBA Supporter
Log Member
...We’ll assume you know the primary datum and the arms for each of the wheels...

I could not make the "assumption" that the datum, nor the reaction points relative to the datum were known. The OP went to some length to illustrate that the OTHER documented landmark areas of this well known kitplane were unreliable... Why would I assume the gear locations were known?

And that, right there, is why I'm not about to hand out a spreadsheet randomly to the WWW. Baseline the aircraft, THEN "plug and chug"

#### HomeBuilt101

##### Well-Known Member
>...illustrate that the OTHER documented landmark areas of this well known kitplane were unreliable.... Why would I assume the gear locations were known?

Thanks for proving my point... again.

Why would anyone ass-u-me that the location areas of a heavily modified kit was "landmarked"?

Would it not be prudent to do THREE easy measurements (tip of nose to axel of nose wheel /left main wheel /right main wheel and the place the airplane in DIGITAL scales.

The logic of not sharing a spreadsheet to the Homebuiltairplanes community to prove some long worded strange point is not just unhelpful but it is also really...just sad.

#### Toobuilder

##### Well-Known Member
HBA Supporter
Log Member
Details matter, my friend. Your initial post strongly suggested that you expected the spreadsheet to do everything. Another post suggested that you were unwilling to make any measurements, let alone baseline the key landmarks on the airplane. You have also since shared that the kitplane is "heavily modified". Add that on top of the somewhat incredible weight and balance threads on this site lately, and the propensity for the RV crowd to "share" W&B data without actually weighing anything...

Well, this former Mass Properties Engineer is not one bit sorry for withholding a magic spreadsheet. Not when there are this many red flags waving.

#### HomeBuilt101

##### Well-Known Member
whatever... talk to the keyboard...

#### TFF

##### Well-Known Member
Come on 101. You are a professional pilot. You are supposed to be teaching us.

Why do you want the datum on the nose tip? So all the math is addition. Add a bag to the nose compartment, you add. If the datum was somewhere like the main cockpit seats , you would have to subtract to add the weight for that bag example. All those big planes you flew and the datum was out beyond the nose? Those big long test probe noses? That tip is the datum. Why? What if they wanted a more pointy nose? No new measurements needed. They gave them some growing room.

You put an improved turbo on your aircraft, CG change is simple math if the plane is mapped out. If not, you have to stop and weigh any mod. Did you buy different brand tires? Move the main battery? I know people too light to fly solo and have to sit on 50 lb of ballast. If the plane is mapped out, easy.

You say you really don’t know where the back seat is without drilling a hole? Ever thought of some masking taped lateral on the outside of the fuselage? Measure to the leading edge of the wing and then measure to the tape?

You are flailing when you should be getting anal. Are you leveling the plane correctly when weighing? The numbers are worthless without consistency.

#### HomeBuilt101

##### Well-Known Member
TFF. Good information and questions...thank you good food for thought.

>You are supposed to be teaching us.

I am always learning so thanks for the information you share...greatly appreciated!!!

>Why do you want the datum on the nose tip?

That is what the manufacture of the kit said to do...I was indeed following the instructions. Measure back from the nose to the center of the axle of the nose/left main/right main wheel. They said to confirm the arm location of the pilot seat, rear seat, fuel and baggage compartment using the known weight of a person and bag. The math they had in the example did not work out...I believe there was a typo.

>So all the math is addition. Add a bag to the nose compartment, you add. If the datum was somewhere like the main cockpit seats , you would have to subtract to add the weight for that bag example. All those big planes you flew and the datum was out beyond the nose? Those big long test probe noses? That tip is the datum. Why? What if they wanted a more pointy nose? No new measurements needed. They gave them some growing room.

My nose job on the airplane is all done now so if I use the nose as the datum it is bench marked in for future reference. My number really closlly match the plans numbers so it is confirmed.

>You put an improved turbo on your aircraft, CG change is simple math if the plane is mapped out. If not, you have to stop and weigh any mod.

Yes new turbo is installed measuring the location of the center of the turbo with a plumb bob is easy. I already know the weight so I can to the math. It is kinda tough to weigh out oil lines and intake charge tubes that have complex and compound shapes.

The ONLY way to confirm the moment of the fuel tanks is to weight the airplane...so why bother doing the math for everything else since I had digital scales.

>Did you buy different brand tires? Move the main battery?

Yes. Yes. And a bunch of other stuff.

>I know people too light to fly solo and have to sit on 50 lb of ballast. If the plane is mapped out, easy.

It is all mapped out now!!!

>You say you really don’t know where the back seat is without drilling a hole? Ever thought of some masking taped lateral on the outside of the fuselage? Measure to the leading edge of the wing and then measure to the tape?

That was a joke...I kinda hoped that was understood because it seems kinda zany for a guy to take a hole saw to their airplane. Guess not.

So a question I really have for everyone but that too guy...if the airplane is up on scales what would be the advantage of physically measuring and mapping out locations of stuff if you have highly accurate digital scales and a spreadsheet. Put 50 pounds in the baggage compartment and the scales all read higher...add up the three increases in weight and they add up to 50 pounds so the scales seem to be doing their job...right???

How would a guy confirm the moment of the fuel in the tanks using a plumb bob???

Would it not be more accurate with digital scales as opposed to measuring tape, framing squares, and bubble levels? Even if I did all of that stuff there is no way I could calculate the moments of the fuel because the delta shape of the wing and the landing gear cut out.

>Are you leveling the plane correctly when weighing?

Yes as per the instructions.

>The numbers are worthless without consistency.

That is why I wanted to benchmark everything.

Again...good questions and interesting bantering...except for the too guy...not so much...

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#### Toobuilder

##### Well-Known Member
HBA Supporter
Log Member
Classic HBA behavior lately:

Member begs for help
Member gets help
Member ignores help
Member "invents" superior method
Member complains of persecution by elitist snobs...

#### Pilot-34

##### Well-Known Member
I didn’t see that