# Weight and Balance Estimation

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#### cavelamb

##### Well-Known Member
Guestimating weight and balance for a new design is one of the
harder parts of the design process.

It can't be done by comparing this one to that one.
If it could, all one would have to do to design a lighter structure
would be to compare the new design to a lighter example!

Weight and Balance Estimation

There is a lot of smoke and mirror magic around weight and balance
because so many people misunderstand it so well!

At the heart of all of it, though, is a rotational force about a
reference point. The rotational force is called a MOMENT, and
the reference point is called the DATUM.

It doesn't particularly matter where the Datum is located, as long
as you use the same location to work the problem.

One reason to place the datum at the tip of the spinner is because
all the station numbers are then all positive. No negative distances to
confuse things.

One reason to place the datum at the main gear axles is because
the datum is station zero.zero. Multiply the weight on the wheel
times zero (the ARM is zero at the datum) and the moments for that
wheel come out to zero. Makes the arithmetic a little easier?

And, the reason to place the datum at the leading edge of the wing
it because that's where we are going to wind up anyway. The results
of our CG calculations will finally boil down to a point some given
distance aft of the leading edge, expressed in percent of chord.

The term STATION is the distance from the datum to a particular place
on the aircraft. Say, for instance, the instrument panel? Or the pilot's
belly button.

The station numbers change according to where the datum is placed.
But the instrument panel stays in the same physical location.
(would that hte pilot's belly button would as well! )
It's all about an offset from a zero point, ok?

CG range is often referred to in terms of a percentage of the wing chord.
Say 25% would be the forward CG limit, maybe 33% would be the aft limit.
So our end number actually refers to a distance aft of the leading edge.
The actual numbers will be different, depending on where the datum is located,
but they all (hopefully) point to the same place on the airplane.

The arithmetic:

weight x distance = moments
pounds x inches = pound inches

So, moments / inches = pounds
and moments / pounds = inches

So how is this used in the design stage?
Easy. And very tedious!

Rather than guessing at the whole airplane all together, we simply
take every single part of the airplane, and it's location, and work
the moments.

In the olde days, this was done with pencil, paper and slide rule.
(and that technology took man to the moon)

So let's use them...

Meet - The Spreadsheet from Hell!
Every piece of the airplane, it's weight, it's location, and the resulting
moment it contributes to the airplane.

Sound like fun?

In the example attached, I've worked a small single seat biplane.
I didn't go down to the nut and bolt level, but that can be done -
IF IT IT NECESSARY. Bolts are steel, and quite heavy for their size.
But for this class of work, it's not necessary.

Also, we are ESTIMATING, remember.
Just because the answer comes out to 8 decimal places doesn't
mean it's that accurate.
Garbage in - garbage out.

I want to direct your attention to column B, named DATA.

This cell is used in different ways in different places.

It can be the actual weight an item, such as engine, mount, pilot...
Or it can be used to calculate the weight of an item, say a wing spar tube?

Look at cell B14.
(PI()*2*0.058*0.1) calculates the weight of 1 inch of a 2"x.058 tube.

PI()*2*0.058 calculates the volume of material, and the 0.1 represents the
weight of 1 cubic inch of that material (in this case aluminum)

Column C is the quantity of these parts (how many of them are at THAT STATION)

Column D is the length of the tube, angle, piece of wood, whatever.

Column E is the station where this piece is located. For a longitudinal piece
like a longeron or diagional brace, the station you would enter is the CENTER
of the piece (that piece's center of gravity). Works ok as long as the piece
is no tapered or ?

Column F works out the actual weight of that piece, and

Column G works out the MOMENTS for that piece.

To simplify working with this monster, I've broken the parts down into
sub-assemblies, like Top Wings, Bottom Wings, struts, etc.

That brings us to Columns I and J
I is the sub -assembly weight
J is the sub-assembly moments

So that's the heart of it.
All the pieces and parts in their correct locations, accounting for
their weights and moments...

At the very bottom of the sheet is the grand total.
There is a line for TARE WEIGHT, which can be used as ballast to
bring the CG into range (for "what if" purposes). It should be
0 unless you want to add ballast somewhere.

We add up ALL the WEIGHTS, we add up all the moments.
We divide moments by weight and get the resulting center of
gravity location expressed as inches aft of the datum.

We get empty weight and empty CG.

Then we add pilot and fuel, entered in that order so that we can
see the no fuel and full fuel CG locations.

That's pretty much it for this example.

The designer would next take those CG locations and work out where
the are in percent of wing chord.
25% to 33% of the mean aerodynamic chord is a good safe starting
range. Outside that range, it's not going to be stable.

This is a biplane, so that part gets a bit messier since we have to
first figure out Mean Aerodynamic Chord, but we'll save that for a
future discussion.

My intent with this example is simply to offer budding designers
an example of how to get started on weight and balance estimation.

That's not the end of the design phase, rather it's a starting point.

Have fun with it...

Richard

#### Attachments

• yb1.xls
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#### cavelamb

##### Well-Known Member
We started with a sketch of the general arrangement of the airplane.

This drawing should be as accurate as possible, and drawn to a reasonable scale.
Using CAD it can be drawn FULL SIZE! Pretty cool.
But if drawn on paper use a reasonable scale where an inch can be easily measured.

The attached sketch is a very early effort. It turned out not to be real great,
but it makes a good starting point (since this is the drawing the weight and

It is drawn facing left so that the stations match a normal mathematical
number line (increasing to the right). In the industry this drawing
would normally face to the right and the station numbers would increase
to the left. Just sayin...

Along the bottom of the drawing is a scale in feet and inches.
Notice that the datum (reference point at station zero) is located at the main
gear axles. It can be located anywhere, but I find this arrangement works
well for me. Also note the inches divided off in the first foot of the scale.

Also note that I've drawn in very few dimensions. Since the drawing is
full scale any dimensions needed can be taken directly from the drawing
without cluttering it up. And those are placed on a different layer so they
don't clutter up the drawing.

We draw in the big pieces... pilot, engine, fuel tank locations, baggage
compartment, instrument panel, wing spars, brake cylinders, etc.
Locate as many of the heavier parts as possible and add them to the drawing.
Working in CAD makes this easy. Drawing on paper is a lot easier of we
use an overlay for adding details. Either way, we need to start filling in
the structural elements of the design.

This fuselage structure is to be built using riveted aluminum angle.
The calculations in the sheet under DATA account for this.
If you want to use steel tube, wood, carbon fiber, or T3-Unobtanium,
the DATA entry will represent that material.

For parts that are added as complete units (brakes, battery, instruments)
the weight of the item is entered in the DATA column, with quantity and
location in their respective columns. While the DATA column can get a
bit involved, this approach helps keep the overall spreadsheet more

My design rules say 3/4 x 3/4 x 1/8 extrusions for most of the structure.
(note: I'm not working a stress analysis here - just the weight and balance)

Lets start with the firewall, which in this case will be 1 x 1 x 1/8 angle.
(starting at line 50)

Two vertical pieces - one each side - share the same station.
Measure length and enter that into the spreadsheet.
Measure width for the lateral (cross) members.

Any significant corner braces? measure the parts and add 'em to the sheet.

Firewall skin itself - .017" stainless steel.
(Missing from the sheet!! OH NO, MR. BILL!!!) Fix it.

Anything else at that station?

The front tube of the main gear leg, the main gear wheels, brakes, wheel pants, etc
are also located at station zero, but the way I built the sheet those pieces will be
entered into the sheet under the main gear sub-assembly rather than the fuselage structure.

Working aft we take each station in turn.

Some parts are not located at a particular station.
Longerons and diagonals, for instance. Or a sheet metal floor. Or skins.

The station number for that would be the center of gravity of that piece, most often
that is the center of the length of that part. If the part is off shaped, tapered
for instance, it would be necessary to actually calculate (or estimate) the location
of it's CG.

Eventually the entire structure is described this way and the end results, the bottom
of the weight and balance report, will be tell the sad tale.
More often than not, early efforts will not be all that happy.

In that case, we start moving things around, until the results fall within the allowable
CG range of the the wing chord.

Yes, it's a lot of work. Or play. Depends on how you feel about it.

But that's what it takes to go beyond just an outline sketch...

#### cavelamb

##### Well-Known Member
It evolved over time...
This is one of the later drawings.

#### Jay Kempf

##### Curmudgeon in Training (CIT)
Supporting Member
It evolved over time...
This is one of the later drawings.

View attachment 22057

Or do all that work to enter the dims and locations into a modeler and get the weight and balance for free at the end.

#### StarJar

##### Well-Known Member
Nice work Cavelamb. I've never seen a tool like that before. Will add it to my humble arsenal of spreadsheets.

#### cavelamb

##### Well-Known Member
Or do all that work to enter the dims and locations into a modeler and get the weight and balance for free at the end.

I dunno, Jay.
Maybe that would be helpful for some people, but I think I prefer a more hands on approach.

In the end, the modeling software is just that...

#### Jay Kempf

##### Curmudgeon in Training (CIT)
Supporting Member
I dunno, Jay.
Maybe that would be helpful for some people, but I think I prefer a more hands on approach.

In the end, the modeling software is just that...

The modeler can load the spreadsheet and update it. So if something looks a miss you can update in either place if you like. Removing a dimension from the 2D CAD machine and loading it manually into a spreadsheet is redundant and redundant efforts are chances for data entry.

With your AutoCAD drawing you could be attributing each block and then extracting the attribute data. But you choose to do it manually. I used to work just like you. Don't have time for that anymore. The older I get the more I look for tools to do things right and automate things that take forever. There is a lot of repetitive and recursive arithmetic in aircraft design. Mistakes have not gone up or down because of automation of tasks. But the ability of one person to do a massive amount of repetitive work that used to take a team is a reality now. Just like your spreadsheet is an automation of adding columns of numbers manually the modeler is an automation of transcribing and then extracting dimensional data. Enter once use it many times. These tools weren't developed randomly. They were developed out of need for productivity. 2D CAD is free now because it is really not used anymore.

#### cavelamb

First up, I use DesignCAD 3D MAX, not (shudder) Autocad. ($60 retail and worth 100x that) Not that it matters to anyone but me. DesignCAD's macro language (BASICCAD) allows one to do exactly what you describe. If I were doing this professionally, I'd do exactly that. I've worked up some of it. But consider, Jay, this whole rant is intended to teach, not do... In that respect, what better what better way to approach it? Richard #### Jay Kempf ##### Curmudgeon in Training (CIT) Supporting Member First up, I use DesignCAD 3D MAX, not (shudder) Autocad. ($60 retail and worth 100x that)
Not that it matters to anyone but me.

DesignCAD's macro language (BASICCAD) allows one to do exactly what you describe.
If I were doing this professionally, I'd do exactly that. I've worked up some of it.

But consider, Jay, this whole rant is intended to teach, not do...
In that respect, what better what better way to approach it?

Richard

I used to use DesignCAD and it is a good program and I recommend it to the budget challenged. Very nice stuff. It lacks the automatic spreadsheet link that is true but it will be a very straightforward leap to get it there.

I agree that teaching is best using hand methods. Hand methods have to be there anyway. Hand method run throughs lead to how to structure spreadsheets, modeling schemes, formulas, estimations of how the outcome should appear... That is what professionals do: they make sure that you have the answer you expected before proceeding further. I always test my spreadsheet formulas for output that is expected. I always test the models for the intended outcome.

#### Pops

##### Well-Known Member
Supporting Member
Very good. On the single seat Cub that I fly, I did a running weight and balance as I built and of course the last thing was determining the length of the engine mount to get the final CG where I wanted it.(non electrical, so no battery) Came within .10 , so I was happy. I enjoy the whole progress. I'm doing the same for the JMR as I build. I keep a piece of tape with a mark on the top longeron and move it as the CG changes in case I lose the papers, not the most organized. pops

#### Autodidact

##### Well-Known Member
this whole rant is intended to teach, not do...

Well that's kinda sad, because that little biplane is about the neatest idea I've seen in a long time!

#### cavelamb

##### Well-Known Member
Well that's kinda sad, because that little biplane is about the neatest idea I've seen in a long time!

Maybe I should rephrase that?
It's not intended to be a professional level (or even advanced amateur level) approach.
But if one has the time, inclination, patience, and desire, it will work just fine.

Imagine young Clarence Johnson holed up in a London hotel room for the weekend
frantically revising the Lockheed Ventura design into the B-37 for the Brits.
Ok, bombs go here. Does the tail gunner HAVE to be all the way back there???
What does a .50 caliber weigh? How much ammo? Look at what that does to the CG!

Nothing but paper, pencil and slide rule.
But then Kelly was an aircraft design genius!

Today we have a heavenly host of software to help out. (Jay is dead right about that)

But without the basic understanding of what those programs are doing in there,
the (so called) designer is nothing more than a glorified key punch clerk.

Auto:
That little biplane, referred to as the YB1 Stealth Biplane (because it's invisible)
has a great deal of potential as an amateur built experimental.

I drew it intending to build it some day. I can't right now. But maybe some day?

Construction would be straight out of the Texas Parasol manual.
Well, fairly close anyway. Rather than build the fuselage as mirror image sides,
I'd do it as top and bottom ladders - due to the splayed cross section of the fuselage.

Riveted extruded aluminum angle truss. Wings could be a buried tube spar (moved
aft of the leading edge, or wood spar/wood ribs (with a weight penalty!).

No reason to build ugly airplanes!

#### cavelamb

##### Well-Known Member
Or do all that work to enter the dims and locations into a modeler and get the weight and balance for free at the end.

I've been thinking about what you said, Jay, and wanted to ask...
I've not played with any of the modeling software out there.
So I don't know.
If you took that approach ...
Can you do that and break out sub assemblies easily?
Find out what a wing weighs by itself? A gear assembly?
Swap out panel configurations (as a block)?
That kind of thing?

#### Jay Kempf

##### Curmudgeon in Training (CIT)
Supporting Member
I've been thinking about what you said, Jay, and wanted to ask...
I've not played with any of the modeling software out there.
So I don't know.
If you took that approach ...
Can you do that and break out sub assemblies easily?
Find out what a wing weighs by itself? A gear assembly?
Swap out panel configurations (as a block)?
That kind of thing?

Yes, yes, and more yes. That sort of stuff makes it a little easier to build the big model if you build it in chunks you can get your brain around. Plus it loads less in memory to deal with sub assemblies.

DesignCAD should be able to do all that. It is just a little less parametric than the $5k brothers. I really like that program for what it is. You are working in 2D. If you worked in 3D and then outputted 2D you would save yourself a bunch of head scratching. Worth some experimenting. As far as blocks, that is 2D thinking. Layers the same way. Stop thinking that way. The industry has moved on. You just build what you want full size in the computer. Then if you want to put something on paper you just rotate the model and cut it up the way you want until the paper looks the way you want. #### cavelamb ##### Well-Known Member Yes, yes, and more yes. That sort of stuff makes it a little easier to build the big model if you build it in chunks you can get your brain around. Plus it loads less in memory to deal with sub assemblies. DesignCAD should be able to do all that. It is just a little less parametric than the$5k brothers. I really like that program for what it is.

You are working in 2D. If you worked in 3D and then outputted 2D you would save yourself a bunch of head scratching. Worth some experimenting.

As far as blocks, that is 2D thinking. Layers the same way. Stop thinking that way. The industry has moved on. You just build what you want full size in the computer. Then if you want to put something on paper you just rotate the model and cut it up the way you want until the paper looks the way you want.

LOL, yep, that's me - left behind.
But I have played around with 3D a bit.
BTW, you should check out the latest DC V22.
They have really hit one out of the park with that build.
This is good stuff, Maynard!

Jay, you mean maybe something like this???

#### cavelamb

##### Well-Known Member
Perhaps bad terminology on my part.
Sometimes simple words had exotic meanings in special circumstances.
By "block" I meant something like this...

This drawing is supposed to "move"... animated GIF.
(shows how far left behind I really am, doesn't it)

But it's not working in my browser. (works in ACDSee)
Might have to save it and use something else to watch.

#### cavelamb

##### Well-Known Member
oops - duplicate post

#### Jay Kempf

##### Curmudgeon in Training (CIT)
Supporting Member
Perhaps bad terminology on my part.
Sometimes simple words had exotic meanings in special circumstances.
By "block" I meant something like this...

This drawing is supposed to "move"... animated GIF.
(shows how far left behind I really am, doesn't it)

But it's not working in my browser. (works in ACDSee)
Might have to save it and use something else to watch.

View attachment 22091

If you have a way to articulate and save sub assemblies then that is all good stuff. Then it's just gaining experience in using the software that gets the rest. Anything that has volume, area and location can have weight, force, stress/strain applied to it.

#### cavelamb

##### Well-Known Member
All of this posted stuff is just Design CAD.
I started using is back in the DOS XT days.
I do okay with it.