First off you can download the C150 TCDS from the
FAA site which gives the "official" loading arms. Never mind that the loading sheet graph doesn't quite match up with the TCDS data ...
I see no reference to the fuel tanks cg arm
If you're running with the normal ICAO/GAMA proforma (as with the chart cited) you are calculating the moment sum and then using the CG graph to figure the final CG. Just saves you the hassle of doing the sums longhand and there is no need,
per se, to know the actual loading arm values.
a graph of the fuel arm can be a very convoluted thing.
Never mind sweptwing jets, any non-prismatic tank can be expected to have a fuel loading arm which varies with fuel volume - starting with small aircraft such as single Beech etc. The secret is to assess at what stage the aircraft is not reasonable for a linearised fuel loading arm.
Now, as to the "constants", there is no great mystery here.
By way of working up to the answer, consider converting a quantity to another quantity by a process of multiplication and division by several items eg -
2 x (6 x 8 / 2) = 48
can be done more economically by doing part of the intervening calculation and using simplified multipliers -
6 x 8 / 2 = 6 x 4 = 24
so we could have done the first sum as
2 x 6 x 4 = 48
and this is what the designer of the spreadsheet has done. Now why he/she did it that way and not go the whole bit and use 2 x 24 remains a mystery ... Perhaps he is an olde pharte like me and others who were brought up on old mainframes and limited significant places in floating point calculations .. which made us use simplified calculations on computers to minimise floating point calculation round off errors in consecutive calculations ? This was a particular problem if one had to do divisions with similar value quantities. Now, if that nonsense doesn't mean much to you, don't worry, it isn't anywhere near as important in these days of fancy PCs.
So, we can play with the numbers and come up with -
(a) for fuel
moment = pounds x arm / 1000
= USG x 6 x 42 /1000
= USG x 6 x 0.042
[More generally, one would refer to IU rather than moment in this case, but the subtlety is not important for the present discussion]
The spreadsheet designer either has used an arm of 42.17 (for whatever obscure reasons) or, more likely, he/she figured that value by doing a series of unit conversions. Either way, 0.04217 is just a minor simplification of the calculation - no more, no less. If you were working from the graph, with an arm of around 38, you would get 0.038, which is pretty close to 0.04217 at the end of the day.
(b) for the loading bays (and using Mach Tuck's read off values to save me the eye strain of doing it myself ..)
0.06346 = 63.46/1000 which is pretty close to the value derived from the graph of
0.064 = 64/1000
and
0.08666 = 86.66/1000 which is pretty close to the graph value of
0.0857 = 85.7/1000
It is not immediately obvious where the small discrepancies in the arms derive. However, if you like to post the spreadsheet, or send me a copy, it will become very obvious, very quickly, what the designer was up to.
As weight and balance seems to be a bit of a black art to many
which is a great shame as it is dead simple .. provided one follows the basics and maintains strict numerical housekeeping ... the black art comes into play when designing trimsheets and, even then, it's a simple exercise once you get the hang of how to go about it.
the manufacturer has probably chosen to present the data in this fashion to simplify the issue as much as possible,
The manufacturer simply is following the recommended practices in the GAMA format POH. In my view, the GAMA format for weight and balance is dreadful but that's just my opinion. The GAMA format also has been adopted as an ICAO recommended light aircraft POH format so I guess I am just a lone voice in the wilderness on this point.
the author of the graph will have obtained it from the manufacturer.
The TCDS is the first port of call and, at the end of the day, if we can't find out by other means, we get the old tape measure out and measure arms directly in the aircraft.
The AFM does give us the stations for the baggage areas, but in this spreadsheet they aren't used at all.
Now, I don't have a copy of the POH but let me guess, the quoted arms are pretty close to 63.46 and 86.66 ?