Well done, that man. Crownies promise noted and logged in the diary for a convivial collection.
With many of the exam question stuff, there are multiple ways to get to the answer. So long as the method is sensible and the working error free, all is well .. and, certainly, if Method A makes no sense, give it away and use Method B.
(Continued from post 14)
(Misplaced this thread along the way, so I'll continue with the tale now. Have misplaced the training notes .. not that that matters as I'm sure that they will have been updated from time to time along the way ..)
E. Shifting Weight to Alter the CG (Reloading the Aircraft)
First point .. ALWAYS sketch a picture to suss out the arrangement.
This situation arises, typically, when a calculated intended load puts the CG outside limits (or outside a desired location) and we need to rearrange the load to achieve the required/desired CG location.
Recall that the CG was calculated by finding a suitable balance location which gave a zero total moment. It follows that, if the CG, now, is "wrong", then the total moment is "wrong" so we need to rework the moment sums to suit and find a sum which meets the need to have zero total moment about the new CG position.
Let's say that the new CG required is located a distance from the old CG which we will call δCG .. this is just the distance between the two CG positions. For convenience, let's put the new CG to the right of the old CG (we can call it the datum position for the next calculations to make things easier to follow) and have, say, a baggage compartment in the nose (at distance - s1 from the datum) from which we can take some weight and another in the back (at distance s2 from the datum) into which it might be put ..
Calculating moments about the new CG position we would get something like ..
total moment = -w x -s1 + w x s2 - GW x δCG (the last term because the old CG is now -δCG from where we want to have the new CG) ..
but, for the new datum position to be the CG, the total moment must be zero, by definition .. a bit of rearranging and we get
w x (s1 + s2) = GW x δCG
and a tad more rearranging ..
w/GW = δCG/(s1 + s2)
This we could describe, generically, as
weight to be moved ____ distance between the two CG positions
---------------------- = -------------------------------------------
gross weight___________ distance between the two load stations
(if you didn't follow the story with ease, don't worry .. the end generic equation is the thing to remember ..)
F. Adding/Removing Weight to Alter the CG (Ballasting)
First point .. ALWAYS sketch a picture to suss out the arrangement.
This is much the same as rearranging some load .. let's say we want to move the CG to the right and we have a suitable compartment in the tail for adding some weight to achieve the required CG change. We can set up a similar total moment expression with the datum at the new CG position ..
total moment = w x s - old GW x δCG (note that s is the distance from the new CG - the datum - to the ballast station location)
putting the total moment equal to zero to force the datum position to be the new CG gives us ..
w/old GW = δCG/s
which, generically, can be described as
ballast weight ________ distance between the two CG positions
--------------- = ---------------------------------------------------
old GW __________distance from the new CG to the ballast station
Again, don't sweat the sums too much .. the end generic relationship is what you are after.
The same sort of generic expression can be used for removing weight from a station.
G. Using Fuel as Ballast
As a general principle, use of fuel for ballast in light aircraft is not a good practice .. small quantities, often poor gauging capabilities and, then, if you have an operational need to go into that fuel in flight, you might find yourself out of control prior to having to demonstrate your Gimli gliding capabilities.
A bit different with heavy aircraft which, generally, have the advantage of being subject to a more rigorous management oversight regarding procedural protocols etc.
Having said that, you can use fuel in the balance calculations in the same manner as described earlier.
H. How about Graphical Approaches to Envelope CG Calculations ?
One typical problem sees the initial aircraft loaded a bit outside either the forward or aft CG envelope limit. Clearly, one needs to fix this prior to flight. The usual way is either to rearrange the existing load to suit or, alternatively, add ballast/offload payload.
If the problem is in the constant CG regions (lower weight forward and all the aft limit range), the previous simple approaches work fine. No reason why you can't do it graphically .. just doesn't make any sense and, generally, ends up less accurate ..
If, however, you are in the higher weight forward limit region where the CG moves aft with increasing weight, such an approach doesn't work with the moving target ballast technique. We can sort out this problem by one of two methods -
(a) this isn't the recommended approach but is noted for those who might have an interest - the CG limit line (on the W-IU limit chart) is a simple quadratic and, by figuring a particular ballast line equation (linear for the Echo .. but not always the case), the two can be solved simultaneously to find the required ballast weight. Although not a difficult exercise, per se, it's just too painful either for exams or real world flying .. so let's not go there.
(b) the pragmatic alternative to (a) is a graphical implementation of the simultaneous solution. Simply plot the incorrect loaded W-IU point (outside the envelope) and then a second ballasted load point (inside the envelope). On the W-IU chart, you can join these two points with a straight line - provided the ballast arm is constant - and read off the intersection with the CG limit to figure how much ballast weight is needed to fix the misload.
I. Miscellaneous Comments on the Echo POH Loading Data
(a) seat loads. Removing seats usually involves a slightly different arm to that used for the occupant. However, since the manual doesn't make the distinction, one uses the one common loading arm. The reference to 82kg max in the (removed) seat position refers to the normal seat structural design load to cover a 170lb/77kg occupant - ie, unless you have further information, the floor limit is presumed to be 77kg + seat weight for simplicity. For the same reason, seat loading is limited to 77kg unless a specific loading design permitting a higher load is implemented.
(b) load charts. The presentation is typical GAMA POH format and one which you will see in many light aircraft POH weight and balance sections. This has an unfortunate consequence of using the OEM FS datum in that the W-IU chart is rather dreadful due to the pronounced slope from lower left to upper right. The main problem arising is that the plotting accuracy in use is compromised.
Compare this chart with, say, the Alpha loading system. In the latter, the datum is a typical trimsheet trim datum (ie not the OEM FS datum) and, although there is not enough information to work out just what the trim datum is, we can observe that it either is, or is very close to, the fuel arm position. A quick look at the resulting envelope in the trimsheet shows a very much better layout for accurate plotting .. this is the main reason we use non-OEM trim datums for trimsheets. Indeed, the larger aircraft OEMs usually schedule the OEM loading systems using a similar trim datum philosophy. The quick way to tell if a chart uses a sensible datum is to observe if the envelope is "squarish" or boxy (such as for the Alpha) rather than very slopey and elongated (as for the Echo and Bravo).
Caveat - with ultra lengthy, complicated posts, there is always the chance of keystroke or similar errors unless the information is peer-reviewed. If you see, or even think you see, something a bit strange, please let me know so that I can check it out ..