Hi all can you help me on this question I used the graphical method and found that 50 kg could be added i then calculated this arm and new weight and it was within limits and was correct I then use the total calculation method and found the answerTo be 38 kg And also correct how was this possible

Sorry page 189

First point - the books vary through different revisions so far as pagination, etc., is concerned. Generally better for the readers if you post a happy snap of the question so that we are all singing from the same sheet of music.

As to the question - and also correct how was this possible ? They can't both be correct so there has to be an error along the way somewhere.

38kg looks to be a good answer (actually just a cigarette paper under 38kg).

If you ballast 50kg to run an iterative solution, the 50kg puts you outside the envelope by a bit over 10mm so it looks like you maybe took a wrong turn in your plotting. Perhaps you can post a happy snap of your arithmetic calculations and the graphical plot and it should be pretty easy to figure out what might have gone awry.

Hi John thanks for the quick response I re did I t on the Envelope and can see that there could be a margin of error on the thickness of the pencil line.and yes you are correct When I added on 50 kg it was 10 mm out is this the reason why Bob says to use the flow chart for adding and subtracting on the aft CG but that being said it also gives the envelope method on page 161 as I Have included in the photo Cheers mark

a margin of error on the thickness of the pencil line

The main problem with a graphical solution is associated with the envelope datum. Typically, GAMA style loading systems use the OEM standard design datum which usually is well forward. This is fine for most purposes but, generally, not really suited to graphical calculations due to the resulting shape of the envelope, as drawn. It is for this reason that heavy aircraft OEMs (and most competent WCOs) usually define a second datum for weight and balance purposes where graphical solution work is required. You can see this in the Alpha loading system where the designer (Norm Overmeyer) has chosen a datum better suited to producing a "boxy" envelope shape.

You will notice on your chart example that the slopes of the lines are similar. This makes for a quite poorly conditioned intersection. (It is for the same reason that, in nav work, we impose angular restrictions on position lines which are to be used for determining a fix). You need to do everything you can to end up with accurately drawn lines -

(a) use a sharp pencil

(b) try to plot the longest line you can to minimise plotting errors associated with the accuracy of plotting end points

(c) be very careful in how you read off intersections. On your example, if you read it more carefully, it is clear that the intersection is well below a 50kg increment

is this the reason why Bob says to use the flow chart for adding and subtracting on the aft CG but that being said it also gives the envelope method

As with many things, there is more than one route to the solution. For this stuff, the usual techniques we might use include

(a) simple plotting

(b) moment balance calculation once you know the target CG. This can be done in several ways, some more complicated than others. Figuring the target CG is easy if the CG isn't varying with weight (for ballasting) or you are just rearranging loads to change from one CG to another. For the typical light aircraft envelopes, such as you are working with in this course, the only difficult section of the envelope is the upper, forward limit where the CG does vary with weight.

The target CG can be figured out using simultaneous solution of equations (this is a mathematical technique which works fine but is a bit over the top for routine pilot weight and balance work.) You can run this sort of calculation for the weight by CG envelope presentation as the upper forward section is a straight line. However, for the weight by moment (or IU) presentation, the segment is a quadratic and the calculations get a bit more involved.

Bob's approach is to use calculations where they are reasonably simple, but to prefer the graphical plotting solution for the upper forward segment for ballasting exercises.

Keep in mind that, as instructors, we are trying to show you reliable ways of doing things but tending toward the simple techniques to facilitate success in the artificial arena that is the exam session.

The Gross Weight and Moment given in this question puts your present condition inside the envelope but close to the aft limit. The questions asks you to find the maximum weight that MAY be added to the rear compartment. Adding weight to the rear compartment will move the centre of gravity aft, so it's the aft limit that must be considered. It can be solved by the 'two point' method, but why do that if you can use the flow chart and get a much more precise answer in less time?

The worked answer on page 217 uses the flow chart. Remember that if you are dealing with the Echo's aft limit, you will NEVER need to plot the two points. because the position of the aft limit is given in the manual. The aft limit does not change with weight, so you can ALWAYS use the calculator to solve an aft limit problem whether you are adding, subtracting or shifting weight.

Once again thanks Bob and John for your quick replies helps greatly