Working through the CPL Performance study program at present.

One point reading through the textbook (8/11/2018 revision - second hand) confuses me a little. The subject topic is weight and balance and correcting an initial misload to put the cg at the forward limit. This is a very straightforward generic physics/mathematics problem familiar to any university technical undergraduate.

On pages 178-179, there is a technique shown to calculate weight shifting to move the cg to the limit. An equation for the high weight section of the forward limit is worked out and used to calculate the target cg for the weight shifting work following which the weight to be moved is calculated.

However, on page 180, where the problem involves adding or subtracting rather than just shifting weight, the problem is done graphically and there is a statement that "you must use the graph to solve the problem". This latter statement is the source of my confusion.

It is clear that there is no reason, technically, why the problem should not be solved graphically, but there are no reasons given in the text why an analytical approach similar to the shifting weight solution cannot be used. I have a reasonable background in mathematics and physics and there is no functional reason why this problem cannot be solved by the use of equations in a manner similar to that shown on page 178 for shifting weight.

I must be overlooking something in the text because I can see no reason why the graphical technique is mandated so strongly when a suitable analytical approach is rapid and provides a more accurate answer.

Perhaps Bob can resolve my confusion ?

Thanks in anticipation, Dave.

Hi Dave.
If you are shifting weight to place the centre of gravity on the forward limit, a simple equation can solve the problem because, if you shift weight you don't change weight, so the required centre of gravity is known at the outset.

However, if you add or subtract weight, the resulting centre of gravity changes with changing weight.

You don't know how much weight to add or subtract until you know the position of the forward limit after the weight has been added or subtracted and you don't know what the forward limit will be unless you know how much weight you are going to add or subtract.

Most of our students are not university technical undergraduates. They don't have a strong background in maths and would find it a bit much to grapple with a simultaneous equation. That's why I recommend that the graphical solution be used for adding or subtracting weight.

It still is possible to check the approximate answer obtained from the graph and 'fine tune' it to find the weight that would result in the new centre of gravity coinciding with the forward limit.

I'm pretty sure that the examiner would apply a fair margin of error to this type of problem.

Bob

Thank you for your reply, Bob. From that, I understand that the textbook direction is only a recommendation and that, of course, is quite reasonable. I agree that the majority of people would be better served staying away from simultaneous solutions of equations.

One other query of trivial note: I presume that the various aircraft used for the course and exam are based on actual aircraft ? It wouldn't make a lot of sense for the examiners to bother with the trouble of working out specification sets of data when they could just pick this or that aircraft from the local Australian fleet at the time.

Some comments, if I may.

In case others are wondering what the previous posts are talking about, Bob's explanation is on the money. It is possible, using a standard algebraic technique usually called 'solving simultaneous equations' to figure out where two lines intersect on a graph. For the upper forward section of the envelope on the weight by IU arrangement, the envelope line equation is a curve (quadratic) while the aft compartment load is a straight line. The line on the graphed envelope looks like it is straight but that is only due to the datum chosen - were we to select a better datum, the curve can be seen fairly easily.

Looking at the example cited in the textbook, the preferred approach for itinerant calculations, such as the line pilot does, is to plot load increments to find the intersection. In the example given, Bob comes up with 40 kg to be added by inspection of the graph. Were we to do the exercise algebraically, the answer is 38.2 kg (to the first decimal) - not much in it, is there ? Certainly, that sort of accuracy is more than fine for practical weight and balance work.

Generally, the pilot is best served by plotting as shown in the textbook.

The folks who would use the algebraic approach are

(a) we instructors - to save time. For instance, I have the various aircraft set up in Excel and, for the example given, all I had to do was type in the starting weight and IU and then look in the solution table for the load change for the aft baggage arm. That took all of, probably, 5 seconds ? Bob, I am sure, would have the same sort of thing set up for his use as would any of the active ground instructors.

(b) small charter operators who can't afford to buy/lease the large operator style load control system packages

So, why don't we just do this generally ? That's easy. The equations have to be figured out for every different aircraft and the software set up to run the sums. Unless you are going to use it over and over and over again, it's just not worth the effort.

In answer to Dave's question on aircraft types, following a search over several coffees some years ago, the story is -

(a) alpha, bravo and charlie are, respectively, turbo Lance, Cheetah, and Sundowner. As a side note, be wary of the alpha trimsheet. The original is a design by Norm Overmeyer (a pleasant civil engineer and weight control officer no longer with us) which was modified, at the then examiner's request, by Bruce Clissold (likewise a very pleasant WCO chap in semi-retirement). The original version, unfortunately, is still floating around - see the following thread for a discussion - bobtait.com.au/forum/performance/5279-we...0-may-2015-book#8645

(b) the echo doesn't map across to any particular aircraft that I could find without spending way too much time on the exercise. My assessment is that the then examiner ran up a list of desired questions/techniques which he wanted to test in the CPL exam. He then started, probably with the Piper Navajo (there are some similarities between the echo and the Navajo), and played with the aircraft data until he arrived at a set of numbers which would produce the desired results for his exam questions.

At the end of the day, it really doesn't matter what aircraft the various exam aircraft may, or may not, be. The loading systems are reasonably typical of what you might see out in the Industry and that is the aim of the exercise. Certainly, you will see plenty of other styles of loading system but one has to start somewhere.