I think we are dancing around the same thoughts ? Some further thoughts, if I may ?
My point was, the calculation was not run using algebraic rules. Yes, jukzizy got the correct answer, but the working and the answer were inconsistent. The algebra requires brackets.
Indeed. However, while Jukzizy has been a little lax in that he omitted the parentheses in his post, he has run the calculations with them. I think, perhaps, you are being a tad hard on the post ?
For the echo, the forward CG limit is not linear, it changes at 2360 kg.
As is the case for the very great majority of light aircraft envelopes.
The equation is correct for all weights between 2360 and 2950 kg inclusive. It falls apart for weights less than 2360 kg.
Which is why I specifically specified that I was addressing the "upper forward limit line" rather than the forward limit, in toto. Indeed, the two equations are identical, if presented a little differently. Your comment applies with equal validity to the use of your own equation, as cited.
I'm guessing that this is what you meant by "one's preferences"?.
Not at all.
My comment related to the observation that Bob's equation is presented in a form which provides a link to the derivation. I haven't discussed this with him but I presume the reasoning is for student understanding and, if so, I certainly have no problem with that. However, it is conventional to represent a linear equation in the form y = mx + b and a simple further step with Bob's equation results in the standard form. From my perspective, the standard form offers the benefit of being simpler for the student to commit to memory.
The reference to "preferences" simply relates to selection of one equation form or the other.
Seeing we are discussing this point, it is worthwhile considering the fact that the use of equations for this purpose is quite unjustified (even inappropriate).
The derivation accuracy and rational precision of the envelope limitations do not warrant going to such lengths. If the examiner so requires for examination purposes, so be it, but students should be aware that it is quite inappropriate for routine use. Indeed, were we to do this in the real world, quite apart from its being a tad silly, one would need a new equation for each successive Type which we might operate. In reality, the accuracy obtained by careful reading of the graphs should provide more than sufficient accuracy for the examination. There is one caveat, however - the engineering world favours rational considerations in which regard, the limits should be viewed with a bit of haziness. The legal world, however, is more concerned with the black and white of the written word. It remains essential that pilots ensure that their steeds remain within the AFM/POH prescribed limits which, in turn, derive from the Type Certificate for the aircraft Type.
As a sideline comment, it is important that students are aware that, while the upper forward limit line for the CG vs WT graph usually is linear, this isn't the case for the alternative presentation as moment (or IU) vs WT. For the latter case, the line segment is a curve (quadratic) although this is not always readily obvious from visual inspection unless a more suitable datum is used than that derived from the GAMA Spec 1 POH protocols. Not difficult to figure the equation but, again, quite silly for general usage.
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