Often there are multiple ways you can approach the solution for a problem. You can run any of these questions using a plot-it-and-check-the-intersection approach, subject to the underlying requirement that straight lines are appropriate. However, some of the loading line slopes are pretty similar to the envelope limit lines so it becomes very difficult to read anything like an accurate answer. If. say, in a question, the alternatives are well separated, this approach may be useful.

The alternative is to run some trial calculations - either

(a) you will have several alternatives and you can run those values to see how you go, or

(b) you start with a couple of guesses (one on each side of the correct answer) and then run a simple bracketing sequence by taking consecutive midpoints to refine the calculation. Using midpoints is the standard computer solution approach - you probably can be a little bit more innovative and guess a little more accurately which will save some time overall. This technique will converge fairly quickly so it isn't too much of an imposition.

Although the 'try each answer' approach works, it has been made much more difficult since CASA introduced the 'type-in' answer questions. If you are adding or subtracting weight to get to the forward limit in the ECHO, the lines often cross at such a shallow angle that you can have no confidence in your answer (especially when you are trying to interpolate between printed chart values in the first place).

That leaves you with no option but to have a guess, then compare the result with the calculated forward limit and decide whether you need more or less weight. Keep doing this until you 'sneak up' on the correct answer. Since CASA refuse to reveal what margins they apply to the 'correct' answer, this could be a long and tedious task. Do you need to be within 1,2 or 3 kilos? Hope you brought a cut lunch!!

As Bob suggests, it is getting to be a bit silly as these numerical approaches have absolutely no place in the real world of aviation. In the real world you plot, read the value, and then apply a little bit of conservatism to give you a reasonable argument in the event of regulatory or legal questioning. Then you go flying.

While the midpoint bracketing approach will keep the number of calculations down to a reasonable pain in the neck, there is another way to approach the problem. This is to solve the problem as simultaneous equations. However, this is even further removed from reality so it probably isn't of great use unless you are pretty good at algebra.

In the real world you plot, read the value, and then apply a little bit of conservatism to give you a reasonable argument in the event of regulatory or legal questioning. Then you go flying.

So true. Thank you John!