Hi all,

Does anyone have any tips or tricks to improve the accuracy when using the echo chart for forward limit problems? Working through questions, I have found that using the echo envelope produces inaccurate answers in regards to weight to add and find myself using alot of time to fine tune answers. I have attached a question below as an example.

Loading data for a given flight in an Echo aeroplane are
Basic empty aircraft weight 1970 kg
Basic empty moment index 480
Load in forward compartment 50 kg
Pilot and three passengers loaded in the front and middle rows
The maximum fuel that may now be loaded in the main tanks only is closest to
[a] 100 gals
180 gals
[c] 33 kg
[d] 33 gals

Does anyone have any tips or tricks to improve the accuracy when using the echo chart for forward limit problems?

Bit of a problem. The options, for the exam, are limited as you can't run the sums on a PC, nor can you bring along your handy set of graphing aids.

The intention is that you just do the best you can on the envelope - accurate plotting/reading, sharp pencil. Problem is that the slopes of the fuel and forward limit are very similar and any plotting errors are magnified for the intersection. It is reasonable to presume that the examiner will tailor the answers to suit the practical realities of the envelope.

The best approach for the exam is to run a quick calculation and plot to get an approximate solution and then run some bracketing iterations with the calculator to refine the intersection to a degree where you can still match the reasonable resolution of the chart. Bracketing homes into the solution fairly quickly so, starting with a reasonably accurate point, the final answer ought not to require more than several iterations. All a bit silly as you would NEVER do that on the line as a commercial pilot.

The poor choice of datum for the loading system doesn't help at all, either.

If you are a dab hand at basic algebra, you could figure and remember the coefficients for the quadratic which represents the upper forward limit, calculate the equation of the straight line for the fuel load, and run a simultaneous solution. Not overly difficult but definitely would be a bit silly for a pilot licence exam.

Side note - re the occupants, you really should not be using standard weights for a small aircraft with only a few seats. Ref the CAAP, John Klingberg's original report (on which the CAAP is based) showed very clearly that the stats don't support using standard weights on small aircraft.

This is a known problem, because the forward limit line for Echo is not a straight line but is very slightly bowed outward (it is a quadratic) in the available envelope graph. I suggest the most practical solution for exam purposes is to first calculate an approximate answer using the graph; then calculate the exact position of the CG for your approximate solution; now use the formula for the forward CG limit, calculate the discrepancy in CG, and use the weight-to-add formula to update the approximate answer. The result will usually be quite accurate.

You can also improve accuracy by improving graph technique (sharp pencils, careful use of ruler etc). However, in the exam you'll be using the materials supplied by the examinations office. If you get a blunt pencil or a damaged ruler, ask for a new one. The charts for the exam will be stapled together and should be un-stapled so you can lay the page flat.

Disclaimer: retired professor of mathematics