Ravi,

Good to see you getting into the CPL adventure.

A bit hard to comment without the whole question.  Might you be able to provide any data additional to that contained in your post, please ?

Hi Ravi,

Thanks for raising this — you have actually picked up an important difference between the flight computers.

Your wind conversion is correct:

120°T with 10°E variation = 110°M at 20 kt.

Using a CR-type computer, it is quite reasonable to obtain about a 7 kt headwind component outbound, giving approximately 173 kt, and then treat that as a 7 kt tailwind component on the reciprocal, which leads you towards 187 kt.

The example on page 114, however, has been worked using the E6B-type flight computer method, which is the method CASA uses for these examination calculations. The E6B solves the complete wind triangle, including the effect of the crosswind and the crab angle required to maintain track. This produces approximately:

Outbound: 173 kt
Return: 185 kt

So the difference you have found is not because your magnetic conversion is wrong. It is due to the slightly different way the CR and E6B computers handle the wind triangle.

For CASA exam purposes, I would recommend using the E6B method for these heading and ground-speed calculations.

It is a good pickup, and we will add a clarification to the text so that it is clear that the example is based on an E6B-type computer.

Kind regards,
Paul

Paul,

Your answer confuses me a tad (although I suspect that the story is very simple and will fall out as soon as I can work the specific problem).   

Both the CR (Jeppesen CR and clones) and the Dalton (E-6B and E6B/E6-B clones) must give the same answer (within reasonable reading/plotting tolerances - which should be only trivially different) if they be used correctly.   They have to as they are both solving the same triangle using mathematically correct and equivalent techniques.  The CR does the bulk of it by resolving components along the TR/GS vector, while the Dalton does the whole thing somewhat more simply and easily by a graphical solution using the basic triangle.

To resolve this, as I don't have the source document, might I ask you to post the whole question for readers' consideration, please ?  Then I can comment with my engineering pilot's hat on.

Asides: 

(a) For what it's worth, one can work the sums backwards and get, near enough, TAS 180kt, GS out 172, GS back 186 for the CR and, for the Dalton, TAS 180, GS out 172, GS back 186.   I see no substantive difference between the CR and the Dalton ?

If I run the question in Excel (ie do the trig sums), I get TAS 180, GS out 172.2, GS home 185.9 which shows a reasonable agreement with both my CR and Dalton solutions ?

(b) One needs to be aware, and keep in mind generally, that the pilot nav computers are manufactured to a price and are not always as good as they ought to be.   Certainly, the average computer is not up to the build quality of the (somewhat more expensive) engineering/scientific slide rules of yesteryear.   Generally, they remain fit for purpose but such manufacturing errors can introduce unexpected errors in use.

Indeed, EBJ related a tale that, when he first took over the rights to Lahr's/United's device, the first few manufacturing runs were so bad that he and family spent numerous evenings around the kitchen table running detailed scale error checks.

(c) The other consideration is ETAS.  In Lahr's workup, he didn't coin the term, preferring just to refer to the trig equation in his patent application, and, most certainly, didn't introduce the 10 degrees nonsense which EBJ did in his user guides.  The Jeppesen approximation process is fine for in-flight use but makes absolutely no practical sense at all and, for the exams, just puts the candidate closer to a point where the CASA computer assigns a "wrong" grade for the question.   

One must set TAS on the outer CD scale against 10 (the TAS index) on the inner CD scale to permit the trig multiplications.  Initially, you must run the sum X/W = TAS x sin (drift angle) to get the drift angle.  You now can, immediately, swing your eyes around to the immediate left of the TAS index to figure the sum ETAS = TAS x cos (drift angle).   This takes all of one second (OK, two seconds if you are drinking coffee at the same time) - why ever would anyone intentionally bother approximating ETAS by TAS ?  As the drift angle gets down to below, say, 5 degrees, you will do so simply because you can't read the ETAS value and, for practical purposes, the two are functionally the same value.

For those who have been mischievously seduced by the user guides and use the ETAS=TAS approximation for drift < 10 degrees, you are deliberately introducing a small, and quite unnecessary, error into the G/S calculation.   

I note that CASA cautions the ATPL candidate against using the approximation but, as a sop to the vast numbers who think it is a "good" idea, goes along with it for drift < 5 degrees as it becomes moot at very small drift angles.