Small piston day VFR charter operation:

Find the ETI to the ETP from alpha, Given the following

Distance from alpha to Bravo- 320 nm
Track 295*M
Tas 140 kts
W/V 250*M/30kts
fuel flow 120 L/hr
Taxi 20L
Etas- 138kts
320×159/280=181.7nm

Time= D/s
= 181÷117kts
= 93 minutes

When doing this type of problem always start with a diagram.



In nil wind conditions, the ETP (CP) will be half-way between A and B. If a wind is blowing the ETP will be displaced upwind from the track mid-point position. Use this to check if you get a sensible answer after the calculations are done.

Track Home = 115 M
TAS = 140 kts
W/V = 250 M/30
GS_home = 160 kts

D_ETP = (Total Dist x GS_home)/(2xTAS) = (320 x 160)/(2 x 140) = 182.8 = 183 nm

Note: 183 nm is more than half-way to B - this is to be expected as we are punching into a headwind on route to B.

Track Out = 295 M
TAS = 140 kt
W/V = 250 M/30
GS_out = 117 kts

T_ETP = D_ETP/GS _out = 183/117 = 1.56 hr = 94 min

If that is one of my questions, could you please let me know where you found it.

it is a question from casa exam one of my friend got last time he sat his exam

A minor comment, if I may.

Some of the processes we use when working the wind triangle depend, for their validity, on the wind speed's being a sensibly small fraction of the TAS. As that fraction increases, things can require a little more care and precision and, in the extreme, the solution doesn't always function well at all.

For this particular case, the wind is 30 kt, a decent proportion of the TAS. The 2 x TAS approximation for (G/S on + G/S home) is starting to unravel a little.

Suggest you rework the calculations to check out the difference. Just for interest ....

Just out of curiosity, I reworked the ETP using the actual GS_out and GS_home

Using TAS
D_ETP = (Total Dist x GS_home)/(2xTAS)
= (320 x 160)/(2 x 140) = 183 nm

Using the actual GS's
D_ETP = (Total Dist x GS_home)/(GS_out + GS_home)
= (320 x 160)/(117 + 160) = 185 nm

Absolute Error = 185-183 = 2 nm
%Error = 2/185 = 1%

An interesting exercise!

Thank you very much..planning to sit the exam this thursday.

%Error = 2/185 = 1%

Hence my comment that the approximation was starting to unravel at that sort of drift angle.

Now run the sums for larger drift angles and you can find yourself rapidly up to errors of 10% or more and the implications on flight management become significant. Generally, this is not too much of a concern for high speed aircraft - the fast jet folks commonly tend not to worry much at all about wind and just point and go - but, at the other end of the spectrum (low speed GA) the effects are much more obvious.

Hence my comment that folks need to be a bit circumspect about blindly following any approximations unless one understands and is appropriate about the application of any limitations inherent in such approximations ...

G'day John

Let me start be saying that the following does not contradict anything that you have said. I am in full agreement. I'm just looking into the practical side of the ETP (CP) calculation.

Once again, out of curiosity, I've reworked this problem with a pure 50 kt x-wind.

Let WV = 205/50
Then GS_out = 131 kt and GS_home = 131 kt .... Drift angle 21 degrees

D_cp = (Dist x GS_home)/(GS_out + GS_home) =(320x131)/(131+131) = 160 nm

Using the approximation (2xTAS)

D_cp = (Dist x GS_home)/(2xTAS) =(320x131)/(2x140) = 150 nm

Absolute Error = 160-150 =10 nm
% Error = 10/160 = 6% .... I must admit, I was expecting a bigger error.

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Playing the "devil's advocate", is 6% a significant error in the bigger picture ?

To my fading knowledge, ARFOR winds were good to within +/- 30 degrees and +/- 20 kts.
With that in mind, let us assume that the "actual" wind was 195/40 kt ..... A forecast wind error of 10 degrees and 10 kts

Then GS_out = 141 kt and GS_home = 128 kt

D_cp = (Dist x GS_home)/(GS_out + GS_home) =(320x128)/(141+128) = 152 nm

Absolute Error_wind = 160-152 =8 nm
% Error_wind = 8/160 = 5%

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Given the intrinsic uncertainty of the forecast winds, is a 6% error significant?

For the CASA exam I would use the calculated GS_out and GS_home.

In the real world, I would lean towards the simplified equation using "2xTAS"; simply because the wind errors will limit the precision of the ETP calculation.

Ah, practical things.

We need to keep very clearly in mind that there are two animals, the theory examination side of things (which is the imperative in this site) and what we might do in operations. For the students coming on, it is imperative that they understand that the two animals have some very different character elements and that the theory side of things takes precedence while they endeavour to score the necessary passes in the various theory examinations.

I'm just looking into the practical side of the ETP (CP) calculation.

And that, of course, is fine, so long as the priority thought is toward the exam.

Playing the "devil's advocate", is 6% a significant error in the bigger picture ?

For the theory exams, I suggest, very much a resounding yes. Recent experience suggests that CASA is treading the speed and accuracy line for the examinations and that the candidate necessarily needs to be more than attentive to precision and arithmetic (if not necessarily rational) accuracy. That is just the way things are and we need to live with the situation.

For me, 2% variation is the boundary between acceptable and a bit rough for general calculations as this figure accords with a number of things which apply in the certification world. I apply that figure, generally, other than for fuel quantities where we can do a tad better in our sums, I suggest. Others, of course, may see things in a somewhat different light and that, of course, is fine.

In the real world of operations, accuracy is not, of itself, the pre-eminent driver, rather that the pilot needs to have a clear understanding of what his/her calculations represent in respect of precision and accuracy. It is essential that he/she then applies those calculations and their results in an acceptable operational manner giving due consideration to regulatory requirements as published and the normal precepts of due diligence.

For this particular discussion, the concern is the relative wind strength, especially where the geometry leads to significant drift angles. The unthinking pilot is at risk of significant error with operational implications if approximations be applied blindly .

Another, reasonably extreme but nonetheless valid and illustrative, example -

TAS 100 kt (ie a typical not so startling GA performer)
W/V 360/50
TR 090

for which I figure a discrepant result in the region of 14%.

Somewhere, one needs to draw a line in the sand. I'm not too fussed exactly where (although I incline to 2% as a general aim) but, clearly, 10-15% is a bit rough around the edges ?

The prime concern is that the student should end up with the ability to understand what he/she is doing with calculations and, should there be some rubberiness, then have a very sound understanding of what variability in accuracy may exist and to what extent it might disadvantage the operational imperative on the day.