Why are the altitudes and distances in the profile view different when calculated with the fpm values in the conversion table on Jeppesen charts? To put it more simply, I find the distance between points according to the speed-fpm table, in how many minutes I will fly. I multiply the minutes I find by the fpm value in the conversion table. But I get values lower than the altitude difference between points and these values may vary in different calculations. To give an example from the image, an airplane flying at 90 knots will fly 3 DME in 2 minutes. If it descends at 478 fpm, equivalent to 90 knots on the conversion chart, it descends 956 feet in 2 minutes (2x478=956). The descent in the 3 DME should be 987 feet (3000-2013=987) in the profile view, while the descent calculations given in the conversion table should be 956 feet. Where did the 31 feet in between go? Or is there an intentional reason for this? I would be glad if you help. The image is taken from page 11-1 of "LTBU" code Corlu Ataturk airport Jeppesen chart.
Why are the altitudes and distances in the profile view different when calculated with the fpm values in the conversion table on Jeppesen charts?
$\begingroup$ I think the problem may be an incorrect assumption about the 3,000'. The 2013' and 740' heights are precise surveyed heights at the respective DME distances. But the chart very specifically avoids calling out a specific height at D7.6. The assumption is that you'll be level at 3,000', and that altitude intercepts the GS at a distance that equals D7.6, rounded to the nearest 10th. If they intended to imply the precise altitude at D7.6 was exactly 3,000, they would have marked it accordingly. Your 31 feet of error represents intercepting the GS about 4 or so seconds after passing D7.6. $\endgroup$– Max RFeb 14 at 4:05
$\begingroup$ If your approach was correct, my calculations for the distance between 2013 and 740 feet should have been accurate. But unfortunately, there is a difference of 30.2 feet again. Considering that we descend at 90 knots ground speed, according to the conversion table, we will fly the distance of 3.9 DME in 2.6 minutes (3.9/90 * 60 = 2.6). If we descend at 478 fpm in 2.6 minutes, we descend 1242.8 feet (2.6*478=1242.8). This means that we will be at an altitude of 2013-1242.8=770.2 feet. But we should have been at 740 feet. The difference is 770.2-740=30.2 feet! @MaxR $\endgroup$– pilot162Feb 14 at 6:57
$\begingroup$ Moreover, if you hold a GS of 3.00° from 2013' to 3000', it will require you a distance of 3.10 NM to do so, and not 3.00. The chart probably accounts for some inaccuracies. $\endgroup$– Al-QorasaniFeb 14 at 8:15
So, I decided to just start from scratch and build a model that started at the TDZ and worked back out. I wanted to determine what would happen if the DME antenna was not precisely collocated with the Glide Slope antenna. I wanted to take into account the slant-range error endemic to DME as well.
As I tinkered with the model, what I stumbled upon is that when I input 3.00° GS, I got the kinds of errors you were describing. But when I solved for minimum error, guess where I ended up? At 3.09° GS, the slope that was actually published on the plate as the non-precision LOC GS.
Here's the data. Note that I used the DME slant range and not the horizontal ground distance, in my altitude computations. Also, I used the plate's 508' elevation for the baseline, whereas the airport charted elevation is 570'.
Table 1 - 3.00° GS
|Degrees||DME||DME Dist||Horiz Dist||Alt AGL||Alt MSL||Expected||Height Error|
Table 2 - 3.09° GS
|Degrees||DME||DME||Horiz||Alt AGL||Alt MSL||Expected||Height Error|
I post this as an "answer" because I needed the space and table capability that the answer block provides... But I acknowledge that this doesn't answer the question of "why?"
1$\begingroup$ +1, this actually makes perfect sense: the exact altitudes are only relevant for the LOC approach (with 3.09° slope). On the ILS you don't care about exact altitude, you just follow the GS (cross-checking altitude is still important, but not at this accuracy). $\endgroup$ Feb 17 at 17:48
$\begingroup$ Your approach to the question and your effort are very good. However, despite all these calculations, I still do not understand the 2-3 feet margin of error, even if it is small. I think the most summary conclusion that can be drawn from these calculations is this: DME-Altitude values seen in the profile view section of the approach represent the LOC approach, not the GS approach. By the way, you mistyped 505 where you wrote "plate's 505' elevation", could you please correct it to 508'? Thanks for everything. $\endgroup$– pilot162Feb 17 at 19:15
1$\begingroup$ @pilot162 As I mentioned in my first comment, I don't see the 3,000' altitude as being "authoritative" whereas I agree the 740 and 2013 should be spot-on. So when I focus on those two, I can arrive at a zero-error solution by making (a) tiny adjustments to the ILS GS angle, and then (b) moving the location of the DME antenna some number of feet forward or aft of the GS antenna. The GS slope through both points is 3.0794°, and the DME antenna would be about 65 feet from the ILS antenna to create a zero-error result, with 7 feet of error at intercept. $\endgroup$– Max RFeb 17 at 21:30
1$\begingroup$ @pilot162 I'm still tending towards Bianfable's thoughts as well, that the shown heights are for the LOC approach and are not intended to make any exact statement for the ILS. In fact, there could be small distance differences between the designated touchdown point, used in calculating the LAC non-precision descent, and where the ILS antenna actually ended up being located. And remember, they are rounding DME distances to +/-0.05nm (300'), altitudes to +/-0.5 feet, and glideslopes to +/-0.005°. There's some play in the solution that we just have to accept as margin of error. That's a D $\endgroup$– Max RFeb 17 at 21:34
1$\begingroup$ Hint: You need to take the curvature of the earth into account if you want to improve the altitude accuracy. As far as I can see you have used a flat earth model. $\endgroup$– DeltaLima ♦Feb 18 at 12:25