Mandatory PBN training (merged)

“the effects of gravity on time according to general relativity.”

And doubtless speed.

Well, while we’re calculating gravitational influences, why not include atmospheric refraction?
That’s a standard geodetic consideration for light, and while the refractive indices will be different for that wavelength, they will have a far greater effect than that of gravity…

Worse, they will be random, given the temporal dependency on the atmospheric variables; air pressure, temperature and humidity…

In 3D space, it doesn’t matter if the flight path is a curve or straight line in either Euclidean or Geodetic space, as long as the Navigation System is calculating everything in a common coordinate system, to which all these vectors have already been properly converted.

Adding to the chaos, are the runways fully mapped in 3D? Or are only the endpoints mapped? Hardly anyone really lands before the numbers.

Peter wrote:

I do expect you to calculate the curvature of the glideslope due to relativistic effects.

That is surprisingly easy and can be done using basic velocity equations, at least over the distances involved here, and the number 2 in weak gravity fields.

A photon needs ~0.0000309 seconds to travel 5 nautical miles [9260 m, divided by ~300,000,000 m/s]

Simply using good old Newtonian gravity and equivalence of acceleration and gravity, light gets accelerated “downwards” at a rate of 9.81 m/s, and because of that it gets deflected downwards by ~0.00000001 (or 1E-8) metres. [ distance = 1/2 acceleration x time squared, so 1/2 3.09E-5 × 3.09E-5 × 9.81 = 9 * 9.81 * 5E-10 = 9.37E-9, round to 10E-9 or 1E-8 ].

Then all you need is the simple knowledge that under General Relativity, the actual deflection is twice that predicted by Newtonian gravity, at least while you are in a weak gravity field such as the Earth’s. So unless you are flying the ILS on a Neutron star, just multiply by 2.

So 0.00000002 (or 2E-8) metres, or 0.00000074 (7.4E-7) inches.

So my jocular guesstimate on the prior page of 0.00002" (2E-5) was off by two orders of magnitude… oh dear!

This is simple because over the distances involved here one can simply use these formulae, which assume gravity acts perpendicular to the ILS beam, and also that it is parallel to the earth; if you want to fly an ILS from the moon it gets more complicated. And Einstein did all the hard work to get to that factor 2 over a century back. For the Neutron star ILS, you will have to calculate your own factor using the more complicated Schwarzschild solution to Einstein’s field equation.

@AF, over to you for the atmospheric refraction…

I think there are too many engineers on this forum

Now I am disappointed that my 500eur EASA approved PBN course did not cover the effect of gravity on light.
Would the European airspace ever be safe without this forum?

If you were taking off from a Neutron star, and the aircraft were on a travelator….

Peter wrote:

How can a straight line which is above the surveyed glideslope be approved or unapproved?

Peter,

The issue is that there is not a surveyed path below the MDA. Hence the advisory glidepath only applies to the portion of the descent between the FAF crossing height and the MDA where the descent is protected. It is not protected below the MDA.

The Advisory glidepath is not just a Garmin or Jeppesen thing. It is an option provided for in the TSO and described in RTCA DO-229C/D.

There is quite a history with the handling of advisory glidepaths. At one point in time, almost all RNAV GPS straight in approaches had an advisory glidepath. The admonition was that it was only to be used above the MDA. But pilots were following it below the MDA and in some cases hitting stuff. So Flight Test started checking below the MDA and found issues on some procedures. They brought the issue to the ACF/IPG (Aeronautical Charting Forum/Instrument Procedures Group). The FAA changed its process and Flight test added notes to the procedure documents (8260) when they could not fly a +V path to the threshold without having to maneuver to avoid obstacles. The VDA (Visual Descent Angle) and TCH (Threshold Crossing Height) were then removed from the affected charts and a note was added “Descent Angle NA” in the profile view. In addition, if there was an LP included with the LNAV, the LP is a WAAS approach and has a FAS Block defining the path. In a misguided attempt to block GPS/FMS systems from using the +V on these procedures, the VDA was coded to a value of zero as a code, not an angle. This caused serious unintended consequences to the Garmin GPS systems (excepting the GNS480) in that the code used the VDA in a calculation as a divisor and a machine check of divide by 0 would occur. Not a good thing to happen on an approach to have your GPS reset. Garmin’s only immediate resolution was to pull any of the affected procedures (about a 100) from the database. Garmin eventually fixed the software and re-enabled these procedures, but it took almost 2 years for most of their systems to have an upgrade available. Then the FAA changed their mind and the note on the chart to read as “Visual Segment – Obstacles” and added the VDA back into the FAS for the LP procedures. Garmin also added +V for LP procedures in a later software update. Jeppesen took the position that if the FAA included the VDA and TCH in its 8260, then they would add the +V. That is where we stand today, so depending on if the new note is on the chart and not the old note, +V will be available in the Jeppesen database. So in the US, you had damn well better understand that +V is different than LNAV/VNAV or LPV and not to use the +V below the MDA.

NCYankee wrote:

But pilots were following it below the MDA and in some cases hitting stuff. So Flight Test started checking below the MDA and found issues on some procedures. They brought the issue to the ACF/IPG (Aeronautical Charting Forum/Instrument Procedures Group). The FAA changed its process and Flight test added notes to the procedure documents (8260) when they could not fly a +V path to the threshold without having to maneuver to avoid obstacles.

This caused serious unintended consequences to the Garmin GPS systems (excepting the GNS480) in that the code used the VDA in a calculation as a divisor and a machine check of divide by 0 would occur.

Really sloppy software design if that could happen. Input data validation, anyone…..

Many thanks NCYankee for your explanation.

I would have never expected to be able to fly the +V glideslope below the MDA, and it surprises me that this bit didn’t get through to some pilots.

Peter wrote:

I would have never expected to be able to fly the +V glideslope below the MDA, and it surprises me that this bit didn’t get through to some pilots.

US pilots do not have training mandated. Too many think it is an equivalent to an ILS.Airborne_Again wrote:

Really sloppy software design if that could happen. Input data validation, anyone…

Definitely, but the value of zero as a code was not part of the specification and invented without checking the impact on the only real provider of support for LP, so you would have thought that the FAA would have checked with the inclusion of the zero code point. I objected at the time it was suggested as zero is not an angle and the field did not allow for codes, just values of angles.