Bank Angles (1) and TCAS (2)

[simonijs]

Hello Hardy,

May I bring up two – completely different – things in just this one post?

For a long time, I noticed that sometimes the bank angle (in LNAV) is "excessive" for the required heading (or...: track) change. Sometimes, because it does not happen all the time.
Example 1: WPT A was approached on a magnetic heading of 207, the next magnetic outbound heading was 210. For a heading change of only 3 degrees, the aircraft rolled nearly 15 degrees to the right that caused an overshoot of the new track. For this to correct, rolling to the left was required to finally capture the outbound track from the last waypoint.
Example 2: WPT B was approached on a magnetic heading of 206, the heading to turn to after this waypoint was 203. This time, the aircraft only banked by a maximum of 4,5 and no corrective turn was required at all. Both turns were recorded by PSX's FDR.
I have seen bank angles of close to 20 degrees for similar small changes in heading. My rule of thumb for our students was to not bank by more degrees than the number of degrees for a heading/track change: so 5 degrees of heading change; do not bank by more than 5 degrees. 10 degrees of heading change; do not bank by more than 10 degrees. Up to the point of maximum bank which for these Seneca-type of aircraft was the Rate-One-Turn (en route: approximately 20-22 degrees).

Re TCAS, I do like the random offset of opposite traffic when I use an offset myself. Thanks for that!
Most airspace these days is RVSM where the next "same direction" traffic would be either 2000 ft above or below. PSX-generated opposite traffic, however, seems to occupy the next higher or lower "same direction" levels designated inside RVSM airspace, i.e. almost always 2000 ft above/below instead of 1000 ft above/below. Would this be easy (as well) to implement? Could it possibly be coupled to pilot selection of the "Step Size" on the CDU: 1000 ft - No Opposite traffic (North Atlantic Tracks, for example); 2000 ft - RVSM airspace; ICAO - outside RVSM airspace (Polar Regions)?

And is it correct that PSX-generated traffic, causing an RA, is not responding with an opposite manoeuvre; so once I get a climb RA, is the other traffic then receiving a descent RA or no RA at all?

King regards,
Simon

[Hardy Heinlin]

Hi Simon,

the turn guidance algorithm is very complex. It seems easy to guide a vehicle along an arc like a train on rails, but trying the same with a flying aircraft is impossible because an aircraft cannot fly a constant radius during the entire turn; there's always a smooth, gradual transition from the straight track to the target turn radius, which results in an exponential curve, and then the same transition vice versa from the turn back to the straight track. Because of this complex geometry, the LNAV guidance computer uses three phases: The turn anticipation phase, the turn phase, and the wings-level anticipation phase.

And because this is so complex and difficult to coordinate under any groundspeed, wind, and weight conditions, it may happen that sometimes an anticipation phase won't look 100% perfect.

I have further fine-tuned this stuff a few times over the past 4 years. It's a never ending story ...

I'm not sure if I can apply your Seneca-type bank angles here. The turn radius is a square function of groundspeed (or TAS when referring to the air mass alone), and when you increase your speed above a Seneca-typical speed, your turn radius will increase enormously while keeping the same bank angle. If you then decrease the bank angle, the radius will increase even more.

In fact, the real FMC draws a larger turn radius on the ND for small course changes in cruise. I haven't yet implemented this detail because it causes difficult side effects, e.g. on short legs the turn will be longer than the actual leg distance.

PSX-generated opposite traffic, however, seems to occupy the next higher or lower "same direction" levels designated inside RVSM airspace, i.e. almost always 2000 ft above/below instead of 1000 ft above/below. Would this be easy (as well) to implement?

Yes, easy.

And is it correct that PSX-generated traffic, causing an RA, is not responding with an opposite manoeuvre; so once I get a climb RA, is the other traffic then receiving a descent RA or no RA at all?

The TCAS commands of the other aircraft will be coordinated with your TCAS commands, therefore the other aircraft will escape correctly indeed. So, yes, it does respond correctly. You may see this in the Rio approach situation. Only if you run one of the "red" training scenarios ("intruder ignores RA") the other aircraft will always escape in the wrong, opposite direction.


Cheers,

|-|ardy

[IefCooreman]

there's always a smooth, gradual transition from the straight track to the target turn radius, which results in an exponential curve, and then the same transition vice versa from the turn back to the straight track.

Aerowinx off-topic, but theory on-topic:

This is almost the same for train tracks. The actual turn section of a train track is preceded and followed by a section where the radius changes from infinite (straight) to the value of the turn radius, and at the end back to infinite radius. Back in the days this was a parabolic section, modern computers allow the use of a hyperbolic section (I think it is... my memories are fading).

Just for info :-)

[simonijs]

Hi Hardy,

Yes, I am familiar with this formula (turn radius, rate of turn, etc.). And all of a sudden I remembered the "S-turns across a road", a long long time ago. Quite a challenge to fly them properly with only 20 logged hours or so...
I do understand that the turn guidance algorithm is complex, and that changing factors do influence it to some extend. But under circumstances that are rather similar (Example 1: weight 274T, GS 466 kts, W/V 256/34, SAT -51; Example 2: weight 267T, GS 471 kts, W/V 256/33, SAT -55) I was expecting to see more or less the same behaviour of the LNAV Guidance Computer for a heading change of only 3 degrees. But good to know that you have looked into this already.

Re TCAS: great if this RVSM-method can be implemented. Hopefully other forum members won't disagree...

So, yes, it does respond correctly.

I was asking, because I found the altitude deviation from the original FL to be quite excessive, also busting through other flight levels until the "Clear of Conflict" sounded. One time, testing this out, I was receiving a Climb RA from a same-level-intruder, which I ignored. The other traffic was not descending either. Two obstinate persons...
From Eurocontrol documents, I understood that a deviation of no more than 300-400 ft - by each aircraft receiving the RA - would be required, causing a total vertical separation of 600 - 800 ft. Enough for a "Clear of Conflict".

Kind regards, and thanks for your reply
Simon

[Hardy Heinlin]

In PSX update 10.36, random non-conflict TCAS targets on our airway now use 1000 ft vertical separation even at high altitudes when our FMC uses a step size of 1000:

http://aerowinx.com/board/index.php?topic=4191.0


|-|ardy

[simonijs]

Thanks for 10.36 and all adjustments that it contains.

Regards,
S.

[Hardy Heinlin]

I made a mistake; the reference in our FMC should be 2000, not 1000. For 1000 ft separation the step size is 2000.


|-|