FPA correction during Cold Weather approaches

[CX-HOR]

I fly the A330 and my Company has just renewed its guidance on how to fly NPA's with cold weather altimetry corrections. As with most guidance it issues important considerations have been left out, and when questioned nothing definitive has been given.

I would appreciate if any TRI/TRE's could share what they suggest in the following example.

Flying either a VOR or RNAV approach to an LNAV only minima with temp below 0'C: Our Company guidance is to correct both minima and FAF crossing altitude in FMC. What they will not say is what correction to FPA should be applied to stay on the profile. Mathematically I would say the same correction as that applied to the altitudes, based on FPA being derived from barometric sources not purely IRS, and so also needing correcting for the cold temperatures.

ie if modifying FAF and Minima by 10% then correct FPA also by 10%. The best I could get from our training dept is "increase it a little".

So, Vilas or any other TRE out there, is there any guidance you have in this scenario?

I fully understand if temp still allows to fly to an LNAV/VNAV minima, then don't correct FAF altitude and stay in FINAL APP mode with the coded FPA if possible. What I am looking for is guidance when having to fly APPNAV/FPA modes.

[underfire]

I am sure there are quick rules of thumb, but here is Eurocontrol take:

http://i63.tinypic.com/20poe95.jpg

[CX-HOR]

Thanks Underfire,

Your formula relates to the altitude correction for cold weather.

My Company already specifies conservative corrections to be added to altitudes depending on ISA dev, what they don't say is if the FPA is also corrected by the same amount. These figures are 10% for ISA-15 and 20% for ISA-30, so are quite significant corrections.

ie In your first example for a temp of 0C at sea level you would increase altitudes (both FAF and MDA) by 6%. So if the normal FPA was 3degrees, do you fly from the corrected FAF altitude at 3x1.06? to stay on profile? This would make sense to me.

[mcdhu]

I think I'm probably being thick here, but.......
if you correct the platform altitude for temperature, you will now be flying at the correct altitude that you would be at if it was ISA temps.
Therefore, do you need to correct the FPA at all?
Dunno. Will try it in the sim.
mcdhu

[BuzzBox]

mcdhu,

Although the actual FPA remains the same, the FPA calculated by the aircraft will be different, because the ADIRS uses barometric altitude in its calculations. For example, to fly a 3° glidepath you might need to set an FPA of 3.3° on the MCP/FCU. The aircraft will think it's flying an FPA of 3.3°, but the true FPA will be 3°.


CX-HOR,

Your approximation is correct. If you need to correct the altitudes by 10%, then you should also correct the FPA by 10%. The actual calculation is:

FPA correction = arctan (altitude correction/distance to the field)

For example, let's say the glidepath is 3° and the FAF is at 1300ft, 4nm from the airfield. If you need to correct the FAF by 10%, then the correction is 130ft. According to the formula above, the FPA correction would be:

arctan (130/4 x 6076) = arctan (130/24304) = arctan (0.005349) = 0.306466° ≈ 0.3°,
so the corrected FPA would be 3° + 0.3° = 3.3°

You can get the same result using the approximation method:
10% x 3° = 0.3°

The same method also works for a 20% correction.

[Capt Fathom]

Back to the original question, where does the FPA come from? IRS or Air Data?

[BuzzBox]

From the A330 FCTM (my emphasis):

In cold weather, the atmosphere differs from the International Standard Atmosphere (ISA) conditions. The parameters computed by the ADIRS are barometric and ISA-referenced. The ADIRS use inertial data and barometric altitude to compute FPA. When the atmosphere differs from ISA, the altitude and FPA computed by the ADIRS and the associated indications on the PFD (altitude, VDEV) are not accurate.

When the temperature is lower than ISA:
‐ The true altitude of the aircraft is lower than the altitude that the ADIRS computes.
‐ The FPA the aircraft flies is less steep than the FPA the ADIRS computes.

[FullWings]

All I can say is that geometric altitude can’t arrive soon enough...

[sonicbum]

Hi CX,

all the barometric altitudes associated with the procedures will be subject to an altimeter error in cold weather ops, i.e your true altitude will be lower than your indicated altitude as you know.
When the OAT falls at 0 deg C and below you will need to apply some corrections to the different altitudes of your procedures, that is as you say the FAF altitude, the minima but the step down fixes altitudes as well. You can get the temperature corrections tables for high and low altitude in your FCOM PER-OPD-GEN-ALTITUDE TEMPERATURE CORRECTION. Airbus has removed a while back the tables for FPA modification as its usage was not practical. It is obviously quite impractical as well to temperature correct all the step down altitudes after the FAF in a NPA, therefore one method that you could use is to correct the FAF and the MDA and from there build your own descent profile, i.e check how many miles you have between the FAF and the last DME check altitude before your MDA and find out how many feet you need to lose per NM. You will definitely have a slightly steeper angle of descent.
In the calculations are correct, you will end up at your last DME check fix altitude higher of the amount of feet that are required from the above mentioned table within +/- 20 ft we could say.

[mcdhu]

Hey thanks BuzzBox. That very same paragraph is in the 320 series FCTM also.
Interesting! I get it now.
Thanks again.
mcdhu

[CX-HOR]

Thanks Sonic and Buzz for your contributions.

[underfire]

Procedure design calculates the low and high temps, based on the published FPA and ISA. NA below is 0.917 FPA, and NA above 1.13 FPA. (so, in reality, you need to correct to .917GPA to have obstacle protection, ie 2.75 instead of 3)

There are components of both temperature and altitude to consider.
http://i64.tinypic.com/4r6jb7.jpg http://i66.tinypic.com/5b1vlu.jpg

[Capt Fathom]

???????????

[sonicbum]

Procedure design calculates the low and high temps, based on the published FPA and ISA. NA below is 0.917 FPA, and NA above 1.13 FPA. (so, in reality, you need to correct to .917GPA to have obstacle protection, ie 2.75 instead of 3)

There are components of both temperature and altitude to consider.


Did not get much of that explanation either...

[BuzzBox]

Procedure design calculates the low and high temps, based on the published FPA and ISA. NA below is 0.917 FPA, and NA above 1.13 FPA. (so, in reality, you need to correct to .917GPA to have obstacle protection, ie 2.75 instead of 3)

There are components of both temperature and altitude to consider.

If I'm not mistaken, those formulae relate to the calculation of the minimum temperature requirements for RNP-AR approaches (ie Special Aircraft and Aircrew Authorisation Required), using Baro-VNAV to LNAV/VNAV minima. When flying such approaches, the DA must be corrected for temperature, but the FAF does not need to be corrected because the final approach path vertical angle (& obstacle clearance) is safeguarded against the effects of low temperature by the design of the procedure. The formulae are described in the following document:
http://www.faa.gov/documentlibrary/media/order/nd/8260_52.pdf

CX-HOR's question related to approaches that are flown to LNAV minima, without vertical guidance, where the pilot controls the vertical profile by selecting an FPA on the autopilot MCP/FCU. In cold temperatures, the aircraft's actual FPA will be less steep than the FPA computed by the ADIRS. In such cases, the pilot should select a higher FPA on the MCP/FCU to ensure the aircraft flies the required FPA, as described above.

[sonicbum]

When flying such approaches, the DA must be corrected for temperature,

Hi Buzz,

RNAV(RNP) usually always have a range of useable temperatures or at least the minimum useable temperature for the procedure, as for example in Kathmandu RNAV RNP RWY02.
No corrections are required to any altitude, include the DA.

[FlightDetent]

No corrections are required .... include the DA. Is that so? For starters, the procedure is published with OCA, not DA, innit?

[BuzzBox]

Hey Sonicbum,

The rules might be different in the US, but my understanding is that when approaches are designed to PANS OPS criteria, the temperature limitation only prevents the angle of the final approach path from becoming too shallow. Pilots still need to correct the DA to ensure sufficient obstacle clearance at the minima.

According to PANS OPS Doc 8168 Vol 1:

Part II FLIGHT PROCEDURES - RNAV AND SATELLITE BASED

Section 4 - Approach procedures with vertical guidance

Chapter 1 - APV/Baro VNAV approach procedures

1.4 OPERATIONAL CONSTRAINTS

1.4.1 Pilots are responsible for any necessary cold temperature corrections to all published minimum altitudes/heights. This includes:

a) the altitudes/heights for the initial and intermediate segment(s);

b) the DA/H; and

c) subsequent missed approach altitudes/heights.

Note.— The final approach path VPA is safeguarded against the effects of low temperature by the design of the procedure.

[sonicbum]

Hi Buzz,

from the ICAO RNAV (RNP) procedure approach design :

"The low temperature limit assures
obstacle protection for the lowest expected temperature and prevents the effective VPA from going below 2.5 degrees.
ISA for the airport may be calculated using the following formulas. (etc..)"

According to the above you are obstacle protected at the promulgated altitudes, therefore I do not see the reason to correct the DA.

Reference RNAV RNP APPROACHES DESIGN MANUAL (http://www.icao.int/meetings/pbn-symposium/documents/9905_cons_en.pdf)

[underfire]

You dont need to correct anything if you are within the temp limits, that is why the chart states uncompensated baro VNAV and there is NA below and NA above. (where ICAO goes to 2.5, FAA goes to 2.71)

Post #12, which no one seems to understand, includes the calculations, should anyone want to understand the temperature limits/protection, as well as how to compensate for temperatures and adjust the FPA accordingly. (ie if you want a 3 degree FPA and the temperature is this, here is the difference)

In the procedure design, you are protected within the limits of the procedure, but outside the procedure, you need to provide corrections. The includes temperature and the effect of turns. I suppose turn protection would be a matter for another topic.

[FlightDetent]

Thank you Buzz for the reference.

Sonic and Underfire: I understand you saying there is no geometrical reason to increase published values in order to maintain the obstacle clearance. Is that right?

The DA, pardon my ignorance, is not published in the AIP and not calculated by the procedure designer.

[underfire]

I think that needs more detail. If you are within the NA abv/bel, then no, you do not need to add or subtract anything. This is calculated by the procedure designer to work within the min GPA to maintain obstacle clearance. Depending on the design, temperature and turn corrections may be included in the design.

DA not published in the AIP? I would guess that you are looking at a particular design. DA/MDA are always calculated by the designer using obstacles in either the approach or the missed approach.
If you are saying that when MDA is shown, DA is not calculated, I suppose that is true, and it leaves it up to the pilot to make sure that the decision altitude is high enough so that with momentary descent, MDA surface is not encroached.

[BuzzBox]

Hi Sonicbum,

"The low temperature limit assures obstacle protection for the lowest expected temperature and prevents the effective VPA from going below 2.5 degrees.
ISA for the airport may be calculated using the following formulas. (etc..)"

That quote comes from a section titled 'Effect of temperature on VPA'. I agree, the low temperature limit ensures obstacle clearance during the final segment by stopping the flight path angle from going below 2.5° (PANS-OPS). But what happens when you arrive at the DA? Under PANS-OPS, the DA is based on a minimum OCA/H of 75m/246 ft. The minimum OCA/H is based on a minimum obstacle clearance (MOC) of 75m/246 ft during the final approach. If you don't correct the DA for low temperature, then you won't have the required MOC when you arrive at the minima.

Some of the information published by the various regulators is confusing and contradictory regarding temperature correction requirements. However, Transport Canada's Advisory Circular 700-024 Required Navigation Performance Authorization Required Approach is very clear. It states the following:

5.2 (10) Navigation System without Temperature Compensation. For aircraft without temperature compensation capabilities, the operation must occur within the temperature limits (TLim) published on the approach chart. Despite being uncompensated, the baro-VNAV path in the final segment will provide the required obstacle clearance. The flight crew members must correct, as required, for the cold temperature effects on minimum altitudes such as IAF, IF, FAF, DA, MA and MSA. In below ISA temperatures the baro-VNAV path will cross the FAF at an altitude below the temperature-corrected FAF crossing altitude. It is permissible to follow the baro-VNAV path from the temperature-corrected intermediate segment altitude.

https://www.tc.gc.ca/media/documents/ca-opssvs/AC_700-024_issue_2.pdf

[underfire]

The DA taken into account the cold temp limit GPA with the associated obstacle clearance.

Under PANS-OPS, the DA is based on a minimum OCA/H of 75m/246 ft. The minimum OCA/H is based on a minimum obstacle clearance (MOC) of 75m/246 ft during the final approach
The operative word here is minimum. In reality, it is a 200' ROC with a 50 foot momentary descent, that is a DA. (slightly different for PANS-OPS) The ROC is a sloping surface, different from the GPA, sloping from the TCH (150' ROC with 50' TCH) to 500 feet at the FAF. As noted by the text, the cold temp limit is accounted for in the calculations.

http://www.airspaceusa.com/images/VNAV_PROFILE.gif

Minimum Sector Altitude

Currently, there is not a European-wide common procedure to deal with adjustments to Minimum Sector Altitudes (MSAs). Some regulators do not specify adjustments to MSAs and consequently ATC providers do not apply a temperature correction to published MSAs for cold temperatures. It is the flight crew reponsibility according to the provisions of ICAO PANS OPS referred above.
Some operators advise flight crews to add 1000 ft to the MSA when the temperature is - 30 °C or colder. (RAF FIH)

Minimum Vectoring Altitude

MVAs are established for use by the Air Traffic Controller (ATCO) when Air Traffic Control (ATC) provide a surveillance service (usually radar). Each MVA chart contains sectors large enough to accommodate the vectoring of aircraft within the sector at the MVA. The minimum vectoring altitude in each sector provides 1000 ft above the highest obstruction in non-mountainous areas and 2000 ft above the highest obstacle in designated mountainous areas.
According to ICAO PANS OPS, minimum vectoring altitudes shall be corrected for temperature. The temperature correction shall be based on seasonal or annual minimum temperature records. In turn, ATC authorities are required, as per ICAO PANS ATM, 8.6.5.2, Note 2, “to provide the controller with minimum altitudes corrected for temperature effect”

[BuzzBox]

Underfire,

Call me thick, but I'm not sure I understand your explanation. I am, after all, a simple pilot.

Let's say we have an approach to a sea-level airport, where the low temperature limit is -20°C. Are you saying that the OCA/H is calculated to ensure the minimum obstacle clearance of 75m/246 ft at the OCA/H is achieved at -20°C, and at higher temperatures the actual obstacle clearance would be greater? In other words, assuming no obstacles, the OCA/H would be something like 286 ft, providing at least 286 ft obstacle clearance at temperatures greater than 0°C and a minimum of 246 ft at -20°C?

[Chesty Morgan]

That's what he's saying.

[underfire]

What I am saying is that the minimum obstacle clearance already takes into account several factors, one of which is the temperature correction.

Another factor, with the design criteria, there are no corrections for turns, which is why the FAA states no turns inside the FAF (unless specially designed). The taper to 500' ROC is one attempt to blanket in turn corrections before the FAF.

There are factors accounting for the accuracy of the nav system/gps.

With the ILS, many factors do not need to be accounted for, and that is why the min ILS is a 150' ROC with 50' momentary descent, or the 200' min.

This may help as well

Vertical Error Budget (VEB).

The VEB is a set of allowable values that contribute to the total error associated with a VNAV system. Application of equations using the VEB values determines the minimum vertical clearance that must exist between an aircraft on the nominal glidepath and ground obstructions within the OEA of instrument procedure segments. When the VEB is used in final segment construction, its application determines the OCS origin and slope ratio.

http://i63.tinypic.com/242c2go.jpg or just give you a headache!

This is from Eurocontrol:
http://i65.tinypic.com/120s4yc.jpg
http://i63.tinypic.com/2lc8h8n.jpg

[FlightDetent]

http://www.ead.eurocontrol.int/eadbasic/pamslight-AF034544E381C3B848CD9EC7CD05A960/7FE5QZZF3FXUS/EN/Charts/AD/AIRAC/EG_AD_2_EGCC_8-14_en_2016-03-31.pdf

no (M)DA.

[underfire]

buzz...wanted to show a basic for the DA and OCS.

The obstacle evaluation surfaces for an aerodrome are fixed. If the procedure is outside of this, you must provide evaluations. Procedure design wants to avoid this, as then, every cycle, the obstacles must be evaluated.

Note that for the OCS, it is a fixed surface. This surface takes into account the low temp limit (FAA 2.71 eff GPA, and 2.5 effective GPA ICAO) ie the surface does not vary with the effective glideslope.
http://i66.tinypic.com/2j0l4dh.jpg

The DA is set by the controlling obstacle. (there are seldom obstacles in the approach, so the DA is usually set by an obstacle in the missed)When there are, it is typical to raise the HAT, hence the DA as illustrated.
http://i63.tinypic.com/2j2vo2a.jpg

This shows an obstacle in the missed (as well as the DA vs OCS, with momentary descent)
http://i63.tinypic.com/9sz2hj.jpg

In a design, when you have turns, you have to adjust the surface to take into account the turn. While this appears simple, it is actually incredibly complex due to the body geometry of aircraft in a turn and the turn methodology between aircraft.
http://i67.tinypic.com/nch15c.jpg

Enjoy!

[oggers]

...none of which has anything to do with the OP which buzz-box correctly and succinctly answered with his very first reply in post #5 after you failed to read the question and gave a superfluous and incorrect answer.

[underfire]

response to buzz box if you can read and comprehend.

Since the OP's question was about cold weather correction standards, the actual calculations should be considered.

[Potsie Weber]

FPA adjustments are still in our manuals

[Capn Bloggs]

Adjust the FPA during the approach if the ISA deviation changes down final... are they serious?!

[FlightDetent]

Bloggs, I read it differently. They suggest that if the (corrected) FPA would bring you below the minimum altitudes, you do something about it. Correct the corrected ;) Why the need for such statement is altogether a different thing.

Now, with the ISA dev being different between the points of measurement i.e. airport thermometer vs. aircraft static port, you put quite a can of worms on the table!

Case 1: -05 AD OAT, FG OVC001, temp. inversion at 1200 feet and 45 kt winds aloft at 3000 AAL. - - - no, I refuse to open that one :*

[oggers]

underfire:

Since the OP's question was about cold weather correction standards, the actual calculations should be considered.

The OP's question was specifically about adjusting the FPA when flying a CDFA to a non-precision approach with LNAV minima. All the stuff you have pasted is about ensuring obstacle clearance when designing an approach with vertical guidance, or simply applying a cold weather altimeter correction which is not what was asked.

response to buzz box if you can read and comprehend.

Yes but the problem is that when buzzbox wrote...

"the temperature limitation only prevents the angle of the final approach path from becoming too shallow. Pilots still need to correct the DA"

...he was correct, whilst your response is incorrect:

You dont need to correct anything if you are within the temp limits, that is why the chart states uncompensated baro VNAV and there is NA below and NA above.

The FAA states in NTAP US Cold Temperature Restricted Airports:

"Pilots must use the corrected MDA or DA/DH as the minimum for an approach...The temperature restriction at a "Cold Temperature Restricted Airport" is mutually exclusive from the charted temperature restriction published for "uncompensated baro-VNAV systems"

That is, pilots have to correct the DA anytime it is cold enough, as defined in the US by the list of Cold Temperature Restricted Airports, and none of the formulas for designing an APV approach you have pasted here override that simple requirement. eg:

KTVC cold weather temperature restriction = -14ºC
RNAV RWY 10 uncompensated baro-VNAV NA below -19ºC

...correcting the DA is mandatory below -14 whilst you can still fly the baro-VNAV.

[Kazume]

Hi all! Sorry I'm busting in here, but seriously, this thread is pretty much the only useful one I found while googling 3 days straight looking for a formula on how to calculate FPA temperature corrections.

@BuzzBox

FPA correction = arctan (altitude correction/distance to the field)

Could you tell me where you got this? Thx in advance ...

[FlightDetent]

Trigonometry, no offence intended, just draw the two triangles. Mathematically precise: FPA corrected = arctan (height corrected/ distance to aimpoint).

[Kazume]

Well, I've been looking at it and isn't the correct formula like this:

https://docs.google.com/drawings/d/12d3KBeB5heSxkyR4qeDIVXKNh6FdK9N8mpz9v4x12Hk/edit?usp=sharing

?

But I suppose the more simple formula comes from small-angle approximation?

Edit: ok, I just saw you actually put height corrected instead of height correction. That kinda was the thing I was wondering about in BuzzBox's post.

Thx!

[FlightDetent]

Neat drawings!

[peekay4]

Kazume looks like you're correcting height above FAF but not the threshold height.

Also I believe just proportionally correcting the FPA as suggested in the original post yields approximately the same answer... e.g. if the FAF correction was 10% then simply correct the FPA by 10% as well.

However the drawings aren't representative of what's actually happening, and I think these approximations may slightly underestimate the required FPA (so you'll tend to end up a little high).

[Kazume]

However the drawings aren't representative of what's actually happening

I'm curious, peekay4 ... apart from the approximation of using the threshold instead of the touchdown point (I could increase x by 954ft for a 3° (= 50ft / tan (3°) ) to get rid of that approximation?), how is the drawing not representative of what is actually happening?

I've tested my way of calculating with a specific example and compared it to the result when using the formula BuzzBox gave and although the difference is small indeed, it is there. LOWW RWY 34, 2400ft height on a 3° GP yields 3,27° vs 3,22°.

The reason I'm interested in getting the most accurate way of calculating this whole bit is because I'd like to write a small app that does those corrections for me. So all inputs are highly welcome ...

[FlightDetent]

... looks like you're correcting height above FAF but not the threshold height. Surely you do not mean to correct the threshold elevation? But what then, exactly?

[peekay4]

What we have is an approximation assuming a linear geometric flight path from (linearly) corrected altitudes.

But that's not what's actually happening. With corrected altitude the plane is physically flying at H, not (H+dh) as in the graphs. What has changed is the air density, and the density gradient is nonlinear.

Plus the gradient itself changes with non-ISA conditions, while an uncorrected FMS will always assume ISA pressure gradients.

So basically the plane is flying a non-linear "barometric" flight path using the "wrong" (ISA) pressure gradient. Hence a geometric interpretation based on straight ratios can only yield approximations.

Here's a table from Transport Canada showing true descent angles for some non-ISA temperatures (sea level):

http://i.imgur.com/MByqb2s.png

What we want to find is the "inverse" of the above, but I think you will find our simple linear geometric models don't quite "match up" to the actual angles.

[FlightDetent]

Kaz: Easy on yourself, use distance to THR and TCH of 50'. It follows the way the approaches are designed and actually flown - so not an oversimplification at all.

FPA.corrected = arctan [ (x+y) / dist.to.threshold ] where

y = FAF.alttitude - (THR.elevation+50ft)
x = ALT.correction.over.FAF /properly calculated from FAFalt-ADelev/

[Kazume]

Thx for the inputs!

@peekay4

As far as the density gradient not being linear is concerned, there's probably no way around that approximation. After all, the ICAO doc 8168 seems to create its height correction tables on an assumed linearity as well, so I guess this is will be close enough for a corrected FPA too.

I still would think that even when some of these calculations are based on approximations they still should be more accurate than a simple rule of thumb.

Your "What we want to find is the "inverse" of the above" got me thinking though (tell me if that's closer to what you suggested): if I want to correct the (wrong) height to reach the charted height, I've got to tackle the problem "from below" (as in, how much do I need to increase the altitude on my altimeter to actually fly the charted height), so instead of putting the dh correction on top of H, I've changed my drawings (https://docs.google.com/drawings/d/12d3KBeB5heSxkyR4qeDIVXKNh6FdK9N8mpz9v4x12Hk/edit?usp=sharing) to add dh to the pressure altitude so as to reach H after correction. And after adding the threshold-to-TD correction I get similar results to those from the more simple formula suggested earlier.

@FlightDetent

Isn't going all the way to TD the more clean way to calculate this? Going all the way down to height 0 eliminates the need for another correction at threshold height (again, based on approximations, however small).

Funny thing about these FPA corrections is that our company has removed the table from the QRH, apparently after someone had messed up after using it. We're now to make the corrections to the FPA "as appropriate" :ok:

[peekay4]

Kazume in the 8168 correction formulas the temperature is assumed to be linear with height, but not the pressure / density factor (which it is essentially calculating).

Hence the formulas aren't in the form y = mx + b, and if you look at the correction tables, the resulting values are non-linear.

I think the idea is to make a conservative estimate and leave it at that.

[Kazume]

As far as the FPA is concerned, does that mean - in your opinion - that it is better to guess the corrected value rather than calculate it using a formula (with linearity assumption)?

[peekay4]

Ideally neither. The FMS should handle cold weather compensation, including flight path corrections as necessary. In fact here in Canada it's required that all new or updated FMSs have cold weather compensation built-in.

As such there is an accepted ICAO-blessed algorithm used by FMSs to compute these corrections, published as part of the PBN RNP standards. Unfortunately I don't have access to these standards to read what they say, but may be you can get them from your company. The algorithm might be a simple linear approximation, but maybe not.

[Kazume]

I'll see what I can get from my company (the best I got so far is "it's really complicated" and getting redirected to someone else). I'm finding this a very intriguing topic. The deeper you dig, the more you realise it seems to be a really deep pit :P