Aussie climb gradients and obstacle height

[sru]

Hi all perf / math people,

1. Given the following, is it possible to calculate the height and distance to the limiting obstacle:-

TODA 1960 (4.49%)……. (full length, climb gradient required to clear obstacles)

STODA 1951 (3.33%)
1934 (2.2%)
1916 (1.6%)

My thoughts are that all combinations of reduced runway length vs. climb gradient should all intersect at the same point (for the limiting obstacle)

2. Is this valid?

3. If it is valid can I work out this intersection point to answer # 1?

I have (I think :ugh:derived my own equation) but would like to validate it.:sad:

Ideas welcome, PM me if you need further info.

Thanks to all that read,
SRU

[Old Smokey]

I don't have a calculator with me to work out the result/s, but..........

If there was only one limiting obstacle (rare), YES, you may by simple geometry calculate the exact height and distance of that one obstacle.

The problem with Australian RDS data, you don't know how many limiting obstacles there are, and, in fact, each of the gradients published may have "their own" obstacle, but all is not lost. By calculating the intersection of each successive STOD or TODA gradient, you may construct a SERIES of intersections, thus creating an Obstacle Polygon, where the intersections are actually "phoney" obstacles, but SAFELY above all REAL obstacles. So there, now you have a series of obstacles to play with.

One very important final consideration in constructing an Obstacle Polygon is that for all Obstacle Clear Gradients published ABOVE the lowest (1.6%), all obstacles will now be considered EXCEPT for a possible more distant obstacle generating the lowest published OCG (1.6%). In this case, you will need to pull out the survey Charts to find a POSSIBLE obstacle which may be generating the 1.6% OCG.

Advice of the Runway Slope would be beneficial, as the OCGs emanate from the runway surface, which, for a sloping Runway, be originating from a different elevation.:ok:

J_T, did I learn well from the master?:}

Regards,

Old Smokey

[sru]

Thanks Old Smokey,:ok:

Nice to know I am heading vaguely in the right direction. The problem is a bit more complicated than I first thought.:eek:

Cheers
SRU

[sru]

Old Smokey,

A couple of questions –if you’re up to it.http://static.pprune.org/images/smilies/smile.gif

Would I be correct in saying if after, I have got the polygon of obstacles, if I pick the most limiting I will clear all other obstacles? (With in the surveyed area)

Quote:-

“One very important final consideration in constructing an Obstacle Polygon is that for all Obstacles Clear Gradients published ABOVE the lowest (1.6%), all obstacles will now be considered EXCEPT for a possible more distant obstacle generating the lowest published OCG (1.6%).”

My understanding is that the above still only applies within the surveyed area? At this stage I am not concerned about out of the surveyed area.

As an aside:-

I do remember back in the F27 days if you ran thru the segments as per ANO / (CAO) requirements to 1500’ (given min. cert. climb gradients for the a/c) then the distance from the aerodrome at which you achieve 1500’ was quite large! Well outside the surveyed area. Therefore SE ‘Escape procedures” to stop you hitting stuff!! (Outside the surveyed area)


Cheers
SRU

[Pugilistic Animus]

Sru I'm glad you put out some bait for the big fish

I knew he'd take the hook:D

I wonder how he deals with those pesky slope elevation problems;)

PA

[john_tullamarine]

A useful question and one for which the general lack of knowledge causes the likes of OS, Mutt and me considerable angst ...

climb gradient should all intersect at the same point

As OS has noted, there may (and generally will) be a number of obstacles .. you may have one which is critical for all RDS data or, indeed, a different obstacle for each OLS. Solving the trig for the published data quickly tells the story. It is worth noting that the trig model required is pretty straightforward .. if you have any difficulties, either OS or I can give you a hand ..

you may by simple geometry calculate the exact height and distance

Generally, the original data is subject to a bit of round off and the runway slope can introduce some approximation errors. However, in general, the simple trig analysis (which must include an approximation for slope to be at all useful) will give results which are of more than sufficient accuracy to be useful for runway analyses.

where the intersections are actually "phoney" obstacles

The intersections may be conservative artefacts of the trig (ie "phoney") or they may be the actual obstacles, depending on the runway obstacle profile .. doesn't matter at the end of the day (unless you are ducking under the planned departure profile .. in which case, as passenger Bloggs in row 95, I would prefer the phoney obstacle).

EXCEPT for a possible more distant obstacle

One needs to keep in mind (at least for Oz) that the bulk of RDS data (perhaps all ?) is based not on inclino survey but, rather, discrete obstacle survey within the prescribed trapezoid. The surveying agency then works backwards to come up with the relevant inclino data. If this is the case, then distant obstacles will not be considered. (For an inclino survey, generally the distant obstacle is not identified as such and will be included by default .. although there would be nothing to preclude known distant obstacles being excluded).

Outside the trapezoid (both laterally and on the extension) .. the pilot is on his own if the operator doesn't do the sensible thing.

did I learn well

.. indeed, old son ...

if I pick the most limiting I will clear all other obstacles?

Yes, and no. Keep in mind that all we are doing here is defining bumps in the departure profile. It is up to you to make sure that the aircraft NFP keeps above them. Main problems -

(a) third segment acceleration which will need to be massaged into the picture.

(b) different segments have different gradients

My understanding is that the above still only applies within the surveyed area

Depends on the survey .. refer to other comments on the matter.

At this stage I am not concerned about out of the surveyed area

I suggest that you should be as that is where 90 percent of the work is involved.

I do remember back in the F27 days

As do we all .. (are you three parts deaf like the rest of us ?). Worst situation will be twin-jets with a large V2/Vcl split. For instance, the DC9, on a similar basis .. is looking at something in the order of 50nm, as I recall (a while, now, since I have played with DC9 RTOW numbers).

I knew he'd take the hook

We can't help ourselves, unfortunately ..

I wonder how he deals with those pesky slope elevation problems

Generally, one can obtain a surveyed centreline profile. Either the actual profile can be used or, more usually, it can be linearised.

Keep in mind that it is usually no great problem to find out who did the survey for a given aerodrome and liase directly with the surveyor to find out what was, or was not, done. While the big airports sometimes can be a little public service in style, most of the smaller airport owners (and the individual surveyors) are a delight to work with and I have no hesitation in singing their praises.

.. and the best bit is that the surveyor, often, will just give you the survey RL data for the obstacles of interest.... and Bob's your uncle ....

[Pugilistic Animus]

We can't help ourselves, unfortunately ..

Two Hooked on the line A Tuna and a Mahi Mahi, Now we Need a Shark:}


PA:8

[Old Smokey]

Beware the hidden obstacle!

I should have been a bit more specific with my comments about the possibility of a more distant (NOT distant) obstacle arising from the lowest published gradient, an example.......

There are two Distance / Gradients available, 1.6% and TODA 1.82%

Two separate obstacles may well have caused these two gradients, one fairly close in, and one more distant (for the 1.6%). By geometry, we can establish one intersection of the 2 gradients, the "phoney" obstacle will be higher and more distant than the one causing the TODA 1.82% Gradient, but will be LOWER and CLOSER IN than the real obstacle causing the 1.6% Gradient.

If, on the other hand, you have 3 gradients available and all produce 2 intersections which are, for all practical purposes, at the same point, there's a 99% chance that we're dealing with only one obstacle.

The conservative way to go if you don't have "good" data close in (like Type A charts) is to assume the 1.6% obstacle at the Survey Limit. If you're dealing with 15,000M Survey Limits, that creates a 'worst case' obstacle of 787.4 Ft above Airport Elevation at 15,000 M. For a 2 engined aircraft, this will require a 1217 Ft 3rd segment, just nudging the type of 3rd segment heights which cause a problem if your engine has a 5 minute limit at Takeoff Thrust / Power.

Of course, there may still be numerous hard bits beyond the Survey limit which may affect both 2nd and 3rd segment performance, time to get out the Topo charts......:{

Regards,

Oldf Smokey

[SOPS]

Sorry..I have to ask..why do you need this stuff????? I mean..if it is really important why is it not provided to you...or is my 30 years out of GA protectected by a major airline showing:}

[john_tullamarine]

Two Hooked on the line

I'm sure that Mutt will be along anytime soon, now ...

Two separate obstacles may well have caused these two gradients

OS' point about hidden/multiple obstacles is very important.. especially when it comes to fitting in the third segment.

For the simplifying calculations referred to, if the intersection of more than two slopes suggests that we have identified an obstacle, that makes life a tad easier (but it doesn't guarantee that the lowest slope is not simultaneously limited by another, more distant, obstacle). If not, there is no way we can infer obstacle triplets without relevant charts or, as sometimes is done, going out to the aerodrome and having a looksee.

The polygon, to which OS refers, has to be treated as a series of rock hard intersecting surfaces above which we need to keep our puny aeroplane .. lest we be smitten and not see retirement.

Is this complex ? .. not really, but you do need to be reasonably tidy with housework and detail.

Sorry..I have to ask..why do you need this stuff?????

Ah .. absolutely the most important question !

Background ...

(a) If your wing falls off - you die - mostly.

As pilots we understand a little about a bunch of limit speeds and g-loads. Generally, most of us respect these (and all the other important things) and get to retire and go sailing.

(b) etc... etc...

(c) If you manage a CFIT (which includes combining OEI with wrong takeoff calculations) - you die - mostly.

As pilots, most of us know a lot less about performance than the stick and rudder stuff (and some would opine that the new breed know precious little about the latter as well).

It appears reasonable to me that we should know (at least) the basics about all the various things which are hiding out there ... just waiting to kill us off ?

I mean..if it is really important why is it not provided to you

Is it important ? .. see (c), above. By my simple life standards, if it is reasonably likely to kill me, I consider it important.

Is it provided ? .. certainly by the reputable operators (although, for some, only for a restricted scenario).

However, many operations give, at best, only lip service to proper takeoff calculations and, for others, the pilot is where it is all at.

The old Perf A studies gave the student a reasonable basic grounding in the discipline .. but that only covered a smallish subset of the pilot fraternity.

...or is my 30 years out of GA protectected by a major airline showing

I think so ....

[sru]

John, OS

Thanks for your enlightenment. It has certainly helped my understanding of it all. Strangely enough when I first started looking at this I was looking at the gradient and height at the limit of the surveyed area as the worst case. Then I started to think :uhoh: ......

Anyway now to look out of the surveyed area to MSA:eek:

Cheers

SRU

[sru]

OS, John,

I have to stop thinking .......:hmm: One last question and I'll stop bugging you both I promise :)

Re the runway slope. I understand down slope is the most limiting, factoring this into the obstacle height, ( worst case 15000m, 1.6%, OH 787') is it valid to add the slope to the published gradient ( and reverse for up slope)? At 15000m 0.1% slope = 49'

Or is it more correct to add the height difference and leave the gradient the same for consistency?

Or are there other things I am missing (as I suspect!!). I know it can't be that simple.

Thanks

SRU

[john_tullamarine]

I have to stop thinking .......http://static.pprune.org/images/smilies/yeees.gif One last question and I'll stop bugging you both I promise http://static.pprune.org/images/smilies/smile.gif

Questions and discussion are the lifeblood of Tech Log ..

I understand down slope is the most limiting

For obstacle considerations, why should this be so ?

is it valid to add the slope to the published gradient

Why would you want to do this ?

Once the aircraft is airborne, it has no interest in runway slope (except for the case where runway slope equals or exceeds climb capability .. which can be of interest OEI). While we need to factor in slope re screen RL what the extended centreline slope might be doing further out is of little interest other than to the extent of providing critical lumpy bits...

Takeoff obstacle clearance is based on screen position, climb with respect to the airmass, and whatever the ground clearance may happen to be.

I suspect that I may have missed your point along the way .. in which case your response should get us back onto the discussion highway.

[sru]

John,
In previous posts, reference has been made to runway slope as a consideration.

From OS first reply:-

"Advice of the Runway Slope would be beneficial, as the OCGs emanate from the runway surface, which, for a sloping Runway, be originating from a different elevation."

And your first reply:-

"...the simple trig analysis (which must include an approximation for slope to be at all useful)"

Not sure what slope you are talking about here but I assumed it was runway slope, hence my last post.

Understand your reply as the aircraft is airborne now and runway slope does not factor into it anymore.

But does runway slope need to be factored for finding the the height and distance of the obstacle in the first place. (via my trig calcs)

Cheers
SRU