Obstacle height calculation
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Obstacle height calculation
Was reading an old practice paper, and came across this statement ."Obstacle height is generally referenced to the elevation at the end of the TODR. Assuming the climb gradient is constant, the flight path of an uphill slope runway will begin at a relatively LOWER elevation relative to a downhill slope runway.
What am I missing here? Can anyone explain this to a simpleton? If you are already going up hill, how can you take off at a relatively lower point than if you are going downhill???
Let the education of Elroy commence!
What am I missing here? Can anyone explain this to a simpleton? If you are already going up hill, how can you take off at a relatively lower point than if you are going downhill???
Let the education of Elroy commence!
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Elroy,
Your question is essentially a 2 part, 2 situation scenario. One relates to the climb gradient required for a given obstacle, the other pertains to assesment of obstacle clearance if the aircraft is at a fixed gradient.
(1) "Obstacle height is generally referenced to the elevation at the end of the TODR." - Consider a 2000 M Runway of Elevation 1000 ft AMSL, Slope is 1% Down, and there is a 1100 ft AMSL obstacle at 1000 M from the runway end. As Elevation (1000 ft) is quoted for the highest part of the airfield, at the beginning of the Takeoff the Elevation is 1000 feet, and at the End of the Down-Sloping (-1.0%) Runway, the Elevation is 65.6 ft lower, i.e. 934.4 ft. To clear the obstacle the aircraft must climb from 934.4 ft to 1100 ft (165.6 ft) in 1000 M, a gradient requirement of 5.05%.
Now consider the opposite Takeoff direction of the same runway, also with a 1100 ft AMSL obstacle at 1000 M from the runway end. At the end of the (UP-sloping) Runway the aircraft is at 1000 feet, leaving 100 ft to climb to clear the obstacle in 1000 M. That's a gradient requirement of 3.05%.
Thus, for the same obstacle data, the Gradient REQUIRED from the Down Sloping Runway is 5.05%, Vs 3.05% for identical obstacle data from the Up Sloping runway. That's why obstacles are referenced to the lowest portion of the runway, and, in assessing Obstacle Limited Weights, a higher Takeoff Weight is possible from the UP Sloping Runway.
(2) "Assuming the climb gradient is constant, the flight path of an uphill slope runway will begin at a relatively LOWER elevation relative to a downhill slope runway." Now consider an aircraft at the WAT limit, unaffected by Runway Length or obstacles. In either Takeoff direction (assuming no wind), the aircraft will have an identical Climb Gradient, say, for example, 6.0%. The assumption is also made that the overall terrain in the area is the same as the Runway Slope.
For Takeoff from the Down Sloping Runway, the aircraft is achieving 6.0% to the horizontal, but 7.0% to the terrain, thus, at any point along the flight path, clearance of the assumed obstacle-free terrain will be 7.0% of the horizontal distance flown.
For Takeoff from the Up Sloping Runway, the aircraft is achieving 6.0% to the horizontal, but only 5.0% to the terrain, thus, at any point along the flight path, clearance of the assumed obstacle-free terrain will be 5.0% of the horizontal distance flown, a LOWER terrain clearance.
Some of the words in the quote that you made must be examined carefully. the words "relatively LOWER elevation" imply HEIGHT (above obstacles), by inclusion of the word "relatively", because all obstacle heights are assesses RELATIVE to the Runway Elevation.
Regards,
Old Smokey
Your question is essentially a 2 part, 2 situation scenario. One relates to the climb gradient required for a given obstacle, the other pertains to assesment of obstacle clearance if the aircraft is at a fixed gradient.
(1) "Obstacle height is generally referenced to the elevation at the end of the TODR." - Consider a 2000 M Runway of Elevation 1000 ft AMSL, Slope is 1% Down, and there is a 1100 ft AMSL obstacle at 1000 M from the runway end. As Elevation (1000 ft) is quoted for the highest part of the airfield, at the beginning of the Takeoff the Elevation is 1000 feet, and at the End of the Down-Sloping (-1.0%) Runway, the Elevation is 65.6 ft lower, i.e. 934.4 ft. To clear the obstacle the aircraft must climb from 934.4 ft to 1100 ft (165.6 ft) in 1000 M, a gradient requirement of 5.05%.
Now consider the opposite Takeoff direction of the same runway, also with a 1100 ft AMSL obstacle at 1000 M from the runway end. At the end of the (UP-sloping) Runway the aircraft is at 1000 feet, leaving 100 ft to climb to clear the obstacle in 1000 M. That's a gradient requirement of 3.05%.
Thus, for the same obstacle data, the Gradient REQUIRED from the Down Sloping Runway is 5.05%, Vs 3.05% for identical obstacle data from the Up Sloping runway. That's why obstacles are referenced to the lowest portion of the runway, and, in assessing Obstacle Limited Weights, a higher Takeoff Weight is possible from the UP Sloping Runway.
(2) "Assuming the climb gradient is constant, the flight path of an uphill slope runway will begin at a relatively LOWER elevation relative to a downhill slope runway." Now consider an aircraft at the WAT limit, unaffected by Runway Length or obstacles. In either Takeoff direction (assuming no wind), the aircraft will have an identical Climb Gradient, say, for example, 6.0%. The assumption is also made that the overall terrain in the area is the same as the Runway Slope.
For Takeoff from the Down Sloping Runway, the aircraft is achieving 6.0% to the horizontal, but 7.0% to the terrain, thus, at any point along the flight path, clearance of the assumed obstacle-free terrain will be 7.0% of the horizontal distance flown.
For Takeoff from the Up Sloping Runway, the aircraft is achieving 6.0% to the horizontal, but only 5.0% to the terrain, thus, at any point along the flight path, clearance of the assumed obstacle-free terrain will be 5.0% of the horizontal distance flown, a LOWER terrain clearance.
Some of the words in the quote that you made must be examined carefully. the words "relatively LOWER elevation" imply HEIGHT (above obstacles), by inclusion of the word "relatively", because all obstacle heights are assesses RELATIVE to the Runway Elevation.
Regards,
Old Smokey
Moderator
While OS' answer may be simplifying some points for convenience ... seems I'm missing something here on a couple of points ...
As Elevation (1000 ft) is quoted for the highest part of the airfield
When one is doing the sums .. other than in a quick and dirty manner to get a conservative answer .. calculations usually are based on the specific MSL RLs quoted in the aerodrome runway and relevant terrain data. Assuming one has this data .. the end elevation/obstacle RL deltas on which the sums are based are then simple differences of values measured from a common datum. Indeed, if one has the actual centreline RL profile then one can be a little cleverer and determine the (approximate) actual RL at end TODR rather than use the end TODA declared figure (or use a somewhat conjectural linearised approximation) if the TODR << TODA.
The ARH is of little direct relevance (although, for convenience, the ARH may well be input as the Hp argument if one is doing the sum manually). If one is going to the trouble of using a number cruncher, then one would input an appropriate RL for the sake of a poofteenth improvement in "accuracy".
If the elevations quoted are MSL RLs, then I have missed something along the way in the leap as to how obstacles are referenced to the lowest portion of the runway.
For the two (opposite direction) examples given, each is quite separate from the other and the lowest portion of the runway appears only to have relevance to the departure in the downsloping direction ?
Answer (2) appears not to be related to the wordiology of the question in respect of will begin at a relatively LOWER elevation relative to a downhill slope runway.
Perhaps it is just a bit late at night and I am overlooking something specific in the wordiology ? Alternatively, having been involved in pilot theory training in another lifetime and having a fairly jaundiced view of Regulatory examination questions .. especially the lack of lucidity relating thereto on many occasions ...... If I may relate an anecdote at my expense .. many years ago .. as a recent graduate I undertook my Oz ATPL exams by my own study .. read the syllabus for each topic .. read the nominated texts .. and then, in the exam, managed to complete the "enter-your-name-in-this-space" question but precious little else. I then found out about past sample papers and the fact that the exams had only a passing relevance to the required subject academic competence ...
signed,
Confused
As Elevation (1000 ft) is quoted for the highest part of the airfield
When one is doing the sums .. other than in a quick and dirty manner to get a conservative answer .. calculations usually are based on the specific MSL RLs quoted in the aerodrome runway and relevant terrain data. Assuming one has this data .. the end elevation/obstacle RL deltas on which the sums are based are then simple differences of values measured from a common datum. Indeed, if one has the actual centreline RL profile then one can be a little cleverer and determine the (approximate) actual RL at end TODR rather than use the end TODA declared figure (or use a somewhat conjectural linearised approximation) if the TODR << TODA.
The ARH is of little direct relevance (although, for convenience, the ARH may well be input as the Hp argument if one is doing the sum manually). If one is going to the trouble of using a number cruncher, then one would input an appropriate RL for the sake of a poofteenth improvement in "accuracy".
If the elevations quoted are MSL RLs, then I have missed something along the way in the leap as to how obstacles are referenced to the lowest portion of the runway.
For the two (opposite direction) examples given, each is quite separate from the other and the lowest portion of the runway appears only to have relevance to the departure in the downsloping direction ?
Answer (2) appears not to be related to the wordiology of the question in respect of will begin at a relatively LOWER elevation relative to a downhill slope runway.
Perhaps it is just a bit late at night and I am overlooking something specific in the wordiology ? Alternatively, having been involved in pilot theory training in another lifetime and having a fairly jaundiced view of Regulatory examination questions .. especially the lack of lucidity relating thereto on many occasions ...... If I may relate an anecdote at my expense .. many years ago .. as a recent graduate I undertook my Oz ATPL exams by my own study .. read the syllabus for each topic .. read the nominated texts .. and then, in the exam, managed to complete the "enter-your-name-in-this-space" question but precious little else. I then found out about past sample papers and the fact that the exams had only a passing relevance to the required subject academic competence ...
signed,
Confused
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I'm a bit confused as well.
What I gather from the original statement is that the aircraft climb gradient is relative to the horizon , so on a uphill slopping runway you will have a lower (relative) obstacle height, and you need a lower climb gradient; if the the runway slopes downhill, for the same obstacle (absolute) height and position, your aircraft constant climb gradient will be affected because your relative height to the obstacle is indeed higher and so is the the climb gradient needed to overcome that obstacle. This can be useful when calculating the MTOW for that particular rwy, is it not?
GD&L
What I gather from the original statement is that the aircraft climb gradient is relative to the horizon , so on a uphill slopping runway you will have a lower (relative) obstacle height, and you need a lower climb gradient; if the the runway slopes downhill, for the same obstacle (absolute) height and position, your aircraft constant climb gradient will be affected because your relative height to the obstacle is indeed higher and so is the the climb gradient needed to overcome that obstacle. This can be useful when calculating the MTOW for that particular rwy, is it not?
GD&L
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John_T,
I'm afraid that this is rather brief, in transit at home between work, and the thread had slipped to page 2 in my absence.
Yes, I did indeed simplify some points for convenience, the most pertinent of these simplifications being -
(1) The aircraft is field limited on a Balanced Field, i.e. the 1st/2nd segments began right at the end of the TODR, and TODR = TODA = TORA
(2) The quoted airfield Elevation is for the highest point on the runway, i.e. the beginning of the Down-Sloping Runway, or the end of the (same) Up-sloping runway.
(3) The effects of 1st segment have been ignored, as being relatively constant in all cases.
In my work (and I'm sure yours too) it's necessary to make very exact obstacle analysis for RTOW production where Effective Operational Lengths (EOLs) will be frequently used in evaluating a "Balanced" Field / 1st Segment / 2nd Segment limit, i.e. the Field Limit and the Obstacle Limit are equal. In these cases, the TODR will be often well less than the TODR. The gradient to the obstacle, then, will be from the point at the end of the TODR, and, on a Sloping runway, this will always be less than the highest elevation of the runway.
In the example that I quoted (a 1% Down Sloping runway of 2000M TODR, with end elevations of 1000 feet and 934.4 ft), the aircraft must climb from 934.4 ft to the 1100ft AMSL sample obstacle in 1000M, a gradient of 5.05%. If, however the aircraft only required, say, 1500M of the 2000M available, the end of the TODR will be at an elevation of 950.8 ft and be 1500M from the obstacle, a gradient of 3.03%, hardly a 'poofteenth' of a difference! Similar arguments hold good for the Up-Sloping Takeoff direction.
It would have been better if I had said "obstacles are referenced to the lowest portion of the TODR" rather than "obstacles are referenced to the lowest portion of the runway". The latter is correct if the aircraft is truly Field limited, the former applies to everyday performance number crunching.
Where the problem lies is when producing "back-up" General Takeoff Charts in the event that the RTOW is invalidated, and I'm sure that this is a part of your work too. The pilot cannot be expected to do an incremental creep along the runway to calculate the Weight / TODR, the elevation at that point, and the relative vertical and horizontal distance to the obstacle to calculate the 1st/2nd segment limits. It then becomes necessary to quote the worst case in instructing the pilot to compare the overall lowest runway elevation against the obstacle, for safety and more often than not, conservatism.
A lot of pre-surveyed data (e.g. STODs in the Australian system) don't require knowledge of obstacle or runway elevations to do the trigonometric calculations, but when 'raw' data is used from obstacle sources such as survey charts etc., elevation AMSL is the original data to be referenced to Runway Elevation, or the lowest point of it. A very wise P/E once suggested that I use obstacle polygons created from multiple STODs (his name slips my mind
), and, if exact elevation from the point on the runway is used, the obstacle horizontal and vertical scatter comes down to less than a foot vertically, and within a metre or 2 horizontally. If simplified trig is used, not considering the runway elevation at each 'STOD point' the scatter can become quite large.
As a footnote, I use the highest Airport Elevation to calculate the Pressure Height / Density Height portion of the calculation (naturally), but the lowest point of the TOD to compare to the obstacle elevation, irrespective of whether the runway be Up-Sloping or Down-Sloping.. As a further footnote, I use the lowest elevation (as described earlier) against the HIGHEST obstacle in the Takeoff Area to find the Delta to be factored in calculating the MAA, and then add it to the HIGHEST Airfield Elevation.
That's still not the complete story, but hopefully a degree of clarification in where I was coming from in the over-simplified earlier response. I'm only applying principals that my earlier teachers taught me, P_T, G_S, and.....J_T.
Regards,
Old Smokey
I'm afraid that this is rather brief, in transit at home between work, and the thread had slipped to page 2 in my absence.
Yes, I did indeed simplify some points for convenience, the most pertinent of these simplifications being -
(1) The aircraft is field limited on a Balanced Field, i.e. the 1st/2nd segments began right at the end of the TODR, and TODR = TODA = TORA
(2) The quoted airfield Elevation is for the highest point on the runway, i.e. the beginning of the Down-Sloping Runway, or the end of the (same) Up-sloping runway.
(3) The effects of 1st segment have been ignored, as being relatively constant in all cases.
In my work (and I'm sure yours too) it's necessary to make very exact obstacle analysis for RTOW production where Effective Operational Lengths (EOLs) will be frequently used in evaluating a "Balanced" Field / 1st Segment / 2nd Segment limit, i.e. the Field Limit and the Obstacle Limit are equal. In these cases, the TODR will be often well less than the TODR. The gradient to the obstacle, then, will be from the point at the end of the TODR, and, on a Sloping runway, this will always be less than the highest elevation of the runway.
In the example that I quoted (a 1% Down Sloping runway of 2000M TODR, with end elevations of 1000 feet and 934.4 ft), the aircraft must climb from 934.4 ft to the 1100ft AMSL sample obstacle in 1000M, a gradient of 5.05%. If, however the aircraft only required, say, 1500M of the 2000M available, the end of the TODR will be at an elevation of 950.8 ft and be 1500M from the obstacle, a gradient of 3.03%, hardly a 'poofteenth' of a difference! Similar arguments hold good for the Up-Sloping Takeoff direction.
It would have been better if I had said "obstacles are referenced to the lowest portion of the TODR" rather than "obstacles are referenced to the lowest portion of the runway". The latter is correct if the aircraft is truly Field limited, the former applies to everyday performance number crunching.
Where the problem lies is when producing "back-up" General Takeoff Charts in the event that the RTOW is invalidated, and I'm sure that this is a part of your work too. The pilot cannot be expected to do an incremental creep along the runway to calculate the Weight / TODR, the elevation at that point, and the relative vertical and horizontal distance to the obstacle to calculate the 1st/2nd segment limits. It then becomes necessary to quote the worst case in instructing the pilot to compare the overall lowest runway elevation against the obstacle, for safety and more often than not, conservatism.
A lot of pre-surveyed data (e.g. STODs in the Australian system) don't require knowledge of obstacle or runway elevations to do the trigonometric calculations, but when 'raw' data is used from obstacle sources such as survey charts etc., elevation AMSL is the original data to be referenced to Runway Elevation, or the lowest point of it. A very wise P/E once suggested that I use obstacle polygons created from multiple STODs (his name slips my mind
), and, if exact elevation from the point on the runway is used, the obstacle horizontal and vertical scatter comes down to less than a foot vertically, and within a metre or 2 horizontally. If simplified trig is used, not considering the runway elevation at each 'STOD point' the scatter can become quite large.As a footnote, I use the highest Airport Elevation to calculate the Pressure Height / Density Height portion of the calculation (naturally), but the lowest point of the TOD to compare to the obstacle elevation, irrespective of whether the runway be Up-Sloping or Down-Sloping.. As a further footnote, I use the lowest elevation (as described earlier) against the HIGHEST obstacle in the Takeoff Area to find the Delta to be factored in calculating the MAA, and then add it to the HIGHEST Airfield Elevation.
That's still not the complete story, but hopefully a degree of clarification in where I was coming from in the over-simplified earlier response. I'm only applying principals that my earlier teachers taught me, P_T, G_S, and.....J_T.
Regards,
Old Smokey
Moderator
.. ah .. your conservatism explains my query ... just two comments .. minor and of no real account but may be of interest to others ?
The quoted airfield Elevation is for the highest point on the runway.. this will depend on the local definition but commonly the ARP need not have an elevation located on a runway ?
i.e. the Field Limit and the Obstacle Limit are equal
.. need that be so ? In general, I would have thought not . .. ie one will usually be more limiting than the other ? noting that, in general, one can probably force them to be equal ..
P_T .. last I spoke with him, Peter was intending to retire to QLD. Fine chap by any standards .. I do hope that his retirement is bringing him the rewards he so richly deserved.
G_S .. the Alzheimers is in full swing today, I'm afraid .. the only GS I can bring to mind was with CASA and not a performance man .. perhaps you can PM me to jog the memory ?
J_T .. dreadful fellow ....
Two other fine chaps from the other hangar .. JW and RG (oh, go on .. we can include FO, RF .. oh dear .. but the memory cells are letting me down tonight .. can picture the faces but the names elude me) .. did you have much to do with any of them .. ?
I have to acknowledge a big learning debt to Peter, John, and Roger .. did you know that Peter originally worked for the other mob as a lad and then jumped ship .. ? .. or was it John worked with Peter and then jumped ship ? .. whichever ..
The quoted airfield Elevation is for the highest point on the runway.. this will depend on the local definition but commonly the ARP need not have an elevation located on a runway ?
i.e. the Field Limit and the Obstacle Limit are equal
.. need that be so ? In general, I would have thought not . .. ie one will usually be more limiting than the other ? noting that, in general, one can probably force them to be equal ..
P_T .. last I spoke with him, Peter was intending to retire to QLD. Fine chap by any standards .. I do hope that his retirement is bringing him the rewards he so richly deserved.
G_S .. the Alzheimers is in full swing today, I'm afraid .. the only GS I can bring to mind was with CASA and not a performance man .. perhaps you can PM me to jog the memory ?
J_T .. dreadful fellow ....
Two other fine chaps from the other hangar .. JW and RG (oh, go on .. we can include FO, RF .. oh dear .. but the memory cells are letting me down tonight .. can picture the faces but the names elude me) .. did you have much to do with any of them .. ?
I have to acknowledge a big learning debt to Peter, John, and Roger .. did you know that Peter originally worked for the other mob as a lad and then jumped ship .. ? .. or was it John worked with Peter and then jumped ship ? .. whichever ..
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John_T,
Ummm, I'm taking a punt on a PM not being necessary when there's only good things to say of people, and it doesn't compromise their anonymity.
P_T, as you correctly figured = Peter E. Turner, a true gentleman and a master of his craft. His parent's must have had a hint of his future when they gave him the initials P.E. Like yourself, I too have a large learning debt to him, along with a good number of my ex colleagues from the old firm. He did indeed retire to Toowoomba, I've been in touch several times over the years, and his answer to the occasional performance question is "I've forgotten all that stuff. I'm a gentleman farmer now". I don't know how good he is as a farmer, but a true gentleman he was, and is. The family legacy lives on, son Mike was a MD-11 captain the last I heard.
G_S = Gordon Stiles (or was it Styles) of British Aerospace. Another fine gentleman to whom I have a learning debt. I never did get to know him personally, only professionally. I listened well in his presence, he had a long and large career in Performance Engineering, including work on such minor types as THE Concorde.
J_T = Another fine gentleman, who exists in cyber land for most, not such a bad chap at all when you get to know him, just don't get him started on directional control problems at Vmcg (Relax, I'm a convert)
Whether it was John or Peter who changed allegiances eludes me, I know that it is true for one of them, my money is on John's having done so.
i.e. the Field Limit and the Obstacle Limit are equal.. need that be so - You're right again of course, they need not. I must admit that it was a tongue in cheek attempt to bring the very balanced Mutt into the debate with a bit of "Balanced Field / Obstacle" takeoff verbiage. (That's my excuse for the day anyway).
Regards,
Old Smokey
Ummm, I'm taking a punt on a PM not being necessary when there's only good things to say of people, and it doesn't compromise their anonymity.
P_T, as you correctly figured = Peter E. Turner, a true gentleman and a master of his craft. His parent's must have had a hint of his future when they gave him the initials P.E. Like yourself, I too have a large learning debt to him, along with a good number of my ex colleagues from the old firm. He did indeed retire to Toowoomba, I've been in touch several times over the years, and his answer to the occasional performance question is "I've forgotten all that stuff. I'm a gentleman farmer now". I don't know how good he is as a farmer, but a true gentleman he was, and is. The family legacy lives on, son Mike was a MD-11 captain the last I heard.
G_S = Gordon Stiles (or was it Styles) of British Aerospace. Another fine gentleman to whom I have a learning debt. I never did get to know him personally, only professionally. I listened well in his presence, he had a long and large career in Performance Engineering, including work on such minor types as THE Concorde.
J_T = Another fine gentleman, who exists in cyber land for most, not such a bad chap at all when you get to know him, just don't get him started on directional control problems at Vmcg
(Relax, I'm a convert) Whether it was John or Peter who changed allegiances eludes me, I know that it is true for one of them, my money is on John's having done so.
i.e. the Field Limit and the Obstacle Limit are equal.. need that be so - You're right again of course, they need not. I must admit that it was a tongue in cheek attempt to bring the very balanced Mutt into the debate with a bit of "Balanced Field / Obstacle" takeoff verbiage. (That's my excuse for the day anyway).
Regards,
Old Smokey
Moderator
GS .. I believe I have heard his name MID many years ago
... indeed, Peter professed to lose all interest in the craft once he retired .. we tried to interest him in doing some work for us at the time but he was adamant ..
.. as for Mutt .. the three of us should, surely, arrange a beer or many before we all get so old that we forget what the bar is for .. and you're quite correct .. likewise, I thought he would wade in on the discussion at some point ..
... tempus fugit ... John must be dead now at least 20-25 years ... both he and Peter were the most scholarly and charming of gentlemen whom one could be honoured to have met along the workaday pathways ..
.. we probably should leave this thread alone .. could get quite maudlin contemplating the "good old days .."
... indeed, Peter professed to lose all interest in the craft once he retired .. we tried to interest him in doing some work for us at the time but he was adamant ..
.. as for Mutt .. the three of us should, surely, arrange a beer or many before we all get so old that we forget what the bar is for .. and you're quite correct .. likewise, I thought he would wade in on the discussion at some point ..
... tempus fugit ... John must be dead now at least 20-25 years ... both he and Peter were the most scholarly and charming of gentlemen whom one could be honoured to have met along the workaday pathways ..
.. we probably should leave this thread alone .. could get quite maudlin contemplating the "good old days .."
