Runway Slope calculation

[4g_handicap]

Hi there,

Had to deal with an ineresting problem the other day.

I know that runway slope is calculated by getting the diff in elevation of the two end and the calculating that as a % of the runway length.

What happens when the slope is not uniform ie starts very steep uphill and turns eventually into a downhill. How does one account for this in takeoff performance calculations(according to above calculation slope could = 0)

I heard someone mention an equivalent slope. Does anyone know what this is and how it is calculated.

THanks

[GlueBall]

We take performance data from Runway Analysis Manual which includes runway slope. At some weird runway sloping as at Quito, Ecuador, (El 9200), where you can't see the opposite threshold for example, no performance allowance for headwind is permissible. Likewise, at Rio Negro, Colombia, (El 7000) and at Guatemala (El 5000) the runway slope is such that one can takeoff at significantly higher gross weights going downhill with a tailwind than to go uphill with a headwind.

[OverRun]

4g_handicap
There is an old ICAO correction method to cope with variable slopes - it calculates the equivalent slope as an index number. Four indices are available.

Are you flying with pistons (either avgas or steam driven) or jets (turboprop or turbofan)? And do you know the actual slopes involved (useful, but not essential). I can then calculate the "equivalent slope".

These days, some authorities simply use the diff in elevation method. It's less accurate, but as they drive to their next airport inspection, they seem strangely unconcerned.

[4g_handicap]

Overun,

I personally am fly a jet at this stage, but our company also operates Jetstream 41. I also recently moved off turbo-props(HS748). Performance has always been a field of interest, so I am not talking of any field in particular.

Authorities here also just use the diff in elevation method, but I think it is inaccurate. What is equivalent slope. I would have thought that a slope that starts off uphill and ends up downhill will have a different effect to one that starts off downhill and end up going uphill.

Also does one factor the slope into the stopway?

Thanks for any help.

[john_tullamarine]

The ICAO approach divides the runway into quarters, where each quarter (of the runway length) slope is multiplied by a factor which increases as the runway is traversed. In this way the latter stages of the runway slope have a increasing weighting .. i.e. the stopping section on a limiting runway is over emphasised.

I don't particularly like the approach for several reasons so I don't routinely use the technique. As I don't have the formula to hand and haven't used it for quite some time, I cannot quote it .. however, I do have it on file somewhere and will dig it out in the next few days for you.

[OverRun]

OK, I've programmed the formula and run a couple of test cases. It doesn't make a big difference, until the slopes get very steep. But if they do get steep, they probably lie outside the parameters of the ICAO study and the study is no longer valid.

Anyway, the formula for turboprop and jet is to divide the runway into quarters, determine average slope in each quarter, and then the slope index as follows:
Slope Index = [first quarter slope + 1.33 second quarter slope + 2.33 third quarter slope + 3.33 fourth quarter slope], all divided by 8. This reflects the greater influence of the runway slope at the high speed portion of the takeoff run.

The per cent runway correction is then 7 times the slope index if it is positive, and 4 times the slope index if it is negative. For piston aircraft, it is about double the turboprop/jet case.

Putting this into the slide rule:
For a runway all uphill at 1%, the length correction is 7% or 140m on a 2000m runway (which makes it 2140m; nothing special about 2000m but it's just an easy example to use). For a runway all downhill at -1%, length correction is -4% or -80m on a 2000m runway.

For a convex/concave runway, it does make a difference if it starts off uphill or downhill:
For a runway with the first half uphill (+1%), and the second half downhill (-1%), length correction is -1.7% or -33m on a 2000m runway. This was compared with your 'difference in runway end elevation method' which gave the correction as +0%.
For a runway with the first half downhill (-1%), and the second half uphill (+1%), length correction is +2.9% or +58m on a 2000m runway.

For the undulating case, first quarter up 1%, second quarter up 1%, third quarter level, fourth quarter down 1%,), length correction is -0.5% or -10m on a 2000m runway. This was compared with your 'difference in runway end elevation method' which gave the correction as +0.25%.

I also tried an extreme case, although this is outside the range studied for ICAO and could well be inaccurate because the aircraft performance may not change proportionately:
first quarter up 5%, second quarter up 3%, third quarter level, fourth quarter down 3%,), length correction is -0.5% or -10.3m on a 2000m runway. This was compared with your 'difference in runway end elevation method' which gave the correction as +1.25%.

From the various runway length studies I've done, I wouldn't get excited about anything less than a runway length change of 100m, or 5% for the 2000m runway case. There are some subtleties about the assumed runway slopes in the ICAO study, which I've also looked at and they can be safely glossed over here. It seems as though the differences between the 'difference in runway end elevation method' and the more detailed equivalent slope are pretty small, although I have to say that I only really realised that once I'd done these calcs. I guess this was what john-tullamarine was alluding to (is that you Diggo?).

So I would think it is true to say that the effects of temperature, headwind and density altitude are probably more significant than runway slope, unless you're bush flying off Lesotho or New Guinea mountain sides.

There is no provision for considering the effect of the slope of the stopway, and looking at the relative lengths involved, I would think it would not be material.

[4g_handicap]

Overun,

Many thanks - that is exactly the kind of gen I am looking for.

If I may ask - where do you get your gen. Any reference material?

4g
:)

[john_tullamarine]

Overrun,

No, but I've been around the countryside a bit .. quite likely that we have met. I certainly wouldn't like to fly into anywhere much in Lesotho .. the Drak is a bit savage for my liking ...

[notcavok]

I am probably being a bit nieve here, in fact I am sure I am.
By taking the difference in threshold elevations and calculating it as a percentage you achieve a mean slope be it +ve or -ve. So where you have lost out by an incline you gain again by the following decline????
This appears to me to be the only accurate outcome?
Please don't shoot me down, I am genuinely cuious.

Cheers the noo.

[OverRun]

4g_handicap
My reference was the ICAO Aerodrome Design Manual, Part 1, Runways. 2nd edition 1984. Their Doc9157-AN/901 Part 1.

Notcavok - the difference between the simple average technique and the more complex equivalent slope technique reflects the greater influence of the runway slope at the high speed portion of the takeoff run. The aircraft acceleration varies with speed, and so the position of the various slope(s) along the runway has a varying effect.

I was surprised at how little difference the more complex method made, particularly since I've been struggling with takeoff performance calculations on a runway which has a big hump in the middle. Surely, I thought, the differential slopes must make more of a difference . . . . . . . I guess not.

What was interesting though was all the obscure performance factors that popped their heads up in the process. One airline has an aircraft performance degradation factor in their system for the effects of age, lose rivets, etc (and can tailor it to the performance degradation factor for a particular aircraft - I presume for a hanger queen, but was too polite to ask). It tends to drop about 5% off the performance. Quite sophisticated, and impressively realistic.

Another, much smaller, airline had the expectation of lower performance because they (not Boeing) had de-rated their engines slightly to reduce maintenance requirements. That subtlety of maintenance is getting outside my field and I suppose it makes economic sense. However I never got to see the performance charts for that airframe/engine combination because no such combination was commonly used. I'm sure the airline had all the necessary charts and performance programmes, somewhere.

What struck me though, which is sort of why I included these rambling anecdotes, is just how tenuous is the link between the aircraft that you are actually flying, and the performance charts you're using. There is such a plethora of combinations of airframe and engines and all sorts, that I'd keep as close an eye out for assumptions or mistakes in the paperwork as I would for all the physical factors involved.

Anecdotes? - well I'm not going to mention a certain airline that had to make extra long flights around the bulge of Africa from Jo'burg and got an under-the-counter deal from P&W to allow an increase in EPR for Jo-burg takeoffs (high altitude, TO weight and air temperature) without loss of warranty. When the deal was eventually wound up, the citizens of Kempton Park (the suburb just past the threshold markings) got Real Close views of the 747 underside for the first few flights.

[john_tullamarine]

The ICAO approach is not a great deal of help for runways with humps in the middle.

If it is giving you sleepless nights ... why not try either modelling the aircraft, or breaking the takeoff down into smaller sections, consulting the AFM to assess slope effects and then summing the results to arrive at a distance, making sure that the answer remains conservative with respect to the AFM used conventionally.

You could always just put in an empirical fudge factor based on experience with a particular aircraft AFM ... which is what most of us do to address these sorts of problems.

Which runway is causing you the problem ?

How long ago since you frequented Kempton Park ?

Three other points in your post ..

(a) it is perfectly conventional to monitor individual aircraft for performance deterioration and adjust the numbers accordingly. While this is not so common for takeoff calculations, it is pretty standard for flight plan fuel burn prediction

(b) the airline involved in its own derating potentially is a worry unless the procedures have been through an appropriate rigorous certification process. If you cast your mind back far enough, an Australian operator got caught out badly at SYD doing just that sort of thing

(c) the comment about the AFM and the real world highlights a standard worry. Pilots have a tendency to believe the RTOW numbers. When one considers that the AFM data is predicated on defined conditions which may not represent the real world all that accurately, there is a very real need for pilots to make sensible assessments for matching RTOW data to particular takeoffs.

Notcavok .. slope is just one of the real world problems faced by ops engineers in doing the sums and pilots in trying not to frighten themselves during the takeoff. There will always be an error involved in the answer, either due to the AFM model's being a little out, or the boundary data containing error. The trick is to keep the RTOW data, as determined, reasonably (ie conservatively) realistic.

[ 20 December 2001: Message edited by: john_tullamarine ]</p>