ILS GP Formula

[airbuslad]

I must have Alzheimer’s because I can not remember this. Can anyone tell what the quickie formula is to figure out how far back in miles you will intercept a 3 degree glide path at certain altitude above ground?

Thanks

[Pegasus77]

3 miles per 1000 feet

ILs starts in 4000' AGL then you will intercept the ILS about 12 miles before the threshold.

P77

[mjudk]

Remember the 1 in 60 rule. 1 degree is 1 feet in 60 feet, so 3 degrees is 3 feet in 60 feet. Go and work it out :)

[FlapsOne]

Although the 1 in 60 rule works, life is far too short to work that out for an ILS.

Stick with Pegasus77's plan, or for round numbers, use 300 ft nautical mile.

2,000 ft = just under 7nm

3,000 ft = 10 nm

4,000 ft = just over 13 nm

5,000 ft = just under 17 nm

etc ad nauseam

[Pilot Pete]

All I do is remember 3 x dist in nm;

i.e. 5nm out 3 x 5 = 15 therefore 1500ft (AGL)
or 4nm out 3 x 4 = 12 ---"--- 1200ft

Use the same rule for straight in visual approaches (remember field elevation if significant) when using QNH.

Also works well if you want to do a constant descent visual approach if high above an airfield. You may declare and be cleared for the visual when high on the profile (if you were going past the field to join the ILS at 8nm and you declare visual you will now be high on a visual approach (obviously you don't want to fly all the way out to 8nm and then come back to land) so how do you decide when to turn base and final?

What I do in the 757 is position to end up a couple of miles out from the field on a downwind with the gear down and flap 20 set. If very high you can take speedbrake as well to really get the rate of descent up. If there is a DME on the field (or a fix in the FMC) that gives you distance out, so for example, as I pass 3 mile downwind I use the same rule which will give me 900ft. Well that's what I should be inbound so I add 1000' for the base and final turn giving a target at 3 miles downwind of 1900'. If I'm at 3000' then it's too early to turn in so I keep going downwind and calculate for 4 nm (2200'). If I'm 'in the ballpark' (say within 500') I can start to turn base, take flap 30 and adjust my rate of descent to give me my 3 degree slope (always remembering to keep an eye on the wind).

For the 3 degree glideslope I use another rule of thumb;

Drop the last zero from the groundspeed and halve the answer which will give you your required rate of descent in 100's of feet per minute;

So, G/S 140kts means 14/2=7 = 700fpm

which I find a lot easier than 5 x groundspeed which works as well.

Sorry if you knew all that, hope it's useful to others.

PP

[BlueEagle]

Worth remembering too that a lot of ILS are only reliable within certain ranges, for example:

Loc = 25 miles or less.

GS = 10 miles or less.

Beware getting 'locked on' too soon!

[Young Paul]

There are two formulae here -
3 miles per 1000', or 330' per mile
and 300' per mile.

Both are very easy to use.
The first is about 10% more accurate, if it matters. Which quite honestly it doesn't really.

[OzExpat]

Yes, I find it simplest to use 3 times altitude divided by 1000 to figure my descent point. I know the description sounds complex but it really isn't. Take today for example. I was at FL210 and wanted to be at 2500 feet at 10 DME.

For simplicity, I said that 2500 feet was really 2000 feet, requiring a net height loss of 19,000 feet by the time I reach the 10 DME point. Dividing 19000 by 1000 gives me 19. I multiply 19 by 3, to give me 57, then add the 10 DME, to give a resultant descent point of 67 DME, which I rounded (today) to 65 DME. I then planned to descend at an initial IAS of 220 knots. I divide 220 by 10, to get 22, then halve that, to give me 11, then multiply that by 100, to give me a rate of descent of 1100 feet per minute to maintain profile.

It almost always works out well, unless you've got very strong headwind or tailwind. It didn't today but that was because I had to make a step descent with a Dash-8. It was a tad behind me and above. I knew it would overtake me if I gave it the opportunity and that would be simpler for both of us. As I was thinking that, ATC asked if I could descend early.

I advised that I could descend straight away - I was still around 74 DME at the time. Rather than do any maths at that stage, I just slowed to 200 knots, to ensure that the Dash would overtake quicker and descended at (200/10 = 20. 20/2 = 10. 10 x 100 = 1000 FPM) until reaching a point where there was enough separation between us, with the Dash ahead of me for us both to descend on our normal profiles.

I was about to work that out when I noticed a "live" Glideslope needle. I was, by then, 50 DME. Before using it, I decided to test the signal by intercepting it (it was above me at the time so it wasn't as if I had to fly down, which I wouldn't have done while still so far out). Then adopted my original 220 knots/1100 FPM profile. The GP signal did the right thing so I didn't have to do any further maths and passed the IAP exactly on profile.

So there ya go. When ya don't get any profile disruption, do it the way my plan started out and you'll get the hang of it in no time and be able to short-cut the calculations before you know that you're doing it. If you get a live GS indication further out than you expect, just check its behaviour against the profile you've planned to fly, as already worked out.

Some days, things just go too smoothly! :D

[airbuslad]

Thanks for the replies lads. The Alzheimer’s must be getting better I seem to remember the one in 3.
Have great weekend

[Pilot Pete]

Forgot to mention, using the 3 x height/1000 to work out the descent gradient from up high also requires us to allow for slowing down in the 757 (a pretty slippery beast!). What works well is 1nm for every 10kts you want to lose. So;

cruise at 37000' with a target of 210kts when intercepting the localiser. 37x3=111nm + 10nm to slow down = 121nm. That works fine as a ballpark check for the VNAV profile.

Once you start going down it's all about energy management, just keep the calculations going to see where you are, it doesn't matter if you are high or low on the profile, just use the energy in the a/c to your advantage; if you are low on the profile and there is the chance of a shortcut at some point don't try regaining the profile using thrust, you'll probably end up on profile when you get the shortcut or even above it and you've just burnt all that extra fuel! If you are not going to get a shortcut then you are better trying to regain the profile earlier rather than later (and lower) where you will burn more fuel

If you are high on profile once cleared you can increase speed in the descent to dive down below that required and once level allow the speed to wash back off to get yourself back on the correct profile just as your speed comes back to the required level. This happened the other night going into Manchester. Initially arriving via Mirsi for a landing on 24L we requested 06L as it was very quiet. At a very late stage our request was granted so all of a sudden we had just lost 25 track miles. My initial reaction was to bin VNAV, go FLCH, wind the speed up (no ATC speed restriction) and pull the speedbrake out, select HDGSEL and point us towards an 8nm final. Quickly rebrief for the VOR/DME to 06L and set up the navaids (although we had the field in sight they still like you to follow the approach aid). Using the MCT DME 'plus a few' as my rough guide to distance to go before the LNAV arrival track was reprogrammed for 06L I could once again see how high I was on the profile. It's not long before you have dived through it and can start thinking about the decelleration, at which point the automatics were ditched and I got the chance to practice a hand flown VOR approach, recalculating all the time using the rules mentioned previously with the added bonus of the PNF calling the descent profile height checks until we had the PAPIS in sight. Works a treat. The idea being to keep the thrust levers shut from TOD to around 4nm when you spool them up in case of the GA. That way we burn only about 0.3T of fuel, whereas if you have to use thrust at any stage that figure goes up dramatically, especially with a level portion low down. Can often be nearer 1.0T

PP

[autoflight]

Earth is not flat. Therefore the height at greater distances from the GP antenna will be slightly greater than if it was flat. If you're operating in hot conditions, like 50C in Kuwait, true altitude will explain pressure altitudes differences vs DME distances. At 10nm these effects are not too great. The curvature of the earth is significant enough to notice if you capture GS at extreme range, and you're prepared to do the maths.

[OzExpat]

All agreed Pete ... guess I should've mentioned, for the benefit of those who didn't check my profile, that I fly a B200, which is a very flexible aeroplane - if somewhat slower than your 757! :D

autoflight ... okay, I've never seen that. I have the advantage of being in the tropics, where the highest temp I've seen is 36 celsius, with the average more like 32 .. by day. At this time of year ... we're in our "dry season", which is something not like "winter" elsewhere, and the temp never seems to get above about 28... brrrrrrrr :eek: :D

[Pilot Pete]

autoflight,

surely, bearing in mind the protected range of a glidepath signal (as pointed out by BlueEagle) the discrepancies are more likely to be due to signal interference at greater ranges than due to earth curvature! How far out are you talking about for earth curvature to become a factor?

PP

ps OZ,

I had a friend who flew a big turbo-prop and it never ceased to amaze me that he said they could maintain some rediculous sounding speed to 4nm before chucking out the prop 'anchors'. Props do have their advantages in some phases of flight!

[autoflight]

1 degree for every 60 miles. Depending what range you actually get the GP, its a bit academic, but nevertheless a factor for those who are more interested in the calculations. Its not too often that there is a post on this subject, and this consideration would otherwise never see the light of day.

[Waste Gate]

Here's a simple rule of thumb I use for monitoring descent profile in a 767. It would probably work well in the 757 too. Here goes . .

Take your indicated airspeed and subtract 200. Divide the answer by 10. For example, for a 300 knot descent, the "number" is 10.

Multiply your altitude to lose by 3, add the "number" and you will get a very accurate required track miles for any given altitude. It also compensates automatically for winds and ties in nicely with the "gates" that most people use, eg. 5000ft/20nm/250 KIAS and 10000ft/40nm/300 KIAS.

So next time you are descending through 11500 ft AAL at 280 KIAS and wondering how many track miles you need, using this rule of thumb you will come up with about 43 track miles.

WG.

[Waste Gate]

Here's a simple rule of thumb I use for monitoring descent profile in a 767. It would probably work well in the 757 too. Here goes . .

Take your indicated airspeed and subtract 200. Divide the answer by 10. For example, for a 300 knot descent, the "number" is 10.

Multiply your altitude to lose by 3, add the "number" and you will get a very accurate required track miles for any given altitude. It also compensates automatically for winds and ties in nicely with the "gates" that most people use, eg. 5000ft/20nm/250 KIAS and 10000ft/40nm/300 KIAS.

So next time you are descending through 11500 ft AAL at 280 KIAS and wondering how many track miles you need, using this rule of thumb you will come up with about 43 track miles.

WG.

[OzExpat]

Pete ...

I had a friend who flew a big turbo-prop and it never ceased to amaze me that he said they could maintain some rediculous sounding speed to 4nm before chucking out the prop 'anchors'. Props do have their advantages in some phases of flight!
He probably had to do that, with yer 757 up his clacker! :D

[Pilot Pete]

Oz,

no, no, no, we're always sedately coming in at 160 to 4! I think he was one of the school who believe that 180 to 2 makes a big difference to his on chocks time!

PP

[OzExpat]

Pete ... ah yeah, now I get it - his apron is off the other end of the runway huh? :D

[4dogs]

Oz,

Multiplying your groundspeed by 5 is the same result as whatever you said, errrr "divide by ten then halve it etc", and potentially easier.

[SixDemonBag]

Hey Wastegate, sitting in YPPH doing the daily gring. I too have heard a heap of different formulas in calculating the track miles req'd. The one I use is a simplified one of yours.

300 kts : 3x Ht +10
250 kts : 3x Ht +7
Ref +80 : 3x Ht +5

Saves on that first step....if you're like me and need every second and cubic millimeter of brain capacity! Catch you on the airwaves. (spoke to devilboy today)

BTW...never thought about the whole 'curviture of the earth' thing on an ILS. Interesting.

[OzExpat]

4 dogs ... agreed. But at the stage where I'm planning my descent, my GS is a bit different to what it'll be during descent. As a result, I've never bothered to include GS in my scan until after passing the IAF/IAP.

[411A]

Operated with a particular F/O a few years ago who started to "plan" his descent about TOC. Twisted his Breitling bezel, spun the wiz wheel, punched the calculator buttons...and still got it wrong.
Hopeless. :rolleyes:

[Pilot Pete]

4Dogs

I suppose it's what you are used to, but I don't see how with a G/S of 160kts multiplying 160 x 5 can be easier than 16 (just ignore the last digit of the GS) divided by 2 to give you your answer of 8(hundred)fpm ROD?

OZ

Good point, I too am not really interested in groundspeed until I am about to capture the glideslope, until then it's airspeed that I need to be concerned with as that's what I have to lose to take flap etc at the right point.

PP

[bookworm]

Young Paul wrote:

There are two formulae here -
3 miles per 1000', or 330' per mile
and 300' per mile.

Both are very easy to use.
The first is about 10% more accurate, if it matters. Which quite honestly it doesn't really.

Full marks for thinking about the accuracy but the true figure is almost slap bang between the two:

For a 3 degree glidepath, the height is 6080ft * sin (3 degrees) per nautical mile from the touchdown point, which is 318 ft/nm.

As you say, I don't think the difference between any of these is likely to be of operational significance.

[Waste Gate]

GDay SDB.

I must have missed you in YPPH by only a day. Left home on Thurs. night for Auckland, and ended up in Perth. Go figure . . . :confused: :confused:

WG.

[OzExpat]

Pete ... humble apologies for the delayed response... was travelling to the UK - and then there was booze... and wimmen. Ya know how THAT goes! ;) Anyway, yes, even tho my machine ain't as slippery as yours, the same considerations apply coz it takes a while to slow a B200 from 220 KIAS to 200 for approach flap, then back to 180 for the gear. I like to have meself sorted at GP intercept.

bookworm ... I appreciate your comments but the fact is that, things are changing throughout the approach. In fact, they're changing right from the moment you leave crz alt. The airspeed is changing a bit, the TAS is changing a lot. It is for this reason that a "close approximation" works so well. But I'm sure you already knew that.

[4dogs]

Oz,

I can't find my old Blue books since she who must be obeyed tried to clean up my study, so I need a procedure designer's help:

Noting that there are some differences in ILS installations, what sort of vertical distance from the glide path would one expect to see at half scale deflection up and down at say 4 miles from touch down (about where OMs are sited, depending on terrain etc) and 10 miles (about the start of the procedure)?

[OzExpat]

4dogs ... I'm several thousand miles away from all my references sources at present. Rather than "wing" an answer that could well be wrong, I'll have to bat this one to someone elsewho may be tuned in here.

I'm not due back at work until 28 August, but sure am having fun in the meantime! :) Sorry I can't be more help right now.

[autoflight]

4dogs
Whatever formula you get, remember the real world is not flat [increased GP altitude by 90 ft at 10nm], and there are true altitude considerations. Otherwise unexplained crossing altitude errors may be more clearly understood if you do more complete maths.

[Max Angle]

Here is my rule of thumb:

Feed the FMC with wind data and any altitude/speed restrictions, get the newspaper back out and go down when it tells you to.

[xpc]

altitude x 3 for the TOD
DME x 3 is the formula i use to check if i am on glide when all else fails