Trigonometry is hard

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Eibwen

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Eibwen
Gaining some increased familiarity with determining flight visibility on instrument approaches at minimums and ran into a difference in how to calculate at a typical DH.

IFR Magazine article: Makes reference to the following…
“For a normal precision approach with a DH at 200 feet, you’ll be about 2800 feet, or a little over a half mile from the threshold.”

AIM 1-1-9 f(2)(b) says this:
“The MM indicates a position approximately 3,500 feet from the landing threshold. This is also the position where an aircraft on the glide path will be at an altitude of approximately 200 feet above the elevation of the touchdown zone.”

Which is it? Or am I missing something?
 
My math says 2800 ft since 200/318 is about 3800 feet from where the glide path intersects the runway at about 1,000 ft down the runway at the aiming markers.

Edit: ok so my math says I’d be at 239 feet on glideslope if the FAA’s guidance is correct. That’s probably pedantic to split hairs that finely on some level except it makes a significant difference in what I expect to see at a 1/2 mile visibility minimum if I do break out at an actual 200 minimum.

My math skills are suspect. Set me straight if I’m cockeyed.
 
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Touchdown zone is usually about 1000' in from the threshold.
Edit: Never mind......but, I see, the quote from the AIM does seem ambiguous, they use both threshold and touchdown zone, seemingly as the same point.
And, FWIW, I get the same numbers as you, with simple trig.
 
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Thanks.

Yeah my conclusion is that paragraph in the AIM is discussing MM placement (barely a thing anymore I know) and from an operational standpoint it made sense to place the MM just prior to minimums as a reminder to the crew on the approach that the decision point was imminent. Not as an indicator that they were precisely at minimum DA.

It still is a strange bit of ambiguity (or actual error?) on something that can be stated precisely and has considerable impact on the following decisions.
 
I'm doing Calculus homework right now and when I saw the title I expected a Secant or Sine somewhere. This seems more like a Geometry question...
 
Well since your chances of flying an ILS that has a working MM in an aircraft with a working audio panel with a MB receiver is probably close to zero, I wouldn’t worry too much about what the AIM says in that regard.
 
tsts4 said:
Well since your chances of flying an ILS that has a working MM in an aircraft with a working audio panel with a MB receiver is probably close to zero, I wouldn’t worry too much about what the AIM says in that regard.
Click to expand...
fair enough. But estimating visibility at 200 or whenever you break out is the actual point of the post. More specifically, the variation in distance at 200.

I think I have a good idea of what led to it now.
 
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I think you are overthinking it. Part 91 visibility is based on what you see when you arrive at the DA/DH. See the runway environment as defined under 91.175 and you land (or if only the approach light system is visible you can go down to 100ft) Distance can cave determined by the runway markings which are a set size and distance from one another. Don’t try and do math in the cockpit especially when on an approach to in IMC to mins.
 
I understand your point, but it’s not overthinking. It’s how the ALS was designed and it’s a tool we have available.

www.ifr-magazine.com

How Far Can You See? - IFR Magazine

Three simple conditions must be met to land from an instrument approach: being in a position to land, having the runway environment in sight, and possessing the required flight visibility. The first requirement is straight-forward and the second is thoroughly articulated in the regs. The third...
www.ifr-magazine.com www.ifr-magazine.com
 
Hmm. I see a lot of wording in the initial question like: "about", "approximately" and "for a normal ..."...
That doesn't lend well to a single, definite mathematical answer. Some variables have to be held constant. But assuming a 3deg GS and 200' DH, wouldn't it just be like this? Forgive my paintshop art and my own rusty math skills lol.

1733079971149.png

I got the 50' AGL from Honeywell Aerospace's glidepath page.
1733080049242.png

But the GS angle can be different as evidenced below. So 3.0 isn't always the case, nor is 200' DH.
1733078162463.png
1733079620906.png
 
Well yes, at a certain level and to tsts4’s point above, this definitely becomes a whole lot of hair splitting that is not useful or worth focussing on to a granular level while actually breaking out at minimums. I don’t think any of us would be engaged in the trig/geometry/whatever this is just to figure out whether or not we have 2,816 feet or 2,743 feet of visibility.

Every approach has slight (or large) differences that would adjust our decision making. Having a good understanding of the ALS and what it shows us, and what we can *expect* to see, when we first break out … is the goal. It facilitates a smooth transition to the final stages of an approach and landing.

This just arose from the large difference between an FAA publication and an article about how to interpret the visuals on short final at minimums. A large enough difference to be, for me, worth understanding so I have a clear expectation … when it’s useful and the need arises. That’s as much as my math needs to tell me. Ymmv.

Thanks all.
 
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Eibwen said:
This just arose from the large difference between an FAA publication and an article about how to interpret the visuals on short final at minimums. A large enough difference to be, for me, worth understanding so I have a clear expectation … when it’s useful and the need arises. That’s as much as my math needs to tell me. Ymmv.
Click to expand...
Sounds to me like the math just proves that there’s confusion in the terminology.
 
hindsight2020 said:
which is never. But I'm not an airline pilot; in my line of work we just send it!TM and hope the crash doesn't embarass the leadership too bad :D
Click to expand...

I just finished reading a Prairie Fire FAC history. Those dudes really sent it.
 
Say the airport is reporting less than 1/2 mile visibility. You elect to fly the approach (part91). If you get to the DH and can see the runway then you have the required 1/2 mile of flight visibility. ATIS, AWOS, or whatever doesn’t know what the flight visibility is. You’re making it harder than it needs to be.
 
Eibwen said:
www.ifr-magazine.com

How Far Can You See? - IFR Magazine

Three simple conditions must be met to land from an instrument approach: being in a position to land, having the runway environment in sight, and possessing the required flight visibility. The first requirement is straight-forward and the second is thoroughly articulated in the regs. The third...
www.ifr-magazine.com www.ifr-magazine.com
Click to expand...
The gist of the article seems to be how to disarm a fed by having a good answer. After you land, measure out the required visibility from the threshold on your approach chart — you saw the runway before that point, right?
 
Busflyer said:
Say the airport is reporting less than 1/2 mile visibility. You elect to fly the approach (part91). If you get to the DH and can see the runway then you have the required 1/2 mile of flight visibility. ATIS, AWOS, or whatever doesn’t know what the flight visibility is. You’re making it harder than it needs to be.
Click to expand...
=) Except it’s not hard. it’s just some calculation to work out. (Trig is hard … that’s why I don’t use it:D) . It’s the details of how the system works which I think is interesting and potentially useful. And if it’s in the AIM I have a goal of understanding it. That’s me. Ymmv.
 
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ArrowFlyer86 said:
But the GS angle can be different as evidenced below. So 3.0 isn't always the case, nor is 200' DH.
View attachment 135787
View attachment 135794
Click to expand...
While neither is always the case, they are the case in the vast majority of instances. You used a pretty extreme example there, 7.75º is higher than the maximum permissible glidepath angle which is why the lower one is a circling-only approach.
 
flyingcheesehead said:
While neither is always the case, they are the case in the vast majority of instances. You used a pretty extreme example there, 7.75º is higher than the maximum permissible glidepath angle which is why the lower one is a circling-only approach.
Click to expand...
Yeah, the thought process behind that ties into the initial wording of "about", "approximately" and "for a normal approach..."...
Not every one will conform, which is why there may have been initial confusion. But I freely admit I chose the most extreme example I could find just for the sake of contrast :)
 
A 3 degree glideslope is 318'/nm away from whatever reference point you ended the 3 degree slope. Round to 300' for inflight calculations of things like "at what distance will I center the GS from this level altitude?" A 4 degree glideslope is 424' nm. Unlikely to see steeper and very unlikely to ever hear or see your MM indication. JFK seems to still have an IM on 22L, so you could shoot that to hear it I guess.

Math is: tan(3) = x/6076 [ft/nm], so x = 6076 [ft/nm] *tan(3) = 318 ft/nm.
 
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