I have a 1952 book that uses 1.23 for the VHF line of sight formula - yet the exams use 1.25.

Paco,

Thanks for the heads up on the path being a pursuit curve. The derivation from first principles in terms of groundspeed coordinates was not going well!

The solution in airspeed coordinates appears to be given on the Wikipedia page for a radiodrome here, pushing the date back to at least the 1730s.

I have just read the reference and two things occur to me.

1. The reference describes an object which is chasing another object which is itself moving. This is not the case with the navigation beacons.

2. If the hare is running directly away from the dog (which sounds like what any sensible hare would do) or directly towards the dog (a mad march hare possibly), the dog's path will be a straight line. This is of course the equivalent of the beacon being directly upwind or downwind of the aircraft.

Keith,

In the airspeed coordinate system the beacon has a velocity vector opposite to the wind vector.

Is it not correct that when the beacon is finally reached the aircraft velocity vector is parallel to the wind vector, in the opposite direction?

My comments were not intended to be taken seriously

But

If we take the river-crossing scenario, if the food is some distance downstream and the current is sufficiently slow, the dog might actually be moving at right angles to the flow, or even in a somewhat downstream direction when it reaches the food.

Or in the case of the Hare running directly away from the dog, the entire path of the dog will be a straight line. Given the range of possible scenarios, we cannot say that the path will always be a spiral or even a curve.

I have not bothered to go through the maths in the link, but if it is correct, then presumably it will cater for the cases examples which I have described above.

Ahah, it's look like i've found someone more mathematical than me !
You're seriously interested in coming up with an equation to describe this kind of curve ?
I'm sure you would be familiar with the brachistochrone curve as well ?
You sound like some of my colleagues in higher education who went on to become math researchers.

For a pursuit starting with a non-zero crosswind component there will be at most only one instant when the headwind component is zero. The crosswind component will only be zero if the beacon is reached.

Nahin, referenced in the Wiki page on radiodromes, for a terrestrial coordinate system with the beacon at the origin and the wind acting along the positive y-axis, provides this function [eqn 1.2.8] for the radiodrome which he refers to as the "wind blown plane's path":

http://mathurl.com/mt4lwns.png

The wind speed is w and the true airspeed is v. At x = a, where the path crosses the x-axis, the heading is orthogonal to the wind. If n < 1, i.e. if the beacon can be reached, then the y-axis is an asymptote for y'(x). Therefore the beacon is reached directly from the downwind position unless it is initially approached directly from the upwind position.

KayPam,

That is a famous variational problem of similar vintage and one that took Newton half a day to solve.

He obviously had trouble with the ADF as well :)

If I am understanding this comment correctly it means that:

Experiment 1. If the starting point is with the aircraft 10 km directly upwind of the beacon it’s final approach to the beacon will be from directly upwind.

Experiment 2. If we repeat the experiment, but with the aircraft displaced even a small distance (1 m, 1 cm or even 1 mm) to the left or right, it’s final approach to the beacon will be from directly downwind.

Is this really the case?

The limits of the resolution of the ADF system should not be a factor in this, because the same equations have been applied to other situations such as the dog and hare.

Yes, I think that would be the case.
It's all about drift angle and not allowing for it.

Strictly in terms of the properties of the curve that is correct. The required rate of turn near the beacon will however often exceed what can be achieved. Arthur Bernhart discusses these curves in a set of papers here.

For aircrafts with wingspan over 60m the formula is: 90m + 0.125D; so 90 + 0.125*1500 = 277.5m

The CAA response to post 1062:

Compressibility is typically considered at speeds above 200 kt CAS or 300 kt TAS.

However, it doesn't appear to be in the database anyway.

Bless them, this is because the FAA documentation says compressibility need not be considered below 200KT (one assumes CAS but they don't specify) and 10,000ft (missed that bit out) and the CRP-5 and its RAF predecessors did not consider compressibility below 300KT TAS. The response is an awkward attempt to reconcile the two given speeds, but sadly misses the point that compressibility is not applied in the conversion between Mach number and TAS. Really.

Hey,

Having just completed my 14th test a few days ago, I'd like to provide you with some feedback.
I started with a French School in mid december, so it took me a grand total of 6 months and one week. That's including the four total weeks I took to revise before sessions 1, 2 and 4.

My country does not seem to be willing to disclose your marks, but I had an average of about 95-96% with my school's final tests (they reused some questions from aviationexam and created some questions, to simulate new questions on the test day)

I spent half my time on the books and half my time on aviation exam.
This was done in parallel with my job, about 1 to 3 hours per day of work, every day during these six months.

About the subjects :
I started with :
Communications, air law, ops proc : just by heart learning, not so many new questions but they could be surprising since it's not easy to not miss anything.
Then, instruments, meteorology, perf and mass&balance : No idea if questions on test day were new or not because they could all be answered with reasoning. I like subjects like these.
Then AGK, PoF, flight planning. The latter two are like the four previous one : I liked them. However I feel AGK is the subject in which the level I reached is the weakest of all subjects : too many many systems and details to learn. Different type of fire detectors, seriously ?
To finish with, gen nav, radionav, human factors.
HF : easiest subject of all, took me 10 minutes to complete the test.
Gen nav : so many calculations, it makes me tired. Thankfully it's quite of an easy subject for an ex math-student like me.
Radionav : worst subject, by far. Many different themes and many new questions about ridiculous little details that no one cares about.. The subject in which I had the worst scores, immediately after having read the books. In the end I think I have a better command of this subject than AGK but it was a pain in the ass. Probably mostly because it was the last subject.

Now i'm on for some bureaucracy to get my official diploma.

I'm very glad it's over, I have no idea what I'm going to do with all the newly available free time.

Hello, I came across a difficult PSR/PNR question while writing SACAA IR Exams and I need your help. Twice infact and all were similar.

I was given a PET Distance of I think 1200nm and distance from point A- B of 2300 NM if I remember correctly. Total fuel was about 15000kg and that was all. No speeds or endurance was given or wind. I was then asked to calculate PSR from point A to B.

Hi there

I started studying from the syllabus learning objectives, means that I learn specifically what they are willing us to know, line by line.
Do you think that's a good technique to pass the ATPL theory exams?! Or I should only study from my notes/books/cbt,... ?!
I am quite worry as the official exams are fastly coming up...

Cheers

In that case you will learn to navigate before you know about Lat & Long......

Not a good idea that. The LOs were never meant to be a syllabus as such.

Hey Pacol, then why put LO's in? What's the point of covering LO's if they don't (at the very least) cover the syllabus? Can you point me to the syllabus per se? That way I won't have to worry about the LO's

There are no syllabuses, that's the rub! They specify an LO, meaning what a student is expected to know after the studying then leave it up to the schools to guess to what level they should teach, thus creating their own syllabus. The only reference to levels or even sources of knowledge is in the question itself, which nobody should be able to see.