VOR DME or TACAN: how does triangulation work?

[JayPee]

One thing I've been struggling with regarding navigation is the following...

 

The VOR DME or TACAN station transmits 360 degrees and it is aware of where the north is. Additionally the distance to the ACFT can be determined. Next to this, the ACFT comes with a compass so the difference in degrees between its heading and the north can be determined as well. So as far as I would summarise it comes down to the following:

 

angle a is known (VOR)

distance Z is known (DME)

angle b is known (compass on the ACFT)

 

Now if the ACFT wants to determine the location of the VOR DME or TACAN station relatively to itself, as is what the HSI shows you, it would need to know angle c to combine angle b + angle c. However, for angle c you would need to know two of the following, all which are unknown:

 

distance X

distance Y

angle d

 

Where am I missing the obvious?

 

If north were just upward for the ACFT and for the VOR DME as well then angle c would simply be 180 minus angle a. But since distance Z is greater than zero, there is a triangle: magnetic north - ACFT - VOR DME.

:pilotfly:

Edited January 17, 2014 by JayPee

[Griffin]

Ok, it's been a while since I have been close to avionics despite that I'm supposed to be an avionics technician.

VOR is not a smart instrument containing complex computer for calculating angles. VOR shows the deviation of an aircraft from the selected radial and it's simply determined by the phase differences in two signals. I don't know exactly how a TACAN operates but it's not too much different IIRC.

HSI combines the functionality of a VOR indicator, an ADF indicator and a compass. ADF is also a very simple using only radio signals to determine the direction.

To know how it works you need to know how each of those systems work. HSI is an excellent instrument that combines all of them into one clear display.

Edited January 17, 2014 by Griffin

[Eddie]

Essentially it's all done by measuring time delays between signal pulses and in somewhat similar in principle to RADAR, only unlike RADAR is doesn't rely on reflected energy. The TACAN and aircraft don't actually "know" any of the things you assume they do, and they don't need to either. There is no triangulation involved.

 

A TACAN antenna transmits two separate signals, one which travels in all directions and is "pulsed", and another that is rotated. An aircraft set to the correct TACAN channel sends a pulse the the TACAN and then the TACAN station sends back a reply to the aircraft with the time delays being used to calculate range. This is also the same for air to air TACAN.

 

Bearing works by having the TACAN station modulate the signal amplitude it sends differently across the antenna by rotating a reflector around the antenna. This gives a rotating signal where one point has a higher amplitude and the opposite side a lower amplitude.

 

As the antenna rotates a fixed reference signal is also transmitted, as both happen at a fixed speed, the amplitude of the modulated signal at the point the reference signal is received is used by the aircraft's TACAN set to determine it's bearing from the station.

 

All pretty simple really. ;) (Although I'm probably terrible at explaining it).

[aaron886]

When introducing this to students, I describe a lighthouse with the usual sweeping white light but also a blinking red light on top. The white light rotates at 1 RPM, and the red light blinks once every minute at the moment the white light points towards magnetic north. By comparing the time between the lights, you can determine a bearing from the station. (Radial)

 

The HSI is really very simple in principle. It simply rotates the instrument face on which the VOR indication is shown, turning it into a Heading Indicator. I can expand if you are confused.

[Eddie]

That's a good analogy, I might have to steal that one.

[Bushmanni]

You have a slight conceptual error in your drawing and it's good that you draw it as this misconception would have probably been very hard to catch without it. Range of aircraft from VOR is minuscule in comparison to distance between VOR and north pole or aircraft and northpole. In effect vectors X and Y are parallel and hence c is simply the opposite direction of a. While this isn't exactly true the error is unsubstantial as long as the assumption of being far away from north pole holds.

[GRUNT -Shrek-]

Marry had roast beef, Marry burped.

 

(MH + RB = MB)

 

you are totally missing magnetic/true bearings, deviation and error.

 

 

Basically you intersect two LOPs having best approximatly 90° offset, so the bearing will be most precise.

[JayPee]

Eddie's explanation

I always thought TACAN worked exactly like VOR+DME, but although the end results are the same (you get your bearing and range), what happens under the hood is different.

 

You have a slight conceptual error in your drawing and it's good that you draw it as this misconception would have probably been very hard to catch without it. Range of aircraft from VOR is minuscule in comparison to distance between VOR and north pole or aircraft and northpole. In effect vectors X and Y are parallel and hence c is simply the opposite direction of a. While this isn't exactly true the error is unsubstantial as long as the assumption of being far away from north pole holds.

Understood. So when flying over Svalbard it would be slightly off but that's about it?

 

When introducing this to students, I describe a lighthouse with the usual sweeping white light but also a blinking red light on top. The white light rotates at 1 RPM, and the red light blinks once every minute at the moment the white light points towards magnetic north. By comparing the time between the lights, you can determine a bearing from the station. (Radial)

 

The HSI is really very simple in principle. It simply rotates the instrument face on which the VOR indication is shown, turning it into a Heading Indicator. I can expand if you are confused.

Are you talking about TACAN or VOR DME?

[Bushmanni]

The error depends on the ratio between longitudinal (east-west component) distance to the VOR and distance to the closest pole. In arctic and antarctic circles with 100km longitudinal distance to the VOR you would have about 2 degrees of error. The direction of error depends on which side of the equator you are and whether you are east or west side of the VOR. This error would cause you to slowly fly off the radial which you would then correct with slight adjustment of the heading and everything would be fine. In effect you are unlikely to even notice this as wind correction is likely going to be much bigger.