lenbrazil
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### What Is The Range Of A Plane Radio?

What is the range of a plane radio broadcasting on a CTAF/Unicom frequency?

More specifically would it be possible for a transmission from a King Air at 1800 ft / 440 AGL be picked up at an airport (Sky Harbor) at 610 ft 45 – 50 miles away? It may have been snowing at the time.

Len

luisca
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### RE: What Is The Range Of A Plane Radio?

It depends on several things, like the conditions of the atmosphere and the altitude of the plane, also the power of the transmitting radio is important.

 Quoting Lenbrazil (Thread starter):More specifically would it be possible for a transmission from a King Air at 1800 ft / 440 AGL be picked up at an airport (Sky Harbor) at 610 ft 45 -- 50 miles away? It may have been snowing at the time.

It is entirely possible.

A good rule of thumb is that the transmitter is line of sight with the receiver you can hear it. I have listened to MLB ATIS from 60 miles away.
If it ain't Boeing (or Embraer ;-)) I ain't Going!

MD11Engineer
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### RE: What Is The Range Of A Plane Radio?

If it is VHF, then it is a direct line towards the electrical horizon (a little bit more than the optical horizon due to different difraction of EM waves at this frequency). So the range depends largely on altitude (up to 2-300 km).

HF (shortwave) transmissions can propogate due to two means:
Ground waves, were the signal follows the shape of earth with increasing loss until it peters out (disappears in the static background noise). This range is usually (depending on the antenna and transmission power) a few hundred kilometers.

Air waves: Depending on the frequency and time of day (solar activity) HF waves can be reflected at the ionosphere layers of the upper atmosphere. They can even (provided the angle of radiation at the transmitting antenna is low) bounce back and forth between the ionosphere and ground, so that HF waves can have a range from between 1000 km and global range.

Jan

[Edited 2006-04-17 19:57:50]
Je Suis Charlie et je suis Ahmet aussi

Dtw757
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### RE: What Is The Range Of A Plane Radio?

Oh I would think you should be able to hear an airplane using the CTAF 50 miles away with no problem at all. At my local airport KDUH we use a CTAF and I have heard calls being made from as far as 100nm while I was at pattern altitude.
721,2,732,3,4,5,G,8,9,741,2,3,4,752,3,762,3,4,772,3,788,D93,5,M80,D10,M11,L10,100,AB6,319,20,21,332,3,346,388,146,CR2,7,

lenbrazil
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### RE: What Is The Range Of A Plane Radio?

Most of you seem to be saying it's possible, how probable is it (definate, probable, possible)? Remember I'm asking about plane to airport not plane to plane. For those of you familiar with Northern Minn the plane in question would have been a few miles east of Eveleth the nearest airport with the same CTAF is Sky Harbor just SE of Duluth.

Len

JetCaptain
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### RE: What Is The Range Of A Plane Radio?

Theoretical VHF reception range (nautical miles) is equal to 1.23 times the square root of the altitude (above the receiver). I presume you mean the aircraft was at 1800 feet above sea level ?

Then 1800 - 610 = 1190 feet above Sky Harbor

Reception range equals = 1.23 times (SQR 1190) = 42 nautical miles (48 statute miles).

JC

[Edited 2006-04-17 21:59:09]

[Edited 2006-04-17 21:59:55]

timz
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### RE: What Is The Range Of A Plane Radio?

By "theoretical" you mean "assuming the earth is a sphere"-- right? In this case the aircraft was 440 AGL so we can't be sure the terrain between it and the airport would allow a line of sight. But presumably the airport antenna is not at ground level, and its height adds a few miles too.

jspitfire
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### RE: What Is The Range Of A Plane Radio?

 Quoting JetCaptain (Reply 5):Theoretical VHF reception range (nautical miles) is equal to 1.23 times the square root of the altitude (above the receiver). I presume you mean the aircraft was at 1800 feet above sea level ? Then 1800 - 610 = 1190 feet above Sky Harbor Reception range equals = 1.23 times (SQR 1190) = 42 nautical miles (48 statute miles). JC

I was just trying to post this exact reply, but the tread was moved here from the Civ Av forum, so you beat me to it. Just one small correction, however, it was actually recently changed to 1.25 instead of 1.23, not that it makes too much of a difference.

Jason

lenbrazil
Posts: 109
Joined: Wed Apr 12, 2006 11:08 am

### RE: What Is The Range Of A Plane Radio?

 Quoting JetCaptain (Reply 5):Theoretical VHF reception range (nautical miles) is equal to 1.23 times the square root of the altitude (above the receiver). I presume you mean the aircraft was at 1800 feet above sea level ? Then 1800 - 610 = 1190 feet above Sky Harbor Reception range equals = 1.23 times (SQR 1190) = 42 nautical miles (48 statute miles).

So 42 nautical miles is a best case senario? according to airnav.com it's 46.1 nautical miles so it would have been just out of range? They also say it's 37.1 from DLH to EVM the plane had been talking to Duluth ATC were they going out of range?

timz
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### RE: What Is The Range Of A Plane Radio?

No, nobody knows whether there actually was a line of sight in this case, since nobody knows about the terrain between. Could be a bit better, could be a bit worse. And in any case you have to apply the formula twice, once for the aircraft and once for the ground antenna height.

JetCaptain
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### RE: What Is The Range Of A Plane Radio?

>> So 42 nautical miles is a best case senario? <<

Not necessarily, but under normal conditions with typical equipment it should be close. How high was the receiving antenna ? A good exterior antenna 30 feet above the gound would add about 7 nautical miles to the reception range.

JC

lenbrazil
Posts: 109
Joined: Wed Apr 12, 2006 11:08 am

### RE: What Is The Range Of A Plane Radio?

What is the range of a plane radio broadcasting on a CTAF/Unicom frequency?

More specifically would it be possible for a transmission from a King Air at 1800 ft / 440 AGL be picked up at an airport (Sky Harbor) at 610 ft 45 – 50 miles away? It may have been snowing at the time.
Sorry if I’m being a bit dense but wouldn’t increasing the height of the transmitter reduce the range? Let’s suppose it’s 30 feet off the ground that would place it at 640 ft. ASL so it would be 1800 – 640 = 1160 Sq. root = 34 x 1.25 = 42.5 (or x 1.23 = 41.8).

But let’s suppose the receiving antenna did add about 7 miles the maximum would be 49 miles but could be less.

If the plane was 44 – 46 miles from Sky Harbor people at that airport might have its transmissions but then again might not depending on terrain weather and other factors correct?

I have no idea what kind of antenna the have there, other than getting in touch with them how could I find out?

Len

JetCaptain
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### RE: What Is The Range Of A Plane Radio?

>> Sorry if I’m being a bit dense but wouldn’t increasing the height of the transmitter reduce the range? <<

No it increases it. You need to consider the reception range at each location, then add them together.

range = (1.23 times (SQR 1190)) + (1.23 (SQR 30))

which is the same thing as saying 1.23 times (SQR 1220)

Terrain could be a factor, but in this case there doesn't appear to be any that would impact the line of sight between EVM (elevation 1378') and DYT (elevation 610').

So I'd say it "could" have been theoretically possible if they had a good antenna and radio at DYT, but the signal would probably have been weak, and the squelch would have had to be turned down or off on their radio.

So what exactly are you getting at anyway ? I'm guessing something to do with this ?

http://www.ntsb.gov/publictn/2003/AAR0303.htm

JC

Mir
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### RE: What Is The Range Of A Plane Radio?

Sky Harbor is a little airport with a little FBO that caters to small GA planes. At bigger FBOs that serve the more corporate crowd, each FBO may have its own radio frequency that pilots can call in on to tell them that Mr. Executive will be arriving in thirty minutes, so have the Mercedes waiting and make sure the air conditioning is set to 72 degrees. You're not going to find that at DYT - there will be a little radio in the FBO, and people will listen to it if they're in earshot, but more often than not they'll be out working on something else on the airport - it's small enough that they can pause what they're doing and help out if they see someone taxiing in. According to Airnav, DYT only gets 38 operations per day on average, so whoever works at the FBO probably has a lot of free time on their hands. I'd put money on DYT having no fancy reciever, and I'd also put money on them not hearing the transmissions that you refer to.

-Mir
7 billion, one nation, imagination...it's a beautiful day

Pihero
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### RE: What Is The Range Of A Plane Radio?

Come on, guys !
The initial formula was wrongly used : 1.23 x SQRT (A) gives a rough estimate of the line-of-sight distance [i.e]the distance to the apparent horizon[/b]. and that's the effective transmission/reception range of any given station antenna
Now, another station is bound to the same earth curvature limitations, governed by the same formula.
That means that you'll have to add-up the two ranges in order to find the maximum distance at which the two stations could talk to each other
In the initial problem, D max = 1.23 x SQRT (1800) + 1.23 x SQRT (610),
or 1.23 x [SQRT (1800) + SQRT (610) ]
so, 1.23 x [42 + 25 ]---->1.23 x 67 = 82.4Nm

 Quoting JetCaptain (Reply 12):range = (1.23 times (SQR 1190)) + (1.23 (SQR 30)) which is the same thing as saying 1.23 times (SQR 1220)

That must be a typo...Right ?
Contrail designer

JetCaptain
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### RE: What Is The Range Of A Plane Radio?

 Quote:The initial formula was wrongly used

No it wasn't.

 Quote:In the initial problem, D max = 1.23 x SQRT (1800) + 1.23 x SQRT (610), or 1.23 x [SQRT (1800) + SQRT (610) ] so, 1.23 x [42 + 25 ]---->1.23 x 67 = 82.4Nm

This is wrong because 1800 feet is the altitude of the aircraft above SEA LEVEL, you need to use the altitude above GROUND LEVEL. And 610 feet is the elevation of the DYT airport, where above ground level would be 0.

In this case the reception range from the aircraft will vary depending on the direction because the ground is not level in this area. The ground rises as you go from south to north. The elevation of DYT is 610 feet while the elevation of EVM is 1378 feet. However it is a fairly constant rise and would not impact the field of view from an aircraft that is 422 feet above EVM (1800 feet ASL).

To get the reception range to the south in the direction of DYT you need to consider the relative altitude between the aircraft and ground in that direction. ie: 1800 - 610 = 1190 feet above GROUND LEVEL. The 42 nautical miles in the first example would be correct looking from the aircraft towards DYT to the south (if the receiving antenna is at ground level).

 Quote:which is the same thing as saying 1.23 times (SQR 1220)

Yes that was a typo.

 Quote:I'd put money on DYT having no fancy reciever, and I'd also put money on them not hearing the transmissions that you refer to.

I would agree that this is probably the more "practical" answer. In my experience little FBO's don't have the greatest radio setup and would have the squelch turned up to block out weak signals. But with good equipment and the squelch turned off I'd say it could be possible.

JC

KELPkid
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### RE: What Is The Range Of A Plane Radio?

Don't forget, too, that a King Air is most likely to have "big" airplane radios that run off the 400 Hz AC bus, and are more powerful (i.e. the radio has a higher output wattage) than your typical GA aircraft radio...

Celebrating the birth of KELPkidJR on August 5, 2009 :-)

JetCaptain
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### RE: What Is The Range Of A Plane Radio?

 Quote: Don't forget, too, that a King Air is most likely to have "big" airplane radios that run off the 400 Hz AC bus, and are more powerful (i.e. the radio has a higher output wattage) than your typical GA aircraft radio...

Yeah but on the other hand in this particular case the antennas were probably iced up and the aircraft was out of control in a 90 degree bank with the antennas possibly pointed away from DYT.

JC

[Edited 2006-04-18 17:57:03]

SlamClick
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### RE: What Is The Range Of A Plane Radio?

 Quoting Jspitfire (Reply 7): it was actually recently changed to 1.25 instead of 1.23,

The geometry has not changed. Probably someone started teaching 1.25 instead of 1.23 because anyone can do the 'one and a quarter' math in their head.

My nephew is a container ship captain and he says maritime use is 1.17 X the square root of your height above the sea. Perhaps that accounts for the bending of light by the increased water vapor in the air just above the sea, I don't know.

The 1.23 is probably not going to work for PHX though, as there are mountains in every direction within the distance he stated.
Happiness is not seeing another trite Ste. Maarten photo all week long.

JetCaptain
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### RE: What Is The Range Of A Plane Radio?

 Quote:The 1.23 is probably not going to work for PHX though, as there are mountains in every direction within the distance he stated.

The last time I checked the earth hasn't changed shape, so the 1.23 factor hasn't changed. He's not talking about the Sky Harbor in Phoenix, he's talking about Sky Harbor, KDYT, in Minnesota (near Duluth).

JC

SlamClick
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### RE: What Is The Range Of A Plane Radio?

 Quoting JetCaptain (Reply 19):The last time I checked the earth hasn't changed shape, so the 1.23 factor hasn't changed. He's not talking about the Sky Harbor in Phoenix, he's talking about Sky Harbor, KDYT, in Minnesota (near Duluth).

Well, my mistake. (that's why they call this forum "tech/oops"

I agree. 1.23 is the proper constant for the formula. I just meant that in mountainous terrain it might not be reasonable to expect the full service volume on radio reception.
Happiness is not seeing another trite Ste. Maarten photo all week long.

Pihero
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### RE: What Is The Range Of A Plane Radio?

JetCaptain,
The formula used is just theoretical.
It takes into account the altitudes -MSL - of both the transmitter and the receiver.Obstacles do not come in it, and neither does the terrain slope. That's for local conditions only.
Earth curvature line-of-sight has MSL as level zero. Just imagine you're standing on the shore, watching the ships roll in and a friend of yours is in the near-by light tower.There is a yellow rubber dinghy on the horizon, coming towards you.Who is going to see it first :You or your friend ?
Now if that dinghy has a mast, how much farther will you be able to see it before you spot the dinghy underneath ?
That's what the maths say, and nothing else.
If I take your understanding of the formula further,an aircraft flying at Mt Everest altitude will never receive a transmitter held by an alpinist who's just made the top, right ? (because the "height" of the aircraft would be zero).
First you reinvent Mathematics, then you come out with a flat earth theory...
Well done, sir!
Contrail designer

lenbrazil
Posts: 109
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### RE: What Is The Range Of A Plane Radio?

 Quoting JetCaptain (Reply 12):So what exactly are you getting at anyway ? I'm guessing something to do with this ? http://www.ntsb.gov/publictn/2003/AA...3.htm

Yes, this is regarding the Wellstone crash.

Conspiracy theorists esp. the author of a book called "American Assassination" make much of the lack of a distress call.

As a layman it seems to me and to pilots on this and other forums that an SOS call would have been unlikely, the pilots who had only flow together 4 times and had no CRM would have been unlikely to have made one trying to save the plane first and a drop from 440 ft. AGL after a stall at 76 KCAS wouldn't give them much time.

Later it occured to me that even IF one of the pilots had made a distress call it's unlikely anyone would have heard it. They were on the EVM CTAF frequency and the only person at EVM went outside to 'do some chores'. The closest airport that uses the same frequency is Sky Harbor so I wondered if it was possible that the call would have been picked up there. That from what I gather here is theoretically possible but unlikely.

Other factors to consider is that the plane would have been about 135 degrees behind the plane and it was heading towards the ground at (approx) 26 degrees. I said the plane was at 1800 ft. ASL but that was before the plane stalled, if the call presumably would have been made only after stall so the altitude probably would has been less.

I imagine line of sight could have been a problem. The plane was only about 440 feet AGL and 1300 feet above Sky Harbor and about 269170 feet (44.3 nautical miles) away. Unless the terrain suddenly dropped off near Eveleth chance that the LOS would have been blocked is quite high.

One more question (OK 2) doesn't the FAA or FCC space airports that use the same frequency so that one won't pick up broadcasts intended for the other*? If not for example wouldn't a plane clicking on the lights at one turn on the lights at another as well?

*If there is a rule regulating this please let me know.

JetCaptain
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### RE: What Is The Range Of A Plane Radio?

Pihero,

 Quote:Earth curvature line-of-sight has MSL as level zero. Just imagine you're standing on the shore, watching the ships roll in and a friend of yours is in the near-by light tower.

Your boat on the ocean logic doesn't work here because RADIO WAVES CAN NOT PASS THROUGH THE GROUND, airplanes are flying over the GROUND here, not the OCEAN, therefore you have to take this GROUND into account, and use the height above GROUND and not above sea level as a reference. Again 42 nautical miles from my first example is correct. Your answer that the reception range is 82 nautical miles is ridiculous.

 Quote:If I take your understanding of the formula further,an aircraft flying at Mt Everest altitude will never receive a transmitter held by an alpinist who's just made the top, right ? (because the "height" of the aircraft would be zero).

In the Everest example the maximum reception distance between an aircraft at say FL350 and an Alpinist at the top at 29,000 feet would be about 410 nautical miles. I don't know what you are talking about when you say I think it would be zero !?

JC

Pihero
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### RE: What Is The Range Of A Plane Radio?

What do you make of this statement then ?

 Quoting JetCaptain (Reply 15):To get the reception range to the south in the direction of DYT you need to consider the relative altitude between the aircraft and ground in that direction. ie: 1800 - 610 = 1190 feet above GROUND LEVEL. The 42 nautical miles in the first example would be correct looking from the aircraft towards DYT to the south (if the receiving antenna is at ground level).

You converted the airplane altitude - 1800 ft - into a height over the airfield - 610 ft-. and you come out with height = 1190 ft, which is correct, value upon which you base your computation,
Or am I seeing things ?

Therefore, following this kind of logic, an airplane at 29,000 ft is at 0 ft AGL, relative to Mt Everest ---> 1.23 x SQRT (0) = 0 Nm.

And as I'm only human, neither does my vision.
Contrail designer

JetCaptain
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### RE: What Is The Range Of A Plane Radio?

 Quote:Therefore, following this kind of logic, an airplane at 29,000 ft is at 0 ft AGL, relative to Mt Everest ---> 1.23 x SQRT (0) = 0 Nm.

This is correct, but only for the area behind the mountain below 29,000 feet, this area is blocked by the mountain therefore reception range is equal to 0. Are we on the same page now ?

JC

JetCaptain
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### RE: What Is The Range Of A Plane Radio?

Lenbrazil,

It sounds like you have a pretty good handle on the reception issue.

 Quote: One more question (OK 2) doesn't the FAA or FCC space airports that use the same frequency so that one won't pick up broadcasts intended for the other*? If not for example wouldn't a plane clicking on the lights at one turn on the lights at another as well?

I don't know what distances the FAA uses when pilot controlled lighting is involved ? On the eastern seaboard there are a lot of smaller airports were the CTAF frequencies overlap. But it's been awhile since I've flown around in small aircraft, so I'm not the expert. A couple of times on a nice clear summer weekend afternoon flying over the northeast US at FL410 I've tuned up 122.800 to hear what it sounded like. Talk about a busy frequency from that altitude, I was probably listening to almost a 100 airports at once.

JC

[Edited 2006-04-19 00:27:48]

Mir
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### RE: What Is The Range Of A Plane Radio?

 Quoting Lenbrazil (Reply 22):One more question (OK 2) doesn't the FAA or FCC space airports that use the same frequency so that one won't pick up broadcasts intended for the other*? If not for example wouldn't a plane clicking on the lights at one turn on the lights at another as well?

Airports certainly can (and do) share CTAF frequencies. In fact, it's good policy not to click on the airport lights from too high up, as you'll turn on the lights at surrounding airports. You'll hear planes at other airports all the time when on a CTAF frequency, which is why starting and ending your radio calls with the airport you're at is so critical.

I think the reason the FAA doesn't try to set up CTAF frequencies so that they are exclusive to one airport in the area is that while it may help those on the ground, those in the air will be able to hear a much wider range, and thus it isn't really practical unless they want to seriously increase the number of CTAF frequencies.

-Mir
7 billion, one nation, imagination...it's a beautiful day

timz
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### RE: What Is The Range Of A Plane Radio?

 Quoting Jspitfire (Reply 7):it was actually recently changed to 1.25 instead of 1.23

Assuming no refraction, the actual figure would be between 1.22 and 1.23, so presumably they decided to allow for some refraction.

 Quoting SlamClick (Reply 18):My nephew is a container ship captain and he says maritime use is 1.17 X the square root of your height above the sea.

That's nautical miles, right? The 1.23/1.25 is statute miles.

timz
Posts: 6163
Joined: Fri Sep 17, 1999 7:43 am

### RE: What Is The Range Of A Plane Radio?

Ah-- now I notice he said

 Quoting JetCaptain (Reply 5):Theoretical VHF reception range (nautical miles) is equal to 1.23 times the square root of the altitude (above the receiver).

Assuming no refraction, and assuming the WGS84 spheroid, the figure for statute miles is between 1.22 and 1.23, depending on where you are on the spheroid.

JetCaptain
Posts: 198
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### RE: What Is The Range Of A Plane Radio?

 Quote:assuming the WGS84 spheroid, the figure for statute miles is between 1.22 and 1.23, depending on where you are on the spheroid.

Yes, except it is NAUTICAL miles.

JC

SlamClick
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### RE: What Is The Range Of A Plane Radio?

Okay, here's how you really do it.

1. Find the distance, in feet, from the center of the earth to the radio transmitter site. Multiply this distance by itself. This is called A-Square.

2. Find the distance from the center of the earth to your airplane. Multiply it by itself. This is called C-Square.

3. Subtract A-Square from C-Square. The result of this is called B-Square. The square root of this is the distance, in feet, at which you could expect to receive the radio station. It corresponds to a tangent across the surface of a spherical earth from your height above it.

If you are closer to the center of the earth than the transmitter site it may complicate the arithmetic somewhat. On the other hand if you are flying lower than the radio site, perhaps math is not your biggest problem at the moment.

I'd advise a quick peek out the window to resolve that last matter.
Happiness is not seeing another trite Ste. Maarten photo all week long.

timz
Posts: 6163
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### RE: What Is The Range Of A Plane Radio?

 Quoting JetCaptain (Reply 30):Quote: assuming the WGS84 spheroid, the figure for statute miles is between 1.22 and 1.23, depending on where you are on the spheroid. Yes, except it is NAUTICAL miles.

So now you know not to trust your source. You can do the Pythagoras for yourself and confirm that 1.22-1.23 is the range for 5280-foot miles. Assuming no refraction, that is.

bhill
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### RE: What Is The Range Of A Plane Radio?

Lenbrazil..I dont' mean to digess from your original question regarding commonly used freqencies, but with all of the "smarts" being built into airplanes nowadays...why not just use all of the other aircraft "zipping" around the Earth 24 hours a day to pass radio traffic as relays? I remember a discussion with Boeing folks complaining about "free flight". i.e let the airplanes computers "talk" to each other about seperation, altitude; for traffic management..at cruise, mind you for better flow control...
Carpe Pices

JetCaptain
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### RE: What Is The Range Of A Plane Radio?

 Quote: now you know not to trust your source. You can do the Pythagoras for yourself and confirm that 1.22-1.23 is the range for 5280-foot miles.

Hmmmmm. Every source I've ever seen has used .....

1.23 for nautical miles
1.41 for statute miles
2.28 for kilometers

As just one example, the website below is using 1.23 for NAUTICAL miles:

http://www.naval.com/sight/index.htm

Have they all been wrong !? Now I'm confused ? Can some mathematician type explain just what factor/units are really correct, in plain language, so someone dumb (lazy) like me can understand ?

I've tested it while flying numerous times (receiving the ATIS) and the 1.23 factor using nautical miles has always been very accurate.

JC

[Edited 2006-04-20 14:24:26]

timz
Posts: 6163
Joined: Fri Sep 17, 1999 7:43 am

### RE: What Is The Range Of A Plane Radio?

 Quoting SlamClick (Reply 31): Okay, here's how you really do it. 1. Find the distance, in feet, from the center of the earth to the radio transmitter site. Multiply this distance by itself. This is called A-Square. 2. Find the distance from the center of the earth to your airplane. Multiply it by itself. This is called C-Square. 3. Subtract A-Square from C-Square. The result of this is called B-Square. The square root of this is the distance, in feet, at which you could expect to receive the radio station. It corresponds to a tangent across the surface of a spherical earth from your height above it.

You can see that explanation needs work-- if transmitter height equals receiver height, reception range comes out zero.

 Quoting JetCaptain (Reply 34): 1.23 for nautical miles 1.41 for statute miles 2.28 for kilometers

Like I said, it's 1.22 to 1.23 for statute miles assuming no refraction. Apparently they all assume some refraction, which no doubt is sensible. It's surprising they all assume the same amount, tho. As I recall Bowditch uses 1.144 for nautical miles, and you saw that 1.17 above.

[Edited 2006-04-20 18:00:59]

bond007
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### RE: What Is The Range Of A Plane Radio?

 Quoting SlamClick (Reply 31): It corresponds to a tangent across the surface of a spherical earth from your height above it.

I don't think so.

Jimbo
I'd rather be on the ground wishing I was in the air, than in the air wishing I was on the ground!

SlamClick
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### RE: What Is The Range Of A Plane Radio?

 Quoting Bond007 (Reply 36):I don't think so.

Okay. What do you think?
Happiness is not seeing another trite Ste. Maarten photo all week long.

SlamClick
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### RE: What Is The Range Of A Plane Radio?

Here's what I mean:

The circle (1) is the earth.
The radio transmitter is on the surface at A
The line PQ is your height above the transmitter.
The line QA which is a tangent is the line-of-sight distance from that height.

Your vertical height has been exaggerated for clarity but mostly because I didn't draw the picture.
Happiness is not seeing another trite Ste. Maarten photo all week long.

timz
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Joined: Fri Sep 17, 1999 7:43 am

### RE: What Is The Range Of A Plane Radio?

Good-- a diagram. Now all you need to add is another radial line, angled downward from the center of the earth ("downward" on the diagram, not on the earth), below line OA, to the transmitter that's at some specified height above the surface, on that same tangent.

Then you've got two right triangles, O to A to receiver and O to A to transmitter. Apply Pythagoras to each triangle to get the A-to-receiver and A-to-transmitter distances.

All assuming no refraction.

David L
Posts: 8552
Joined: Tue May 18, 1999 2:26 am

### RE: What Is The Range Of A Plane Radio?

 Quoting Pihero (Reply 14):That means that you'll have to add-up the two ranges in order to find the maximum distance at which the two stations could talk to each other

This sounds remarkably like the way maximum radar range is calculated at sea. In that case you assume (not unreasonably) that the horizon is at sea level and there are no significant obstructions. You use the transmitter's height above sea level to calculate the distance to the horizon and you do the same for the receiver. Add those two distances together and you get the maximum transmitter to receiver range. This, of course assumes that the transmitter's signal is strong enough to be detected by the receiver (a separate issue).

SlamClick, it looks to me that the QA line represents the aircraft's line of sight distance to the horizon (definitely a "tangent" issue). If you continue the QA line down into the lower, right quadrant you can place the receiver anywhere on that part of the line at, say, point B. Thus, QA gives you the aircraft to horizon distance and AB gives you the receiver to horizon distance. Add them together and that gives you the theoretical maximum range between transmitter and receiver, ignoring refraction and Mount Everest getting in the way.

Is this what we're talking about? I'm going to feel so dejected if it isn't.

SlamClick
Posts: 9576
Joined: Sun Nov 23, 2003 7:09 am

### RE: What Is The Range Of A Plane Radio?

 Quoting David L (Reply 40):SlamClick, it looks to me that the QA line represents the aircraft's line of sight distance to the horizon (definitely a "tangent" issue).

Which I assume to be, on a smoothly rounded earth to be the same line-of-sight we use for radio reception.

Man I hope so! Hey! Maybe if I'd been able to cut-and-paste I'd have done better in geometry.

* * *

 Quoting Timz (Reply 39):Then you've got two right triangles, O to A to receiver and O to A to transmitter. Apply Pythagoras to each triangle to get the A-to-receiver and A-to-transmitter distances.

We had a great discussion of exactly that point once, on the flight deck, while motoring northeast over Twin Falls Idaho. We could see a distant mountain peak in the sunset. We both agreed it was Mount Hood, near Portland Oregon. Somewhere near 400 nautical miles away but with our altitude and the mountain's height . . .

We could not see the rest of the Cascades, not even Ranier. We also could not agree on exactly why that was. Never did the math for the somewhat greater distance. Empirically, Hood was the most distant. Don't know what the math says.

One of many reasons why I so enjoyed my flying career though.
Happiness is not seeing another trite Ste. Maarten photo all week long.

timz
Posts: 6163
Joined: Fri Sep 17, 1999 7:43 am

### RE: What Is The Range Of A Plane Radio?

That does sound unlikely, depending on where you were exactly. There are lots of 7000-9000 ft mountains, closer to you-- even if Mt Hood weren't hidden, it wouldn't stand out among the closer peaks.

David L
Posts: 8552
Joined: Tue May 18, 1999 2:26 am

### RE: What Is The Range Of A Plane Radio?

 Quoting SlamClick (Reply 41):Quoting David L (Reply 40): Is this what we're talking about? Man I hope so! Hey! Maybe if I'd been able to cut-and-paste I'd have done better in geometry.

But cut-and-paste in our day involved scissors and glue. I don't know about you but we weren't allowed scissors and back then we hadn't discovered what happened when you sniff glue (although it would explain a lot).

I just wasn't sure if there were two completely different things being discussed. The business about the height of the aircraft above the ground station threw me.

SlamClick
Posts: 9576
Joined: Sun Nov 23, 2003 7:09 am

### RE: What Is The Range Of A Plane Radio?

 Quoting David L (Reply 43):I just wasn't sure if there were two completely different things being discussed. The business about the height of the aircraft above the ground station threw me.

Yeah, it is really not precisely the height above the transmitter site but the absolute difference between airplane (receiver) altitude and the nominal elevation of the transmitter site - both referenced to sea level.

For my dispatcher students I did a module I called 'the mathematics of flight operations' and I had a two-sided 8.5 x 11 sheet of formulas. We would do problems related to flight planning both with a whizwheel and a pocket calculator until they were comfortable with both. Then they could use whichever they preferrred. I always stressed though, that even if they worked it to twenty seven decimal places the answer was nothing more than an approximation in the real world because there are so many wildcard variables out there.
Happiness is not seeing another trite Ste. Maarten photo all week long.

David L
Posts: 8552
Joined: Tue May 18, 1999 2:26 am

### RE: What Is The Range Of A Plane Radio?

 Quoting SlamClick (Reply 44):even if they worked it to twenty seven decimal places the answer was nothing more than an approximation

Calculator Syndrome! If you have to work out each decimal place yourself you tend to think about how many are relevant.

timz
Posts: 6163
Joined: Fri Sep 17, 1999 7:43 am

### RE: What Is The Range Of A Plane Radio?

 Quoting SlamClick (Reply 41): on the flight deck, while motoring northeast over Twin Falls Idaho. We could see a distant mountain peak in the sunset. We both agreed it was Mount Hood

Supposing you were at 41000 ft at 42.5 N, 114.5 W, and assuming no refraction, you would see

Steens Mtn 181 nm in azim 274 degrees
Strawberry Mtn 214 nm in azi 302 deg
Rock Creek Butte 210 nm in azi 313 deg
Sacajawea Peak 204 nm in azi 325 deg

All of those would reach about a half-degree higher than Mt Hood, which would be 356 nm in azi 301.4 deg.

SlamClick
Posts: 9576
Joined: Sun Nov 23, 2003 7:09 am

### RE: What Is The Range Of A Plane Radio?

 Quoting Timz (Reply 46):Supposing you were at 41000 ft at 42.5 N, 114.5 W, and assuming no refraction, you would see Steens Mtn 181 nm in azim 274 degrees Strawberry Mtn 214 nm in azi 302 deg Rock Creek Butte 210 nm in azi 313 deg Sacajawea Peak 204 nm in azi 325 deg

Well if I can't see Three-Fingered Jack I'm not going up there!
Happiness is not seeing another trite Ste. Maarten photo all week long.

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