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802.11, Horizon Drop-Off And Range
tadghin writes: "Rob Flickenger at O'Reilly Network has written a neat little piece about the range of wireless networks and how high antennae need to be to reach the maximum promised range, given factors such as the earth's curvature and the fresnel zone." Not that most people have solid transmitter disks and clear lines of sight to a wireless reciever miles away, but the more the better when it comes to bypassing modems and expensive per-computer hookups.
We once thought the world was flat, and we did alright.
And then, the scientists came along and pursued their righteous agenda of proving that the world wasn't flat. But we didn't mind, since we were busy milking our cows and scratching an existence out of the ground.
But the same scientists who took away our earth's flatness are now telling us they're running into trouble. They say they can't handle the curvature they invented. Their antennas aren't long enough. They can't even master what they themselves have wrought.
Why couldn't they have left us in peace?
I am a customer, as is my company and 3 co-workers. We run a VPN over the wireless network so we can comfortably work from home. Of course, most of their other customers are brainless Windows lusers with unprotected file sharing, but we sure get great throughput outside the 9-5 moron window.
In case you're wondering, the residential service provides bandwidth-limited internet access, but the bandwidth limiting is done at the ISP. Internal communications over the wireless network run at whatever speed the network is currently capable of. Typical speeds in the evening are in the 2.5 - 3.0 mbit/s range, with latency between stations of about 10 - 15 ms.
These guys run on an all-wireless network, with access points scattered all over the Ogden, Salt Lake City, and Provo area. The access points are connected to each other via 802.11 links also. The network is, of course, sensitive to rain and snow, but is quite reliable. Most of the service outages I've experienced in the past year have been human (operations) rather than weather or technology failures.
Does anybody get 150' indoors at home using 802.11b? Through walls and floors?
The reason I ask is that I just switched from HomeRF (Intel Anypoint/Symphony RangeLan) to 802.11b (Apple Airport/Linksys WPC11)
My indoor line-of-site range with the 802.11b gear is only about 30' at 11Mbs. Might be caused by the el-cheapo Linksys card, I'm not sure. I'm going to try a 3Com card just to try to eliminate that possibility.
The HomeRF gear gave me much better signal quality out to about 150' in every direction (including past my yard). I'm curious why my 802.11b results seem to be so terrible. I've tried turning off every RF source in my house and still see crappy signal quality.
For now, I've got two access points set up and I'm roaming between them but I'd still like to figure this out.
What type of cable were you using? Using LMR-600, we get about 10 miles tops. Using 1200, I could see more, but still doubt I would see 25 miles *reliably* out of our 2.4 stuff. When you did this stuff, did you amplify over FCC regs? What was your total output db? Just curious...
Instant Karma's gonna get you...
Networks will be free when they don't cost anything to build. My company http://www.mvn.net is currently bringing wireless Internet access to the home. It's not perfect yet, but it's getting better. And we do use encryption/authentication on our network. We do radius-based authentication, as well as MAC-layer authentication via our equipment. But, in answer to your first paragraph, we're broadcasting everywhere...not just to corporate customers. It'll get to everyone soon enough. It's too cost-effective/profitable not to.
Instant Karma's gonna get you...
I see that frequency hopping is limited to 1 watt, but did not see anything regarding direct sequence. In fact, none of the categories I saw in that document really fit direct sequence. From what I've read in the past, the rules as they apply to point to point are the same for direct sequence, but I could be wrong.
Instant Karma's gonna get you...
I found it:
(1) For frequency hopping systems operating in the 2400-2483.5 MHz or 5725-5850 MHz band and for all direct sequence systems: 1 watt.
Instant Karma's gonna get you...
Yes. But the same trends. Everyone wants something for free. They want other people to pay for the stuff, and then let them use it for free. And if they don't let them use it for free, the lusers hack into it anyway. But, it's human nature. I've, unfortunately, gotten used to it being in the ISP business.
Instant Karma's gonna get you...
We run a network that covers a town, and stay within the FCC regs. We amplify well below the one watt EIRP rule, and we're still able to cover a 4 mile radius with no problem, and have seen even more distance. It is possible to do networks across small towns within the current FCC regulations using unlicensed 2.4Ghz equipment. However, you are very right about long distance stuff. Licensed freqs are the only way to go. DMC Stratex has some good long-distance, high bandwidth, licensed equipment.
Instant Karma's gonna get you...
It was a joke. Lighten up fuckhead.
Instant Karma's gonna get you...
Ahh. No problem. I could see how my pun comment may make some things seem a joke and others not. I hadn't had my coffee yet when I wrote the "fuckhead" comment. My apologies :D
Instant Karma's gonna get you...
I am part owner of an ISP that does wireless service. 25 miles is not feasible from what we've seen. It is possible, but with the stuff we're using (2.4Ghz unlicensed), it's not going to happen. Even with most of the licensed stuff, you're only going to see around 15 miles. The most we've seen reliably from our 2.4 stuff is 10 miles, and this was with an 80 foot tower at the customer location. We also use 5.7/5.3 Ghz equipment for 8mbit point to point service. This is in the UNII band. We have gotten a max of 11.1 miles from this stuff. Could probably get 15 miles with 2-foot dishes.
Hills and things do improve the situation with the equipment that we use with our 2.4 network. The perfect situation is one where you have some sort of blockage just a little before the end of your range. This helps to prevent your transmitters from interfering with their counterparts in case they're transmitting just a bit farther than they should be able to. The best idea would be a cellular style delivery. No reason to go 25 miles with a link. Why not saturate a town or city with transmitters? Build the system (as we are beginning to build ours) where the customer only has to have a small, inexpensive 11db (or lower) flat-panel antenna on their house, without an expensive amplifier or huge LMR-1200 cable.
Wireless is in its infancy, and it's probably going to give us all cancer, but I like being able to take the telco out of the loop (no pun intended).
Instant Karma's gonna get you...
They both operate in the same frequency range.
This is where you lose me. 802.11b is not upcoming, it is here and there are products on the market for it. It is an extension to 802.11 to increase the data rate, change the encoding and some other things. Many times when people are talking about 802.11 they are referring to 802.11b. There is an upcoming 802.11a that will be a significant change but that is a ways off yet.
Chris Cothrun
Curator of Chaos
Bleh!
However what about the loss due to cable length. I work with microwave equipment and if you have a cable with say .5dbm of loss per 10ft of cable and you have an antenna with +2.5dbm gain and u're running a 30' cable, then you have no need to tune down your transmitter. Now these numbers are not real, however it gives an idea.
---- Fight to protect your right to keep and arm bears! ummmm... ya I think that's right....
Interference with other users of the radio spectrum can result in a fine from the FCC. Story about a wireless ISP being investigated by the FCC.
This is hillarious. The story is about the FCC clamping down on a wireless Internet provider using 2.4 GHz devices in an apartment complex for interfering with amateur radio television.
While the Hams are clearly in the right legally, morally I cannot equate 2 guys doing ATV (probably a static image of their callsigns) with an entire apartment complex's high-speed Internet connectivity. If they really wanted to send video, why don't they get the 2.4 GHz Internet service and use Netmeeting???
-ex N3HAU
You are so right about plug and pray. It's like welding the hood shut.
I see even classic Slashdot is now pretty much unusable on dial up anymore.
Unfortunately the phrase "Microsoft Quality Hardware" sounds too much like a marketing slogan and would likely be misinterpreted by the average person to mean hardware manufactured by Microsoft to the same high standards as so many have been fooled into thinking that Microsoft has achieved in their software (in what can only be a triumph of advertising over user experience), especially since for the most part hardware that Microsoft has put its name on seems to be of the quality that many of us really wish that their software would have achieved as long as circumstances conspire to make its use unavoidable.
I see even classic Slashdot is now pretty much unusable on dial up anymore.
Correct, I fumble-fingered on the d/b. I'd like to know the exact type of cable. I just looked up, and the best heliax cable I can find is ~4.5dB/100M. Better than LMR-400, but not as good as LMR-600. The 1dB/100 sounds like a 900MHz rating...
A 14dB amp would amplify noise, but if you can put a higher signal into the cable, you will have higher signal comming out at the other end.
Without amplifiers, there is no "free-lunch." If you're going to increase gain, you're going to reduce coverage somewhere. In the case of omni-directional antennas, when you increase gain in the antenna, you're narrowing the coverage angle. With a Uni-Directional, you're directing all the energy and energy capture to a very small (15 degree X 8 degree for 24dBi) area.
There are ways to configure diversity antennas so that one supports transmit only, one for receive. Then you can put amps on each. You do have to make sure you are not exceeding the FCC gain limits. Usually if you're using amps, you have to do a point-to-point application. Any one interested in wireless network design should check out some of the documents on Breezecom's site. They give a good tutorial on how to increase range and still stay within the FCC requirements....
If you check out Cisco's site, they have a nice range-calculation utility that takes this into account.
We've been using long-range 802.11d for about a year. We have demonstrated good connections (5.5Mb) between a 5dBi omni-directional and a 24dBi Unidirectional across 17 miles. However our main tower is 165ft in the air, and has a feed line of 10ft to limit cable losses.
We see a number of installations where the users have put up an antenna, run 200ft of feed line, and wonder why they can't get a connection. A good rule of thumb is 7dB/100ft. For each 3dB your signal losses double, so a person with a 200ft feed line has a signal level 1/16th of the antenna level. You would need 14dB of antenna gain just to recover from your feed line losses.
Basically, if you're trying to run wireless, don't expect miracles. If you play by the posted rules things will work, but if not, don't blame the equipment...
Some buildings aren't short of roof space, but the taller buildings are in high demand, at least here in Minneapolis.
When I first started here, one of our clients was an ag business that advertised on DTN and another sat-delivered weather info station. The guy in charge of the account had a station installed in his office and said getting the dish onto the roof was a major hassle.
He said that the entire roof space was actually leased out by the building to a third party whose business was renting roof space for communications. They actually did the installation and placement of the dish, and of course collect a healthy fee for the square footage.
I think it mostly depends on the building, ours is 38 stories with excellent southbound LOS. I notice that some buildings that are ~20 and surrounded by much taller buildings have one or two DirectTV dishes but nothing else, just acres of tar...
>Story about a wireless ISP being investigated by the FCC.
:)
Oh, man...this couldn't happen to a better person.
I went to middle school with Jeff Wellemeyer (the article mis-spelled his name I believe), and he is *SUCH* a twit. He was a twit in middle school, and in past dealings with my company he has been a twit, and even criminal.
Of course, it probably doesn't help that Darwin is in Chapter 11 right now.
Jeff
But hills and mountains migth as well *improve* the situation as getting in the way, for the simple reason that all smart access-providers will put their transmitters on one of those high spots.
With a 25 mile range, all you need to do if there's moutains around is put the transmitter at the top of a high one, and everyone who can see that peak, and is closer than 25 miles will get access. Doesn't sound half bad to me.
I'm a lot more skeptical to if the 25 mile range actually is realistical, even taking into account weather and such and not just some laboratory-theoretical limit.
I've done near that anyway.. yes it's theoretical, but it's also practical.
Though to get 25 miles, you'll need precicion installation... good cable, solid connections.. 2.4Ghz is very succeptible to small errors in cabling.
Also.. having a high point is good.. but you'll need to cover several channels in order to service many people from that distance...
Everyone has to jump in like they're some kind of expert. Anyone and everyone who has ever fired up a Logitech wireless mouse is now a full-blown wireless engineer with years of experience.
This article is rather useless. First of all, Cisco's coverage range (supposedly) goes beyond LOS (that's Line Of Sight). This is due to VOFDM modulation that is using multipath signals in a non-LOS environment. Yes, this may be total marketing hype, but the author of the article doesn't have a clue about this and totally misses the point, assuming that LOS is the only issue.
Slashdot should really give up any attempts at covering wireless technologies. The editors don't know what is valuable information, and the resulting discussions are rather useless as well.
Tired of being "punished" by the Slashdot $rtbl since 2002. I'm now over at http://soylentnews.org/ .
Take a look at Western Multiplex gear sometime
They have nice stuff but it doesn't appear to be all standard 802.11b, which is what I was talking about.
Of course, the round trip delay effects are of little consequence if your MAC has been designed to take that into account. 802.11b has not.
In fact, standard 802.11b will fail completely at 50-60 miles distance, because every transmission will result in an ACK timeout.
Vendors of long-distance bridge links will either use a different MAC, or modify 802.11b in a non-standard way to increase things like ACK timeout.
The 802.11 was designed for operation over short distances only. All the timing calculations assume that the air propagation delay is negligable.
If you're going to use 802.11 for outside links, you have to take the propagation delay into account. For every mile between the two stations, there is a >10 usecs round trip delay. The 802.11 standard uses a 20 usec time as a slot length. These slots are the basis for the random backoff procedure, and can also be found in the difference between the various inter frame spaces. When the total round trip delay (air+rx+tx delays) becomes greater than 20 usecs, you'll get (some) performance degradation.
The degradation in DCF mode is graceful, but the PCF will basically break down completely in the face of long delays. Fortunately, most vendors don't even support PCF.
Things get worse if you have more than a simple point-to-point link.
In short, 802.11 can work over long links, but don't bet the farm on it, and results may vary with equipment.
This doesn't suprise me. Most buildings aren't short of roof space, and removing them would take effort & dollars. However, if a building did get short on roof space, I guarantee that an audit of what's up there would take place, and anything that a tenant wouldn't justify & probably pay for, would be removed.
You get 1 watt. If you use an antenna you have to turn the power down on the card to compensate for the gain.
. 4G_Band.index
FCC regs and explanation:
http://www.lns.com/papers/FCCPart15_and_the_ISM_2
Those conditions really aren't that bad, especially in any area that has a few tall buildings. I was the systems manager for a hotel management company that had several properties in the Miami area. Most of our buildings were over 12 stories (roughly 130 feet) and none of them were more than 10 miles apart.
You'd be surprised at how little owners know about their rooftops. We had several defunct satellite dishes up there for years, just taking up space. No one knew nor cared. On most buildings, a person could stick an antennae/satellite dish and no one would be the wiser. If enough sys admins that run the networks for large buildings got together, it would be relatively easy to pull this off in even small cities.
"Study your math, kids. Key to the universe." -The Archangel Gabriel
As a side note, it's gotten me on some interesting rooftops. The most memorable was a mental institution in southern VA. They didn't keep me, so I guess it turned out okay...
-Omar
I currently live just outside of good DSL range, but I have a friend close to the CO. I've been considering buying a wireless bridge (like Cisco/Aironet 340), but I'd like to know if its going to work before I spend >$5k on equipment! I've got a low hill just obscuring LOS, but the straight distance is only about 3 miles. Are there are low cost ways to determine the quality of the signal path? I can't find anyone who can loan me the equipment, are there any other options? Thanks!
I understand that it's cheaper for the networking people if they don't lay cable. However, I can't adequately allow for the management of our desktop computers on a shared 11Mb/s network, even if only 10 people use each wireless node.
I can understand the benefits for mobile users, but we've only a small number of those, and we can accommodate them with wireless if necessary.
Has anyone else come across similar issues? I'd put a wireless network in my home, but not at work... is this issue being addressed by forthcoming protocols?
I think this gentleman is great at highschool level mathematics, but lacks any experiance in dealing with wireless networks, they are not near as cumbersome as he makes them out to be.
Perhaps this gentleman should stick to wired networks, maybe recalculating the maximum lenght of cat5.
You can get antennas from such places as HyperLink Technologies that can give you up to a 24 dBi improvement. A combination of a good antenna with good outdoor placement can do wonders for a lot of people.
[Disclaimer: I don't work for HyperLinkTech.]
-----
Rob's calculations are a little flawed. The horizon for RF signals is not the same horizon for a laser beam.
McGraw Hill's "Electronics Engineers' Handbook" gives and effective earth radius factor "k" as 4/3 for frequencies greater than 30 MHz. This would extend the distance of Rob's calculations significantly.
When doing path calculations, there are a number of other factors that affect reception such as conductiviity, permittitivity, roughness and curvature. Reflected signals which also change the receptive strength are dependant on polarization, grazing angle and ground constants.
In general, creating RF paths can be considered black magic, based on the FM principle (magic). The 25 mile figure is really a best case scenerio, where only atmospheric attenuation is hampering the signal. Still, with some adequate hieght, RF communications can be established near 25 miles if the system is set up properly (ie minimizing signal loss at every stage as was pointed out earlier).
It should also be noted that the system discussed is only point to point and would have little value in reaching a mobile user. Mobile use is severly limited by the type and directionality of the antenna and the amount of RF power on the mobile computer. My own 801.11b link is good for 150 feet and most of that is due to the 10mW on an omni antenna sticking out of my laptop.
machinator omnis sine licentia
[Boy, do I feel stupid!]
-- @rjamestaylor on Ello
Check out NASA's history with balloons. And Richard Branson (and various others)'s attempts at round-the-world. Balloons are _not_ the easy option they look...
Grab.
Ahh but if the atmospheric conditions are you you can get a great skip and maybe someone's wireless LAN in NYC will be used by someone in Toronto! Conditions are pretty good right now cuz of Aurora ;)
It seems that this would be hampered a lot more than current 802.11 hardware due to the length. With these long lengths there are many factors due to the weather. What happens when there's a storm passing by inbetween your little network? Or any cloud interferance for that matter. This doesn't even seem remotely possible as i'd be listening to radio stations on the other side of the world now. Also you can get further lengths by bouncing your signals off the atmosphere. This would seem like the best way, as it is already a proven method. Police, hams, and scanner enthuisasts use this to extend their length of radio signals.
But... Bluetooth and the upcoming IEEE 802.11B (note the B) are going to go head to head. It doesn't have the cool name or logo, but it does have the backing of both IEEE and Intel. You may hate Intel, but they have a lot of weight to throw around.
I must admit that I was really excited about the Bluetooth standard, but I would always choose an IEEE standard over an industry consortium. I'm still ticked off that USB has gained wide acceptance.
Unrelated but worth noting: There is some chance of interference between bluetooth and 802.11.
-- null
In some cases, the wireless towers would be 1000 ft tall. But that only gets you to just under 38 miles to the horizon. As noted in the article 10k feet gets you 126 miles. There is a diminishing returns factor here.
second minor nitpick point. The formula in question is very practical but only works for near earth heights. The geometry it uses is in fact based on the shape of the parabola (note the simple square root element). The higher the object, the less accurate it is, but it doesn't get bad until you get to hundreds on miles high above the surface. At which point alot of other factors are getting in the way as well.
Check out the Vinny the Vampire comic strip
"It is a greater offense to steal men's labor, than their clothes"
The 25mile figure was probably extrapolated by measuring the output wattage of the solid dish antenna. This is done by measuring the distance over which the signal is so weak, it can not be distinguished from surrounding noise (at any frequency). It's a basic high school physics problem.
:)
It's also a benchmark. Does this mean it can ever be reached? Looking from the comments of the obviously intelligent slashdot community, I don't think so. But benchmarks are just that. Theoretical performance indicators. All it means is that 802.11b has nifty error control protocols and other stuff that allows you to keep communications integrity at 25miles in a very hypothetical situation. Isn't that what Ph.Ds are supposed to do? As in generate some number from some obscure formula somewhere using obviously hypothetical situations.
However, to look on the bright side: It would be interesting if every 200foot high structure had a dish mounted as relay points in, say, a metro or even suburban area. You are no longer limited to 25miles, regardless of topology. In fact, 802.11b can replace traditional LOS microwave dishes (the huge telco ones) and lower the cost of transmission across borders. Imagine GTE beaming 802.11b from the US to Canada. FCC and CE violations anyone?
The referenced article doesn't give any prices, but Google is my friend.
The 25-mile antenna (most expensive) has a list price of $1,069.00. The others are cheaper, going as low as around $100.
Reference: ScanOnline (the Bridge Antennas link, in particular)
ObDisclaimer: I'm only referencing ScanOnline because they came up "lucky" in Google.
K45
This signature has eleven vowels.
Nope. It would be easy. And the tether wouldn't get in the way of air traffic, either. Plus, think of the fun when a ballon burst and laid a mile of cable across the landscape. Or lightening striking the same place, over and over (think Ben Franklin). Sounds good to me. Let's use your money to do it. Get really great insurance and start building now.
- - - If the sun is a star, why can't I see it at night?
If the jets can't fly over major metros, how do they land at La Guardia?
- - - If the sun is a star, why can't I see it at night?
I live in major metro area. Jets fly almost directly over the center of town. I've been in 'em and looked straight down on a city of 300,000. The medivac chopper comes and goes from all directions as well. But yes, there are "roads" that they fly. They're not for safety mainly, but for "noise abatement." It's so the neighborhoods can take turns sharing thunder.
- - - If the sun is a star, why can't I see it at night?
Maybe that would be one point builder's would start highlighting to govts. opposed to high rise buildings.
There's always sufficient, but not always at the right place nor for the right folks.
http://www.ydi.com
http://www.netnimble.com/products/index.html
http://www.superpass.com/
HTH! :-)
http://www.netnimble.com/products/index.html
"Maybe if the technology could be improved to be a fraction of that of land lines, we wouldn't need ISPs in the first place and connections would be maintained by users themselves for their own personal benefit, but also contribute to the overall system - ala distributed aggregate like Napster. Completely free, diffuse, and powerful. Wireless is the natural medium because it doesn't require any land licensing or other utility fees."
Ummm...if you wouldn't need ISP's how would you be able to share your connection via a wireless infrastructure in the first place? Curious...
If anyone (i.e. not an electical engineer) wants to learn about radio frequency (RF) propogation, I suggest finding some amateur radio publications such as The ARRL Handbook (2001 edition). It provides plain english explaination and particial experience about the operating in the microwave bands.
Typical 802.11(b) usage is under license-free operation for local "ad-hoc" networks. The equipment is designed to operate locally such as a college campus or a company building, not across town. This relates to the license-free usage exemptions (Part 15 or 11, I believe).
If you want higher power or higher gain antennas, you will need a license from the FCC (in USA) or similiar government agency in your country. Interference with other users of the radio spectrum can result in a fine from the FCC. Story about a wireless ISP being investigated by the FCC.
I am the owner of a HyperGain 24 dB Heavy Duty Grid Antenna, from HyperLink Technologies.
I purchased it to provide extended converge of my 802.11 network through as much of the surrounding city. Currently, I do not have an amplifier but I am planning to get one.
I have the antenna on top of my Condo, which is about four stories high at the roof. When I first got the antenna and hooked it up I was disappointed with the performance. This, however, is due to the highly collimated beam (8 degrees). The problem was you could get a very good connection for miles away, but you had to have relative line of sight. That is, you had to be facing the direction of the antenna, and vice versa.
This provided limited, unidirectional coverage. I ended up fixing the problem by attaching a rotating stage to the Antenna and having it do 360 degree constant rotations and a few degree pan/tilts. This is controlled by the network, which looks for a signal. Once one is found, the antenna is adjusted to get the best reception and left in that position. This was all done with a simple C program, a bit of math, and a DAC card to control the motor.
This has increased the range significantly and given the simulation of a cell with a radius of equal reception. I was even able to maintain a good connection while driving and changing directions in a car; The system "tracking" the signal as it changes.
Some limitations include the fact it can only track one user at a time, although multiple users could be given equal amounts of connectivity "bust" time by spinning the antenna continuously, similar to the way a streaming server "bursts" data to a local streaming cache which then relays it to the slower client. This might be difficult (on the network), as a connection would be in a constant state of variation going on and off, but is still interesting.
What would really be interesting is if home users connected their wireless networks to one another, forming another totally separate network, analogous to ham radio IP, except a lot faster. Maybe if the technology could be improved to be a fraction of that of land lines, we wouldn't need ISPs in the first place and connections would be maintained by users themselves for their own personal benefit, but also contribute to the overall system - ala distributed aggregate like Napster. Completely free, diffuse, and powerful. Wireless is the natural medium because it doesn't require any land licensing or other utility fees.
One can only dream ~
"I'll just chip in a bit for RedHat: I actually have that installed on my university machine." - Linus, '95
Assuming that the angle subtended is small (say .1 radian, not more than a few hundred km/miles at the earths surface) then the following equation not only works identically, but gives you a better insight into where the magic numbers come from.
The assumtion above permits us to make the approximation
sin(t) = tan(t) = t (+ parts per thousand)
cos(t) = 1 - t^2 (+ parts per ten thousand)
The angle subtended at the earth's surface by two locations r apart is r/R where R is the earth's radius.
Therefore the ratio of the the radius of the earth to the radius plus the tower required is cos(r/R):1.
We approximate this to (1-(r/R)^2):1
However, the radius R is the known quantity, we want to know the height of the tower (which we'd get from the right hand side of the ratio).
The ratio becomes R:R/(1-(r/R)^2)
Now 1/(1-x) for small x is 1+x, and we've agreed that (r/R)^2 is small. Therefore the ratio becomes
R:R*(1+(r/R)^2)
So, the contribution of the tower to the RHS is
R*(r/R)^2 = r^2 / R
So h= r^2 / R
Or hR = r^2
The assumtion here is that h, R and r are measured in the same units. As some deal with values in 'human sized units' (the height), and the rest are far larger (particularly the planetary radius), you can either start throwing conversion factors in, or use metric values where the conversion factors are no more than powers of 10. I'll chose the latter.
I'll assume the mean earth's radius is 6370km. Adjust to taste as you move towards the poles, or vary angles at the equator.
h*6.37e6 = r^2 (h, r both in meters.)
So one way round gives
h = r^2 * 1.57e-7 if r is meters
= r'^2 * 0.157 if r' is in km
(h here is in meters)
The other way round
r = sqrt(h * 6.37e6) gives r in meters
r'= sqrt(h * 6.37) gives r' in kilometers
The guy's equation had already combined foot to mile conversions with the earth's radius in miles, and then applied the square root. That's why the 1.224 (or whatever) may have appeared a bit mysterious. However, the h~r formulations are more transparent as they show the physical constant in the equation rather than some mysterious magic number.
For those worried about the approximations, you don't need to really, because the parts in a thousand and parts in ten thousand were for a 637km range. At a 63.7km range, where r/R is 0.01 the part in a thousand term becomes a part in a million! (and hundred million for the 10000 one).
Enjoy.
THL.
--
Keeping
What we need is a 768 Terabit wireless thingy in every city center. But that will probably never happen since even cell phone radiation seems to be enough to fry your brain, according to some people. Imagine what a wireless link that fast will do to your brainstem.
Guacamole dip, anyone?
-- Si hoc legere scis nimium eruditionis habes.
Although most corporate Wavelan users are considerate enough to not use encryption or passwords to protect their networks, a few paranoid companies have begun to implement these revolting practices.
Don't they understand that networks want to be free?
[Insert the usual disclaimer here]
Perhaps we could look at our current cellular phone infrastructure and realize it doesn't seem implausible... The Earth's curvature be damned!
Why can't we use the same idea (multiple antennaes used as repeaters ) for the wireless lan / wan idea?
the only reason not to that I could imagine is the signal strength. But cellphone's signals are relatively weak... I don't see why they're isn't any sort of talk of this.
Reason, free market capitalism, and individualism