Monday, June 12, 2006 11:41:41 PM
I asked a question a few days ago about the radio transmitter to be used in the strat and the types of services that will be offered. Going on today's release, I'd like to post some speculation that I had been tossing around in my head for a while. Others may have done this before, but after some searching I couldn't quite find the same thoughts stated I had been thinking.
First, let's take note that Bob Jones states that the 4010 "is exceptionally capable of transmitting broadband signals for extended distances — well beyond the distances required for use in the Stratellite airship.”
Well, Strawberry peak is 6,143 feet about sea level and near the town of Twin Peaks:
http://www.fs.fed.us/r5/sanbernardino/volunteering/lookouts/strawberry.shtml
The airport in Riverside, CA has an elevation of 818 ft. This is near where the Operations center is to where the Strawberry Peak 4010 is transmitting.
http://www.airnav.com/airport/RAL
The distance between these points appears to be about 32 miles by road:
http://maps.google.com/maps?f=d&hl=en&saddr=Riverside,+CA&daddr=twin+peaks,+ca&ie=UT...
For this estimate, let's round and say it's about 30 miles (it's probably less). Given these facts (and assuming my geometry isn't that rusty):
We can see that the hypotenuse of the triagle involving Riverside and Strawberry Peak is still about 30 miles. It's a long distance with very low rise. It's similar to the way a strat will cover an area (note that these are certainly not to scale).
Down on the lower left, we see my makeshift strat hovering at 13 miles with the maximum radio distance of about 35 miles shooting out at an angle. Given these, the ground distance under the strat that can receive broadband has a radius of about 32 miles or about 3,216 square miles. Other transmissions are different, so this is just the broadband component.
Ok, that means that each strat, given these estimates, provides broadband to 3,216 sqaure miles. Usually we hear about "line of sight" or other terms indicating what is below the horizon for the strat.
But 30 miles is well beyond what they are planning? Hmm. I doesn't seem to quite match up, but I'll continue with this figure to see where it leads us.
There is a lot of work in of Satellite Clusters; that is, how does one optimally provide coverage to a specific region given several circular areas of possible coverage. Also, how is redundacy to be provided according to some expected level of down time. (See for instance: http://ssl.mit.edu/spheres/motivation.html )
I'm not going to pretend to know the optimal way to arrange this coverage, so I am going to use a fairly simple arrangement.
The Chicago Area:
Above is a hypothetical coverage of the Chicago area with 4 strats. The idea is to have complete coverage of the central circle while also having redundancy in the case that a single strat is out of service. Ok, so we have perhaps 4 strats per circle with a radius of 32 miles.
We could also think about it a little differenly. Each central node (or area of coverage) needs three additional strats to provide full redundancy. So, each central node is borrowed from the previous cluster adding on three more to complete its redundancy group (StratZone, to coin a term). So, the total number of strats needed to cover an area is
((total area)/3,216)*3 + 1
That is, we just take the total area and divide it by the coverage of one of our StratZones. We know we need three strats for each zone plus and an additional node borrowed from the nearby one (the first one doesn't have anything nearby so we add 1).
Well, you might ask, why not just put two over the same area instead of 4 (just put two right next to eachother)? Amoung other reasons, in this scenario, each circle forms part of an interlocking whole so that no area is without coverage. Each of the edge circles could be a new central node, except it will only take three more strats to provide fully redundant coverage.
We need 2 strats over every location with no gaps in coverage. I'm sure this is an overestimate and that there are more optimal ways to provide coverage.
Below is the "add-on" StratZone.
Now, let's compare our original coverage area to that of a circle with a radius of 400 miles:
Ok, so that's pretty good coverage of a hunk of the midwest. A circle with a radius of 400 miles has a total square mileage of about 500K miles.
Using our above formula, ((502,654)/3,216)*3 + 1 = (about) 470 strats.
This doesn`t line up with 5 strats for Columbia. Columbia is 707,685 square miles (http://www.cia.gov/cia/publications/factbook/geos/co.html) which involves each strat having a broadband radius of about 202 miles, not the 32 miles that we seem to be dealing with above. Are they only targeting populated areas with this?
8, 400 mile circles can cover the US = 3,760 strats
3,760 strats * $15 million per strat = 65 billion for the entire US.
So, what am I missing? Are the HotZone units capable of tramsmitting WiMax at a range of 200 miles?
First, let's take note that Bob Jones states that the 4010 "is exceptionally capable of transmitting broadband signals for extended distances — well beyond the distances required for use in the Stratellite airship.”
Well, Strawberry peak is 6,143 feet about sea level and near the town of Twin Peaks:
http://www.fs.fed.us/r5/sanbernardino/volunteering/lookouts/strawberry.shtml
The airport in Riverside, CA has an elevation of 818 ft. This is near where the Operations center is to where the Strawberry Peak 4010 is transmitting.
http://www.airnav.com/airport/RAL
The distance between these points appears to be about 32 miles by road:
http://maps.google.com/maps?f=d&hl=en&saddr=Riverside,+CA&daddr=twin+peaks,+ca&ie=UT...
For this estimate, let's round and say it's about 30 miles (it's probably less). Given these facts (and assuming my geometry isn't that rusty):
We can see that the hypotenuse of the triagle involving Riverside and Strawberry Peak is still about 30 miles. It's a long distance with very low rise. It's similar to the way a strat will cover an area (note that these are certainly not to scale).
Down on the lower left, we see my makeshift strat hovering at 13 miles with the maximum radio distance of about 35 miles shooting out at an angle. Given these, the ground distance under the strat that can receive broadband has a radius of about 32 miles or about 3,216 square miles. Other transmissions are different, so this is just the broadband component.
Ok, that means that each strat, given these estimates, provides broadband to 3,216 sqaure miles. Usually we hear about "line of sight" or other terms indicating what is below the horizon for the strat.
But 30 miles is well beyond what they are planning? Hmm. I doesn't seem to quite match up, but I'll continue with this figure to see where it leads us.
There is a lot of work in of Satellite Clusters; that is, how does one optimally provide coverage to a specific region given several circular areas of possible coverage. Also, how is redundacy to be provided according to some expected level of down time. (See for instance: http://ssl.mit.edu/spheres/motivation.html )
I'm not going to pretend to know the optimal way to arrange this coverage, so I am going to use a fairly simple arrangement.
The Chicago Area:
Above is a hypothetical coverage of the Chicago area with 4 strats. The idea is to have complete coverage of the central circle while also having redundancy in the case that a single strat is out of service. Ok, so we have perhaps 4 strats per circle with a radius of 32 miles.
We could also think about it a little differenly. Each central node (or area of coverage) needs three additional strats to provide full redundancy. So, each central node is borrowed from the previous cluster adding on three more to complete its redundancy group (StratZone, to coin a term). So, the total number of strats needed to cover an area is
((total area)/3,216)*3 + 1
That is, we just take the total area and divide it by the coverage of one of our StratZones. We know we need three strats for each zone plus and an additional node borrowed from the nearby one (the first one doesn't have anything nearby so we add 1).
Well, you might ask, why not just put two over the same area instead of 4 (just put two right next to eachother)? Amoung other reasons, in this scenario, each circle forms part of an interlocking whole so that no area is without coverage. Each of the edge circles could be a new central node, except it will only take three more strats to provide fully redundant coverage.
We need 2 strats over every location with no gaps in coverage. I'm sure this is an overestimate and that there are more optimal ways to provide coverage.
Below is the "add-on" StratZone.
Now, let's compare our original coverage area to that of a circle with a radius of 400 miles:
Ok, so that's pretty good coverage of a hunk of the midwest. A circle with a radius of 400 miles has a total square mileage of about 500K miles.
Using our above formula, ((502,654)/3,216)*3 + 1 = (about) 470 strats.
This doesn`t line up with 5 strats for Columbia. Columbia is 707,685 square miles (http://www.cia.gov/cia/publications/factbook/geos/co.html) which involves each strat having a broadband radius of about 202 miles, not the 32 miles that we seem to be dealing with above. Are they only targeting populated areas with this?
8, 400 mile circles can cover the US = 3,760 strats
3,760 strats * $15 million per strat = 65 billion for the entire US.
So, what am I missing? Are the HotZone units capable of tramsmitting WiMax at a range of 200 miles?
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