What-If 0113: "Visit Every State"

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Kounosuke
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Re: What-If 0113: "Visit Every State"

Postby Kounosuke » Sat Sep 27, 2014 8:58 am UTC

bigglesworth wrote:
Kounosuke wrote:I spent a couple of hours tinkering away at Google Earth trying to create the solution for Europe, and the best I can get is with 6. There's a lot of tiny countries to get through, doubt a 5 solution exists.
You're lucky that one of your vertical lines goes through western Ukraine.


The horizontal line that hits Andorra and Monaco hits the part of Ukraine south of Odessa next to where it cuts through a tiny bit of Moldova, along with the line that goes from Finland through the Baltics and Belarus that hits a tiny section of Ukraine. Moldova and Slovenia were much tighter

I finally managed to get my solution down to 5 lines after finding a way of hitting Ireland, Liechtenstein, Slovenia, Bulgaria and Cyprus with the same line (It only just hits Ireland and Bulgaria), making the Iceland-Cyprus line redundant. The Finland line didn't need to be adjusted, but I moved it so it hit Montenegro just in case the Ireland-Cyprus line didn't.

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penguinland
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Re: What-If 0113: "Visit Every State"

Postby penguinland » Sun Sep 28, 2014 5:19 am UTC

One could prove that it's impossible to do with 4 satellite passes if one could find a set of 9 states such that no three of them were colinear (i.e., you couldn't cover any 3 of the 9 in a single satellite pass). By the Pigeonhole Principle, we'd need at least 5 passes to cover these 9 states (and thus at least 5 passes to cover all the states).

Unfortunately, I don't know enough about geographic data to programmatically determine whether three states are colinear, and I don't want to do this out by hand. If anyone else wants to take a crack at it, they're welcome to. I imagine that a good starting place is to put Hawaii, Alaska, Rhode Island, something on the west coast, something in the south, and something in the midwest in the set, and see what's left over after that.

Gil-Galad
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Re: What-If 0113: "Visit Every State"

Postby Gil-Galad » Sun Sep 28, 2014 6:18 am UTC

keithl wrote:You should now IMMEDIATELY switch to 10 gee deceleration, or you will fire out of the hole into the atmosphere for a brief high gee deceleration, then a fast trip out of the solar system.

The earth does that for you. You can’t „fall out“ of a tunnel through the earth, you’ll oscillate from one end to the other for all eternity (assuming zero friction).

Great idea otherwise.

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Re: What-If 0113: "Visit Every State"

Postby Flumble » Sun Sep 28, 2014 1:44 pm UTC

Gil-Galad wrote:
keithl wrote:You should now IMMEDIATELY switch to 10 gee deceleration, or you will fire out of the hole into the atmosphere for a brief high gee deceleration, then a fast trip out of the solar system.

The earth does that for you. You can’t „fall out“ of a tunnel through the earth, you’ll oscillate from one end to the other for all eternity (assuming zero friction).

You missed the part where he said to accelerate with 10g downwards (using "maglevs" is a bit peculiar though, as that name suggests canceling gravity). That's quite a bit faster than the 1g you experience by just falling down.

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Re: What-If 0113: "Visit Every State"

Postby Gil-Galad » Sun Sep 28, 2014 4:55 pm UTC

Flumble wrote:
Gil-Galad wrote:
keithl wrote:You should now IMMEDIATELY switch to 10 gee deceleration, or you will fire out of the hole into the atmosphere for a brief high gee deceleration, then a fast trip out of the solar system.

The earth does that for you. You can’t „fall out“ of a tunnel through the earth, you’ll oscillate from one end to the other for all eternity (assuming zero friction).

You missed the part where he said to accelerate with 10g downwards (using "maglevs" is a bit peculiar though, as that name suggests canceling gravity). That's quite a bit faster than the 1g you experience by just falling down.

Oh, sorry. Read that as 10m/s² and assumed he just meant normal gravity.

illandancient
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Re: What-If 0113: "Visit Every State"

Postby illandancient » Mon Sep 29, 2014 12:33 pm UTC

Such a mathematician / physicist answer, ignoring the size of the satellite.

From an engineering perspective, clearly if you take into account the size of the satellite it changes everything. With a really really wide satellite, you would only need one line to cover all the states. One big satellite with a footprint the same size and shape as the USA, not even a line would be required, just a single point.

burnthills
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Re: What-If 0113: "Visit Every State"

Postby burnthills » Mon Sep 29, 2014 7:50 pm UTC

Might save some time if some small body parts were removed and travelled separately - now it becomes a Descartes problem...

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Re: What-If 0113: "Visit Every State"

Postby CharonPDX » Mon Sep 29, 2014 9:19 pm UTC

stoppedcaring wrote:How are we doing on coming up with a 4-pass route over the Lower 48? I can get everything but Washington if we allow a pass over the Four Corners Monument to count for all four states. Of course, I'm using straight lines, not great circles; I don't know if that would affect the final result or not.

Image

Avoiding intersection of the lines seems to be the best approach, as this avoids crossover and wasted airspace. In this example, the only states visited more than once are New York and California.


I like this one. This one makes an SR-71 possible to beat satellite.

Start just over the Southern tip of Alaska, wing down over Washington, Oregon, and join the Northernmost line somewhere in Oregon/Idaho so you hit the line in time to pass over Wyoming. That should be possible on one tank, in about an hour and a half.

Then turn over the Atlantic and mid-air refuel, and hit the Southernmost line, turn around over Texas and hit the middle-South line. A little over an hour, one tank of fuel.

Turn again over the Atlantic and mid-air refuel, and hit the last line to pass over Four Corners. That's a smidge over an hour.

Refuel again over the Pacific, and run to Hawaii, about an hour, single tank of fuel. Four lines, only two "curves" needed from your lines, three refuels, about five hours, including refuel slowdowns.

myrcutio
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Re: What-If 0113: "Visit Every State"

Postby myrcutio » Tue Sep 30, 2014 2:34 pm UTC

I'm surprised Randall didn't mention the explosion option, maybe he doesn't want to draw a bit of someone's foot landing in Alaska. Similarly, you could take the pinball approach where you descend from space in a sealed container at intense speeds, and bounce off strategically placed kinetic missiles at various points during the descent. The fastest spacecraft to reenter the atmosphere reached 29000mph, and the US is about 4600 miles at its widest (not including Alaska or Hawaii, but those can be the starting and ending points), so if you could maintain that speed across six passes you could complete the trip in around an hour or two. You'd be a liquified pulp at the end of it, but you'd have crossed over each state's airspace at least.
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Re: What-If 0113: "Visit Every State"

Postby Jérôme ^ » Tue Sep 30, 2014 5:44 pm UTC

[quote="topynate"]My strategy for a brute-force mathematical solution would be something like:
Get GIS data for state boundaries at high resolution.
/quote]

This interesting, but you can definitely do better by using the parameter space for great circles, which is the projective space (or, in this case, one hemisphere): you can represent a great circle by one of its two centres (say, the one in the Northern Hemisphere, so that you can overlay Siberia above all of this). In this way, you can associate to each state the set of all great circles going through it, very simply: if the state is a closed polygon with vertices Pi, then the centres of all great circles going through this state belong to the closed polygon with vertices Ci = centre of the great circle (Pi, Pi+1). This transforms the original problem into a problem of intersections of polygons, which is an easier rephrasing.

Then, you need to find maximal elements of intersecting polygons in this set. I don't know much about lattice programming, but for the 48 contiguous states, you will probably not have more than 16 intersecting polygons, and therefore at the very most binomial(48, 16) ~ 2^41 maximal intersections (this is an extremely rough bound! the actual number is probably much less).

You now only need to find minimal coverings in this set of maximal intersections. Use collision detection algorithms here.

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Re: What-If 0113: "Visit Every State"

Postby Barstro » Tue Sep 30, 2014 6:23 pm UTC

illandancient wrote:With a really really wide satellite, you would only need one line to cover all the states. One big satellite with a footprint the same size and shape as the USA, not even a line would be required, just a single point.

I believe that, mathematically, a line has no width. Changing the parameters of the question does not answer the actual question. Even if we allowed that, the curvature of the Earth would probably such a sized satellite to be too low for orbit if it is to be in the airspace of each state. Not sure where true orbit starts, but it might be high enough that the spaceship would need to be wider than the planet's diameter.

illandancient wrote:From an engineering perspective, clearly if you take into account the size of the satellite it changes everything.

Perhaps. But from an attorney's perspective, the question was "(what) Maps route... visits as many US states as possible", changed to "minimum number of curved lines". This puzzle involves lines of zero thickness. At best, you could argue (as stoppedcaring seems to have) that the line has a thickness of the person (thus allowing Four Corners to count as four states instead of two or three). Your solution could work if you found a person the size of the United States. You must then insert some horribly intellectual "yo' momma" joke.

The other easy solution is to no try to enter the airspace of each state, but to enter the mineral rights area of each state and just dig down to a depth such that an average sized adult is below each state. I'm guessing that spot is warm.

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Re: What-If 0113: "Visit Every State"

Postby Pfhorrest » Tue Sep 30, 2014 6:38 pm UTC

Barstro wrote:some horribly intellectual "yo' momma" joke.

Like "Ol' Flat Top" from the classic Beatles song "Come Together", yo' momma is so attractive that she's difficult to see.

Because any light which reaches her is unable to escape.

Because her attractiveness is gravitational.

...cause she fat.
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Re: What-If 0113: "Visit Every State"

Postby stoppedcaring » Tue Sep 30, 2014 7:06 pm UTC

CharonPDX wrote:This one makes an SR-71 possible to beat satellite.

Start just over the Southern tip of Alaska, wing down over Washington, Oregon, and join the Northernmost line somewhere in Oregon/Idaho so you hit the line in time to pass over Wyoming. That should be possible on one tank, in about an hour and a half.

Then turn over the Atlantic and mid-air refuel, and hit the Southernmost line, turn around over Texas and hit the middle-South line. A little over an hour, one tank of fuel.

Turn again over the Atlantic and mid-air refuel, and hit the last line to pass over Four Corners. That's a smidge over an hour.

Refuel again over the Pacific, and run to Hawaii, about an hour, single tank of fuel. Four lines, only two "curves" needed from your lines, three refuels, about five hours, including refuel slowdowns.

Excellent!

I reworked the path in Google Earth to trim down distance as much as possible. Here's the final path, in all its glory:

Spoiler:
Image


All the curves have a turning radius of at least 100 miles so that there won't be any loss in speed. The turn from DC and New Jersey up to Rhode Island is by far the sharpest, but it's still within this limit...and of course this is also a likely point for aerial refueling and thus could have reduced speed for a sharper turn. According to Google Earth, the whole route is a cool 18,828 km. Since an SR71's peak cruising speed is just about 1 km/s, this means the route itself would take five hours, fourteen minutes. Unfortunately, I don't have a good idea of how much time would be lost to refueling. The KC135Q was modified to allow refueling at the tanker's maximum speed of 933 km/hr or 0.26 km/s, sadly still a crawl compared to the SR71. I don't know how long refueling takes or how much time would be lost in slowing down and speeding up. According to this naval pilot who flew F14s, he would factor in about ten minutes for docking, fueling, and undocking, but that doesn't give us any data about the slowdown or speedup.

However, I'm guessing that the twin engines of the SR71 are more than capable of producing high-gee acceleration, so if we just choose to limit horizontal acceleration to 1G for the sake of the pilots, then the delta-V of 0.74 km/s will take just over a minute. If we simply write off the distance covered during acceleration/deceleration then each refuel will add 12 minutes to our flight time, bringing our total up to 5 hours 50 minutes. Still should be able to beat out a satellite, and in controlled airspace to boot.

I'll try to attach the .kmz file (renamed to a .doc to allow upload) to this post if I can, just in case someone wants to play around with it. Be sure to rename to .kmz before loading.
SR71 Flight Path.doc
Google Earth File; rename to dot kmz
(1.9 KiB) Downloaded 472 times


Barstro wrote:At best, you could argue (as stoppedcaring seems to have) that the line has a thickness of the person (thus allowing Four Corners to count as four states instead of two or three).

Yeah, you could say it like that. I was more thinking that a line tangent to a curve touches the curve, and so simply touching the border of a state is enough to say that you have "crossed" that state. A line crossing over Four Corners is tangent to all four borders.

Relaxing to tangency will not produce any dramatic advantages and, I think, should be allowable.

EDIT: Reworked the path somewhat. I realized that NY, VT, NH, ME, MA, RI, CT, NJ, PA, DE, MD, DC, VA, and OH can all be hit in sequence by one curve with a radius that never goes under 100 miles, so I reversed the loops. Added enough points to the line so that the actual curves taken will be less distance than the line describes, rather than more.

Image

Brought the total distance down to less than 16,310 km, for a total flight time (requiring only two refuels at a time loss of 12 minutes each) of 4 hours, 56 minutes. Nailed it.

Here's the new .kmz file!
shorter SR71 path.doc
A shorter flight path (Google Earth .KMZ file, rename)
(1.19 KiB) Downloaded 471 times

helo darqness
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Re: What-If 0113: "Visit Every State"

Postby helo darqness » Wed Oct 01, 2014 6:59 am UTC

Okay, I'm probably going to get laughed at for this for asking such a stupid question.

But if satellites count, why not the moon? If one stood on the moon, in the right position, wouldn't they be over all of the States at once, or could at least within a few hours (because of rotation and orbits) have the entire country covered?

:oops:

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Re: What-If 0113: "Visit Every State"

Postby january1may » Wed Oct 01, 2014 10:34 am UTC

stoppedcaring wrote:EDIT: Reworked the path somewhat. I realized that NY, VT, NH, ME, MA, RI, CT, NJ, PA, DE, MD, DC, VA, and OH can all be hit in sequence by one curve with a radius that never goes under 100 miles, so I reversed the loops. Added enough points to the line so that the actual curves taken will be less distance than the line describes, rather than more.

Image

Brought the total distance down to less than 16,310 km, for a total flight time (requiring only two refuels at a time loss of 12 minutes each) of 4 hours, 56 minutes. Nailed it.

Shouldn't it be slightly faster to cut off the parts where the two passes cross as curves? It doesn't work out the obvious way because Indiana, but, depending on how much time the curves take, looks like it would be slightly better anyway.

(I've made a mock-up in Paint, but I'm not sure on how the curves work out in particular.)

helo darqness wrote:Okay, I'm probably going to get laughed at for this for asking such a stupid question.

But if satellites count, why not the moon? If one stood on the moon, in the right position, wouldn't they be over all of the States at once, or could at least within a few hours (because of rotation and orbits) have the entire country covered?

:oops:

You can probably see multiple states at once from a satellite, too (or, for that matter, from the spire of 1 WTC - of which there isn't much dispute what state it's in, though it's awfully close to New Jersey).
That doesn't mean you can be over them at the same time, either. :wink:
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Re: What-If 0113: "Visit Every State"

Postby mewo2 » Wed Oct 01, 2014 12:32 pm UTC

I wrote some code to play around with this, and managed to come up with a 5-line set (great circles, not orbits) which covers all 50 states, DC, Puerto Rico, and the US Virgin Islands. No luck on Guam as yet. Would post an image, but I'm newbie-restricted.

I also had a go at covering the contiguous 48 in 4 lines. I haven't found it yet, but it's tantalisingly close. There are a whole host of 47s - you can miss out any of Arizona, Arkansas, Delaware, Florida, Kentucky, New Mexico, North Dakota, Ohio, Rhode Island, South Carolina, Tennessee, Texas, Vermont or Washington.

This rules out the idea of finding a set of 9 states with no colinearities, as any set of 9 states is included in one of these 47s. The minimum set of states (from the 48) that it's impossible to cover with 4 lines must contain at least these 14.

As for covering all 50 in 4, I'm fairly certain that's impossible. I haven't yet been able to find even a way of doing 49.

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Re: What-If 0113: "Visit Every State"

Postby stoppedcaring » Wed Oct 01, 2014 4:01 pm UTC

january1may wrote:
stoppedcaring wrote:EDIT: Reworked the path somewhat. I realized that NY, VT, NH, ME, MA, RI, CT, NJ, PA, DE, MD, DC, VA, and OH can all be hit in sequence by one curve with a radius that never goes under 100 miles, so I reversed the loops. Added enough points to the line so that the actual curves taken will be less distance than the line describes, rather than more.

Shouldn't it be slightly faster to cut off the parts where the two passes cross as curves? It doesn't work out the obvious way because Indiana, but, depending on how much time the curves take, looks like it would be slightly better anyway.

(I've made a mock-up in Paint, but I'm not sure on how the curves work out in particular.)

Wow, impressive. Here I was saying earlier that it's better not to cross lines, and look what I did.

I cloned your mockup in Google Earth and adjusted some of the paths -- for example, I pulled the upper route down to catch IA, IN, IL, and OH, allowing the lower route to only barely clip the eastern corner of KY and the southwest corner of MO. All curves have been smoothed to be well within a 100 mile turn radius. Sure enough, it's dramatically better:

Image

The total distance has been reduced down to just 14,775 km. Ferry range for an SR71 is nearly 6000 km, so three tanks (two refuels) should be no problem. It would probably be best to run the route in reverse: starting with a full tank over HI, refueling somewhere over CO near the Air Force Academy, and then picking up the final tank over Lake Erie. All in all, the trip will take only 4 hours and 30 minutes. Beat that, satellite.

I also learned that if you rework the route to go from Hawaii up to AK and then down to California, you can make the loop all the way back around to Four Corners in under 14,000 km...but the turns are tighter, and expanding those turns out to allow a 100 mi radius makes this route longer than the 14,775 km route shown above.

Could we do the short route in less time? The X15 is much faster than the SR71 but only has a range of 450 km. It does carry liquid rocket fuel rather than solid rocket fuel, so it could conceivably be set up for in-air refueling (though this would be painfully complicated). At maximum speed, it could navigate the full route itself in just over two hours (setting aside the lower turn radius), but it would need at least 32 refuel stops, which would bring refueling time alone to well over 6 hours.

Finally, if you're part of the 99%, this doesn't quite beat out the road warrior route that Steven Worley gave us. His was 6,813 miles. This one would be significantly longer if mapped onto the closest roads, since you traverse the entire US twice rather than only once.

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Re: What-If 0113: "Visit Every State"

Postby Tyndmyr » Wed Oct 01, 2014 8:01 pm UTC

It seems the best way to optimize travel is to pose the question to this forum.

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Re: What-If 0113: "Visit Every State"

Postby Xenomortis » Wed Oct 01, 2014 8:29 pm UTC

Image

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Re: What-If 0113: "Visit Every State"

Postby mathmannix » Wed Oct 01, 2014 8:41 pm UTC

helo darqness wrote:Okay, I'm probably going to get laughed at for this for asking such a stupid question.

But if satellites count, why not the moon? If one stood on the moon, in the right position, wouldn't they be over all of the States at once, or could at least within a few hours (because of rotation and orbits) have the entire country covered?

:oops:


No. Although you can potentially see the whole country from the moon, the moon is directly over a much smaller part of the earth - check out comic 1276. It's a circle about 35 ¾ miles (57 ½ km) in diameter. And I don't know how far north of the equator it gets, but the sun's "shadow" never goes above the Tropic of Capricorn (by definition, more or less), so that only includes Florida, Texas, and Hawaii. The moon's orbit being not exactly in the same plane as the sun's earth's (although it's very close) might get you another few states, or it might not, but it definitely wouldn't get you the northern half of the lower 48, or Alaska.
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Re: What-If 0113: "Visit Every State"

Postby Moose Anus » Wed Oct 01, 2014 8:44 pm UTC

mathmannix wrote:
helo darqness wrote:Okay, I'm probably going to get laughed at for this for asking such a stupid question.

But if satellites count, why not the moon? If one stood on the moon, in the right position, wouldn't they be over all of the States at once, or could at least within a few hours (because of rotation and orbits) have the entire country covered?

:oops:


No. Although you can potentially see the whole country from the moon, the moon is directly over a much smaller part of the earth - check out comic 1276. It's a circle about 35 ¾ miles (57 ½ km) in diameter. And I don't know how far north of the equator it gets, but the sun's "shadow" never goes above the Tropic of Capricorn (by definition, more or less), so that only includes Florida, Texas, and Hawaii. The moon's orbit being not exactly in the same plane as the sun's (although it's very close) might get you another few states, or it might not, but it definitely wouldn't get you the northern half of the country, or Alaska.
While I think you're mostly right, I don't think the sun has anything to do with being "over" any particular state. It's more of a normal of an idealized sphere of Earth. That said, I doubt the moon would ever be "over" Alaska or most other states.

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Re: What-If 0113: "Visit Every State"

Postby mathmannix » Wed Oct 01, 2014 8:47 pm UTC

or watch the first season of the Drew Carey show.
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Re: What-If 0113: "Visit Every State"

Postby stoppedcaring » Wed Oct 01, 2014 8:54 pm UTC

One consideration is that the refuel time may be a little longer than I estimated; the SR-71 is a much bigger bird than the F-14. I was able to find anecdotal references to the fuel capacity of the SR-71 being roughly 40 short tons, and given that this pilot says a B2 takes up to half an hour to gulp 50 short tons, it may be that 25 minutes or so is a better estimate of refuel time for the SR-71. This would increase the time to as much as 4 hours and 55 minutes.

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Re: What-If 0113: "Visit Every State"

Postby Flumble » Wed Oct 01, 2014 11:32 pm UTC

stoppedcaring wrote:One consideration is that the refuel time may be a little longer than I estimated; the SR-71 is a much bigger bird than the F-14. I was able to find anecdotal references to the fuel capacity of the SR-71 being roughly 40 short tons, and given that this pilot says a B2 takes up to half an hour to gulp 50 short tons, it may be that 25 minutes or so is a better estimate of refuel time for the SR-71. This would increase the time to as much as 4 hours and 55 minutes.

Instead of a lengthy refueling, you can just swap planes. Of course you should first decelerate the fighter to a speed at which the pilot(s) can "safely" get out and hop to the other one. It works in BF2, so I expect it to work in real life. :D

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Re: What-If 0113: "Visit Every State"

Postby Moose Anus » Thu Oct 02, 2014 1:08 pm UTC

Flumble wrote:
stoppedcaring wrote:One consideration is that the refuel time may be a little longer than I estimated; the SR-71 is a much bigger bird than the F-14. I was able to find anecdotal references to the fuel capacity of the SR-71 being roughly 40 short tons, and given that this pilot says a B2 takes up to half an hour to gulp 50 short tons, it may be that 25 minutes or so is a better estimate of refuel time for the SR-71. This would increase the time to as much as 4 hours and 55 minutes.

Instead of a lengthy refueling, you can just swap planes. Of course you should first decelerate the fighter to a speed at which the pilot(s) can "safely" get out and hop to the other one. It works in BF2, so I expect it to work in real life. :D
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Re: What-If 0113: "Visit Every State"

Postby stoppedcaring » Thu Oct 02, 2014 4:25 pm UTC

Flumble wrote:Instead of a lengthy refueling, you can just swap planes. Of course you should first decelerate the fighter to a speed at which the pilot(s) can "safely" get out and hop to the other one. It works in BF2, so I expect it to work in real life. :D

Good luck pulling that off at Mach 3.

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Re: What-If 0113: "Visit Every State"

Postby Flumble » Thu Oct 02, 2014 4:36 pm UTC

stoppedcaring wrote:
Flumble wrote:Instead of a lengthy refueling, you can just swap planes. Of course you should first decelerate the fighter to a speed at which the pilot(s) can "safely" get out and hop to the other one. It works in BF2, so I expect it to work in real life. :D

Good luck pulling that off at Mach 3.

I believe Mach 3 is not a speed at which the pilot(s) can "safely" get out and hop to the other one.


Moose Anus wrote:James Bond knows a faster way to swap planes.

That's an even better method, if you can solve that weird spontaneous combustion effect after moving into the new fighter.

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Re: What-If 0113: "Visit Every State"

Postby clarkbhm » Sat Oct 04, 2014 4:03 am UTC

I've come up with a nice 48 state solution that excludes only Rhode Island. Unfortunately, the 5 post limit keeps me from sharing the image right now. Sigh.

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Re: What-If 0113: "Visit Every State"

Postby clarkbhm » Sat Oct 04, 2014 5:29 am UTC

Ok, I'm back from coming up with five thoughtful and inquisitive posts on other forums. The link below clicks through to an image I created from google maps which calculates distances using great circles. I was able to get at least a sliver of every state with the exception of Rhode Island. I had two other 47 state solutions as well, one that left of Washington, and one that left off Wyoming, but I'd much rather be accused of leaving off the smallest state in the union.

Now to go tackle the "all of Europe" challenge... ;-)
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47 states.gif

dtilque
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Re: What-If 0113: "Visit Every State"

Postby dtilque » Sat Oct 04, 2014 10:51 am UTC

helo darqness wrote:Okay, I'm probably going to get laughed at for this for asking such a stupid question.

But if satellites count, why not the moon? If one stood on the moon, in the right position, wouldn't they be over all of the States at once, or could at least within a few hours (because of rotation and orbits) have the entire country covered?

:oops:


The ecliptic (path of the sun) is inclined about 23.4 degrees from the equator. So the sun will only be directly over areas between the latitudes 23.4 degrees North and South. These latitude lines are known as the Tropics of Cancer and Capricorn, respectively. The Moon's orbit is inclined about 5.1 degrees from the ecliptic. So it never gets more than about 23.4 + 5.1 = 28.5 degrees from the equator. It'll sometimes be directly over Hawaii, Texas, and Florida, but never over any other state.
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stoppedcaring
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Re: What-If 0113: "Visit Every State"

Postby stoppedcaring » Tue Oct 07, 2014 5:12 pm UTC

Success!

Using clarkbhm's solution as inspiration, I was finally able to hit 48 states (and one minor outlying island, Wake Island) in just four great circles. Rhode Island and Alaska are the only ones missed. I was able to hit Hawaii thanks to the tiny uninhabited island of Nihoa which is technically part of Honolulu County and thus part of the State of Hawaii.

It's not the Lower 48, but it is 48-in-4. I'll call that a win.

got 48.png
48 states, 4 circles

helo darqness
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Re: What-If 0113: "Visit Every State"

Postby helo darqness » Tue Oct 07, 2014 9:43 pm UTC

You know if you guys made the lines wider / broader, you'd get everything in.

I'm half joking but really

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Re: What-If 0113: "Visit Every State"

Postby sigilToNoise » Thu Jan 29, 2015 12:28 am UTC

I know this is an old What If, but I had an idea about it: The U.S. territory technically extends down to the center of the earth, so if you went far enough underground, the arc length of each state would be small enough that the entire area of the country would be small enough to fit under the sole of one foot, and then you would be visiting every state simultaneously.

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Re: What-If 0113: "Visit Every State"

Postby PinkShinyRose » Thu Jan 29, 2015 12:43 pm UTC

sigilToNoise wrote:I know this is an old What If, but I had an idea about it: The U.S. territory technically extends down to the center of the earth, so if you went far enough underground, the arc length of each state would be small enough that the entire area of the country would be small enough to fit under the sole of one foot, and then you would be visiting every state simultaneously.

Any ideas on getting the foot there in one piece?

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Re: What-If 0113: "Visit Every State"

Postby mathmannix » Thu Jan 29, 2015 2:06 pm UTC

PinkShinyRose wrote:
sigilToNoise wrote:I know this is an old What If, but I had an idea about it: The U.S. territory technically extends down to the center of the earth, so if you went far enough underground, the arc length of each state would be small enough that the entire area of the country would be small enough to fit under the sole of one foot, and then you would be visiting every state simultaneously.

Any ideas on getting the foot there in one piece?

Well...
You could stay there for a few nanoseconds. (The center of the earth is roughly the same temperature as the surface of the sun. Maybe a thousand degrees hotter (°C or K) according to recent studies, but that shouldn't matter too much.) So really, we just need to work on our teleportation skills.
I hear velociraptor tastes like chicken.

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Re: What-If 0113: "Visit Every State"

Postby Beavertails » Thu Jan 29, 2015 2:08 pm UTC

sigilToNoise wrote:Any ideas on getting the foot there in one piece?


No problem. I just need Brendan Fraser, a bad script, and 5 cups of coffee.
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mathmannix
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Re: What-If 0113: "Visit Every State"

Postby mathmannix » Thu Jan 29, 2015 2:10 pm UTC

Beavertails wrote:
sigilToNoise wrote:Any ideas on getting the foot there in one piece?


No problem. I just need Brendan Fraser, a bad script, and 5 cups of coffee.

Or Hilary Swank and Aaron Eckhart. It's hard to say which script is worse.
I hear velociraptor tastes like chicken.

Jakec
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Re: What-If 0113: "Visit Every State"

Postby Jakec » Thu Jan 29, 2015 6:26 pm UTC

sigilToNoise wrote:I know this is an old What If, but I had an idea about it: The U.S. territory technically extends down to the center of the earth, so if you went far enough underground, the arc length of each state would be small enough that the entire area of the country would be small enough to fit under the sole of one foot, and then you would be visiting every state simultaneously.


Somehow I am skeptical that any country has claimed the center of the earth.

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Re: What-If 0113: "Visit Every State"

Postby mathmannix » Thu Jan 29, 2015 6:43 pm UTC

Dibs! (for the USA!)
I hear velociraptor tastes like chicken.

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Re: What-If 0113: "Visit Every State"

Postby Pfhorrest » Thu Jan 29, 2015 6:49 pm UTC

The center of the earth is a point, and technically nobody has claimed that point, but basically every country claims all the ground below the surface of their territory, to arbitrary depth — no country is going to let you off the hook for digging a tunnel under their territory on the excuse that you dug it really really deep — so effectively, because the Earth is round, they're claiming a somewhat conical chunk of the Earth as their territory, the volume between the point at the center of the earth and the surface borders of their territory.

And it doesn't matter that the exact actual point isn't claimed by anyone for the point that that the whole (two dimensional cross-section of the three-dimensional volume of the) country will have an area smaller than your foot at some point before that point.
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