how many caches fit in a square mile

[+bigredmed]

I have to sympathize with BassoonPilot's earlier comment, though not totally agree. I would like to see us experiment with cache type over lays.

 

Take a park that is 1 sq mile. You could place 100 cache points into this square (10 0.1 mile increments to a side making a 10X10 matrix). Deduct road surface, maintenance facilities, ponds/lakes and the number goes down variably, but closer to about 50. Of these 50 points, maybe 20 of them are useful for caches (the others being in the middle of a baseball diamond or soccer field, etc). Of the 20 that are that are good sites, some number are going to be less good than the others. Maybe we get 10 really good sites. 10 of 100 is not going to be "riding roughshod" over anything, and to me, this comment sounds like the hyperbolic mating call of the eco-fascists.

 

If there are only 10 really good sites and 10 OK sites in this park, why not try to use them in an intentionally mixed manner. Layer multis, micros, and trads in a way that doesn't use up the park by taking 3 of the 10 good sites for 1 multi and allows cachers with different interests or ability all use one park. This means WE monitor and regulate our behavior. It means caches don't get placed somewhere without locals having input into the location/type. It means more eyes for the approvers, so caches that are sort of questionable from the level of mapquest can be sorted out live. It means more work for local cache groups to decide how to do this for given parks and training new cachers on how to hide them.

 

It also means that we can have a system in place that autoregulates the sport and makes this stuff less common.

[+geoSquid]

Take a park that is 1 sq mile.  You could place 100 cache points into this square (10 0.1 mile increments to a side making a 10X10 matrix).

Actually, you could place at least 114. Square packing is not the most efficient use of space. Try hexagonal packing of the caches.

Edited August 30, 2004 by geoSquid

[+cachew nut]

Take a park that is 1 sq mile.  You could place 100 cache points into this square (10 0.1 mile increments to a side making a 10X10 matrix).

Actually, you could place at least 114. Square packing is not the most efficient use of space. Try hexagonal packing of the caches.

Actually you could fit 121 in an 11 x 11 matrix.

[ju66l3r]

Not to go too far off-topic, but here's a post that I gave the saturation equation in:

 

Hexagon Algorithm

 

In it, I describe the equation to be y = 3k(k+1)+1 where y is the number of geocaches that fit in a k-deep hexagon.

 

Now...you can fit more than a perfect hexagon into a square space. But building on these parameters (concentric circles with radius of 264 feet...meaning no center of any circle will come within 528 feet of another circle's center), you can fit 11 caches along a single 1 mile stretch (including both endpoints). The next hexagonal packing line above that one will contain 10 circles. You can continue alternating rows of 11 and 10 for 23 total rows. The centerline of the circles in each row is 228.63 feet from the row above and below it. That makes 5258.5 feet of the second dimension covered with circles (the remaining 21+ feet is lost space).

 

With 12 rows of 11 circles and 11 rows of 10 circles, you can have 242 caches in 1 square mile. A more complicated packing algorithm *may* yield 243.

 

EDIT: For topicality, CO Admin, you may want to point out that in Boulder, CO there are only 1092 caches (some virtual/webcam/etc) within a 100 mile radius of Boulder's 80301 zip code. In over 30,000 square miles, there's only enough caches to cover about 4 square miles of space. Hardly an epidemic worthy of the committee/council/whatever's time.

Edited August 30, 2004 by ju66l3r

[+cachew nut]

With 12 rows of 11 circles and 11 rows of 10 circles, you can have 242 caches in 1 square mile.  A more complicated packing algorithm *may* yield 243.

Either I'm not following you, or your formula is screwed up. In a 11 x 11 matrix you can fit 121. Using your method, I could only fit 126. See the two examples below.

 

I think you meant to say 6 rows of 10 circles.

 

In other words, I can't get the 23 rows you speak of. In the examples shown, the blue box represents one square mile and the circles are 528 ft in diameter.

 

The blue boxes are the same size, but the lower photo is slightly larger, thus it appears bigger.

 

 

Edited August 31, 2004 by cachew nut

[+Fireman78]

You guys are killing me with your math issues ROTFLOL