Central Ohio is probably not the best place to be located if you are trying to get in shape for hiking or backpacking somewhere with mountains. But I do have a favorite place to do as much as I can.
That would be Alley Park, just south of Lancaster, OH. It has about 300 acres so it’s not really all that big. But it is fairly close to me. I can get there in just over half an hour.
It is also rather hilly. It’s really just on the northern edge of Hocking Hills, so it has the same Blackhand Sandstone, and there is even a recess cave in the area. Here’s my topo map of the park.
While there are a lot of trails, they are really pretty separated. You really don’t see any of the other trails until you are right upon them. So it’s still a fun hike. You can also see that there’s at least a bit of elevation change. The low point is down around 860 feet above sea level, and the highest point is around 1070 feet. That’s something . . . at least in central Ohio.
But you can also see that the trails allow you to go up-and-down, up-and-down.
So I got to wondering just what sort of hiking route I could come up trying to maximize the total distance and/or the total elevation climbed. My major criterion was that I don’t repeat myself. Because I hate repeating myself.
What I am looking for is a “simple” path solution of the Longest Path Problem (or at least something close). This is one of those problems that is NP-Hard. It probably cannot be solved in polynomial time as the size increases, but they don’t really know.
In my case, I was just hoping that the number of nodes in Alley Park weren’t too many for my computer to handle in searching through all of the possible routes to find the longest (or nearly the longest).
Here’s my map showing all of the nodes (which I then encoded into the computer program I wrote to do the searching).
A couple of comments on that map. You’ll notice that points 22 and 23 appear to be the same on my original topo maps. In reality, they are about 15 feet apart, which means that that provides an opportunity for not repeating if you choose your path wisely. You’ll also notice points 37 and 38. Obviously, there’s really no choice there—if you come in one side you have to go out the other. But they are local high points, and by including them I was able to easily compute elevation gains.
So, this is a graph with 37 points (note that the Parking Lot is point 0).
It turns out that I was able to do the computation. It turns out that there are 48,192 different unique paths that you can hike through the park without repeating yourself (on that particular hike). There are actually twice that since you can do any path in either direction, but I really don’t want to count those.
The shortest one is a mere 0.74 miles (0, 1, 3, 4, 5, 6, 0).
The longest path is 4.68 miles, with a total elevation gain of 870 feet. (Obviously, that’s not all at once. Also, obviously, there also has to be a total elevation loss of 870 feet to end up back where you started.)
But it turns out that’s not what I would consider an optimal path. There is another path (4th longest) that is 4.61 miles and has an elevation gain of 1040 feet. That’s the path with the greatest elevation gain. It’s still plenty long (only 390 feet shorter than the longest one).
And here it is.
I have hiked it and it is a great route.
Back when John O’Meara was preparing for his trip to Mount Everest, we did a bunch of organized hikes at Clear Creek Metro Park. See, e.g., O’Meara’s O’Venta Hike; A Snortin’ Good O’Meara O’Vencha Hike; O’Meara O’Vencha Hike: Thorn Patrol; O’Meara O’Vencha Hike: Reconditioning; and O’Meara O’Vencha Hike: Spring. In those hikes the focus was on distance (usually around 12 miles), though there were elevation changes. But I like my new route at Alley Park. Sure, it’s a lot shorter than Clear Creek, but climbing all those hills with a heavy pack is and entirely different sort of conditioning.
I plan on heading to the Grand Canyon later this summer and camping down at the bottom. Now I just need to be able to do 5 of those Alley Park longest hikes in a row to be able to get back to the rim.