Additional Math Pages & Resources

Friday, February 3, 2012

Take a Hike, Part II

Yesterday we visited some hiking trails on Cowles Mountain in the city of San Diego, California. (See Take a Hike, Part I.) Today we'll take a look at the elevation gain of some of the trails up this mountain.  With its 933 foot vertical ascent, Cowles Mountain is located in Mission Trails Regional Park and has become one of the most popular hiking destinations in San Diego County. Started in 1974, Mission Trails Regional Park has become one of the largest urban parks in the United States.

Today let’s see how elementary math can help us compare the elevation of various hiking trails on this mountain. If you need a refresher course in elementary math, check out the Excel Math website.

In the meantime, let's start our hike. Here are a few trail options from the base of Cowles Mountain at Barker Way:
The Barker Way Service Road is one of the trails up Cowles Mountain where bikes are allowed. However, you may have to get off and walk up some of the steepest slopes. It has an elevation gain of 870 feet. This map shows the trail up Barker Way:

Barker Way also has a narrow hiking trail that passes over a small bridge and joins the more well-traveled trail from Golfcrest about a mile up the mountain. This trail is much less traveled and becomes quite narrow where brush and trees have encroached on the trail, but it’s very well marked.

One of the most well-traveled routes up the mountain begins at the parking lot on Golfcrest Drive. Pick up a plastic bag at the trailhead if you bring your dog, and be sure to bring water for your pet as well as for yourself. There are no water fountains at the top (but there is a recycle trash can for your empty bottles):

Another route up Cowles Mountain starts in Santee at Big Rock Park. The total vertical elevation from Big Rock Road is 1,176 feet. Not only does this Santee Park offers lots of fun activity areas including basketball, volleyball, and tennis courts, it has gazebo picnic benches, restrooms, grills, two playgrounds and an open green space, pictured below. The park is dog friendly and hosts a trailhead to the top of Cowles Mountain:

If you want a challenging bike ride, begin at Big Rock Park, then take the Barker Way service road to the peak of Cowles. After a brief rest, start back down the service road a short distance and follow the signs out to Pyles Peak and back to Golfcrest for an elevation gain of 1866 feet.

Make sure you stop at the top of Cowles Mountain before continuing down. From the top you have an amazing view of San Diego county. Here's a photo of Lake Murray—another nearby hiking and biking spot—as seen from halfway up the mountain. Lake Murray has an elevation gain of just 10 feet.

This chart shows the elevation gain of various trails in the Cowles Mountain region. The faster the elevation gain over the miles hiked, the more challenging the hike:

If you'd like to calculate your time to hike any of these trails, a science teacher and software developer has put together a hiking time calculator based on the distance in miles (see Take a Hike Part I for more on distance) and the elevation (in feet) of your trail. If you're a regular hiker, your speed up and down the mountain will be faster than these calculations show, but the hiking time calculator is a fun place to start:

This chart recaps the length (in miles one way) of each of these trails on Cowles Mountain:

Now let's fly over to Europe and visit Austria. Here's a lush hiking trail outside Salzburg, in Leogang. We'll save that hike for another day: