Costa Rica pictures, finally!

31 August 2009

I’ve finally put some pictures of our honeymoon in Costa Rica on my Flickr account: here they are.

I thought I’d also put a few of my favorite Costa Rica wildlife photos here.

Iguana
Iguana on the beach.

Crocodile
A crocodile, from the bridge above it.

Toucan
Toucan in the forest below Volcano Arenal.

White-faced monkeys
White-faced monkeys in the forest below Volcano Arenal.


When will I ever need to use trigonometry? (Or, how to avoid avalanche terrain.)

21 August 2009

I sometimes tutor high school math, and as anyone who has done this knows, a common question is ‘But when will I ever need to use blank?’. This came up last year, where the blank was trigonometry.

When will I ever need to use trigonometry? It’s a legitimate question. As an instructor, you could explain how it’s a foundation of mathematics, or how you’ll need to understand it for any career in science or math, or so on… (They’re both true, and are probably close to what I said, but neither are an answer that your student is likely to care much about.) Think about it: what practical problem, in day-to-day life, have you solved by applying trigonometry? (Comment if you have a good one!)

So, when I was backcountry skiing last winter and my friend Erik and I actually applied trigonometry to decide if it was safe to ski a certain slope, we were proud.

It’s generally accepted that if a slope is 30 degrees or less, it’s probably not steep enough to avalanche. Slopes around 40-55 degrees are the most dangerous. We were about to cross a slope, but we weren’t really prepared to be in avalanche terrain: we didn’t have our beacons, probes, and shovels. In short, we wanted to avoid avalanche terrain by staying off slopes that were 30 degrees or greater.

We didn’t have a slope meter, but we did know trigonometry. If we could make a right triangle where one of the legs (i.e., sides not opposite the right angle) was double the length of the other leg, the slope of the opposite side (the hypotenuse) would be less than 30 degrees. (We did need a calculator to figure out exactly what that angle would be.) What could we use to make the two legs? Ski poles!

Figure 1: Identifying a 26 degree slope with two ski poles.

Figure 1: Identifying a 26 degree slope with two ski poles.

Here’s how it works. Plant your first pole vertically, and try to make a 90 degree angle with the second pole beginning halfway down the vertical pole. If the tip of the horizontal pole touches when the poles are at 90 degrees with one another, you’re on a roughly 26 degree slope (Figure 1). If you can’t make a 90 degree angle because the horizontal pole hits the slope too high, the slope is steeper than 26 degrees (Figure 2). If you can make an angle smaller than 90 degrees before the tip of the horizontal pole hits the snow, the slope is less than 26 degrees (Figure 3).

Figure 2: Identifying a slope greater than 26 degrees with two ski poles.

Figure 2: Identifying a slope greater than 26 degrees with two ski poles.

The rule-of-thumb is this: If the poles can form a right triangle with the horizontal pole exactly halfway down the vertical pole, and with the slope as the hypotenuse, the slope is less than 30 degrees and you are probably safe. This is the situation depicted in Figures 1 and 3. If you can’t form the 90 degree angle because the slope is too steep, as in Figure 2, you’re in possible avalanche terrain so make sure you know what you’re doing!

Figure 3: Identifying a slope less than 26 degrees with two ski poles.

Figure 3: Identifying a slope less than 26 degrees with two ski poles.

Finally, you can also use this trick to identify a 45 degree slope (which is absolutely in avalanche terrain). To do that, this time place the horizontal pole at the top of the vertical pole rather than halfway down. If the tip of the horizontal pole just touches the slope when you have a 90 degree angle between the poles, the slope is just about 45 degrees (Figure 4). If it doesn’t touch, it’s less than 45 degrees. If you can’t make a 90 degree angle because the second pole hits the slope too high, you’re on some steep stuff!

Figure 4: Identifying a 45 degree slope with two ski poles.

Figure 4: Identifying a 45 degree slope with two ski poles.

There you have it: a field application of trigonometry. We’re not the first ones to figure this out — I’ve since heard that the Norwegians have been doing this forever. It’s a neat trick.

And of course, there is a lot more to avalanche safety than this. This is a basic rule, but by no means definitive. Be scared of avalanches, and don’t assume that if a slope is less than 30 degrees it can’t slide. If you’re planning to travel in avalanche country take a class, check the avalanche reports, and if you’re not scared of avalanches, watch some videos.

Skiing out from Ken's Cabin
Skiing out from Ken’s Cabin

More photos from this trip.


Twenty 14ers done!

9 August 2009

Yesterday Ingrid and I climbed Mt. Bierstadt and the Sawtooth over to Mt. Evans (Map, credit: 14ers.com). We had both done Bierstadt before (maybe the most popular 14er hike in Colorado?) but the summit of Mt. Evans marked my 20th and Ingrid’s 6th 14er.

This was a long but very fun hike, with four distinct sections: the Bierstadt ascent, the Sawtooth, the Evans ascent, and the descent. The hike from Guanella Pass to the Mt. Bierstadt summit is a 3.5 mile climb, from the trailhead at 11,669′ to the summit at 14,060′. Since it was a beautiful Saturday morning, this section was PACKED with people.

The Sawtooth and Bierstadt from the Bierstadt Trail
The Sawtooth and Bierstadt from the Bierstadt Trail.

From the summit, we scrambled across the Sawtooth. We ran into very few hikers in this 3.5 hour section of the hike (with a lunch and nap break), so it was a nice change from the Bierstadt Trail. This was sketchy in spots but doable.

Ingrid on the Sawtooth
Ingrid on the Sawtooth with the Bierstadt summit in the background.

Once across the Sawtooth, we hiked through a boulder field for about 2 hours up to the Mt. Evans summit at 14,264′. There is a paved road up to the Evans summit — the highest paved road in America — so, of course, the summit of Evans was packed.

Mt Evans Observatory from Mt Evans Summit
Mt. Evans observatory from the Mt. Evans summit.

We quickly left the summit to make our way back to the Guanella Pass parking lot as we were starting to get tired. Rather than cross the Sawtooth again, we hiked down an alpine meadow, into a gully, and then through the infamous willows. The route finding was straight-forward in this section, and there was a decent trail through the willows (albeit a little soggy).

Waterfall
Waterfall just above the willows.

I now understand why everyone warns of how terrible it could be to get lost in the willows. Before there were decent trails through this section the willows could have been a slow, wet end to a long hike. The hike ended up taking us just under 12 hours, from trailhead to trailhead.

Twenty down, thirty-two to go… A map of Colorado 14ers with the ones I’ve hiked in red.

More photos from this hike and photos from my other 14er hikes.


The longest Sunday drive from the mountains I’ve ever had…

28 July 2009

This Sunday was the slowest trip back from the mountains I think I’ve ever had. We were camping for the weekend at a friend’s ranch just on the west side of McClure Pass. We left camp at about 11am for the 5-hour trip home. About an hour and a half into the trip, we ran into this:

Mudslide on CO-133
Mudslide on the Hwy 133, just east of McClure Pass.

About five hours later, when it finally got cleaned up, we were able to head on to I-70 through Glenwood Springs. We’d heard about an accident on I-70, which turned out to be a flipped oil tanker… So, another few hours was then spent in Eagle, Colorado having dinner. We finally decided to brave the traffic and head into the detour through the town of Edwards. We got lucky, and the highway re-opened right around when we got there. So, another few hours on the I-70, and we finally made it home at about 1:30am on Monday morning.

Of course it could have been worse, but a long day nevertheless.