I sent the link to this comic
to physics professor, Eric, so he could explain the solution to me. Instead, I sidetracked him from his real work. Oops.
Bad Dad and I took our 12 yo and a borrowed 11 yo to Salt Lake City for some skiing and snowboarding over the long weekend. The snow conditions were poor by Utah's (high) standards, but we managed to ski safely and have fun. I almost nerd sniped myself.
The first two days were incredibly sunny and bright and we took advantage of the sun to ski Milly's east-facing slopes each morning. The snow started out crusty and hard and we had to pay close attention to where we could find loose powder to turn. The parts of the trails that faced the sun the longest softened up first.
At 10,000 feet, under cloudless skies, the solar irradiance must have been >1000 watts per square meter. In fact, the solar irradiance plot for Cedar City
, elevation 1675 meters (5500 feet), half the elevation of the top of the Milly lift, exceeded 1000 watts on Feb 15. Look at the smoothness of that curve. There was literally not a cloud in the sky.
Round to the even number of 1000 watts/m^2, and assume the snow has an albedo
of 0.9--it reflects 90% of the incident solar spectrum. Let the snow be in equilibrium with the air temperature of -5 C. How long does the sun have to hit a patch of hardpack (icy snow) for it to soften enough to be skiable (by me)?
Recall that 1 watt is 1 Joule/sec. The specific heat of ice
at -5 C is 2.027(kJ/kgK). Utah powder has about 13:1 snow:water equivalence
. But hardpack would be considerably lower. Let's use 5:1.
How warm does the hardpack need to be to give my ski edges something to dig into? Let's just use 0 C as a placeholder until someone who knows better leaves us a comment.
I asked a ski instructor who is a retired engineer and then he said that I underestimated the complexity of the problem. He said that it also depended on the wind and sublimation. Grrr! Let's just ignore those for a first pass.
I got so wrapped up in this, I almost caught an edge on a patch of ice. Hmmm, the second busiest ski weekend of the year and I needed to concentrate on skiing--not thermodynamics.
On the third day, it snowed horizontally. A gust of wind created white-out conditions while we were descending a crowded, steep and narrow section. I knew that I had to keep going forward (albeit slowly) to avoid being hit by a skier above. It's like driving in heavy fog. You can't stop abruptly. You have to control your fear and keep going until you reach a spot where you can stop safely.
Iris lost her nerve and spent the rest of the afternoon at the lodge. After the storm, the skiing was beautiful. My camera battery complained about the cold, but our 11 yo guest snapped this picture with her iPhone.
On the second day, I left the others to join the "ski with a ranger" tour, where I learned a ton of interesting facts about the natural and human history of Cottonwood canyon. When they realized I was a ringer, the rangers let me give the snow water equivalence and climate change portion of the lecture.
On the fourth day, I ran into one of the rangers and she introduced me to a "ranger in training". He took me on a two hour private lesson where he taught me how to ski moguls. My legs are rubber and I am exhausted. But, it was so much fun. And that was even without learning that he met Paul Dirac at Stonybrook, when Dirac came as a guest lecturer for their undergraduate physics class.