tue, 31-jan-2012, 19:05
Skiing at -34

Skiing at -34

This morning I skied to work at the coldest temperatures I’ve ever attempted (-31°F when I left). We also got more than an inch of snow yesterday, so not only was it cold, but I was skiing in fresh snow. It was the slowest 4.1 miles I’d ever skied to work (57+ minutes!) and as I was going, I thought about what factors might explain how fast I ski to and from work.

Time to fire up R and run some PostgreSQL queries. The first query grabs the skiing data for this winter:

SELECT start_time,
    (extract(epoch from start_time) - extract(epoch from '2011-10-01':date))
        / (24 * 60 * 60) AS season_days,
    mph,
    dense_rank() OVER (
        PARTITION BY
            extract(year from start_time)
            || '-' || extract(week from start_time)
        ORDER BY date(start_time)
    ) AS week_count,
    CASE WHEN extract(hour from start_time) < 12 THEN 'morning'
         ELSE 'afternoon'
    END AS time_of_day
FROM track_stats
WHERE type = 'Skiing'
    AND start_time > '2011-07-03' AND miles > 3.9;

This yields data that looks like this:

start_time season_days miles mph week_count time_of_day
2011-11-30 06:04:21 60.29469 4.11 4.70 1 morning
2011-11-30 15:15:43 60.67758 4.16 4.65 1 afternoon
2011-12-02 06:01:05 62.29242 4.07 4.75 2 morning
2011-12-02 15:19:59 62.68054 4.11 4.62 2 afternoon

Most of these are what you’d expect. The unconventional ones are season_days, the number of days (and fraction of a day) since October 1st 2011; week_count, the count of the number of days in that week that I skied. What I really wanted week_count to be was the number of days in a row I’d skied, but I couldn’t come up with a quick SQL query to get that, and I think this one is pretty close.

I got this into R using the following code:

library(lubridate)
library(ggplot2)
library(RPostgreSQL)
drv <- dbDriver("PostgreSQL")
con <- dbConnect(drv, dbname=...)
ski <- dbGetQuery(con, query)
ski$start_time <- ymd_hms(as.character(ski$start_time))
ski$time_of_day <- factor(ski$time_of_day, levels = c('morning', 'afternoon'))

Next, I wanted to add the temperature at the start time, so I wrote a function in R that grabs this for any date passed in:

get_temp <- function(dt) {
    query <- paste("SELECT ... FROM arduino WHERE obs_dt > '",
        dt,
        "' ORDER BY obs_dt LIMIT 1;", sep = "")
    temp <- dbGetQuery(con, query)
    temp[[1]]
}

The query is simplified, but the basic idea is to build a query that finds the next temperature observation after I started skiing. To add this to the existing data:

temps <- sapply(ski[,'start_time'], FUN = get_temp)
ski$temp <- temps

Now to do some statistics:

model <- lm(data = ski, mph ~ season_days + week_count + time_of_day + temp)

Here’s what I would expect. I’d think that season_days would be positively related to speed because I should be getting faster as I build up strength and improve my skill level. week_count should be negatively related to speed because the more I ski during the week, the more tired I will be. I’m not sure if time_of_day is relevant, but I always get the sense that I’m faster on the way home so afternoon should be positively associated with speed. Finally, temp should be positively associated with speed because the glide you can get from a properly waxed pair of skis decreases as the temperature drops.

Here's the results:

summary(model)
Coefficients:
                     Estimate  Std. Error t value Pr(>|t|)
(Intercept)          4.143760   0.549018   7.548 1.66e-08 ***
season_days          0.006687   0.006097   1.097  0.28119
week_count           0.201717   0.087426   2.307  0.02788 *
time_of_dayafternoon 0.137982   0.143660   0.960  0.34425
temp                 0.021539   0.007694   2.799  0.00873 **
---
Signif. codes:  0***0.001**0.01*0.05.0.1 ‘ ’ 1

Residual standard error: 0.4302 on 31 degrees of freedom
Multiple R-squared: 0.4393,    Adjusted R-squared: 0.367
F-statistic: 6.072 on 4 and 31 DF,  p-value: 0.000995

The model is significant, and explains about 37% of the variation in speed. The only variables that are significant are week_count and temp, but oddly, week_count is positively associated with speed, meaning the more I ski during the week, the faster I get by the end of the week. That doesn’t make any sense, but it may be because the variable isn’t a good proxy for the “consecutive days” variable I was hoping for. Temperature is positively associated with speed, which means that I ski faster when it’s warmer.

The other refinement to this model that might have a big impact would be to add a variable for how much snow fell the night before I skied. I am fairly certain that the reason this morning’s -31°F ski was much slower than my return home at -34°F was because I was skiing on an inch of fresh snow in the morning and had tracks to ski in on the way home.

tags: skiing  R  statistics  PostreSQL 
Meta Photolog Archives