Texas Summary

 We've back from our winter escape from Texas, so it's time for a summary. The first thing that comes to mind is that is was cold. Before 2021, winters in Corpus Christi would follow a pattern of 3-4 warm days, with sun and temperatures in the 60s or 70s, followed by 3-4 cold days, where temperatures dropped to around 50 F (10 C). Quite often, we'd also get decent sessions on the colder days, since the water would remain comfortably warm for the first couple of cold days.

This year was different: the cold spells lasted longer, often 5 to 7 days, and the warm spells seemed shorted. On January 20, the air temperatures dropped below 40 F, and it took until February 2 before it got up to 70 again ... only to drop down to below freezing two days later, and then remain below 70 for another couple of weeks. Interestingly, the colder weather is likely to be a consequence of global warming, which weakens the jet stream and thus causes more "blocking", where weather remains "stuck" for longer times. I find it scary that this seems to have become an easily observable trend already .. and that it's effect of making winters in Texas colder may prevent locals from realizing that climate change is real, and carbon emissions really must be reduced.

After having experienced 6 freezing cold days without power in Texas last year, we escaped the cold period in February by driving to Florida. That was an astonishingly long drive (1,260 miles), but well worth it. We visited our friend Joanie, foiled and winged at a few new spots, and I even got to take a one-day wing clinic with Andy Brandt, which was great. I got a few longer rides and can now at least imagine that winging could be fun.

In March, it finally got (mostly) warm, and we had a lot of days with wind in the 20-30 mph range, and temperatures in the high 60s and low 70s. After getting onto the water only about every third day in January and February, I got 21 sessions in March. 11 of those were speed sessions on slalom gear, mostly at Grassy Point and with Nina. I ended up getting above 35 knots a couple of times, which I had previously not done in the USA, and set a new personal best for the nautical mile (32.12 knots) on the last day. But my speed improvements paled against Nina's.

In the last couple of years, Nina had been stuck at a top speed just below 32 knots in Corpus Christi. But after a few successive speed sessions in March, something clicked, and she got a 2-second top speed above 34 knots on March 18. She also set a new PB for the nautical mile (30.448 knots) the same day. After this session, she had no problem getting above 33 knots, proving that she had indeed learned to go faster. 

Towards the end of our trip, we got lucky: 3 windy days in a row, with low tide levels which meant flat water at Grassy Point. On our last day of sailing, Nina set a new top speed PB with 36.103 knots, easily beating my speed for the day. She also improve her nautical mile PB again, to 30.962 knots. For her top speed, she had found a spot of very flat water right next to the shipping channel near Padre Island. She later showed me the spot, but by then, the wind had dropped.

Since we had so many cold days in the first two months of our trip this year, we ended up with a new hobby: bird watching. Corpus Christi may be one of the best spots to get started with taking bird pictures, since it has lots and lots of impressive water birds that are not shy at all. We ended up with photos from more than 40 different bird species, and a few other animals like coyotes, deer, and crocodiles. Here are a few of my favorites:

    Willet - a common sight

    Royal Terns. Love the hairdo.

    Roseate Spoonbills and Little Blue Heron

    Reddish Egret

    Long-billed Curlew. A few often hang out near the Bird island windsurf launch.

    White Pelican

    Windsurfer and a flock of Ibis

    Great Blue Heron and Great Egret, two very common sights.

    Black-necked Stilt. Elegance defined.

Measuring Speed Errors: Sampling Frequency

This is the first of several posts where I look at the accuracy of speed measurements and the sources of errors in detail. To get started, let's look at the tracks and speed graph from an impressive speedsurfing session (click on images for a larger version):

This is the track from a recent speedsurfing session in Tasmania, Australia, available at ka72.com. The section for top speed runs right next to a sandbar is quite short: the blue line in the image is only about 220 m long. But despite the short runs, the speedsurfer hit more than 40 knots in every speed run, and reached a top speed of 44.3 knots. 

I am using this session as an example because it has some very rapid speed changes: each speed run took only about 40-50 seconds. With rapid speed changes like this, we obviously must take speed measurements often enough to get the correct speed, or our measurements will be off. In signal processing, the term "Nyquist theorem" is often used to describe this issue; "sampling rate" that are too low for the signal create "aliasing errors".

A zoom-in on the top 10 second speed run illustrates this:

The blue curve shows the original speed measurements, which were done ten times per second (at 10 hz). The red curve used only every second point of the original data, corresponding to measuring the speed at 5 hz. The green curve used just every 10th point, and shows what the data would look like at 1 hz (the rate of the Locosys GT-31 that was the "Gold standard" GPS device for many years). 

The graph shows clearly that measuring speed just once per second does not capture the details of getting faster and slowing down very well - but how much "aliasing error" do the slower sampling rates introduce? Here is what the calculated top speeds at 1 hz, 5 hz, and 10 hz look like for the categories used in the GPS Team Challenge:

Interestingly, the differences relative to the 10 hz numbers are quite small: 0.064 and 0.026 for the top 2 seconds; about 0.01 knots for the 5x10 second average; and about 0.02 knots or less for the other categories.

But looking at just one result for each categories leaves us a bit at the mercy of chance - perhaps the difference were low for the fastest 2 second run, but larger for other speed runs? So let's have a look at the fastest 5 runs in the 2 second, 10 second, and nautical mile categories:

That's a lot of numbers, but we can just plug them into a spreadsheet, calculate the differences relative to the 10 hz numbers, and then find the average and maximum differences. Here are the results for the speed session:

The average differences measured for the 5 hz data range from about 0.06 knots for 2 second runs to 0.002 knots for the nautical mile. The largest observed difference is 0.131 knots for the 4th-fastest 2-second run. Here's a zoom in of this region (again with blue = 10 hz, red = 5 hz, green = 1 hz):

Basically, most 5 hz values used in this region happened to be higher than the points that were not used, so the 5 hz average ended up higher than the 10 hz average. Over longer periods, point-to-point variations will not show the same "up-down-up-down" patterns as this region, so it will become less and less likely that the sub-samples are mostly higher or lower values, which leads to the drop in the observed differences.

The numbers above are for just one file. What happens if we look at more GPS tracks - from other spots, other people, other units? To find out, I repeated the analysis above with a total of 10 files, which include 40+ knot sessions from Albany and Lake George, as well as a number of slower sessions from other spots. Here are the results:

The numbers cover quite a range - from an average "aliasing error" of 0.004 knots when comparing 5 hz and 10 hz data for nautical mile results, to a maximum of 0.349 knots when comparing 1 hz data to 10 hz data for 2 second runs. Of the 10 files in this analysis, 4 showed differences near or above 0.2 knots for 2-second runs (when looking at the top 5 runs in each file). In other words, the chances that a 2-second result obtained from 1 hz data is off by 0.2 knots or more are quite high. 

In contrast, the observed differences between 5 hz and 10 hz are much smaller - typically around 0.02 knots. One one of the fifty runs included in this analysis had a difference of 0.131 knots; all other runs had a measured difference below 0.1 knots.

But what do these numbers mean? To put them into perspective, I looked at differences from runs that were recorded with 2 GPS units at 10 hz speeds. I included a total of 10 files from 5 different sessions, recorded by 3 different speedsurfers. Here are the results:

The next graphs compare our measured estimates of "aliasing" errors to the measured differences between 2 units - first the average differences:

In each category, the measured "aliasing error" is at least twofold lower than the observed difference between two units. The picture for the observed maximum differences is similar:

The analysis above is the first actual measurement of "aliasing error" in speedsurfing. The result indicates that, compared to the current accuracy of the best GPSTC-approved units, the aliasing error is small for 5 hz data. In contrast, the measured error for 1 hz data is larger than the typical "2 unit difference". In absolute terms, this primarily affects 2 second results, and to a lesser effect 10 second runs. 

What the analysis above did not address was the impact of sampling rate on the accuracy estimates of the final results due to random and non-random errors in the speed measurement from other sources. This is a topic that can appear very simple ("more is better"), but can actually be quite complex when looking at the underlying assumptions and error sources in detail. I plan to address some of these issues in future posts.

Two days, three foils

The last couple of days were great for foiling. On Tuesday, we got WSW wind with averages between 18 and 23 mph, and gusts to 29. Since strong WSW wind means plenty of chop, I went out on my Slingshot Time Code 68 wing, which is my favorite for playing with swell. I though the swell was rather unorganized, but it was still plenty of fun pinching upwind and writing squiggles into the swell back downwind - here are the GPS tracks:

Our friend Joanie was out, trying to learn winging, and it looked quite hard to stay on the board in the chop. So we figured we'd head to flatter waters the next day, when the forecast predicted more southerly wind in the high teens: Waquoit Bay. The water in "Wacky Bay" is nice and flat since it is protected from the ocean chop:

Here is the speed graph for this session:

Since Wacky Bay has so little chop, the water was warm, and the wind just right, I decided to give winging another try with Nina's 6.0 m wing and the i84 foil on my Stingray 140. I managed to get up onto the foil quite quickly, and then had a 2 minute, 600 meter run where I stayed up on the foil and even managed to go upwind nicely. But it was a lot of work - it seems foiling uses some muscles I never use any other time. It also felt very slow, and the speed graph confirms that my speed mostly remained below 10 knots, which is the slowest I have foiled in a couple of years. By the time I turned around, those newly discovered muscles started to hurt, and I did not have the energy to pump back up onto the foil. This seemed very much like work to me, not like fun, and I decided that winging is definitely not something I want to do.

Once back on shore, I rigged my 5.6 m freestyle sail and moved the foil back a bit, and went out for some windfoiling. Now that was an awful lot of fun! The flat water made jibes super easy, so I pretty much foiled through almost all of my jibes. My typical speed now was around 13-14 knots - about 50% higher than it had been on the wing. But since I was well powered and the chop was almost non-existent, I figured I had to also give my freerace foil a try.

So I went back and switched to my Starboard GT-R plus foil with the 95+ fuselage. I picked the short (75 cm) mast since it was shallow near to shore, and I did not know the water depth in other areas. I also put the cheap phone with speed announcing software on, so that I could hear how fast I was going. Since foiling is so quiet, that works well using the phone speaker, whereas windsurfing usually requires head phones. Right away, I heard 17 and 18 knots - speeds that I often don't reach at all in sessions where I use my Slingshot foils. And I was trying to go slow!

This was an entirely different feeling - whereas the slow freeride foil is pure, relaxing zen, this one was adrenaline! But on the flat water, the foil was quite easy to keep under control. The first big surprise was how easy it was to get going. Even though I need about 12 knots speed to foil stably on the 800 front wing (that's only 40% of the surface area of the i84!), and even though I had used this foil only 3 or 4 times (compared to more than 200 times for the Slingshot foils), it was at least as easy to get going. The next surprise came when I tried jibing the foil, which I had not tried before on the GT-R+. The very first jibe was not just dry, but I kept enough speed to pop right back up onto the foil without pumping - nice! I had entered the jibe quite cautiously, and had set the board down onto the water mid-jibe before switching the feet, but the board seemed to be loosing a lot less speed than I was used to.  

I remained cautious in my jibes for the remainder of the session, and tried out different things that I "learned" to screw up jibes, but the foil seemed to insist that, being a race foil and such, it should keep speed. Looking at the minimum speed in the jibes, I ended up with my second-best ever foil jibe, keeping almost 10 knots speed of my 17 knot entry speed. Here's a boom cam video of this jibe:

Compared to some of my better jibes on the i84 foil, it's really not great - the board makes a lot of contact with the water for a relatively long time, and more than once, but all that barely slows things down. I had read about high aspect foils, and in particular race foils, keeping the speed better in jibes (and lulls), but seeing and feeling it happen was still pretty amazing. The short 75 cm mast worked well enough on the flat water, with only one memorable crash when I tried to push the speed a bit ... with enough success that I could not stop the upward tendency from the higher speed in time, and overfoiled.

Two days of windfoiling, great sessions on three different foils - I think I'll be perfectly fine without winging.

Silly Ideas

 Today was the day of silly ideas. It started before we even got to the beach, when Jay thought a 3-piece mast might work even better than a 2-piece mast. Silly! At least the water was warm enough for a 30 minute swim back to shore. 

I was barely foiling for 20 minutes when I came up with a silly idea of my own. After seeing Nina winging so nicely in so many sessions, I tried to partially imitate her. A key thing about winging is that the wing is not connected to the board. That can easily be copied with a windsurfing sail:

I forget a couple of little details though - the most important one being the to leashes that wingers use, one for the board and one for the wing. My board instantly realized my mistake, and took off to enjoy its newly found freedom. With a little help from chop and wind, it easily outpaced my tepid attempts of catching it again by swimming "fast". So I turned around and swam back to the rig, so I'd at least have some company. Fortunately, this being a nice summer weekend and all, a couple of motor boats quickly stopped by, after realizing I was not just swimming and waving at them to be friendly. The first one picked up my boat, the second one offered me a beer (just kidding!). Well, the second one asked if I was ok, and what they could do to help. They then drove to the other boat and told them to please, please deliver the board back to me, which they promptly did (big thanks to both boaters!). No major harm done, except perhaps for my ego.

On the way back to the launch, it was time for my foil to join the silly idea club. Apparently, the front wing was getting sick and tired of always being a foot or more under water, and decided to end the continuous drowning. Quite successfully so - after a surprise crash, I saw it happily swimming on top of the water. But I cut its dreams of escaping short by swimming after it, putting it on top of my board, and  stepping on it:

By then, the wind had picked up into the mid-20s, and my 5.0 m sail and Slingshot 84 wing had gotten a bit large, anyway. I actually planed a little bit on the way in - I guess the 90 cm mast is big enough to work as a fin. The foil setup looked a bit sad now:

That was my second Slingshot fuselage that broke. I blamed myself for the first one since I had drilled an extra hole to move the front wing further forward. But this time, the fuselage was not modified, and the screws were still nice and tight. I checked the GoPro video, and there was no obstacle in the water, either. Sure, the Slingshot fuses are relatively cheap, but replacing them on a somewhat regular basis because they break seems like a silly idea - and I've had it with silly ideas right now. I think I'll pay a little extra from more solidly engineered gear from other brands in the future.

Here are the GPS tracks from today's session: