Sunday, August 23, 2015

Maximum Speed

My apologies. If the title of this post attracted you, you've been lured here under what you may consider "false pretenses". Yes, this post deals with speed while windsurfing. But it's mostly a geeky article that looks at some of the physics underlying windsurfing. So you may want to stop reading now.

But let's put the blame where it belongs. It started when someone asked the question:
Can we really say that a longboard cannot exceed by much its hull speed, NO MATTER the size of the sail? 
That seemed to be an important question for him. He asked on both the iWindsurf forum in the US, and on the Seabreeze forum in Australia. How that developed was typical for the two forums.. but let's not go there.

Instead, let's ask the questions:
  • Does the concept of "hull speed" (very similar to maximum speed") apply to windsurf boards?
  • If "hull speed" has some relevance, what is the hull speed for a typical longboard? How about a shortboard?
  • What can we learn from this?
To get started, let's look at GPS speed tracks from a shortboard session. The wind in this session was marginal, and dropped from about 17 mph (where I was just able to plane) to about 14 mph, not enough for me to plane anymore. Here is what the speeds looked like:
When planing, my speed was about 15 to 20 knots. When the wind dropped a few miles below my planing threshold, the board speed dropped dramatically, to about 4 knots. Instead of going about as fast as the wind, I was now going a lot slower. Even with what felt like plenty of power in the sail, the board did not want to go faster than 4 or 5 knots. I tried to pump up onto a plane a couple of times, which cost a lot of energy, but the speed dropped again as soon as I stopped pumping.

So from this, there seems to be a "hull speed" that is very hard to exceed when not planing - at least on a shortboard. Before we discuss longboards, let's have a closer look at the "hull speed" concept. It comes from traditional sail boats, where boaters and builders observed that the top speed of displacement boats was limited. Past a certain point, more win or adding more sail would not result in any significant speed increases. What this maximum speed or "hull speed" was depends on the boat length - it higher for longer boats.

The reasons behind the hull speed limit are easy to understand. As a boat travels through the water, it creates a wave at its bow (front end), and a second wave at its stern. These waves are traveling forward at exactly the same speed as the boat. Here is an example of what the waves look like, seen from the side:
The laws of physics describe the relationship between the speed S of a wave and the distance between subsequent wave crests (the wave length WL): 
WL = (S/1.34)^2 
The formula above give the wave length in feet when using the speed in knots. When a boat doubles its speed, the wave length will increase four-fold.

When the boat speed increases so that the wave length of the bow wave equals the length of it's waterline, we get the following picture:

 The boat has dug itself into a hole! Quite a bit hole, too: the second crest of the bow wave is where the stern wave crests, so the waves add up and become extra tall. It the boat goes any faster, the wave length of its bow wave increases further, and the crest of the second bow wave falls behind the boat. As a result, the stern (back) of the boat will sink deeper into the water, and it will look as if the boat tries to climb up its bow wave - sailing uphill! Just like walking uphill, that takes a lot of energy, so it becomes nearly impossible.

Turning the wave formula from above around, we can calculate the speed at which this will happen:
S = 1.34 x SQRT(WL)
This is the "hull speed". For typical displacement boats, it is a good indication how fast a boat can go. For a 15-foot boat, it gives a hull speed of 5.2 knots; for a 60-foot boat, we get a hull speed of 10.4 knots.

If this formula would apply for windsurfers, it would be bad news: a typical 8 foot shortboard would have a hull speed of 3.8 knots, and even a 12 foot longboard would have a hull speed of just 4.6 knots. So adjustments are needed!

Let us look back at the waves a boat creates. Looking at similar boats with different weights (or "displacement"), we can see that the height of the wave the boat creates is proportional to the boat's weight. A lighter boat will have to "climb" a slope that is not as steep as a heavier boat, and therefore has an easier time exceeding the "hull speed" that was calculated with the simple formula above. Indeed, it is well known that lighter boats are able to go faster than heavier boats of a similar shape (note that we are still only talking about displacement boats - we'll get to planing designs in a little while!).

Fortunately for us windsurfers, a boat designer has developed a better formula that takes the weight of a boat into account when calculating hull speed.  A typical sail boat like the Catalina 22 weighs in at close to 2500 pounds, even before we add the crew; a windsurf board with sail and sailor will typically weigh in at less than 1/10th of that, while having about 1/2 of the waterline length. So if we use the "Better Way to Estimate Hull Speed", we get quite different results. Here's a graph comparing the calculated hull speeds for windsurf boards with a total (board+sail+sailor) weight of 200 lb:
For an 8-foot shortboard, the difference is not big, but the numbers match better what we seen in the GPS data. But for a 12-foot longboard, the numbers differ a lot: instead of a maximum speed of 4.6 knots, we now get a maximum speed of 8.4 knots!

This is where things get interesting. When I analyze my jibes, I take 8 knots as the minimum speed for a jibe that I cleanly planed through. The weight-adjusted hull speed formula predicts that I should be able to reach 8 knots, the planing threshold, easily on a longboard in displacement mode, but not on a shortboard! And that's exactly what it feels like. Here is a GPS track from a longboard session in marginal planing conditions:
Just like in the shortboard session above, the wind dropped shortly after I started sailing. But instead of a graph with two clearly separated speed ranges, you can see a wide range of speeds. There are runs with top speeds of 6, 8, 10, 12, 14, 16 and 18 knots - the entire spectrum is covered. The maximum speed in the second half of the session, when I was not planing anymore, was around 10 knots - reasonably close to the 8.4 knots predicted "hull speed", but still a bit faster. During the non-planing parts, I was going about twice as fast on the longboard as I was on the shortboard, in similar wind and with the same sail. The fun-factor was way more than 2 x higher!

Another way of looking at this is by plotting the board speed against the wind speed:
In this example, the longboard is faster until the wind reaches 18 mph; after that, the shortboard is slightly faster. The speeds diverge the most between 5 and 15 mph. In this range, the shortboard reaches a plateau, and speed barely increases, even though wind speed increased 3-fold. In contrast, the longboard keeps picking up speed over the entire range. The shortboard sailor feels a lot more pressure in the sail, but the board feels "stuck", unable to convert the pressure into speed. Frustrating! In the same range, the longboard sailor sees the increasing wind nicely converted into higher board speeds, and the longboard slowly starts to switch from displacement mode to semi-planing and finally planing. Fun instead of frustration!

I think the two curves above explain why windsurfing has been on a long downward slope in many parts of the world, including the US. Yes, planing is more fun than sailing in light wind, but we have been way to single-minded in our pursuit of planing. We have made our boards shorter and wider, so that they plane earlier and turn better once planing. Not a big problem at first, when most windsurfers had a longboard in addition to the "funboard". But 10 years later, the longboards were mostly forgotten. Windsurfer drove to the beach with their short funboards on weekends, only to discover that 5 to 15 mph wind is far more common than planing conditions - and that funboards are absolutely no fun if they don't get enough wind to plane.

Even if we have a new windsurfer who has mastered light wind sailing, and is now wants to plane, shortboards can make life more difficult. Instead of gradual acceleration (the blue curve above), she has to first learn to handle a lot of sail pressure without going much faster, and then be willing to go at least three times as fast as before. Not a problem for young daredevils - but I have seen more than one brave soul struggle quite mightily with this transition.

There is clearly a big bump to overcome when getting a shortboard to plane. Whether you think about it as "climbing up the bow wave" in the "hull speed" paradigm, or as having to climb the plateau and steep slope in the diagram above, I don't care; but climb it you must. We need some extra power to get over the bump, so a lot of intermediate sailors end up using a sail larger than what an efficient sailor would need. That is not per se a big problem; but more often than not, it creates problems later on. For example, one logical thing to do when sailing with a larger sail than necessary is to not sheet in fully. Again, not a big problem per se - until you want to learn a planing jibe. As you enter the jibe with a partially open sail, oversheeting to spill the power becomes impossible. Nor are you going at full speed, so you probably are sailing slower than the wind, even at your fastest point in the jibe. Therefore, the sail will alway keep some power in it, and you'll have to lean back to counter the power, instead of adapting a balanced surfing stance. When you then flip the sail, the tail sinks ... and so do your chances of planing out of your jibe.

Finally, back to the question: What can we learn from this? Several things, methinks.
  • If you are living at a "normal" windsurf spot (that is, not the Gorge or the Rio Vista / SF area), consider getting a longboard. The Kona One is a great board with a soft top, wonderful for learning, light wind freestyle, or racing; but old longboards from the 80s and 90s can be just as much fun. Get one, and "no wind" days will become a thing of the past. Sailing a longboard in 10-15 mph wind is a lot more fun than desperately seeking to plane.
  • If you are struggling with planing comfortably and in control, despite having had good instruction, also consider a longboard - it might make your life easier. But I'd suggest to try before you buy :-).
  • If you are on a shortboard, especially in marginal conditions, learn ways to get over "the speed bump". Got chop? Use it! Going downhill is always faster.  Learn to pump! Yes, it's hard when you start, but you may well save energy in the long run. Learn a few ways to pump; learn to really get a feeling for what it takes to get planing, both with effort and with minimal effort; and you may just see that you'll need a knot less wind to get going on the same gear. This can go on for a few years!


  1. Have to agree with the get a Kona comment. I've been having fun with mine this summer.

  2. Would you share what boards you used for the longboard and shortboard charts? Also, your weight would be helpful to compare this information with my own experience. BTS: great post.

    1. Giuan, the GPS graphs are from a Fanatic Skate 110 (237 cm) and a Mistral Pandera (353 cm, 185 l). I weigh about 190 lb.

      The speed graph summarized what I think happens, based on many sessions on these and other boards. It is intended to illustrate a point, and not directly linked to hard data. But if you could deal with issues like getting the actual wind where you sail, chop, changes in angle to the wind while sailing, and so on, I think you'd end up with very similar curves.

  3. Nice job with this analysis, Peter. I really like the graph of longboard speed and shortboard speed vs. wind speed.

  4. Well done, Peter. Hope to see you this fall.