Fizix of sailing

[klb67pgh]

My wife is a high school physics, earth science, and other assorted science classes teacher. Her senior physics class students know we have an Ericson 25 and have asked about sailing. My wife decided to give them a day on the water towards the end of the school year. They did some class work on what makes a sailboat go, true and apparent wind, a few vector problems, etc., and today was our day on the water. Our sailing club owns several Flying Scots (and Sunfish, and Hobies). I'm a U.S. Sailing instructor and agreed to do the crash course chalk talk on sailboat and sail parts, points of sail, right of way rules, tacking, how to get out of irons, etc. We launched 3 FS boats and walked through rigging the boats at the dock. I lined up 3 of our good FS sailors and instructors to take 2 or 3 kids out in each boat and off they went. Most students got some tiller time. Unfortunately our great wind and 0% chance of rain forecast turned into a cold steady rain by late morning and we were chased of the lake for an early lunch inside the race garage with several kids finding blankets and towels to try to dry off and try to warm up. A few hearty souls wanted to go back out after lunch and I managed to get a few pics - the captain definitely hauled in the mainsheet for the last photo. The kids had a great day despite the weather, we had a good lunch discussion about their on the water experience, the next phase of school/life, and great advice from an engineer/sailing instructor on a career in science related fields (his team builds moon landers), and we did some knot tying too. Despite what you might perceive from traditional news sources, I don't think we are quite doomed yet with this generation. Sure they need to know where their phones are at all times, but they still ask insightful questions and some of them have a pretty good can-do attitude.

 

[N.A.]

Nice!

In case they are useful, two nice physics problems one can do:

- What force must one hold a line with after a couple of wraps on a winch, assuming the line is initially under some given tension? (It's exponential benefit dependent on the coefficient of friction and number of turns, if I remember)

- Why does the force on the sails/an object scale like the square of the wind velocity (and not, say linearly or something).

Both within easy reach of high school physics.

 

[Teranodon]

I wish I had been there, maybe I could have learned something. I have been sailing for more than half a century. I have a PhD in elementary particle physics from an Ivy League university. Every few years, I try to understand how a sailboat goes to windward (something I was doing this morning in the San Juan Channel) and I always fail. I've had it with Bernoulli, all those phony airfoil diagrams, the contrived vectors that give the "right" answer. It's a mystery.

 

[Christian Williams]

I am left with "the keel pushes on the water and it pushes back." An airplane "pushes the air down and the air pushes back up." I was trained as an English major. We tend toward Aristotle: an acorn wants to be an oak. A sailboat wants to go to windward.

In general aviation the flight instructor goes through the usual explanations of Bernoulli, wing shapes, then the even-a-barn-door-will fly example, and then, the smart ones add, "nobody really agrees but that's what to say on the test."

In a recent thread on where to put the reflector when using an optic tachometer, I had to stop and think about whether the radius position on the flywheel mattered.

Seemed like it ought to, until I thought about it. It doesn't. The rpm is the same at the axle as at the rim of a wheel. What's different is the rotation speed of the location point. I had to go to Google to reveal the useful difference: torque.

It took all that to recognize why the alternator pulley can't measure engine RPM with an optical tach, and why larger sheaves in a block make more purchase at the cost of speed.

There is some value to every puzzle, although I may be more often puzzled than most.

 

[Kenneth K]

What's different is the rotation speed of the location point.

A bit of semantics mainly, but the "rotation speed" (usually measured in RPMs) is still the same. It's the "linear" speed that increases with circumference (diameter), but people don't like the term "linear" when dealing with a wheel. It's easier to think in terms of "linear" when you consider how far a belt must move (linearly) across the pully when the pulley rotates one full circumference.

So, a technical geek would say, "What's different is the linear speed of the rotating point,"--the first measured in ft/sec, the latter measured in RPM.

I had to go to Google to reveal the useful difference: torque.

Again, semantics, but torque is a measure of force, not speed. Together, a given torque (F), applied at a given speed (V), equates to a resultant Power (P). A diesel engine could drive a small pully very quickly to create 25 hp or a larger pulley at a lower RPM to produce the same power. It's the basic prop-sizing problem.

 

[Christian Williams]

Very good. Thanks.

 

[Kenneth K]

Yep.

But it still does nothing to help explain sailing to windward. I was going to add the "pinching a watermelon seed with two fingers analogy," but that only helps some visualize sailing on a beam reach, which most people seem to get regardless. Still scratching my head over the "to windward" analogy.

 

[Christian Williams]

Aristotle saw a sort of destiny for everything (Telos), which everything tended toward or longed for. Perhaps an equivalent in reverse of entropy, which in pop understanding means everything tends to fall apart.

Is it a good sailboat's destiny to claw to windward in defiance of Stefan's desire to calculate the forces?

Just a joke analogy nowadays, when we are skeptical of forces we don't understand.

 

[Marlin Prowell]

Mentioning this topic and also Mike Jacker’s book in different threads today reminded me of another Mike Jacker adventure as a teen with a homebuilt hydrofoil sailboat. Another great read.

 

[HerbertFriedman]

Unfortunately, the simple theory based on Bernouli's theorem is wrong for sailing. The idea that the airflow over the top of a sail is faster than at the bottom, and by Bernouli's theorem, the pressure on the top side is less than the pressure on the bottom size, thereby giving lift and forward motion to the sail, may explain lift for aircraft where the speeds are high, but not for sails where the speed is low. Looking at the cross section of a sail which is just the thickness of the material, there is no difference between the path going along the upside (convex) versus the down side (concave) so there is no difference in speed. Bernouli's theorem does not apply.

If fact the idea that even if the sail had thickness, like an aircraft wing, the argument is usually made that the air at the leading edge must meet at the trailing edge, hence the difference is speed top and bottom, is not true either. The lift in a sail has been modeled some time ago by a mathematician at Boeing, please see the attached file, one of many. The issue is that the aerodynamics of sail (low speed flow) is dominated by friction and that is a nonlinear process, best handled by Computational Fluid Dynamics.

 

[Teranodon]

...Looking at the cross section of a sail which is just the thickness of the material, there is no difference between the path going along the upside (convex) versus the down side (concave) so there is no difference in speed. Bernouli's theorem does not apply. ....

That's one point. Another: the force vector is always shown as being (roughly) orthogonal to the curve of the "airfoil". So, to go into the wind, the sail should be eased so as to bring the vector forward! I tried that on my boat - it didn't work. Yes, yes, I know that the magnitude matters as well, but there is no intuitive way to know what it is. In popular "explanations", the magnitude is adjusted (as a function of orientation in the airstream) just enough to produce a desired "lift" component. Sheer handwaving.

 

[HerbertFriedman]

I think the effect you are describing is usually termed "angle of attack" and that is also a very complicated issue, again best explained by CFD.

 

[Teranodon]

I think the effect you are describing is usually termed "angle of attack" and that is also a very complicated issue, again best explained by CFD.

I think you're probably right. I just wish that there was a good intuitive explanation. Alas, air and water are fluids, that is, they need to be understood in terms of the mysterious quantum inter-molecular forces that produce collective behavior. It would be nice if they could be viewed as just ensembles of independent molecules, randomly banging around in a stream. But that view will not get you to windward, I'm afraid. Or maybe it could - I'm not sure.

Simple-minded, but incorrect, explanations abound in our nautical world. Thus, for example, high and low tides are described as bulges of water that are attracted by the Sun and Moon. That gets you one high tide each day. But how to get two? Understanding that takes you much deeper into some tricky physics.

 

[Kenneth K]

I just wish that there was a good intuitive explanation.

I've always thought the intuitive explanation lies somewhere in here:

1. First, the original question itself is part of the problem. Sailboats cannot sail into the wind.

2. On average, they can't get any closer than 30 degrees to the wind, and this is the key. In a 20K wind lying 30 degrees off the bow, you have a 17K direct-headwind component and a 10K direct-crosswind component.

3. But the headwind profile (resistance, form, windage, etc) of a sailboat is much, much smaller than the crosswind profile, so the crosswind effects dominate. The headwind can largely be ignored in the "intuitive explanation" (though it is holding the boat's speed back somewhat, and it's definitely contributing the most to our sensation of speed and thrill).

4. From here, it's not as hard to see how a boat propels itself forward, roughly perpendicular to the 10K wind from its beam, as most of us understand how sailing on a beam reach works. This also explains why the sail has to be trimmed in further, rather than eased, to make the best use of the crosswind component.

That's a more intuitive than technical explanation, but it has too work for me. CFD is beyond me. Is a technical explanation really necessary for most sailors? Columbus sailed to the Far East (well, almost) knowing far less about aerodynamics.

 

[HerbertFriedman]

The equations governing fluid dynamics have been known for more than 100 years at this point and they accurately describe all observed fluid dynamics behavior. With all the effects included, as they must be under low speed conditions, these equations are non linear and therefore not subject to much in the way of analytical results, which are the basis for simple "intuitive" explanations. For the case of aircraft wing profiles, viscosity in negligible and the equations simplify and intuitive explanations are indeed possible. But it is unfortunately wrong to extend these explanations to low speed sailboat conditions.

Before the advent of fast computers, these nonlinear equations made the reputation of numerous fluid dynamics folk, who defined certain "numbers" such that when these numbers were either very small or very large, simplified these equations such that some analytic and therefore intuitive results could be obtained. Examples are the Bernoulli, Reynolds, Prandtl, Mach, etc. There are some intuitive explanations, although not too simple, that can be obtained from numerical solutions of these equations, that is the beauty of CFD, please refer to the extensive papers by Gentry included.

OOPs I just noticed that the second paper is too large for this platform but the reference is "December 1999 The Application of Computational Fluid Dynamics to Sails Arvel Gentry The Boeing Company Seattle, Washington Proceedings of the Symposium on Hydrodynamic Performance Enhancement for Marine Applications, Newport, Rhode Island, October 31 - November 1, 1988" if any of you have access to a technical library. This paper models several America Cup rigs, mast cross sections, etc. and has lots of "intuitive" explanations altough, I do not find them simple. I probably can send this under the regular e-mail platform, is anyone wants the long and gory details.

 

[Nick J]

Unfortunately, the simple theory based on Bernouli's theorem is wrong for sailing.

Thanks for posting the papers. It took me a while to actually open them up and read because most arguments against the the standard theory of sails and lift point to the Newtonian theory or some version that basically says Bernouli is wrong and the sail just redirects the air flow to go directly behind the boat which propels it forward when opposed with the force form the keel (watermelon effect). The problem with this theory is it doesn't account for any force pushing the boat forward. Even the watermelon example relies on some small component of force pushing the seed forward. The comment on how Bernoulli's theory is wrong doesn't sit well with me. After all, Bernoulli said nothing about foils, airplanes, or sales, so how can it be wrong for sailing. all it says is an increase in the speed of a fluid occurs simultaneously with a decrease in static pressure or the fluid's potential energy. That can't be wrong. It bugged me so much, I googled Arvel Gentry in hope of finding counter arguments calling him a quack, but turns out he's an extremely intelligent person with more than enough experience to be writing on the topic (unlike me).... crap, this means I need to actually read.

The answer, as I read it, is Bernoulli's principle is alive and well and actually one of the fundamental components that contributes to lift. The difference between the old theory and what Gentry writes about is how the difference in velocity is accounted for. I still don't fully understand circulation around a foil, but this is an idea I can get behind. It accounts for a forward force component and finally explains why the "speed" bubble I get in my main can exist while I'm going up wind at hull speed.

For anyone who was in the same boat as I was, READ THE PAPER! This isn't the same old "my hand lifts when I stick it out the window of my car" counter to Bernouli. Really cool stuff, Thanks @HerbertFriedman!