# Calculating the forward force of a sailboat

## Main Question or Discussion Point

Sails can propel a boat in two ways.
The first occurs simply when sailing with the wind (downwind) where the sail is set perpendicular to the wind to proved the greatest surface area. The air decelerates as it hits the sail omitting a force onto the sail. As a result, according to Newton's 3rd, there is an equal and opposite force that propels the boat forward.
The second, occurs when sailing upwind or perpendicular to the wind. Here the sail acts as an aerosol and redirects the wind. The wind arrives at an angle to the sail at the front of the boat and gets redirected to its rear (See image)

My question: How can I calculate/predict the end resultant force that propels the boat forward? - I have designed an experiment where I measure the resultant force of the sailboat at different points of sail, and hence, I would like to identify the accuracy and reliability of my measurements and could possibly find the efficiency.

For a downwind sail this is easier as I know the volume and mass of the wind acting on the sail per second...
How would I approach this problem when sailing upwind or perpendicular?

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BvU
Homework Helper
Hello duck, welcome to PF !

There seems to be something missing in your diagram: this way the boat would move downwind and to the right (following ##\vec F_w). There must be something that manages to convert this to a forward force. Any ideas ?

Vector F_w, is the force the wind applies onto the sail. This direction is downwards and to the right yes. However, Newton's 3rd Law calls for an opposite force that counter acts the force of the wind (F_w) which acts on the boat and moves the boat a little bit forward and a lot to the left. Hence sailboats have a keel which creates a very large amount of drag when the boat moves sideways yet little when the boat moves forwards ( and creates a bit of lift as well). The force of the sailboat = mass of the air (m_a) * acceleration of the air (a_a).

Hope this clears any queries :)

BvU
Homework Helper
I have no queries, was just fishing for the realization that it's the keel that allows sailing upwind. To me that means it will be a pretty complicated calculation.
Curious after the design of your experiment. Did you (like I did) google physics of sailing ?
Some pretty exhaustive litterature pops up !

Not quite the same website, but same ideas! - Although I'm not entirely sure if Bernoulli is the more important factor whilst sailing upwind - In sailing we are dealing with relatively small speeds ( 5-20 knots most of the time). In Bernoulli's Equation, the decisive component is velocity as it is the only component which is squared, hence I think its only secondary effects which I will not include in my calculations. Yes as you said its all relatively complicated and thats why I decided to ask for some help!
Being a first timer at Physics Forums, is my question in the right forum and under the right Prefix (B) - Or is this physics a bit more complicated?

For my calculations, I don't really mind if its not 100% accurate - I just need to do some calculations which can back up my experiment's results - It was done in a lab on a ramp ( no keel, just slits to keep the boat in place)...

Just read parts of the document you passed regarding the physics of sailing... The conclusion summons it all up ;
"Ultimately, as has been mentioned, the determination of the lift and drag coefficients for actual yacht components must be left to experiment or numerical computation."

BvU
Homework Helper
You posted an interesting question in the right forum (I think). It's just that the answers aren't all that easy, and the bulk of your readers are mere physicists and other technical folks. I hoped you could find some quantitative stuff in the article, or else perhaps some real expert on this subjecet helps you further.

Note that the speed in the bernoulli thing is the wind speed, not the boat speed. And If I guess the forces on the sail tissue, they do quite a bit. But with a little hole in the sail (or pressure measurements) you might be able to quantify that...

Ok thanks.

If I were to simply calculate the ideal force of the sailboat sailing directly downwind with an open sail, where the wind interacts with the sail at an angle of 180 degrees, would one be able to calculate the force of the sailboat if there was no drag? I've tried this and the furthest I have got is found a value for the total amount of energy the wind carries that interacts with the surface area of my sail per second (0.18J). How could I translate this into the ideal force assuming the boat and sail had a 100% efficiency converting kinetic energy from the wind into force?

SteamKing
Staff Emeritus
Homework Helper
Sails can propel a boat in two ways.
The first occurs simply when sailing with the wind (downwind) where the sail is set perpendicular to the wind to proved the greatest surface area. The air decelerates as it hits the sail omitting a force onto the sail. As a result, according to Newton's 3rd, there is an equal and opposite force that propels the boat forward.
The second, occurs when sailing upwind or perpendicular to the wind. Here the sail acts as an aerosol and redirects the wind. The wind arrives at an angle to the sail at the front of the boat and gets redirected to its rear
Just a couple of nitpicks here:

"The air decelerates as it hits the sail omitting a force onto the sail." "Omit" means "to leave out".

"Here the sail acts as an aerosol and redirects the wind." An "aerosol" is a substance suspended in the air, like the mist from a spray can. I think you mean "aerofoil".

There's several books on the physics and aerodynamics of sails and sailing. The late C.A. Marchaj wrote several books on this one topic.

I might suggest that you also visit the forums at www.boatdesign.net. There are several forums on that site which deal with sailing, and the members over there can also provide more practical experience.

anorlunda
Mentor
Ok thanks.

If I were to simply calculate the ideal force of the sailboat sailing directly downwind with an open sail, where the wind interacts with the sail at an angle of 180 degrees, would one be able to calculate the force of the sailboat if there was no drag? I've tried this and the furthest I have got is found a value for the total amount of energy the wind carries that interacts with the surface area of my sail per second (0.18J). How could I translate this into the ideal force assuming the boat and sail had a 100% efficiency converting kinetic energy from the wind into force?
When you sail downwind, the wind blows on the sail with velocity wind speed minus boat speed. When boat speed matches wind speed, the net wind is zero. But if you assume zero drag of the hull, then downwind boat speed will exactly match wind speed no matter how big or small the sail. That is why assuming zero drag is not useful.

The important concept is aerodynamic lift as distinct from drag. A sail is a kind of wing. As others already said, look up the physics of sailing.

The key design feature of a sailboat is the keel. The ideal keel should have zero drag moving straight ahead, but infinite drag for sideways movement. Without a keel, you have only a raft.

The fun part is that there is no defined upper limit to boat speed when sailing upwind (other than the speed of light). Only drag limits speed. The record for a low drag ice boat I think is about 125 mph in a wind speed of 30-40 mph.

BvU
A.T.
The record for a low drag ice boat I think is about 125 mph in a wind speed of 30-40 mph.
I guess you mean this land yacht:

Ice boats get also very fast, but there is no well documented record higher than this.

BvU
Homework Helper
The word sandblasting gets a new meaning !

A.T.
Just read parts of the document you passed regarding the physics of sailing... The conclusion summons it all up ;
"Ultimately, as has been mentioned, the determination of the lift and drag coefficients for actual yacht components must be left to experiment or numerical computation."
Yes, these are not simple shapes (the sail isn't even rigid). So it's not trivial to predict their aero- and hydrodynamics. But once you know their lift/drag ratios, you can compute how fast a boat can go.

A.T.
The word sandblasting gets a new meaning !
The alternative is getting really wet:

BvU
Homework Helper
Yes, or freeze your behind off in an ice boat. Or worse (but they are all wearing helmets, I wonder why...)
But we are digressing from the OP . Your post #13 must be encouraging for EpicDuck, though...

The fun part is that there is no defined upper limit to boat speed when sailing upwind (other than the speed of light). Only drag limits speed. The record for a low drag ice boat I think is about 125 mph in a wind speed of 30-40 mph.
This isn't correct. The fastest point of sail is (roughly) when the wind is perpendicular to the boat (beam reach). When calculating the force that the wind exerts on the sail it's important to calculate the wind velocity relative to the boats velocity (apparent wind).

When sailing up wind your angle relative to the wind decreases as you speed up. This will decreases the "lift" on the sail, and it eventually forces you into irons. Sail boats cannot sail directly into the wind. When you sail to close to into the wind you'll lose lift and you stall. This is called in irons.

Similarly when sailing down wind, you're relying most on the wind to push your sails. Thus you're limited by the wind speed.

However, when sailing directly perpendicular to the wind, the wind speed perpendicular to your boat won't change as you speed up. However, there is an apparent wind due to your forward motion. If you go fast enough this will eventually force you into irons. So even here there is a limit to your maximum speed. However, if your drag is low enough you can easily sail faster than the wind.

In my experiment, I have a sailboat tied to a forcemeter. This means it doesn't move as I apply a wind strength, but I can measure the force output and record this. Because my boat isn't moving, the wind that I apply to it acts as the apparent wind because this is the wind strength and direction the boat always experiences. The purpose of my calculations, is simply to find the force of the wind acting on the sail with a certain wind speed. I know the actual force that my boat produces due to my readings, and hence I could compare these results and find the efficiency.

For example, if I had a triangular shaped sale, 10 x 20 cm (area = 0.01 m^2) with a constant flow of air at 3 ms^-1, the total volume of air that interacts with the sail would be 0.03m^3. Multiply this by the density of air (1.3 kgm^-3) and we know around 0.04 kg of air interacts with the sail every second. Now using e=.5mv^2 we can calculate that the kinetic energy that interacts with the sail in one second is 0.18J.

This is as far as I get. The problem is, I measure the forward force of the sailboat, and do not know how to compare this as I do not know the speed of my sailboat.

Any help???

rcgldr
Homework Helper
If you look at that diagram in the first post in this thread, you can see that from the boat's perspective, the force the wind exerts on the sail is to the side and a bit forwards, and from the water's perspective, the force that the sail exerts onto the true wind contains an upwind component that slows down the true wind affected by the boat, requirements for any sail craft to operate. Not shown are the forces from the water, if the boat is not accelerating, then the net force from the water is equal in magnitude and opposite in direction with the net force from the wind.

Note that efficient sail craft can out run the wind. From the sail craft's perspective, that the apparent wind can be split up into to components, an apparent headwind and an apparent crosswind. The apparent crosswind equals true wind speed times sin(beta), where beta is the angle between the true wind and the sail craft's heading, which is independent of the sail craft's speed. Another way to consider this situation is to realize that although the sail craft out runs the wind, it continuously sails into a fresh wind ahead of the sail craft (sort like a continuous series of collisions between the wind and the sail). Or think of the situation as the sail craft being squeezed from the wind on one side and the water on the other side, diverting some of the wind aft of the sail crafts heading. Wiki article:

http://en.wikipedia.org/wiki/Sailing_faster_than_the_wind

In the article linked to that mentions Bernoulli's principle, instead of cause and effect relationship, the relationship between pressure and speed is coexistent. On the downwind side of the sail, and if the flow is attached (not a stalled condition) the air tends to follow the convex surface since otherwise a void (zero pressure) would be created. (In a stalled condition, vortices form to fill in what would otherwise be a void). This curved flow coexists with a pressure gradient and acceleration perpendicular to the flow (Bernoulli doesn't directly deal with curved flows), coexisting with reduced pressure along the convex surface (which in turn coexists with acceleration of air in the direction of flow).

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anorlunda
Mentor
This isn't correct. The fastest point of sail is (roughly) when the wind is perpendicular to the boat (beam reach). When calculating the force that the wind exerts on the sail it's important to calculate the wind velocity relative to the boats velocity (apparent wind).
Sorry, I disagree. For sailboats, the fastest direction is with apparent wind about 40 degrees off the bow. Iceboats can go very much closer to the wind. That's how they achieve fantastic speed. By the way, I'm familiar with being in irons. I've lived and cruised full time on my sailboat for 60,000 NM and 10 years.

More important, the exact thing I said is "there is no defined upper limit to boat speed". If you think there is a defined upper limit, tell me exactly what the definition is; 2x wind speed? 10 knots? hull speed? What do you think is the defined upper limit?

rcgldr
Homework Helper
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A.T.
Similarly when sailing down wind, you're relying most on the wind to push your sails. Thus you're limited by the wind speed.
This is true for exactly downwind. Once you go downwind and somewhat across (broad reach), you can go faster than the wind, and outrun a free floating balloon.

anorlunda
Mentor
Wikipedia iceboats says the following. I guess it is true that the record is unconfirmed.

Modern iceboats designs are generally supported by three skate blades called "runners" supporting a triangular or cross-shaped frame with the steering runner in front. Runners are made of iron or steel and sharpened to a fine edge, most often cut to an angled edge of 90 degrees, which holds onto the ice, preventing slippage sideways from the lateral force of the wind developed by the sails. Once the lateral force has been effectively countered by the runner edge, the remaining force of "sail-lift" vacuums the boat forward with significant power. That power increases as the speed of the boat increases, allowing the boat to go much faster than the wind. The only seeming limitations to iceboat speed are windage, friction, the camber of the sail shape, strength of construction, quality of the ice surface and the level of skill, athleticism and fearlessness of the sailor.[1] Iceboats can sail as close as 7 degrees off the apparent wind.[2]

Modern designs of iceboats are very efficient, utilizing aerodynamic designs and low friction, and can achieve speeds as high as ten times the wind speed in good conditions. International DN iceboats often achieve speeds of 48 knots (89 km/h; 55 mph) while racing, and speeds as high as 59 knots (109 km/h; 68 mph) have been recorded.[3] Skeeters and older large stern-steerer iceboats can exceed 90 knots (170 km/h; 100 mph). The rumored, but unconfirmed, top speed of an iceboat is over 130 knots (240 km/h; 150 mph). One reference to a timed run on Lake Geneva, Wisconsin reported an "E-Skeeter" as having reached 137 knots (254 km/h; 158 mph). The same reference reported clocking a DN 60 iceboat on a closed course over black ice on Green Bay, Wisconsin at 94 knots (174 km/h; 108 mph). The stern-steerer Debutaunte, recently rebuilt, was timed over a measured mile at 124 knots (230 km/h; 143 mph) on the ice of Lake Winnebago, Wisconsin in 1938.
But what I really had in mind were curves such as the one below that are hull specific. It looks like what rcgldr said was correct for most hulls and weather.

But I stand by what I first said. There is no defined speed limit sailing upwind.. Only drag limits.