# Hydrodynamic forces on a foil, Reynolds number, viscosity

• Ittiandro
In summary: I am not sure how to reconcile them.In summary, according to windsurfing experts, the mechanical stress on the hydrofoil wing moving through a relatively dense ( viscous) medium like water can break the housing of the wing, particularly the one of my board, which is not designed for speed and high performance and isn’t therefore strong enough to withstand the mechanical stress.
Ittiandro
Hi!
I know little about physics, but I am very well educated , with an inquisitive mind.

First the context, then my specific question

A. Context

The practice of windsurfing has brought me to try and understand the principles of hydrodynamics, in order to make my sailing more efficient.

As explained below , in this post I am enquiring on the fluid viscosity issue, more particularly about the Reynolds number .

I am currently working on a prototype of a DIY hydrofoil wing to attach to my windsurfing board, as per photo.

Currently, these hydrofoil wings are commercially available, but very expensive, because made in carbon. This is why I was thinking to make one myself either in plastic, fiberglas or other suitable material using a 3D printer., or even in fiberglas-reinforced wood , to be shaped by hand.

Windsurfing experts, who are not necessarily trained in physics, say that the mechanical stress on the hydrofoil wing moving through a relatively dense ( viscous) medium like water, is such that it can break the housing of the wing, particularly the one of my board, which is not designed for speed and high performance and isn’t therefore strong enough to withstand the mechanical stress.

B. Question
The reason why I am bringing up this issue in your Forum is that I can’t understand why a windsurfing board moving in water at only 18-20 knts/hr , can create such a mechanical stress on the hydrofoil wing as to rip it off the fin housing..at the bottom of the hull.

As an experiment, I tried to push, pull and twist ( with moderate force) on the fin ( and the housing) , but the fin box withstood the action pretty well. I would have probably succeeded in breaking or damaging it by applying full strength or leaning on the fin with half (or even all) of my body weight , which means at least at least 40 kg, but I can’t see how a 40 kg force can be exerted on the hydrofoil wing , simply on account of the water resistance: the hydrodynamic flow of water encountering the leading edge of the moving wing is not orthogonal to the its surface,( in which case I would perhaps understand ) but practically parallel, as it follows the curved chord of the wing cross section. More specifically, my question is :

Can this alleged stress ( or force) be measured, in kg/cm2 of surface, once we know the angle of attack of the wing., its surface , thickness, the density /viscosity of water at a given temperature.?
Can it be calculated from the Reynolds number?

I discovered that there is a number called Reynolds number, expressing, as I understand, the viscosity coefficient of water or air in function of the velocity of the wing foil, the density of the medium,(air or water) the length of the wing chord and the temperature .

I googled up this number at http://airfoiltools.com/calculator/...0.2&MReNumForm[kvisc]=9.7937E-7&yt0=Calculate
This site has a calculator. To obtain the Reynold number , it is sufficient to enter the data in the calculator and click on the button.

For a hydrofoil having a wing chord of 0.20 m( or about 8”), moving in 20° C water at 20 knts/hr, the Reynolds number is 2,042,129.

Since the viscosity of a medium resists the movement of a body through it ( and can therefore be viewed as a force exerted on it) , I wonder if there is a formula allowing to extract this force ( kg/cm2) from the Reynolds number .

For some reasons, to obtain the Reynolds number, one is not required to provide the length( wingspan) of the wing, neither does the thickness enter into its calculation.

If necessary, let’s assume the length to be 28”, i. e.t the wing has the shape of a rectangle of 8” x28”, from which the surface can be derived. This would be the approximate dimension of my hydrofoil wing.

As to the thickness, if required, we can assume that it varies between 0.50 “ at the leading edge( center wing) to about 1/8” at the trailing edge and at the tips, since the wing tapers down both crosswise and lengthwise.

The angle of attack of the wing, i.e. its pitch is 0 ( zero) because the hydrodynamic flow of water encountering the leading edge of the wing is not orthogonal to the wing surface, but practically parallel to it as it follows the curved chord of the wing cross section. Possibly the drag may have to be taken into consideration, too, but for me all this would be too complicated.

Perhaps a physicist can do it relatively easily, unless there are some missing data.

At worst, the board may not lift above the water, but I am willing to try my project if I have sufficient reasons to believe that , on the basis of the estimated load in kg/cm2 extracted from the Reynolds number, these forces are not great enough to break anything..

Or am I am perhaps asking the wrong question or a question that cannot be answered? I hope not..Thanks for your help

Ittiandro

Ittiandro said:
why a windsurfing board moving in water at only 18-20 knts/hr , can create such a mechanical stress on the hydrofoil wing as to rip it off the fin housing..at the bottom of the hull
"only"?! That's pretty fast by sailing standards.
What sort of failure would you expect with a wing? I haven't seen sailboards with a wing keel - only fixed mast dinghies (going past too fast for me to see too much of what they're doing!) There could be a lot more stress on their keels than with an articulated mast. I guess that you supply all the 'righting' force by body balance but there could be high stress when changing the depth of the wing in the water. In any case, the steady state stresses would be a lot less than transient effects as the wind changes or when you steer.
PS I can't see a photo on your post. Could you try again? Use the UPLOAD button and follow the instructions or can you use a link to a web page somewhere?
PPS The knot (kt) is the unit of speed. 1kt = 1nautical mile per hour.
PPPS I forgot to say that I doubt the viscous forces are relevant, compared with the bernoulli generated forces.
(end of PPPPPS's - sorry)

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Thanks Sophiecentaur
Sorry! 20 kts is the wind speed , not the speed of the board in the water!
Actually, good windsurfers are able to plane at even higher wind speeds.
It is quite common, though, that people sail in sub-planing mode ( by choice or by necessity) in winds as low as 12-15 knts with large enough sails up to 9 m2.

There must be a relationship between wind speed and the velocity of the board, but it may be difficult to calculate, because it depends on a few variables, like the angle of attack of the sail in relation to the wind ,its size, the weight of the sailor, the shape of the hull and the lateral resistance.

In the end, the forward motion of the sailboard, as you may know, results from the combination of two vectorial forces at an angle with one another and having different directions: one is the forward lift engendered by the sail as a foil and the other is the lateral resistance, engendered by the rear fin and the daggerboard in the middle.The direction of the board will be somewhere between these two vectorial directions.

So:

1.For the present purpose, the velocity of the board for a given wind-speed less than 20 knts, can be more realistically set at around 10 kt.
2. What failure do I expect on the wing?
According to many windsurfers the wing itself may not fail, if resistant enough, but the fin box in the hull, housing the fin (or the vertical shaft on which the wing is attached ) may break, because the fin box, in my board , which is not a high performance board, is not secured by screws across the hull and is not strong enough to withstand the alleged stress of the hydrodynamic forces. It can come off.

2.For the type of hydrofoil I am considering, please refer to the enclosed photos : my prototype would be the one in the very first photograph, with the wing mounted directly on the fin ( in some of the photos you can see the housing of the fin, or fin box at the heart of the controversy. )

Normally, however, the most popular ( and expensive) commercially available hydrofoil is the the dual foil type shown in the other photos , having a front wing and a rear stabilizer wing. With this type of foil, the board rises about 1 m. above the water and the speed is stunning, probably close the windspeed, because there is no friction of the board with the water and very little lateral resistance.

3.Depth of the wing in the water :
the commercially available dual wing carbon foil is mounted at the end of a shaft( mast) dropping to about 1 m below the water surface and when fully powered, it rises with the board to about 1 m. above the water.
You seem to think that the stress is proportional to the depth of the wing in the water. It may well be. In my case, I cannot go any deeper than 36 cm ( 15 inches) because this is the length of my fin. This may help in reducing the stress on the fin box. I can mount it even further up closer to the fin box, to decrease the stress on it, but then maybe I risk that there will be little or no lift .,,

4, Viscous forces vs Bernoulli forces
We seem to agree that viscous forces are not relevant here. This is what I thought., at least intuitively,

As to the Bernoulli forces, I looked them up, because,as I said, I am not familiar with physics.. .
As I understand, they may have something to do with the lift ( or upward thrust) of a wing going through air or water.
In other words the air or water streams along the the upper and lower faces of the wing at a different speed s( lower on the down face and higher on the upper face , because of the respective different lengths) . This creates a pressure differential, resulting in vertical lift.
If the Bernoulli forces have something to do with this, I still can' t see how can they break the fin box, if I was unable to do it by hand!

I hope this helps you in ..helping me

THanks

Ittiandro

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• Wing Forum.docx
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Ittiandro said:
2.For the type of hydrofoil I am considering, please refer to the enclosed photos
I looked at the Word document. It is far better to use PDF or even just insert JPEG images. Starting up Microsoft Word is a pain and, believe it or not, not everyone actually has Microsoft Office installed in their devices.
I really don't know enough about this subject apart from having a great respect for just what forces boats are subjected to. What I could say is that your foil would have to be strong enough for you to suspend it between two chairs at its ends and then be able to jump on one edge of the board with your full body weight. Stressing it with your hands would not be a tough enough test to represent the possible forces when moving from wave to wave when you're surfing in a force five. The one thing in your favour is that the wing is not very wide. Nonetheless . . . . .

The "right" way to design a hydrofoil is to first take a course in fluid dynamics, followed by a course in aerodynamics, along with courses in strength of materials, followed by researching airfoils and materials of construction, followed by learning construction techniques. On the other hand, you could just go ahead and build something that seems like it ought to work, then try it. At best, it will work. At worst, it will be a good learning experience. Correction, make that an excellent learning experience.

How do I know this? Back in high school, I had the idea of making a small boat with a jet pump drive where I would sit on it like a snowmobile. I got the hull built, and converted an old outboard motor engine from vertical to horizontal, before realizing that I was in over my head. So I gave up. It was an excellent learning experience and directly led to me going to engineering school. That was in 1969 and before I had heard of Jet Skis.

sophiecentaur
I'm not getting it. Are you designing something like the Moth as shown in this picture?

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I would certainly go ahead and build the wing without asking these questions on physics if all I risked was that the hydrofoil doesn't rise because of the wrong design, (which would be the same as not having the hydrofoil on the board!). This I can always correct.

As a matter of fact, I have already cut out and shaped a wing out of a pine wood board. It looks nice, aerodynamically and I was planning to reinforce it with a fuberglass layer and test it on the water by next summer, until I started seeing warnings in the Windsurfing Forums that I may have problems..

This was enough to slow me down and make me inquire about the physics aspect, because if I really broke the wing or the fin box when out in the water, it could have a problem in controlling the board and making it safely back.

Certainly if, as Sophiacentaur suggests, I suspend the wing between two chairs and I stand on it, with my 85 kgs, it will break, unless it is made in carbon, no question about this!

The real conditions on the water are, however, quite different:, because when I sail, I am not standing directly on the wing, which is underwater , but on a 220 lt board floating on the water, enough volume for TWO people!. So there are really no forces weighing on the wing . On the contrary the only forces acting on it are the hydrodynamic forces producing the upward lift.
Actually the greater these forces, the better, because they would increase the lift of the board .

As to taking courses in fluid dynamics, aerodynamics, etc, to me they are beyond the purview of a relatively simple project like this , which is not a N.A.S.A. . spacecraft project., after all.
Besides, for the wing itself , small as it is, there are websites offering various design options and for each design all the specs related to the optimal aerodynamic ( or hydrodynamic) characteristics are given. These specs can be fed into a 3D laser printer, which can and will produce an aerodynamically perfect prototype and eventually, even the final small scale wing ( 28" wingspan) by printing and joining several sections of the wing, one after the other.

The problem is not building the wing to the right specs, but the interaction of the wing with the board, at the place where it connects ( the in box), the weakest point.
I was hoping that somehow the magnitude of these forces risking to break the fin box could be calculated either from the Reynolds number or in some other ways, but I understand that this is not possible.f you see a way, please let me know.

The largest shear on the connections I imagine will occur in off-nominal transient conditions such as the board nosing down into the water, or the foil becoming airborne in the trough of a wave, or running aground on a rock/bar/beach.

anorlunda said:
The largest shear on the connections I imagine will occur in off-nominal transient conditions such as the board nosing down into the water, or the foil becoming airborne in the trough of a wave, or running aground on a rock/bar/beach.

Thanks Anorlunda
I am glad that perhaps I begin to see the light...I don't foresee any of the off-nominal transient conditions to occur : I don't think that my board ( and wing) wiill become airborne with my 11.6 ft Windsup! I would be lucky if , at best, the hydrofoil wing can raise the board just above the water , if I get enough lift with my contraption, which I am not too sure.
As to running aground, this can happen with any board, even one with a regular fin , without the hydrofoil wing. As to nosing down, I think that this too is unlikely, or at least it will be minimal, when the board glides a few inches above the water.

The important thing which I glean from your comment is that there is no mention of any other forces affecting the wing and originating from the water streaming across the wing in its natural hydrodynamic path producing the upward lift.

Ittiandro

anorlunda said:
I'm not getting it. Are you designing something like the Moth as shown in this picture?

View attachment 222084

I just answered to your other post, but I didn't see this one.
No. the Moth is way beyond what I intend to do and I don't plan to rise that high on the wing..
You can have an idea of my hydrofoil wing by looking at the photo I have submitted to Sophiacentaur. I resubmit them for you, My model would be the one in the 1st photo.

Ittiandro

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• Wing Forum.docx
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Ittiandro said:
You can have an idea of my hydrofoil wing by looking at the photo I have submitted to Sophiacentaur. I resubmit them for you

Thanks but no thanks. I would never open a .DOCX file coming from a stranger on the Internet. Doing to invites malware.

If you have a picture in a form like JPG or PNG, you can upload it directly to the post with the UPLOAD button.

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sophiecentaur said:
I looked at the Word document. It is far better to use PDF or even just insert JPEG images. Starting up Microsoft Word is a pain and, believe it or not, not everyone actually has Microsoft Office installed in their devices.
I really don't know enough about this subject apart from having a great respect for just what forces boats are subjected to. What I could say is that your foil would have to be strong enough for you to suspend it between two chairs at its ends and then be able to jump on one edge of the board with your full body weight. Stressing it with your hands would not be a tough enough test to represent the possible forces when moving from wave to wave when you're surfing in a force five. The one thing in your favour is that the wing is not very wide. Nonetheless . . . . .
If it is easier for you, I am uploading the phooto , just in case

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Ittiandro said:
So there are really no forces weighing on the wing

anorlunda said:
The largest shear on the connections I imagine will occur in off-nominal transient conditions such as the board nosing down into the water, or the foil becoming airborne in the trough of a wave, or running aground on a rock/bar/beach.
My suggestion to stand on the board was based on the fact that the forces (transient, as @anorlunda suggests) when you are on the board are more than capable of moving you and the board upwards (bumping). If you are planing on the wing, it's the only thing in contact with water and the forces would be passed through the wing. The torque with a wing could be higher than with a simple keel.
There are two possible reasons that these things are made with carbon fibre. One is that it sounds sexy and would help to sell the board. The other is that the forces actually justify it. That could just be true. It could be worth while trying it out but you need to be prepared to have it break on you. As you say, it could be embarrassing if you are offshore with no support boat. Can you run your tests somewhere where there could be some support. (Buy an EPIRB and someone will get to you eventually. )

PS In my ideal style of boating, you can go below and make a cup of tea whenever you like. You have to be mad if you base your sailing experience on a guaranteed swim during your trip.

Thank you Sophiecentaur,

Yes, I see now why you suggested laying the wing between two chairs and standing on it : if the board is planing off the water, the sailor's weight is no longer supported by the floating board , but directly by the underwater hydrofoil wing, which could indeed break, except (perhaps) that a part of the force exerted on it by the sailor’s weight would be offset by the opposite upward hydrostatic force of the water and probably be proportional to the surface of the wing..
I see Newton’s 3rd law here.. May be I should increase the wing’s surface, but there are limits to it.

How much of my 85 kg weight on the wing would be offset by the upward hydrostatic lift and the pressure differential between the upper and lower faces of the wing, causing lift?

I have absolutely no idea! Perhaps your expertise in physics can help me here.

Is it possible to calculate the upward force ( in N or Kg) acting on the wing from below knowing:

a) the fluid velocity (or the velocity of the wing through the water),

b) the wing’s surface and its chord ,

c)its thickness at the leading and trailing edges,

d) the angle of the wing’s plane in relation to the water ( angle of attack)

e) the pressure differential between the upper and lower surfaces of the wing ( if it is possible to calculate it) ?

If so, I'll provide you with this information, as a working hypothesis

From your comment I glean that the risk of breaking the wing would therefore arise only when the board is planing off the water, because , as I said before, if it is floating , the sailor’s weight would be entirely ( or mostly) absorbed by the board and not by the hydrofoil wing..

This is assuming that there are no other forces acting on the wing, outside the sailor’s weight, or other transient forces, like running aground or the board flying and falling in water,( like wave sailors do.), capable of exerting enough torque ( or stress) on it to break it or pulling off the fin box..

To prevent breakages out in the water I'll paddle the board first, without the sail, just the board, to see how it goes. with the hydrofoil wing.

I have a hunch it will not be indicative, though, because when paddling the speed will be very low and the board will therefore not rise off the water to plane, which would be the only way to ensure that hydrofoil wing is safe.

I’d appreciate your comment on the calculation issue, if the data I mentioned above ( a,b,c,d,e) are sufficient to quantify the forces acting on the wing..

I am approaching the problem from another angle: the total weight of the board on the water is about 110 Kg, including the weight of the board ( 15 kg) ,the rig and sail ( 10 kg) and my own weight ( 85 kg).

I want to calculate if the upward Lift force of my hydrofoil wing, based on the Bernoulli principle, is sufficient to offset the downward weight of the board and lift it off the water .

The Lift formula is L= 1/2ρ x v2xS x CL

Where ρ ( rho) =density,( kg/m3) A=Area( cm2) V =velocity ( m/s) , CL= lift coefficient , q= dynamic pressure( Pascals)

For ρ= 1000 kg/m3 ( water) V=10 kmh, A=1200 cm2 and Cl= 1.005215,

L=4,650,125 N=474 kg Note: Cl=L/(q x A) where q= 1/2ρ x V2

I read that the angle of attack affect the Cl, but I can’t see how to fit itin the calculation.

The best angle of attack of the wing is 10°C-15 ° C for the smallest drag.

Am I correct in deducing that the board will hydrofoil off the water because the lift force ( 474 Kg) is greater than the downward force of board, rig and myself ( 110K).?

If so, I see why a force of 474 kg on the wing can break it.

Since I am new to physics, my reasoning may be wrong.

I’d appreciate it if you can help me to clarify thisThanks

Ittiandro.

The lift coefficient is a function of the angle of attack. The lift and drag plots for a NACA 2412 airfoil are shown below for Reynolds numbers from 3E6 to 9E6. The lift force is whatever you make it by changing the angle of attack, with an upper limit when the wing stalls. You choose the airfoil to get the highest L/D (ratio of lift to drag) at the angle of attack at which you normally operate.

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Thanks for the observation , Jrmichler
In my post I calculated L =ρ/2 x V2 x A, then I calculated separately Cl=L/qA,( where q=(ρ/2) *V2 ) which yields CL=1.005215, I then added this CL value to the original L equation.

True, the angle of attack was not considered in the L equation because I didn't know how to do it, but my value Cl=1.005215 is very close to the one corresponding to an angle of attack of 10 ° in one of the graphics /charts I have seen and which is the one with the lowest drags.

Bottom line, is my L calculation right in showing a Lift force of 474 kg ( 464994 N) ? If not, can you please tell me why?
If it is correct, am I right in assuming that there is enough Lift 1) to raise the board, the rig and myself ( total 110 kg) off the water, and 2) hopefully without breaking the wing, the fin or the fin box?
I didn't consider the hydrostatic force. Should I have ? Does it affect, perhaps increase the lift? How?

Thanks

Ittiandro

## 1. What is a hydrodynamic force on a foil?

A hydrodynamic force on a foil is a force exerted by a fluid on a solid body, in this case a foil, due to the movement of the fluid around it. These forces include lift, drag, and side forces.

## 2. What is the Reynolds number?

The Reynolds number is a dimensionless quantity used to characterize the flow of a fluid over a solid body. It is calculated by dividing the product of the fluid's density, velocity, and characteristic length by the fluid's viscosity. It is used to determine whether the flow is laminar or turbulent.

## 3. How does viscosity affect hydrodynamic forces on a foil?

Viscosity is a measure of a fluid's resistance to deformation. In the case of a foil, higher viscosity fluids will result in higher drag forces, while lower viscosity fluids will result in lower drag forces. Viscosity also plays a role in determining the Reynolds number and whether the flow is laminar or turbulent.

## 4. How do hydrodynamic forces on a foil affect its performance?

Hydrodynamic forces on a foil, specifically lift and drag, can greatly impact its performance. Lift is the force that lifts the foil out of the water and provides stability, while drag is the force that opposes the motion of the foil. These forces must be carefully balanced to achieve optimal performance.

## 5. How can the hydrodynamic forces on a foil be calculated?

The hydrodynamic forces on a foil can be calculated using various mathematical models and simulations. These models take into account factors such as fluid flow velocity and viscosity, foil shape and size, and angle of attack. Experimental testing can also be conducted to measure the actual forces on a foil in a real-world setting.

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