# Dihedral hydrofoil lift calculations

Discussion in 'Hydrodynamics and Aerodynamics' started by vejas, Nov 19, 2018.

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One of the great books around on practical hydrofoil design and building is "Hydrofoils Design Build Fly" by Ray Vellinga.
Dihedral is defined on page 99 as "where the wing tip is higher than the wing root.." Anhedral is defined on page 102 as a wing whose tip is lower than its root.
The effect of dihedral and anhedral on a moving foiler is described from page 99 to 113.
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Sometimes I've heard beginning sailors complain about all the different names for parts of a sailboat and the lines that control them. For instance :"grab that line"is not very specific and may result in problems. Specific names for lines and parts becomes second nature and pays off when it gets hairy out on the water.
The need to be specific also applies to foils where we have appropriated many words developed in aerodynamics -such as chord, camber, span, tip, root,t/c ratio, and more
including dihedral and anhedral.

C-Fly ocean test foiler:

Last edited: Dec 22, 2018
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### HeimfriedSenior Member

I own this book and read it. It is very helpful espacially as an introduction to this subject (I also found some small errors in it). Vellingas definition of dihedral and anhedral is ok, because it refers to sketches. But the wording alone is questionable. At katamarans for example you sometimes find the wings mounted on the hulls looking inwards (towards the center plane). In this case the "wing tip higher than the wing root" is not dihedral, but anhedral.

Going with Vellingas definition is fine, but one should know, that there are different definitions to avoid beeing missunderstood or missguided.

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Are you saying this is anhedral?

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### HeimfriedSenior Member

Assumed the symmetry plane of the vessel is to the left (out of the pic), to me the wing has two different parts: from its root towards the deepest point of the "V" it is dihedral, from that point towards the tip it is anhedral.

Edit: changed

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### Doug HalseySenior Member

You could say the same thing about aircraft wings or V-foils, but everyone would laugh at you.

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### HeimfriedSenior Member

That is quite possible.
I'm not a foiler at all much less an expierienced foiler like probably you. I have got nothing but the quoted definitions from Vellinga complemented by the sketches and his explanation of roll stability. He only refers to straight wings. Also the examples given by Doug Lord (#11, first pic) referring dihedral or anhedral only to straight wings. Wings with different angles in it are called "gull wing" and "polyhedral".

The explanation Vellinga gives, tells me that the effect of a wing depends on its angular orientation (related to the midships plane).

Last edited: Dec 22, 2018
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### Doug HalseySenior Member

Reading my previous post, I realize that I should have said "laugh about it," instead of "laugh at you." I think all the confusion is funny, but there's nothing personal about it.

At least for V-foils & similar shapes, I always consider the dihedral to be positive on both sides of the deepest point.

But maybe the best policy is to try to include a diagram whenever there's any doubt about what is meant.

revintage and Doug Lord like this.
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### HeimfriedSenior Member

OK. I add a sketch I just made after a Picture in a publication
The Hysucat Development Dr. K.G.W. Hoppe - PDF https://docplayer.net/22516538-The-hysucat-development-dr-k-g-w-hoppe.html
Page #51, bottom

The author calls the angle dihedral. Because there is no support in the middle, it should be right, the attaching points of the wing to the hulls consider as roots. There are no tips, because only one wing is attached to two hulls. If you would consider the wing center as tips of two wings, the Vellinga definition leads to anhedral.

Edit: The sketch shows a cross section of an asymmetrical hull katamaran. Looking from ahead.

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Last edited: Dec 23, 2018
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Wouldn't you have to view the foil from ahead to know whether it dihedral, anhedral or no hedral?

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### HeimfriedSenior Member

The sketch is meant as a cross section, so the view is from ahead (or from abaft, which in this case makes no difference). Did you look at the pic page 51 in the Hoppe paper?
Did I understand your question right?

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### HeimfriedSenior Member

I will try to explain my thoughts with an attached sketch.
To the left is shown a monohull with dihedral wings (tip higher than root). It heels towards starboard. As Vellinga explains, the starboard wing develops more vertical lift than the portside wing and therefore the wing forces tend to correct the heel.

Right sketch also shows wing tips higher than roots and following only the wording of the rule they should be also dihedral. But looking at the influence of the wings in the same situation as before, you will find, the portside wing is developing more vertical lift and as a result the wing forces tend to enhance the heel.

For this reason I would prefer to look at the hydrodynamic effect of a wing angle rather than stick to the formal rule (tips higher or tips lower) to judge if it is dihedral or anhedral.
I don't know, if an aircraft with wing tips pointing to the symmetry plane exists. I only know aircrafts with wings looking outwards. So I think, in aviation was no need to say, the rule "tips higher than root" includes the unexpressed condition "wings looking outwards". But regarding boats it is very common also to use inward looking wings.

Last edited: Dec 23, 2018
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A strut with a dihedral wing attached can be placed so that it is pointing in or out. On sailboats the side with the most lift, in either case, is determined by leeway.
Vellinga's rule stands -as best I can tell.
----
I now understand what you were showing in the sketch in post 23. I think in a configuration like that common sense would dictate that the foil has dihedral*. The "root" is at the center of the foil and the tips are attached to the hulls. Vellinga's rule stands......

* isolate the foil before attaching it to the boat: it is clearly a dihedral foil-attaching it to the hull at the tips doesn't change that.

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### HeimfriedSenior Member

OK. In my eyes you redefine root and tip to save Vellinga'a rule. A rule is helpful in cases of doubt. Espacially a beginner should see what is obviously root and what is tip - to decide if the wing is dihedral or anhedral. Your way would require already to know if it is dihedlal or anhedral an then find out, what must be root and what must be tip to fit the rule.

Agree. That is in essence the same as to say dihedral or anhedral is decided by the angle between foil and symmetry plane of the vehicle (regardless where is tip and where is root).

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### philSweetSenior Member

This is starting to sound like the old question "how come a mirror reverses the image left to right, but not up and down".

As quoted earlier by Heimfried, the ITTC says "Dihedral, Angle (vessel geometry and stability) (-) [-]
The complement of the acute angle between the plane of symmetry of a craft or body and the axis of a hydrofoil attached to it projected on to a transverse plane." Thus dihedral is defined without regard to the choice of body reference frame - leaving us only the problem of measuring it. Measuring it requires you to define the axes.

Notice that we really only have a semi-space in 3D due to symmetry. Two axes go from -infinity to +infinity, and the beam-wise axis goes from 0 to +infinity.

How do you measure an "angle ... projected on to a transverse plane" (using right hand rule)?
As I said in my first post, " The angles are positive x to y in xy, y to z in yz, and z to x in xz.". Let me be a bit more explicit. The angles are positive going from +x axis to +y axis in xy, from +y to +z in yz, and from +z to +x in xz. The angles are negative going from +x axis to -y axis in xy, +y to -z in yz, and +z to -x in xz.

2. Label your axes and indicate the positive and negative directions. Beam-wise is positive by default. Draft-wise can go either way.
3 Draw your foil projection on the transverse semiplane.
4. Use definition of dihedral and the measurement conventions of RHR to measure the angle from the (positive) beam-wise axis to the foil. (This is the complimentary angle of the acute angle to the plane of symmetry measured in the conventional way).

Whether it is positive up or positive down depends on how you arrange your axes in the transverse plane. This is rather important when you start asking computers to do your math for you, since they are notoriously bad at guessing which way angles run if you don't tell them. Matrix functions such as rotation transformations rely on this sort of consistent treatment.

The key here is to realize that you don't get to choose the definition, but you do get to choose how you measure it. Your choice will effect every other component fixed to the body in the same way.

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Well, in fact, there are at least two widely used definitions of dihedral. Dihedral and anhedral are used in aerodynamics. For instance, in Darrol Stintons book "The Design of the Airplane" they are defined as: "The rise of an aerofoil from root to tip is called dihedral; when the tip is lower than the root, anhedral."
Ray Vellinga uses this definition in his book "Hydrofoils Design Build Fly".
Seems like the ITTC definition does not include the word "anhedral".
BMcF in his post #7 on page 1 of this thread defines "dihedral" in the same way that Vellinga and Stinton define "anhedral".
Surprisingly to me, James Grogono, author of the classic on hydrofoils: "Icarus The Boat that Flies", defines dihedral in the same way as does BMcF and further elaborates that it is "the angle of entry into the water"[of the foil](page 19). There is no mention of anhedral in his book.
A possible reason for this is that Grogono's boats all used surface piercing foils for the main foils.
So which definition is correct? And what is meant by "correct"?
It seems to me that "we"use the aerodynamic language much of the time when discussing foils--span, tip, camber, chord, aspect ratio, flap etc. So why would we not use the aerodynamic definitions of dihedral and anhedral when discussing hydrofoils attached to a boat, board or whatever?

from catsailingnews(and other sources)--

Last edited: Dec 26, 2018
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