Need help with FEA of a rudder

[pamarine]

Originally Posted by Ad Hoc

"...Or a I making it more complex than it needs to be?.."

Yup...massive over kill. (A rudder calc shouldn't take more than about 30mins or 1~2hours if you're not familiar)

Just establish the max lift and quarter chord moment, from the CoE, and the rest is simple 'static analysis'!

quarter chord would be 1/4 of the mean chord from the leading edge?

[Ad Hoc]

With foils (Daiquiri can correct me if i'm wrong, as its been a while since i did the theory of this)...The 25% (1/4) chord moment is called the aerodynamic centre because of the varying lift and location of the lift vector, and can be modeled as the lift force always being at the AC together with a constant moment (nose down usually).

M = 1/2 * rho* V^2*A*Chord*Coeff.

So your section has the lift, drag and moment action on it....the stock will take the load as well as the rudder. Hence, locating the stock as close to the AC as possible, if you have the charts of the foil, reduces the load on the stock.

[Knut Sand]

Originally Posted by pamarine

Well that last part is what I thought. I'm thinking I need to distance myself from this builder. Against my advice, he has rushed head-long into building a boat without any testing or engineering to speak of other than his own experience and what I'm able to sneak in under his nose.

Welcome to this world. btw; Where've you been?

Builders of any kind of products often do just that, leap forward, start the building process, then start the design/ strength considerations. It's normal. Not ideal, but normal...

Ad Hoc has given you some pretty useful hints here. I'll add in a few details to the same issue;

Make a folder, with a contact log;
Date, time, who, what...
Everything in written, or as much as possible. activate the "confirm button" on any important emails you send, come to think of it, do it on most emails, then they'll get used to clicking "accept"...
Hook your phone up to the computer, download related SMS' to the same folder.

Normally you won't need the "folder" but use it without hiding it, in a meeting or two, "we did agree to that issue on..... let me see.......; 18 of august...". Then they'll know that they will need hard evidence / proof to go after you.

If your gut feeling (calculations), tells you that this doesnt hold, inform in written asap. If they continue, inform (in writing) that this issue; you consider it to be out of your scope of work.

It's not always a rainy day.... Sometimes there's snow too....

KnutS

[daiquiri]

Originally Posted by Ad Hoc

With foils (Daiquiri can correct me if i'm wrong, as its been a while since i did the theory of this)...The 25% (1/4) chord moment is called the aerodynamic centre because of the varying lift and location of the lift vector, and can be modeled as the lift force always being at the AC together with a constant moment (nose down usually).

Something like that.
For airfoils (or hydrofoils, if you like) of general shape (camber, thickness, their chordwise distribution etc.) the resultant aerodynamic force vector R (which is the sum of Lift and Drag force vectors) will act through a point called "center of pressure", or CP. For a given foil running at a given speed, the chordwise position of CP (which is called Xcp) will vary as the angle of attack (AoA) changes. The aerodynamic moment Ma acting around an arbitrary point A is given by the vectorial product between R and the vector distance between Xcp and A:
Ma = R * (Xcp - Xa)
It has been established by convention that all the distances are to be measured from the leading edge of the foil, and the moment will be positive when acting in such a way as to increase the AoA.
If we decide that "A" is the quarter-chord point, the correspondant moment will be called M1/4.

Now, the Thin Airfoil Theory (TAT) says that there is a point around which the aerodynamic moment Ma is invariant vs. AoA. That point is called "Aerodynamic center" and is placed, according to this theory, at 1/4 chord from the leading edge. Experimental research has shown that although this result is generally not exactly true for airfoils of arbitrary shape, it is true for symmetrical ones - which are the ones we use for rudder design.
The moment around aerodynamic center is thus called Mac and for symmetrical airfoils (zero camber) TAT tells us that Mac = M1/4 = 0. It means that (for symmetrical foils only) CP is placed right there, at 1/4 of chord, and will not move with AoA (at least up until some 6-8°), which is a nice simplification of calculus.
But please note that when dealing with AoA close to the stall the aerodynamic moment will be different from zero - you are in a regime well beyond the validity of the linearized airfoil theory.

Now Pamarine, about your rudder...

The things seen above are valid for airfoils, which are 2D objects. The results of 2D foil anaysis can still be used (through a strip-theory) for a design of high-aspect-ratio (high-AR) keels and rudders, but I guess you don't have a high AR rudder over there. Low-AR rudders have some very peculiar characteristics which are strongly dependant on the vortex system formed at the leading-edge (if swept-back) and around the tips. In case of very-low-AR rudders, this vortex system (dependant mainly on rudder planform shape) will probably be more important for the hydrodynamic behaviour of the rudder than the choice of airfoils.

And since we are talking about very high speeds, I also presume that you have a surface-piercing prop / rudder there. If that's the case, you will also need to take into account the loss of lift due to ventilation and the increase of inflow velocity due to propeller.

I invite you to download form internet and read the paper titled "Rudder Design data For Small Craft" by Dr. A.F. Molland of Univ. of Southampton. It is free and can be easily found with google.
You will find many numbers and answers to your questions over there. If you don't, feel free to get back here and ask.

[pamarine]

The rudder has a 1.5:1 aspect ratio. The boat is a conventional inboard design, so the prop and rudder are completely submerged.

[daiquiri]

Originally Posted by pamarine

The rudder has a 1.5:1 aspect ratio. The boat is a conventional inboard design, so the prop and rudder are completely submerged.

That is a low-AR rudder.
From the pubblication I had suggested you to read, and for all-movable rudders (no skeg in front), you can calculate:

Vr = 1.2 Vs = 66 kts = 34 m/s (inflow velocity at the rudder, due to the propeller)
ARe = 3 (effective Aspect Ratio - please check this against your actual rudder planform)
max AoA = 23° (stall angle)
Cl = 1.32 (lift coefficient at stall - overestimated but it's ok)
Cd = 0.23 (drag coefficient at stall)
Cr = 1.34 (total hydrodynamic force coefficient)
Cn = 1.30 (coefficient of force perpendicular to chord - you need it to calculate torque acting against the stock)
Cm,1/4 = 0.049 (moment coefficient at quarter-chord - note that it is positive, so the center of pressure is fwd of 1/4 chord)
Xcp,c = 0.21 c (longitudinal position of center of pressure is at 21% of the chord)
Ycp,s = 0.49 h (vertical position of cen. of pressure is at 49% of rudder span, measured from the root).

Knowing that forces and moments are calculated with usual formulae (c is the mean rudder chord, S is rudder area, rho is water density):

L = (rho/2) Vr^2 S Cl
D = (rho/2) Vr^2 S Cd
R = (rho/2) Vr^2 S Cr
N = (rho/2) Vr^2 S Cn
M1/4 = (rho/2) Vr^2 c S Cm,1/4

you can find forces and torques acting on the rudder stock and tiller:

T = N (Xcp,c-Xst) (torque countered by the tiller, where Xst is the chordwise position of stock axis, more fwd respect to Xcp,c)
M = R Ycp,s (bending moment at the root)

and from these, and knowing the materials used, you can find the dimensions of relevant rudder structures.

As a final remark, please bear in mind that these are all static forces and moments. But, due to high operative speed and high wave encounter frequencies, your rudder structure should be dimensioned for fatigue. Though it might be questionable whether fatigue criteria should be applied to the max. deflection angle or to some smaller operative angle. If you decide to play safe and go for the first case, it would mean that the above values will have to be multiplied by an adequate coefficient which could be something between 2.0 and 2.5, as a first hint and depending on material used. That is in addition to the usual "coefficient of ignorance" we use for scantlings, which should be at least 1.5-2.0 .

[Ad Hoc]

Ahh...Daiquiri

You beat me to it!...ok, in addition to the above, i would add

If using ally, use a value of 10~20MPa, for fatigue
If using steel, then a factor around 5 would be more appropriate.

But the detailing, how you actually design it, how it shall be built etc , is far more important than just knowing what stress limit to use!

[daiquiri]

Originally Posted by Ad Hoc

But the detailing, how you actually design it, how it shall be built etc , is far more important than just knowing what stress limit to use!

Beyond any doubt.

[Raggi_Thor]

Lots of interesting stuff here!
I think this is a classic example.
The loading conditions are a guesswork, or different konds of estimates at best.
Then why try to calculate tensions and deformations exactly? (With FEA!)
Why not just look up maximum lift (before stalling) for that profile, and then calculate maximum bending moment at 55 knots? Then a roygh hand calculation should tell you if the rudderstock will bend or the bearings be torn?

[daiquiri]

Originally Posted by Raggi_Thor

The loading conditions are a guesswork, or different konds of estimates at best. Then why try to calculate tensions and deformations exactly?

Because, if something goes wrong and someone else with a shiny metal badge comes to find out who is responsable for the failure, it is always smart to have a calculation sheet which will demostrate that your scantlings have been done with a scientific method, based on some reasonably estimated intial load data.

Of course, the concept of "exact" is always questionable. Nothing is exact in this world.
Or better - everything is exact up until the moment we try to measure it.

Originally Posted by Raggi_Thor

Why not just look up maximum lift (before stalling) for that profile, and then calculate maximum bending moment at 55 knots? Then a roygh hand calculation should tell you if the rudderstock will bend or the bearings be torn.

But that's what has been done in the above post!
First, aerodynamic forces and moments have been estimated, based on a research data available. Then, these forces and moments have been transformed into torque and bending moments acting on the rudder stock. Finally, mechanical behaviour (tensions, deflections) of the stock has been evaluated, either with the use of FEA or by hand.

[Raggi_Thor]

Originally Posted by daiquiri

.. that's what has been done in the above post!
First, aerodynamic forces and moments have been estimated, based on a research data available. Then, these forces and moments have been transformed into torque and bending moments acting on the rudder stock. Finally, mechanical behaviour (tensions, deflections) of the stock has been evaluated, either with the use of FEA or by hand.

YES, and OK :-)
I just meant that pen and paper or a spreadsheet can be scientific enough, and ofte safer than FEA that is not completely understood.

[Ad Hoc]

FEA is always always an overkill for about 99% of the time it is used. Simple hand calc's are quicker and easier. But looks nice, fancy colour plots etc.... just like all the other "design" software