Hydrofoils and Lift

General Discussion
41

[quote="$1"]

...that would probably make an engineer feel quite ill.

[/quote]

Been thinking Lennox, and I want to thank you (seriously) because statements like that really motivate me to search and think on a deep intuitive level.  

I did some casual research last night before going to bed, went to bed with some thoughts in my head and woke up with lots more thoughts and a bunch of answers. By 9am, I pretty much have it all sorted out in my head with one exception. I will attempt to fill this hole with an engineering colleage of mine. If my theories hold water, I may publish them here on this website.

Unfortunately, publishing it would require lots of explaining and diagrams, which would be laborious and take up much of my time. But I'd be willing to do it for the sake of clarity and fact finding.

It might be too early yet but I will make some conclusions:

- surfboard lift is mostly Newtonian, and much less Bernoullian.

- yes, DT is "probably" correct when he states that when the velocity increases, pressure decreases and causes board lift, BUT with certain conditions in place.

- DT's boards likely do better than other designs, at speed, level/trim on plane, on the flats, off rail; Lis fish does well here too. This might represent less than 20% or modern surfing, maybe far less than that.

- on rail, or off speed, its Newtonian. This might represent almost 100% of modern surfing.

Opinion: as far as I can see, DT has used and combined previously developed design elements (Simmons, Lis) and has added some modern features. Simply reducing the weight of the finished product can have very dramatic affects, which from what I can tell he has done using more modern materials. Dont know how long hatchet fins have been around but Im betting its been a very long time. Setting twin fins parallel (no toe, no cant) on a short low rockered pushed forward planshape board is nothing new, in fact its quite old. However the use of hatchet fins on a modernized Lis type fish is probably a unique idea, or maybe not?. Throw in some controversial marketing and here we are. 

Again, explaining these conclusions here would be very time consuming. Not sure if Im up to the task to spend the time.

42

Anbody know?  Assume 2-d flow.  Assume that the foil is prevented from moving in the horizontal direction and prevented from rotating but is free to move in the vertical direction.  Assume a foil aspect ratio of 1/10.  The white fluid and the blue fluid are both moving in the same direction at the same speed.  Assume both fluids are equally viscous.  Ignore gravity and weight of foil.  Assume the shape is an arc of constant radius of curvature.  I don’t think it matters if they are compressible or not, momentum equations apply in both cases…right???

What Force (F) needs to be applied to keep the upper edge of the foil level with the blue fluid?

 

43

Newton’s three laws form the basis for Bournelli’s Principle (as a special case when energy is conserved).

As far as “Newtonian” and “Bernoullian”…I assume that by “Newtonian” you mean that most of the calculation of lift involves the direct application of Newton’s Three Laws, while by “Bernoullian” you mean that the calculation of lift is done using Bernoulli’s Equation. Correct?  (there are other definitions for these names that are sometimes used)

(1) OK. What are the “certain conditions” that are required?

(2) And since the lift force is caused by pressure, how do you (and DT) reconcile or associate a reduction in pressure with an increase in lift?

(3) Why, if you say lift is “mostly” Newtonian, are you commenting on a Bernoullian approach–(esp. since BT warned in his initial post that it was easy to be misled by this approach, or to misinterpret the results)? And this is especially the case if / when the computation involves unconstrained flow (unlike in the case of pipe or duct flow, which is pretty straight-forward)

(4) …plus what do you mean by lift is “mostly” Newtonian?

44

 

I may be goint out on the limb here, but I don’t think that it is possible for a foil to travel at a zero AOA across the boundery layer of two fluids. Once the object starts moving the AOA will change, either negative or positive, and the object will begin to rise or fall (plane or plow). I think that this is why plaining is called “hydroDYNAMIC” lift and floating is called “hydroSTATIC” lift. Once the object starts moving the system becomes dynamic and changes in one variable, like velocity, effect other variables, like AOA.

45

Move along – nothing worth seeing here!

(My error- Wrote response to a different topic)

 

46

[quote="$1"]

Anbody know?

[/quote]

1. Bernoulli's Principle is only applicable where the fluid is incompressible; ie uniform density.

2. Your foil has an angle of attack (yeah weird)

Your diagram and points #1 and 2 depicts why Bernoulli cannot accurately explain surfboard planing.

mtb, i mentioned in my post there is huge hole to fill, which BTs diagram partly demonstrates.  By Bernoulli I mean conservation of energy, by Newton I mean mechanics, pressure force. There is tons of debate about the two on the www. I may also have to retract some of my earlier "too early" conclusions, esp about the part about DT being correct. The reduction is pressure he references is a pressure force downward, a reduction of this downward pressure would create more lift. Im only guessing at what he is saying, but Im not saying he is correct, even tho I said "probably" last time.

I say Newtonian, you say AOA, its the same. I want to agree with you but your on another level and Im skeptical by nature so if I dont understand you I just cant assume you are correct in everything you say. But i think I agree with most of what I do understand. I also digest things much easier using figures and diagrams instead of words and math. Thats just me. I may post some diagrams soon. Carry on.

http://amasci.com/wing/whyhard.html

 

47

We discuss some of this stuff here. 

http://www2.swaylocks.com/forums/trade-offs-modern-toedcanted-multiple-fin-systems

48

I'm on the Newtonian/deflected flows/resultant force side of this. I've been talking to engineers, physicists, assorted NASA guys, etc. about these things for 35+ years and this is one of the most cogent discussions I've ever seen. Congratulations, gentlemen; carry on....

49

I’m  starting to think Mr Bernoulli is getting a bad rap in all of this.

I’m quite certain Bernoulli’s theorem is nothing more than an expression for  conservation of  energy  for a parcel of fluid anywhere along its path.

rho*g*h + ½ rho*V^2 + p = constant

He is simply describing the parameters of a known flow field (streamline)

(any change in the fluids velocity along its path will be accompanied by a change in elevation or static pressure to maintain a constant energy)

 

I do not believe Bernoulli actually predicts the flow field. For that you would need to apply the continuity equation (conservation of mass) for frictionless flow or the famous derivative of Newtons (F=ma )  known as Navier-Stokes.

If you are adverse to math, you are free to measure local pressures or velocities, empirically.

Regardless, once you have quantified the flow field of interest, it is perfectly acceptable to apply either Bernoulli or Newton  to calculate local  force vectors ( lift and drag) 

 

Force = pressure * area

Force = mass * acceleration (which quickly transforms into the rate of change in momentum ( F=dmv/dt).

They are all equivalent.

 

Specifically, if you know the local pressure and area you can determine forces.

By necessity that means  locally there has been a change in momentum ( you have redirected the flow). calculating or measuring the magnitude of that change will  yield the same forces. 

You dont get one without the other.

They are the same and you are entitled to calculate forces with whichever method is most convenient.

 

IMO (and mr bernoulli’s)

-bill

50

Regarding your question.

Mind you, one has to fill some of the details, the precise nature of the fluids, etc. .-i.e. all the standard assumptions when faced with such a sketch of a problem.  So, lets take both mediums to be Newtonian, and incompressible at that. And I'll interpret your diagram literally, at least  those parts of it that can be. Further, I'm going to assume this experiment takes place in a gravitational field -i.e. on Earth for example. If it doesn't than the problem is equally as trival, see below.

So, lets say the under static conditions (no flow) the object is completely balanced by the buoyant force. Pressure under such static conditions being isotropic, the only forces with any discernable directionality being the weight of the object, that force which you've indicated which I assume moves with the object, and the 'buoyant force' from the medium below.

Now we start the flow, very slowly at first.

When you start the flow of the lower medium, the object will likely experience a shearing force arising from the upper medium. Given the that the flow is intially very slow, it's a reasonable assumption that given the respective differences in densities of the two mediums, the shear arising from (significantly) less dense medium can be neglected. But if the shear forces from the upper medium can be neglected the object will simply move with the flow as there is no force opposing the motion. In fact until that time in which the viscous force from the upper medium is such that it  poses a counter-force, the object will continue to move with the lower medium.

To be any more precise would require a lot more information.

Jeez, I hope this wasn't the point to be made by your problem.

kc

 

51

My problem statement has been modified.  I left way too much for interpretation.  No, I’m not sure where this is going.

52

[quote="$1"]

My problem statement has been modified.  I left way too much for interpretation.  No, I'm not sure where this is going.

[/quote]

 

i always mess up with the brain teasers.

may i ask for a few more initial conditions while i stall a bit?

gravity vector?

viscosity of fluids?

velocity of fluids?

'depth' of fluids?

foil geometry (circular, elliptical, fore-aft symmetry, other)?

... or is froude # and reynolds # relavent  (bow wave,wake, skin friction, separation etc)?

is the 'flat' fluid/fluid interface a boundary condition or just an initial condition?

rotational and lateral constraints, right?

 

 

oh well,

despite the fact that  i'm sure you could surf it, i'm inclined to think the resultant force vector would try to pull it into the "blue".

 

 

 

 

53

thanks zfennell, I modified the problem statement again.

54

Actually Ben, I believe I solved your hypothetical. So rather than asking another, why not just make your point.

kc

55

 

I’m not sure what answer you are looking for, but it seems obvious to me that it would have to be an upward force (like your red arrow suggests).  Otherwise the foil would be sucked down into the water.  This is kind of like the spoon and the flowing water tap experiment.  Is your pretend surfer holding a hot air balloon, and wearing foot straps?

56

 

How can you ignore gravity and the weight of the foil if you are looking for the force required to move the object in the opposite direction of gravity?

 

 

57

 

Right, I think that if the curvature of the rocker is greater than the curvature of the surface of water that you are plaining on, it would pull the board into the water.  Therefore, angle of attack, is the source of lift…as pretty much everyone already agreed…now I agree.  People were expecting something big out of the question…sorry.

Now…

MTB, how much does flow transverse to the longitudinal axis of the surfboard contribute to lift?  Sharp rails maximize this lift and rounded rails diminish it, because the round rails curve the flow upward, right?  Just in terms of transverse flow, do the fins create lift?

58

I don’t necessarily agree. I think that the curvature of the rocker can create a, built in, positive AOA, creating lift. As far as I know, the suction created by the curved surface is created at the trailing edge of the object because of the attachment of the boundary layer causes the flow to turn, creating negative lift, or suction.

59

 

It creates lift as long as it has a positive AOA because it changes the direction of the flow.

Sharp rails allow the flow to release, so that the boundary layer doesn’t stay attached, and create drag, and negative lift (or as you said curving the flow upward).

The fins create lift because they curve the flow, albeit, in a different direction (maybe similar to the direction of the negative lift created by the curved rail, i.e. suction).

 

60

Correct.  At least to a first approximation (there will be second-order effects, but those will generally be smaller). If a surfboard has rocker that precisely matches the curvature of the wave face is placed on the face of a wave face such that it is congruent with the curvature of the wave face, no lift will be generated. The reason is that the direction of the flow / momentum) is not affected by the presence of the surfboard hull. Rotate the curve representing of the hull of the board (about the point where the hull first contacts the water and you’ll be adding a non-zero angle of attack (either positive or negative, depending on the direction of the rotation) and you’ll have the first-order analog of a flat hull on flat water.

Similarly, increase the rocker of the hull and you’ll be redirecting the momentum so as to reduce (or reverse) the lift (as you noted). In extreme cases the lift vector may become so negative at high flow speeds that the craft may sink in the water column to the point where it becomes swamped. Conversely, less rocker will often increase the lift generated. Note that since the curvature of the wave face varies with position on the face of the wave, wave speed, pathline, proximity to the advancing curl, etc. there will be no single “ideal” rocker for all situations.

Your question assumes that there is a flow transverse to the longitudinal axis of the surfboard (and that its magnitude is significant). In that respect, you have lots of company. However, I would argue that while there are some transverse flows, they are largely second-order in magnitude and primarily associated with the small aspect ratios that characterize  surfboard hulls, and with the spatially-variable, compound curvatures comprising the face of a wave.

The transverse flows associated with aspect ratio arise from water that is flowing toward the hull can escape being redirected downward by flowing off to either side of the hull. This results in a reduction in the momentum change associated with the hull. That, in turn, reduces the magnitude of the momentum of water redirected downward and a resulting reduction in the lift generated.

You are essentially correct.

Flow past a fin will cause the generation of a pressure force whose direction is close to perpendicular to its plane. The component of the pressure vector that is orthogonal to the velocity vector constitutes “lift”. It is given this name independent of whether or not the force is directed up or down, or left or right. However, there will be one angle of attack that doesn’t produce any lift. While symmetric fins the zero lift angle corresponds to an AOA of 0 degrees. Cambered foils, however, typically produce some lift when the AOA is zero. In general, for common asymmetric fins the AOA for zero lift is around - 4 degrees).  In regard to “lift”, keep in mind that although a fin at an AOA of 90 degrees may be generating a large pressure force, by the definition of lift, it is not producing any lift.