Kaplan Propeller Drawing

[Mitch1990]

Hi All,

I am hoping someone with propeller design and drawing experience can assist in something I have been stuck on for a week now. I think I am missing something simple. I am using the data provided for the Kaplan Ka4-70 profile in Marine Propellers and Propulsion by Carlton. I can easily create a blade with zero pitch using the ordinates provided in the table and it looks roughly as it should although would be rather useless. What must I do to the ordinates provided to incorporate pitch into the blade profiles. I have been trying to use the equations at 3.18 which I found on this forum previously, although I am failing. I use thetaS as Zero which I think is wrong based on Cartesian coordinates but thetaS according to the parameter definition is skew angle. I understand that a Kaplan propeller is of constant pitch.

Simply put, what must I do to the ordinates to incorporate the design pitch? I have also read PNA Vol 2. I also apologize for being a Mechanical Engineer trying to do Naval Architecture but work is work.

Any help is much appreciated.

Mitch

 

[jehardiman]

From what I read above, you seem to be missing the major concept of a Kaplan or any other prop. Until you understand how the pitch helix at any radius is developed, I can understand that you got nowhere.
Don't start at the complicated stuff, go look at Figures 7 & 8 in PNA Vol 2, Chapter VI. ​

Once you have the blade sections simply developed for the helix surface at any given radius, there are only two things to change: the pitch and the skew. Any propeller blade is fully developed in reference to the radial development line. At any point radially there will be a pitch and a skew. The face to back centerline of the simply developed blade section at any given radial point is identically on helical development line at that radius. The leading edge to trailing edge centerline of the simply developed blade section at any given radial point is located at the point swept back/forward from its normal position by the skew. This is because there is no rake in a Kaplan propeller.

Edit to add, FWIW, most Kaplan propellers are not of constant pitch. The pitch is twisted off at the root to limit the length of the hub the same as the centerline being advanced to add root strength.

On second thought, you need to comprehend that the term "pitch" is used differently depending on context. While a propeller may have a constant "pitch", the pitch angle at each radial helical development surface will be different. Is that clear?​

 

[Mitch1990]

Thanks for the detailed response. I think the below is where I was going wrong and am still going a little wrong. I need to get the ordinates into an XYZ form for a curve in Solidworks. The profile is in XY plane and the Z value is constant for a given r. What I have done which is visually reassuring but still incorrect as I am using the x ordinates and the pitch angle to adjust the y ordinates in this case to a 15 degree pitch angle. I believe what I am trying to do is go from an expanded profile to a developed profile. The issue that I can see is that the chord length has increase as I have used simple trigonometry to get this and not adjusted the x ordinates. It has been 10 years since I did any real engineering and it really shows. What do I do to the x ordinates to translate the expanded profile to the developed profile. As I understand, the expanded profile is a zero pitch profile on a plane normal to the radius of the propeller, the developed profile is the profile along the helix line generated at a given r.


My apologies if this sounds like nonesense.

Mitch

 

[Mitch1990]

Am I correct in saying the developed chord should be longer than the expanded chord? If so, I have managed some more simple trigonometry to get the correct chord length at the correct pitch angle. I will plot my final profiles tonight/tomorrow morning and post them here for those who are interested. I would really appreciate some feedback if anyone is interested. I didn't edit my previous post to allow people to follow if they too are struggling with the basics.

Mitch

 

[jehardiman]

I believe what I am trying to do is go from an expanded profile to a developed profile.

Actually, your going the other way. Notice I said simply developed, and fully developed. Simply developed is the section you would like presented to the water. Fully developed is the shape in 3 space necessary to get that section.
I am going to shift to customary NA nomenclature here.
Stop thinking in cartesian coordinates; X,Y,Z. Start thinking cylindrical coordinates, x,theta,r. x is the ahead direction along X, r is the distance from X along the z' axis, and theta is the angle of z' from Z. Any point in 3 space can now be defined in 3 terms, x,theta,r. where theta and r are functions of Y and Z.
First, imagine an airfoil section of a prop at radius r moving through the water (inviscid, irrotational, uniform, non-wake adapted...yada,yada,yada…) as it advances at a given speed equal to P, the pitch. That section, relative to the water is 2d, and on the surface of a cylinder of radius r. In one rotation, x -> x+P and theta goes 0 -> 2pi. The z' axis, then sweeps out a helix projected on that cylinder, r. If we were to remove that outer 2d layer and lay it flat, that helix line would appear as a straight line with an angle to cartesian Y of phi, the pitch angle. Yes, on this "local" surface the simply developed section is moving with a zero AoA to the water and can be defined as cord, c, to thickness, t.
The problem comes when rolling that flat surface back onto the cylinder. In 3 space, the helix line is curved in 3 dimensions. This will cause stretching or shrinking of the actual surface based upon whether the coordinate is leading or trailing z' and on the face or back.
In actuality, this is really a lot easier, and quicker, to do on a drafting table using methods shown in Figure 25 PNA Vol 2, Chapter VI. In a 3d modeling program you will have to calculate the projected length along the cylindrical surface in both theta and x |r, phi. As an ME, is really easier to think of this as going on a 7 to 9 axis vertical mill than to try to convert it to cartesian. This is what makes the Toshiba-Kongsburg sellout so important to the political situation in Europe right now.

Edit: X-post.

Am I correct in saying the developed chord should be longer than the expanded chord?

No, the developed cord is foreshortened because of the view.

 

[Mitch1990]

Thanks again for your feedback, I honestly can't believe you put so much time into responding. It is greatly appreciated. In my own words, the nomenclature is likely not on point.

Projected view: The view of the propeller profile looking from aft or more correctly, normal to the thrust vector. What we can see in the radial profiles has components in 3D and the projected view is defined by these profiles.

Developed view: My understanding of the developed view is essentially removing the helicoidal component of each section to produce the developed outline. This is the view I struggle with the most.

Expanded view: Is the opening of the cylinder at a particular r and laying it flat which is where we see the traditional foil shape.

Unfortunately it is not possible to define a curve profile in cylindrical coordinates for Solidworks, so I have to work in cartesian and I am using excel to produce the coordinates for my curve profiles. In solidworks, to my knowledge I cannot project a curve profile onto a cylindrical surface. The main issue is producing a 3D object using the tables that is dimensionally correct without having the ability to wrap the foil profile around a cylinder at a given r.

The chord length derived from the tables is measured at a constant r from theta and z to theta' and z'?

What is the purpose of the formulas provided at 3.17 under fig 3.18 in carlton?

 

[jehardiman]

Projected view: The actual view of the propeller profile looking normal to the thrust vector. In this view blade section cord is laid out on the cylindrical development surface along the pitch helix line. On a flat piece of paper, this is the shortest the cord will appear to be because it is most foreshortened: it is on the surface of the development cylinder and rotated to the local pitch.

Developed view: In this view the helix development line for each radius is rotated until it is flat to the paper, i.e. normal to the thrust vector. The blade section cord is laid out on the pitch helix line (which will be curved) but think of it as if the development cylinder from the projected view has been rotated about the Z generatrix line. This will generate the true shape of the actual physical face of the blade; i.e. if we taped a piece of paper to the blade and traced the outline, this is what we would get.

Expanded view: Correct, this is the opening of the cylinder at a particular r and laying it flat which is where we see the traditional foil shape. This shape is not physically possible and is only used to develop t, c, and (greek) psi for the desired thrust at that radius

The chord length derived from the tables is measured at a constant r from theta and z to theta' and z'?

What is the purpose of the formulas provided at 3.17 under fig 3.18 in carlton?

OK, these two questions lead me to ask if you already have a set of t, c, and (greek) psi for your radiuses? Equations 3.17 and 3.18 refer back to Eq. 3.14a/b which is about the normal mathematical development of a thin airfoil. Also note that a true Kaplan sections are not NACA standard. Perhaps I'm wrong, but I assumed that you had the propeller geometry and were just trying to draw it. Because you first have to design or select the thrust and torque of the propeller before you can start drawing it.

 

[Mitch1990]

The question regarding the equations in Carlton was general. I already have a set of t, c and psi for my current constraints. I read a post previously from yourself that these equations were not really applicable to the Kaplan section.

This will likely make the NA out their squirm, but this where I am as far as foil shape. Note I haven't included Ig values and the chord is twice as long as it should be. There is a one for each r/R values

 

[johneck]

Here is some VB code to turn radial data (pitch, chord, rake, skew) and section offsets into X,Y,Z coords

For i = 1 To nr 'calculate blade surface X,Y,Z coords at nr radii
radius = RR(i) * Diameter / 2# 'RR(i) is non dimensional radius
phi(i) = Atn(Pin(i) / (2# * pi * radius)) 'phi is pitch angle, Pin is pitch
sib = Sin(phi(i))
cob = Cos(phi(i))
skew = skp(i) * dtor 'skew is expanded skew, skp is projected skew
For j = 1 To nc ' nc are number of chord points
dxmid = (pc(j) - 0.5) * CHD(i) 'dxmid is distance from midchord to current point, pc is %chd, CHD is chordlength
For n = 1 To 2 ' suction side is 1, pressure side is 2
dtheta = (EO(i, j, n) * sib + dxmid * cob) / radius 'dtheta is location for specific point from the generator line,
'EO is the local section offset from the nose-tail liine
XO(i, j, n) = XK(i) + dxmid * sib - EO(i, j, n) * cob 'XO, YO, ZO are coords
YO(i, j, n) = radius * Cos(skew + dtheta)
ZO(i, j, n) = radius * Sin(skew + dtheta)
Next n
Next j
Next i

 

[Mitch1990]

Thanks John, I have put together something similar today so it is good to see that I am least on the right track

 

[johneck]

One thing I just noticed is that "skew" is projected skew in radians, not expanded skew as it says in the comments. "dtor" is simply the concersion factor.

it should say
skew = skp(i) * dtor 'skew is skew in radians, skp is projected skew

 

[Mitch1990]

I am just going through your code to compare variables, for future reference, what is the significance of sib and cob?

 

[johneck]

that came from sine(beta) and cos(beta). People usually use beta for pitch angle, but for various reasons used phi here

Old guys used to try and save cpu time, so if a calculated number was used repeatedly, it was assigned to a variable