Kruschke 3v radial and axial angles

[Michael Goodhart]

We are planning to build a 30 ft geodesic dome greenhouse and would like to use the Fuller-Kruschke 3v design but I have only been able to find the chord factors online and not all the radial and axial angles involved. We will be pre-fabricating every triangle to make up all the pentagons and hexagons with the polycarbonate already installed. If anyone has this information along with the chord factors (just to double check that I have the right figures) I would greatly appreciate it , as it has been REALLY difficult to acquire this data. Thanks.

Michael

[TaffGoch]

Michael, welcome to the Geodesic Help Group.

 

Last month, we had a discussion that included the benefits of Kruschke's design, regarding truncations at the ground plane:

http://groups.google.com/group/geodesichelp/browse_thread/thread/2f9e55f8a0858ded/3325dca7add9e89e#3325dca7add9e89e

 

I produced a SketchUp model to demonstrate the differences between a typical method-1 subdivision and a Kruschke subdivision:

http://sketchup.google.com/3dwarehouse/details?mid=11523bfa33e6123d2137e32e8ebf2b1

(Image attached below.)

 

SketchUp can be used to scale the model (unit radius) up to 30-feet, and can be used to measure axial angles, dihedral angles and face angles. There is an article that describes how to make these geodesic measurements...

http://groups.google.com/group/geodesichelp/web?hl=en

...but you may have some trouble, if you're not familiar with SketchUp (which, BTW, is available from Google, for free download.)

 

I'll be glad to provide additional help with the angular measurements, should you need it.

 

-Taff

[Richard Fischbeck]

Hi Michael

Did you check google "dome calculator" ?

[TaffGoch]

Michael,

 

"Gerry in Quebec" has also contributed, to the group "Files" section, a PDF file that includes his calculations for some of the vertex angles:

http://geodesichelp.googlegroups.com/web/hubs-3v-icosa-Kruschke-vs-method1.pdf

 

So, you may find what you need, already documented. (Time permitting, I can measure the SketchUp model, to double-check & confirm the angles.)

 

-Taff

[TaffGoch]

Michael,

 

You will find that the Kruschke chord factors in the SketchUp model confirm Gerry's calculations, even though the model was generated by different means.

 

This confirmation bodes well, for SketchUp model angle-measurements potentially matching Gerry's calculated angles.

 

Do the chord factors you have match the chord factors documented at the bottom of Gerry's PDF file?

 

-Taff

[TaffGoch]

 

The face-angles in Gerry's PDF and my SketchUp model do, indeed, correspond favorably.

 

-Taff

[Michael Goodhart]

Thanks so much Taff for all this great information. I have had some difficulty in getting used to the Sketch Up model measurement process and I just want to say how much I appreciate everyone's input and help. Gerry's PDF was helpful , but I have a question: if I will be fabricating the triangles and cutting compound miter cuts in the ends of the struts to make each triangle and bolt them together (1x4 strut triangles bolted to adjacent ones) wouldn't the radial angles be the same as the face angle if there is no hub connector involved. Also, are the dihedral angles for a Kruschke dome the same as a Class 1 Icosohedral 3v dome or different? Thanks again guys.

Michael

P.S. I'll check out the Google dome calculator tool.

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[TaffGoch]

Michael,

 

The dihedral angles are not likely to be the same.

 

Now that I know that you'll be using 1x4s (3/4"x3-5/8") for the triangle frames, I can whip up a quick model that depicts the geometries, including dihedrals and axial angles. I should be able to do this in short order.

 

Question -- When you say 30-foot diameter, is that 15 feet, radius, measured from the dome center to the outermost vertex of the 1x4 corners? Or, alternately, does that include the polycarbonate panels?

 

How thick are the panels, anyway? I've seen some that are honeycombed, so they're 3/4-to-1-inch thick.

 

It would help to know as many materials dimensions as you can provide, otherwise, my model won't be accurate enough to use for construction plans. I'll wait, until I hear back from you.

____________________________________

 

Attached is an image of dome panels I drafted for a 4v dome. Note that the frame edges incorporate the half-diherals, and are not perpendicular to the panels. I assume this is the panel-construction method you plan to use. I can produce comparable panel depictions for a 3v Kruschke dome.

 

BTW, are you going for the low-profile or high-profile dome (4/9ths or 5/9ths truncation) ?

 

-Taff

[Michael Goodhart]

Hi there Taff,

We would be going with 30 ft floor diameter (15ft radius) not spherical radius measured from dome center to outermost vertex of the 1x4 corner with  4/9ths truncation on probably a 3 ft vertical riser wall (normal stud layout). We wanted to pick a dimension near 30 ft that would minimize waste of the expensive polycarbonate glazing (which is 16mm thick) and comes in 4 or 6ft wide sheets up to 24ft. long, so if you know of a more efficient diameter near that , that would be great. The triangles would be built with the half-dihedrals cut (just like your cool sketch-up drawing) and the polycarbonate would be layed right into a rabbit cut so as to be flush with the upper edge of the struts comprising the triangles. Thanks again for helping me with this. Can't say how much I appreciate it.

Sincerely,
Michael

 

-Taff

--

[TaffGoch]

Michael,

 

That appears to be enough info. I'll model it tomorrow, first thing.

 

I'll concentrate on how the triangles can be most cost-effectively cut from the polycarbonate sheet, to provide ~30-foot diameter footprint. (16mm sounds like the extruded "honeycomb" or "channeled" polycarbonate sheets I've seen.)

 

A rabbet, cut in a 3/4"-thick board, might not provide enough "shelf" support, considering expansion/contraction. Might you consider, instead, providing a tacked-on support trim "shelf," to supplant the rabbet? Perhaps, a 1x2 (3/4"x1-5/8"), tacked to the inside of the 1x4 frame triangles?

 

How are you planning to retain the panels in the frames?

 

-Taff

[Gerry in Quebec]

Hi Michael,
Looks like Taff has given you most of the info you'll need to build
this dome. You asked about radial angles, face angles and dihedral
angles. The dihedrals for the Fuller-Kruschke dome differ from those
in the 3v class I, method 1 dome. (Actually, the Fuller-Kruschke
layout is class I, but not method 1.) Taff will be supplying you with
the dihedral and axial angles.

But this is a panel dome you're building, so you'll also need the
compound angles for cutting the ends of the struts to create tapered
triangular panels with butted joints, as shown in one of Taff's
drawings. The miter setting to dial on your compound miter saw to cut
the strut ends is simply 90 minus the axial angle of that strut type.
The bevel setting angles for cutting the ends of struts in a panel
dome are closely related to the radial angles (i.e., the angles needed
for building hubs in a hub-&-strut arrangement). At a given corner of
a triangular frame, the bevel setting angle for that end of the strut
is 90 minus the radial angle.

If all this sounds too confusing, I can send you a list of angles and
a diagram showing the compound angles for each end of each strut in
the dome. I assume you'll be including some internal bracing inside
each triangular frame, maybe 2x4s??? If so, you will also need the
compound angles to cut those pieces. There are various ways to
reinforce the frames. For example, you can use a T blocking
arrangement like that used by Timberline Domes. Or you can just put in
a couple of studs running vertically from the base of the triangle to
the two equal sides. In that case, some of the bevel settings to cut
the studs are greater than 45 degrees, so a home-use compound miter
saw may not be able to handle the job.

By the way, I once built a very small panel dome (3v icosa, class I,
method 1, 4/9ths) using 1x4 lumber just like you're planning. I used
butted joints for all the frames and bolted them together. The whole
thing was covered in plywood and asphalt shingles. We made this little
cabin to serve as a "bear proof" tent for my daughter and her friends
when she was little.

Cheers,
Gerry Toomey

On Jul 20, 9:32 pm, Michael Goodhart <michaelgoodha...@gmail.com>
wrote:

[Gerry in Quebec]

Michael & Taff,
I've just looked more closely at Taff's drawing of the triangular
wooden panels. I see that his don't involve any compound angles. The
dihedral angle between triangle faces is accommodated by ripping
through the full depth of the strut at the correct angle (e.g., 3.5"
of a 2x4). This is a lot of work, probably requiring industrial
equipment. If memory serves me well, this is the method used by Oregon
Domes.

The method I mentioned in my earlier post is different. It involves
cutting the ends of struts at compound angles to create the necessary
tapering of the frame to accommodate the dihedral angle. In this case,
you have a choice.... You rip the narrow edges of the struts (the 1.5"
edge rather than the 3.5") to allow the sheathing (polycarbonate) to
sit flat on the panels. Or, you don't bother at all to rip the edges,
and just let the polycarbonate straddle the strut edges, as is.

Gerry in Quebec

>  GeodesicWoodDome4V.png
> 231KViewDownload

[Michael Goodhart]

Taff,

Good point about the possible problem with that rabbet cut idea. We thought though that if we used a marine sealant all the way around with a small gap for expansion and aircraft tape over the joints,  that it may work. Maybe the "shelf" idea is better , although that entails a lot more cutting. Anyways, it should'nt matter that much for the overall design and model I would think. The important thing is getting the layout so the dome would sit perfectly on a 30 diameter riser wall ring (15 sided). We believe the 1x4 construction would be sufficient. What is your opinion on this guys?

Michael

 

-Taff

--

[Michael Goodhart]

Hi Gerry,

Thanks for the feedback on your experience with designing a dome like this. As a neophyte of dome building , it may be better as you mentioned to send me a list of all the axial,radial, and dihedral angles used in a Kruschke 3v 3/8 dome.  Does the radial angle differ from the axial angle if one is building the dome via pre-fabbed triangles with no connector hubs? Luckily , I have a very experienced carpenter friend who is helping me build the dome so as to ease the complexity in a lot of this process.  A diagram would really be nice that shows the cuts needed. Once again, thanks for all your help and advice.

Sincerely,
Michael

[Ken G. Brown]

There's another easier way to make panels, used by John Rich from New Zealand I believe. Make the panels with 90 degree sides then make filler strips of the proper V shape to fit and fill the spaces between the panels.

Ken,
from my iPhone

[Gerry in Quebec]

I like that method, though I haven't tried it. I expect you'd need
good hoisting equipment to position the panels temporarily until you
can install the wedge fillets and bolt the panels together.

Gerry

On Jul 21, 10:44 am, "Ken G. Brown" <kbr...@mac.com> wrote:
> There's another easier way to make panels, used by John Rich from New Zealand I believe. Make the panels with 90 degree sides then make filler strips of the proper V shape to fit and fill the spaces between the panels.
>
> Ken,
> from my iPhone
>

> > For more options, visithttp://groups.google.com/group/geodesichelp?hl=en- Hide quoted text -
>
> - Show quoted text -

[Ken G. Brown]

Perhaps the wedges could be pre-attached to one panel of each joint pair.

Ken,
from my iPhone

[TaffGoch]

I've only done a quick scale-up, to see if the polycarb-triangles can be cut efficiently from 4' or 6' sheets. A 30' footprint can, indeed, be produced with panels restricted to these sheet widths. (Image attached.)

_______________________

 

I've attached a few more photos of a greenhouse utilizing such panels. This dome looks to be about 30', as well.

 

-Taff

[Michael Goodhart]

Wow, the scale -up model looks great, Taff. Someone mentioned ripping the whole length of each 1x4 to create the necessary half dihedral angles, although we thought that if we simply cut the ends of each strut with the appropriate compound angle in order to cant each strut top outward, that it would create the necessary dihedral angle. Anyways, thanks for the work and I look forward to seeing the remaining necessary measurements. That Google sketch up help tutorial has really been a help. Need more practice with it though.

Michael

--

[Gerry in Quebec]

Hi Michael,
You could possibly rip 2x4s along the wide side to make 2 tapered
quasi 1x4s. (It would be very difficult to to rip a 1x4 at the right
dihedral angle.) But unless you have really good equipment, I would
deal with the dihedral by cutting the strut ends at the right compound
angles.

I will now upload a data sheet to the files section. It's an Excel
file named 3v-icosa-classI-Fuller-Kruschke-data.xls. It contains a few
diagrams and dimensions:

1) Compound angles at which to cut struts for the three triangle types
2) Dihedral angles
3) For a given radius (plug your desired radius into the green box),
the calculator will give you the edge lengths (before shortening to
accommodate butted joints), the dome height, the floor radius, the
floor surface area, the dome surface area, and the dome volume.

There are still a few bits and pieces of info that you might need for
the framing, such as compound angles for supports within the
triangular frames. I'll see what I can find.

There's probably a big overlap between the info in this Excel file and
what you get from Taff and his SketchUp models. But this is good as it
provides a double-check on the various numbers.

One last thing. For a 30 foot panel dome, I think it might be wise to
use 2x4s, not 1x4s. Are you in an area of high winds or heavy
snowfall? I assume you'll have to get the design approved by the local
building authorities. Good luck.

Gerry in Quebec




On Jul 21, 3:34 pm, Michael Goodhart <michaelgoodha...@gmail.com>
wrote:

> Wow, the scale -up model looks great, Taff. Someone mentioned ripping the
> whole length of each 1x4 to create the necessary half dihedral angles,
> although we thought that if we simply cut the ends of each strut with the
> appropriate compound angle in order to cant each strut top outward, that it
> would create the necessary dihedral angle. Anyways, thanks for the work and
> I look forward to seeing the remaining necessary measurements. That Google
> sketch up help tutorial has really been a help. Need more practice with it
> though.
>
> Michael
>
>
>
> On Wed, Jul 21, 2010 at 2:16 PM, TaffGoch <taffg...@gmail.com> wrote:
> > I've only done a quick scale-up, to see if the polycarb-triangles can be
> > cut efficiently from 4' or 6' sheets. A 30' footprint can, indeed, be
> > produced with panels restricted to these sheet widths. (Image attached.)
> > _______________________
>
> > I've attached a few more photos of a greenhouse utilizing such panels. This
> > dome looks to be about 30', as well.
>
> > -Taff
>
> > --
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> > --

[TaffGoch]

Michael,

 

All the angles, cuts, etc. are incorporated into this model, but are not labeled with degree measurements. That, I'll develop further, showing each triangle frame and polycarbonate panel, "exploded."

 

I've also incorporated a 36" skirt wall, to give you an idea of what the completed greenhouse profile and footprint would look like. You can easily examine the model with SketchUp, even though you haven't mastered measurements (yet.)

 

-Taff

[Gerry in Quebec]

Michael & Taff,
I've just uploaded a new version of the Fuller-Kruschke data file
(same file name). In the earlier version, I had inadvertently locked
the main input box for spherical radius. It is now unlocked, allowing
calculations of a few dimensions.
Cheers, Gerry

On Jul 21, 4:00 pm, Gerry in Quebec <toomey.ge...@gmail.com> wrote:
> Hi Michael,

.....

[Michael Goodhart]

Taff,

This is truly an awesome model of the exact design I had in mind. We'll just have to figure out the best way to frame out the door and make all the cuts. Do you agree that the dihedral angles can be cut on the ends of the struts to cant out the top edge of each strut so as to make each triangle meet the next at the proper angle. Some people talk about ripping the whole length of the chord but that does not seem necessary to me. Maybe I'm missing something though. Much gratitude for all your great work designing this for me!

Michael

 

-Taff

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[TaffGoch]

On Wed, Jul 21, 2010 at 9:12 PM, Michael Goodhart wrote:

> Do you agree that the dihedral angles can be cut on the ends of the struts
> to cant out the top edge of each strut so as to make each triangle meet

> the next at the proper angle?

Michael,

That's precisely how it's modeled. (And that's how Gerry configured
adjacent triangle-frame-planks in his spreadsheet, as well.) It should
be more evident, once I break out representative triangles, frames and
panels.

-Taff

[TaffGoch]

 

I've completed the breakout, and will work on adding dimensions (including angles) tomorrow.

 

-Taff

[Gerry in Quebec]

Michael & Taff,
I've uploaded another file: Compound-angles-internal-supports-
Kruschke-3v.xls. Although it's in Excel format, it's just a string of
jpg images, including a few line drawings, showing the angles to cut
for corner braces and studs inside the triangular frames.

Michael, were you planning to include such internal supports under
your polycarb sheathing?

Note: Some of the vertical supports (studs) have a bevel angle
significantly greater than 45 degrees.

Gerry

[TaffGoch]

Michael,

 

I've revised the model, to include angular measurements, from a carpenter's point of view. (I have, and use, a 2-axis compound miter saw, myself.)

 

You should have no problem measuring lengths, directly from the model, using SketchUp's "Tape Measure" or "Line" tools.

 

If you choose to scale the model, to make the dome larger or smaller, you don't have to worry about the angles changing. Regardless of chord lengths, the angles will stay the same.

 

(Now, I need to double-check Gerry's spreadsheet, to confirm that our angles are equivalent.)

 

-Taff

[Michael Goodhart]

Hi Gerry,

Is the file you uploaded with all the other sketch-up models? I can't wait to check it out. We were not planning to add internal supports under the polycarb except perhaps at the top of the dome for snow-loading or to save on waste of the leftover polycarb.

Michael

[TaffGoch]

Michael,

 

Gerry's spreadsheets can be found in our "Files" section:

http://groups.google.com/group/geodesichelp/files?hl=en&&sort=date

 

I cross-referenced his latest spreadsheet and my last model, and found the angles equivalent. (His were calculated, mine were produced "manually," in a 3D virtual environment.)

 

-Taff

[Gerry in Quebec]

Taff,
Very nice model showing the compound angles. I'm glad to hear the
angles match. I'll try to let David Kruschke know a SketchUp model of
this 3v flat-base configuration is available here.
Cheers,
Gerry in Quebec

[TaffGoch]

Michael & Gerry,

I posted a copy of the model, to Google's "3D Warehouse":
http://sketchup.google.com/3dwarehouse/details?mid=fe572326700e392a2137e32e8ebf2b1

The 3D Warehouse posting will ensure that the latest model revision is
more-widely available, at a well-maintained URL location. A 3D
Warehouse cross-link, to this discussion, will permit easy reference
to the details provided in this Geodesic Help Group thread, including
Gerry's spreadsheets.

-Taff

[Biagio Di Carlo]

Dear Taff,

do you think that 'Growing Spaces' 

is using the Method Kruschke ?

bdc

[Michael Goodhart]

I've seen the Growing Spaces Domes in person, and am almost certain that they are using the Kruschke geometry.

Michael

[Biagio Di Carlo]

Thank you very much for the info.

Biagio

Biagio Di Carlo
Via Berlino 2
Villa Raspa, Spoltore
65010  PESCARA

http://www.biagiodicarlo.com
biagio...@gmail.com

Tel. 085 411588  -  3405310750

  skipename: biagiodicarlo

[TaffGoch]

It looks like Kruschke to me, as well.

[Michael Goodhart]

Hi there Taff,

Thanks again for all your wonderful work with the Kruschke  all-wooden construction model. I was just wondering if I could get a breakdown of the number of each of the four strut types (A,B,C, and D) along with a diagram showing the different triangles which these struts create which would display the angles on each triangle also. Take care,

Michael

P.S. Would you agree that it is a good idea to build a smaller scaled model before the final finished dome?
        Also, is a 26' floor diameter Kruschke 3v dome an efficient size to minimize waste of the polycarbonate?

On Tue, Jul 27, 2010 at 3:32 PM, TaffGoch <taff...@gmail.com> wrote:

It looks like Kruschke to me, as well.

--

[TaffGoch]

Michael,

I've added a color-coded diagram, which depicts the numbers of
triangles required.

The struts are color-coded, as well, to permit a count of planks
needed. Equivalent plank color equates to a triangle edge having the
same cut-angle. (So, there are only 4 plank "definitions," including
length and end-cut-angles.)

I've uploaded the revised model:
http://sketchup.google.com/3dwarehouse/details?mid=fe572326700e392a2137e32e8ebf2b1
____________________________________

If you use 4'-wide polycarb sheets, cutting the "tallest" triangle,
across the sheet (4' triangle height,) then the dome would be about 23
feet in diameter (footprint.)

If you use 5'-wide polycarb sheets, then the dome would be about 29
feet in diameter (footprint.)

The orientation of the hollow-core channels, which I used in the
model, is the orientation of the 4' and 5' triangle measurements
above. If you "mix up" the orientation of the channels, you could
change these results, but they would be within, approximately, the
same range of results.

-Taff

[TaffGoch]

BTW, making a scale model always helps, even if only to reinforce your
confidence in the length & angle specifications.

[TaffGoch]

On Mon, Aug 2, 2010 at 9:14 PM, TaffGoch <taff...@gmail.com> wrote:
>
> (So, there are only 4 plank "definitions," including length and
> end-cut-angles.)

Well, that's certainly wrong! I neglected that there will be mirror-image planks, which will increase the count of unique planks.
 
-Taff

[Gerry in Quebec]

Hi Michael,
As Taff said, it's a good idea to build a model before tackling the
full-size project. However, for a panel dome, which is the
construction method you've chosen, a wooden scale model is a LOT of
work. Hub-&-strut models are much faster to put together, at least to
give you that pre-construction "comfort" you need, especially if
someone else is going to build the panels. Taff's virtual SketchUp
Model, combined with a simple hub-&-strut scale model, should give you
a good feel for the overall shape of the dome.

I've uploaded a 2-page file on how to build a hub-&-strut model of the
3v icosa Kruschke dome (5/9ths truncation) using plastic drinking
straws, wine corks and furniture nails. The dome is a little less than
3 feet in diameter. File name: Krusckke-3v-dome-model-
straws&corks&nails.pdf. Note of caution: You have to drink quite a bit
of wine to get the required number of corks for hubs :-).

Cheers,
Gerry in Quebec

On Aug 1, 10:02 pm, Michael Goodhart <michaelgoodha...@gmail.com>
wrote:
> Hi there Taff,
.........

> P.S. Would you agree that it is a good idea to build a smaller scaled model
> before the final finished dome?

On Aug 1, 10:02 pm, Michael Goodhart <michaelgoodha...@gmail.com>
wrote:
> Hi there Taff.........