Calculate curve to make two curved panel fit together

[franksbedford]

It matters, it is 0.23262" or about 6mm longer.
We scale the Fit-Point splines before trimming, before converting them to polylines.

Regards,
CVH

Thanks for this. That's more than I would have thought and it explains why the panels are slightly too long in real-world cutting. When you cut the top of the panel, the top edge gets wider, and the fit with the small octagon gets worse.

[CVH]

Thanks! Can you explain (1) how you calculate the fit points, so I can do it myself at home.

Already explained earlier: https://www.qcad.org/rsforum/viewtopic. ... 725#p44210
In a Spreadsheet:
- Column A: Row 10-82 = values 0-72 (nn below is 10-82)
- Column B: = Ann multiplied by 5 => Degrees
- Column C: = Bnn divide by 180 and multiplied by pi() => Radians
- Column D: = COS(Cnn)
- Column E: = Dnn multiplied by Amplitude divided by 2 (Amplitude is calculated in E2, in Excel we refer to $E$2)
- Column F: = Cnn multiplied by Diameter divided by 2 (Diameter is calculated in F2, in Excel we refer to $F$2)
- Column G: = Enn concatenated with your list separator concatenated with Fnn (In Excel: =Enn&","&Fnn for Dot-Comma style)
Presuming that your values are converted to strings with dots.
Otherwise you need to replace them string-wise before concatenating to match your QCAD preferences.
In Excel you can enter the formulas in row 10 and drag-fill them all down to row 82, '$' ensures that it remains a fixed reference.

For the fixed values:
When A1 is the required radius entered as value:
- F2: = A1 multiplied by 2 => Diameter
- E2: = TAN(22.5/180*pi()) multiplied by Diameter => Amplitude

The concatenated strings in G10-G82 are your coordinates for QCAD, I need to copy/paste that into a text editor before copy/paste to QCAD.
In rows 3-7 you could add additional formulas for R(exterior), Arc length by given Sweep and so on.
And if you are good at it, estimated length when segmented by segment length => Elongation factor.

(2). How do I import the 73 points into Qcad to create the fit point spline?

From the same reply and a later one:
- Start the spline from fitpoints tool (SL), opt for NOT closed in the Option Toolbar.
- Paste the copied coordinates list to the Command Line. (R-click .. Paste)
- Terminate the spline tool. (Twice R-Click or Esc ... Don't press ENTER as that repeats your last entry)
- Ensure that you have a spline with 73 Fit-Points ... It may duplicate the last one depending if there is a CR/LF carried over or not.
Select (only) the spline and see Property Editor.

Thanks for this. That's more than I would have thought and it explains why the panels are slightly too long in real-world cutting.

Because of interior wrinkling an xxx long flat panel would not fit an xxx long arc, it would be to short.
What you say here is just the opposite
Hoping that you don't use the length of the arc with R + 0.15 ... There that would be slightly to long because of segmentation.

Elongating it 1.15% as per example would ensure it is longer but remains as wide as required also matching your top octagon ...
... Only, the 1.15% is an educated guess.

Each material has such a specific gain factor depending the bend.
Because cardboard doesn't really stretches it is a negative factor, there is nothing gained, it shrinks at the interior.

I've been experimenting with your previous spline on the new drawings, and see how it fits.

They won't fit I presume ... Each cylinder has a circumference and amplitude ... Each dome requires a different sweep angle.
You can uniformly scale the master cosine wave in regards with the original used radius ... In full floating point notation.
Scaling origin is point #36, the factor can be given as an expression.
When point #36 is set on the corner of the base octagon it should then traverse the corner of the top octagon withing minute tolerance.
Why bother? ... Enter the radius and you get a new set of Fit-Points that should match perfectly.


Regards,
CVH

[franksbedford]

CVH,

I cannot say how much I appreciate your help with this.

I have attached the Excel spreadsheet and the Qcad drawing for the 32" model. It's close, but not correct, and I can't find my mistake. In the end, I'm planning on building a single spreadsheet for the fit points for all four oven sizes.

Thanks again!
FB

[CVH]

Within 0.8414" I can't call close at all. I call that way off.
It should be almost not noticeable, better than 1e-10, only detectable with specialized measuring tools.

There are faults in your spreadsheet:
- Missing point #0 - 0 degree - 0 radians on row 10.
- 72 times 5 = 360, the 73th point #72 is on row 82, eliminate row 83.
- Missing the arc S-E radius field.
- E2 is the diameter of the cylinder or twice the arc from S to E and not the dome type or dome radius.
- Eliminate F2, it must be the same as E2, there is but one diameter to refer to, where you refer to F2 change that to E2.

The arc drawn in d32_dome_cover_0,1.dxf is incomplete and incorrect.
I have no recent data on how you constructed the arc S-E for a 32" dome.
Form the drawing I can only determine that the arc length is 17.6854687.

fit_points_revCVH.xlsx

(24.19 KiB) Downloaded 13 times

Green backgrounds are inputs. (With as many digits as possible, 15-17 in my case)
Light blue backgrounds are outputs.
Arc length is derived from sweep angle what is more precise than the rounded length in the Property Editor.


Regards,
CVH

[franksbedford]

I will now go study your spreadsheet and mine. Thanks again. And again...

Here is the v0.2 32 arch design I am working with. I thought it was correct.

FB

[CVH]

Here is the v0.2 32 arch design I am working with. I thought it was correct.

Yes, and the arc has radius 11.97825461, diameter 23.95650922, sweep 84.59518924, length 17.6854687048369
Not diameter 32 because 32 is your dome designation.

A spline from the correct numbers fits within 0.0000000000001

fit_points_revCVHv2.xlsx

(24.8 KiB) Downloaded 16 times

Elongation factor explained:
- Cardboard type C with 40 flutes per foot or flutes of 0.3" wide.
- Fitting a 0.3 long segments on an exterior diameter:
The top angle of the isosceles triangle is 2*ASIN(0.3/2/12.12825461)
That fits N time on a full circle: N = 2*Pi()/(2*ASIN(0.3/2/12.12825461)) (We can omit the multiplication by 2)
- For an arc of 84.59518924 degrees we divide N by 360 and multiply by sweep in degrees:
N' = Pi()/ASIN(0.3/2/12.12825461)/360*84.59518924
- N' times the segment length is the total segmented length of the exterior curvature:
Lseg = Pi()/ASIN(0.3/2/12.12825461)/360*84.59518924*0.3
- Comparing that with the internal arc length we get a factor:
Lseg/Lcirc = Pi()/ASIN(0.3/2/12.12825461)/360*84.59518924*0.3/17.685468704837 = 1.0125

=> The flat face sheet panel Type C, 0.15 thick for d32 must be 1.25% longer to fit at its interior curvature, and that is 1.16% for d36

Regards,
CVH

[franksbedford]

A spline from the correct numbers fits within 0.0000000000001

It's a thing of beauty. Thanks also for generalizing the spreadsheet. I added the 40" mold and drew the cover panel. Files attached.

Now I will print the drawing at full scale, cut eight panels using the template and piece them together. Laser cutting after that.

FB

[CVH]

d40_dome_arch_0,2.dxf
- The fit is (again) found to be not that great, within 0.0321".
- Your top octagon center is (again) placed 0.00128791164035932 to the right of the lower/larger one.
.... Same horizontal offset as here: https://www.qcad.org/rsforum/viewtopic. ... =15#p44276
- #36 is placed 0.99997027" below the corner of the base octagon.
.... I hope that your are acquainted with snapping and all the methods at your disposal.
.... Because the dome arc is defined differently one should match #54 with the corner of the top octagon.
After fixing these things the fit is within 0.0000014" ... What is already acceptable.
.... Why 'already acceptable'? Remark that the radius of Dome type 36 is given with 15 digits.

d40_dome_cover_0,1.dxf
- The arc is (again) tangent to the top plane instead of tangent to vertical at the top of the slot.

But another issue is that with keeping the top octagon steady in size the center as before will now be left of that.
.... See: Intersection between middle orthogonal to the chord and the horizontal.
Also meaning that you get an arc of over 90 degrees (93.68238761) and that this 'overshoots' your top plane by 0.02881".

Being tangent to vertical at the left was just a proposal that worked for d36 and below.
I also remark that you did not adapt height to account for the thickness of the top panel.

You need to make a design choice here: Enlarge the top octagon with dome size or keep the arc as you drew it.
It can't be AND, it is OR tangent to the left, OR tangent to the top.
For the latter, Fit-Point #54 (270°) will match with the corner of the top octagon.

fit_points_v3.xlsx
- I presume that the third dome type is 40 instead of 36 ...
- Corrugated cardboard flute size is an estimation based on Type C
.... Please measure up the number of full flutes waves per foot and enter a real world value. (12/N)
.... The elogation factor will not change much below flute width = 1.000. (For short arcs the arc length ≈ chord)

Regards,
CVH

[franksbedford]

These are all good comments. Here goes:

1. Obviously my snap skills are lacking.
2. I should have adjusted the dome arch for height from the start, and will do that now.
3. For the 40", being tangent to vertical at the left and increasing the size of the top octagon seems like the best solution. I will see if going to 12" does that.

In the physical world, I printed the 40" dome cover as a template and hand cut 8 panels. The intersections were good, but the panels were short by about 1/4". I'm not sure why. Perhaps the fluting. The fluting is more math/design I need to learn.

Overall, excellent progress. Once I start laser cutting I will learn what is bad manual cutting, and what tweaks I need to make to the Qcad files.

In the long, long run, I'm thinking of using FreeCad to do a 3D version of these pieces. And maybe designing an exploded view. All good fun.

[CVH]

The intersections were good, but the panels were short by about 1/4". I'm not sure why. Perhaps the fluting.

From the spreadsheet data:
Required elongation for a 22.418203541554" long arc is 1.01% or 0.226424" more and that fits the 1/4" ....

Your flat face needs to be scaled 1.01% up in length but nothing in width ... Xfactor = 1 & Yfactor = 1.0101.
Scale the Fit-Point splines along with the distance between octagons, before trimming them, before converting to polylines.

Regards,
CVH

[franksbedford]

Here's an interesting way of thinking about this project.

I had originally thought it was a good idea having a standard 10" octagon as the top of all four sizes. But that's "old world" thinking where there is a metal mold, or die, that costs real money to produce. One mold, lots of uses -- in the traditional manufacturing world. But this is modern production, where there is no die, and each piece is cut from a Qcad file, which is free to develop. Each octagon can be a custom size that works best for that mold. The octagons can even be accurate to fractions of an inch, because I'm not giving the design to a welder who can't work at that degree of accuracy.

You might be thinking, of course. I'm getting there.

[CVH]

In the long, long run, I'm thinking of using FreeCad to do a 3D version of these pieces. And maybe designing an exploded view. All good fun.

Probably good for solids but I don't think that there is a corrugated cardboard method and rendering engine included.

Being a 3D concept and preferring FreeCad then why did you not used that in the first place?
It would have intersected 2 cylinders at an angle with ease and that 8 times including cropping to a dome.
Unsure if FreeCad has a developing engine to 'unfold' .. 'unroll' your cardboard design.

Signing off.
CVH

[franksbedford]

Last post on this thread to give a big thanks to CVH. He not only resolved the original question (fitting curved panels together), he de-bugged my drawings, gave me Qcad lessons, answered questions I didn't even know I had, and had excellent design ideas. Incredible.
Also signing off.
FB