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Modelling Paragon 34/44 tapered head tubes

How do folks go about modelling the paragon tapered head tubes like this one: https://www.paragonmachineworks.com/steel-tapered-ec34-ec44-choose-lengt... ?  Onlike the Columbus ones I am used to, there is no obvious upper section, lower section, and taper between them that can be easily input into the head tube dialog box.  It's just one big taper and it does not appear to even be straight.  I think there is some curve to it.  

There are some tubes listed in the "standard" head tube library that are labelled "paragon tapered", but they are are incorrect, so they cannot be used.  As seen below, the lower diameter is way off from what it should be, somewhere around 46mm.

Paragon EC34-EC44 head tubes

I've added these head tubes to the next update of BikeCAD. All I've done is configured the existing tapered head tube input fields to best approximate the actual profile of the Paragon head tubes. Below is a drawing of the 120mm length Paragon EC34-EC44 (HT0510, HT2510) head tube. Below that is the same drawing with the BikeCAD head tube superimposed. At the very bottom is the BikeCAD head tube alone. I think you'll agree this is a pretty good match. The dimensions for this head tube are as follows E=16.5, d=36.4, B=84.5, ∅=47.2 .

Thanks Brent!  You are right,

Thanks Brent!  You are right, that is a near perfect match.  So what dimension changes with each different stock length of these head tubes?  Does B just get proportionally longer or shorter?  So for example, the B for a 110mm tube would be 74.5mm?

Paragon EC34-EC44 head tube range

Yes, that's correct. These head tubes will be available in BikeCAD version 18.5. But until then, you've figured out how to get the numbers yourself. Remember the other point with these head tubes is that the length is not actually defined in the tubing dialog box. It can be defined in the primary dimensions dialog box if you choose to configure the front end geometry by Front center and head tube length. Alternatively you can choose one of the other methods for configuring front end geometry in which case you'll have to massage some of the dimensions until you arrive at the desired head tube length.

On top of that, is there an

On top of that, is there an option to show the actual TT and DT miter angles for these tapered tubes? I've resorted to using Fusion 360 to mock up these miters and to print miter templates because I don't believe BikeCAD provides this info. Maybe I'm wrong though.

Miter templates for tapered head tubes

BikeCAD does account for the tapered profile of the head tube when calculating miter templates for top tubes and down tubes. No need to resort to Fusion 360.

Oh great! That saves me

Oh great! That saves me probably 10-20 minutes of unnecessary work.

I'm still unsure if BikeCAD shows that actual miter angle of tapered tubes though. For instance, if I tick on the "Down tube front miter angle" and switch between a 44mm straight head tube and a Paragon EC34/44 tapered tube, the front miter angle stays the same. Maybe I'm missing another checkbox that shows this change. I can create a simple spreadsheet formula to figure it out if necessary.

I figured out how to

I figured out how to calculate the miter angle for anybody interested using geometry principles from good old SOHCAHTOA:

In the mitering tab I turn on the values for "miter to center of BB measured along top (+ bottom) of down tube". Subtract the top value from the bottom value to get the "adjacent" value. The "opposite" value is the down tube diameter. That's the O and A in SOHCAHTOA, which means we'll be using the formula: TAN(x) = opposite / adjacent


Miter to center of BB along top of down tube = 753.3

Miter to center of BB along bottom of down tube = 733.1

Down tube diameter = 38.1

TAN(x) = (753.3-733.1) / 38.1

TAN(x) = 0.53

x = ARCTAN(0.53)

x = 27.9 degrees

So instead of mitering the value given by "down tube front miter angle" at 24.5 degrees, I'll miter at 27.9 degrees! Math is fun!

Hint: In case you're trying to set this up in a spreadsheet and your ATAN formula is spitting out the wrong number, it's because it's assuming you want the answer in radians. The spreadsheet formula should be =DEGREES(ATAN(.53))

Tapered head tubes miter angle

I suppose I should clarify what I mean by miter angle. The miter angle would be the angle you'd set your mill to if you're cutting your miters with a hole cut saw. Once you start using a tapered head tube, a hole cut saw won't work anymore. This is where the miter templates really come in handy. However, you could theoretically still cut a miter for a tapered head tube using some sort of tapered cutting tool. If you used such a thing, the miter angle would still be measured with respect to the centerlines of the tubes. Therefore, the miter angle should not change as a head tube gets more or less tapered.

What I'd like to do is use a

What I'd like to do is use a round hole saw with a diameter closest to the diameter of the HT at its smallest diameter where the DT meets it and then cut the tube at the appropriate miter angle. This sets the right angle and phases the cut. Then I can use the BC paper template and a half-round file to widen the tube to fit the HT. Does that make sense? In order to do that I need to know the actual miter angle for the tapered HT.

Since I can calculate the angle in a spreadsheet using the existing BC values, I guess I don't need BC to provide the info, but it would be convenient.

Unique approach to mitering

I know that you understand all this, but I still want to push back on your use of the term "actual miter angle". BikeCAD shows the actual miter angle. What you're looking for could be helpfull, but it is definitely not the actual miter angle. I could add a new dimension called head tube taper angle which you could use in cunjunction with the miter angle to get what you want. Although that assumes your down tube is entirely placed along the tapered section. I could also make the very dimension you're asking for. I'm just not sure what to call it. I"m open to anything except "actual miter angle".

BikeCAD shows the miter angle

BikeCAD shows the miter angle for straight head tubes. If you set your milling machine setup to that angle and make the cut there will likely be a big gap between the top of the down tube and the tapered head tube.

How about "down tube front miter angle for tapered head tubes"? It's a mouthful but it's clear. Then you can have a "top tube front miter angle for tapered head tubes".

If I'm the first person to request something like this then I'd love to know how others quickly and accurately make these types of miters. Thanks Brent for taking time to respond.

Miter angle for tapered head tubes

Again, I really don't think we should be suggesting that the miter angle changes when the head tube is tapered. Yes, if you use the smaller diameter hole cut saw you can get a good starting point for your miter if you adjust the miter angle to account for the angle of the tapered profile. But as you've said, that's not going to give you the finished miter you need. You are still going to have to finish that up with a miter template. I would think you'd be better off just going straight to the miter template. You can fairly quickly rough out the shape of the miter with a hack saw and then move on to a file.

If others are particularly keen on this first pass with a small diameter hole cut saw idea, I'd be interested to know.

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