I download FreeCAD because I discovered the rocket workbench. While it is a neat tool in theory, I found it far too limited in practice; you can't make blunted shapes. The database is also full of wildly incorrect shapes; I don't think I found a single accurate cone.
FreeCAD is simultaneously an exemplar of both the good and bad of open source. It's really very impressive for a bunch of volunteers to implement and offer up for free a full, functional, useful parametric 3D CAD system. I personally put CAD among the most complex classes of software to develop, because it runs the full gamut: Serious math, computation & optimization, large data, complex feature sets, deep UI, complex 3D user interactions, etc..
On the other hand, I find it terribly difficult to work around FreeCAD's user interface. Granted, I'm not invested in using it day in & day out by any means. But even trivial tasks are difficult, and I often wind up at some dead end whereby my best recourse is to simply restart the app, because I can't figure out how to get back where I was---and that's just talking about navigating & manipulating the UI, setting aside entirely actual model manipulations.
But no doubt it's a very useful tool to know.
So, I took on the task of learning FreeCAD instead. I have since replicated a few nose cones, but haven't quite got them to the point I feel comfortable publishing STL files.
This looks good to me. For whatever my opinion's worth I think the CAD modeling here is at least on par with all the various nosecone STLs and such floating around, so don't hold back.
I took my 55AC and scaled up the dimensions. The key to making a secant shape is to anchor your arc centerpoint below the axis of your shoulder. How that translates to alpha values
@tjkopena referenced, I'm not sure. This model anchors the center point 2" below the shoulder. If you want to make it "more" or "less" secant, you can increase or decrease that constraint in the first sketch.
That is basically the action of the parameters I mentioned, their visual geometric interpretation.
Say the radius of the circle defining an ogive is ρ. For a tangent ogive with length l and radius r, ρ = (l^2 + r^2)/2r and the circle will have its center aligned with the rear line of the ogive. A secant ogive will have a radius ρ greater or lesser than that and the center correspondingly below or ahead of the rear line of the ogive. Define the tangent ogive radius for a given l, r as ρ′, then you can define a shape parameter α such that the ogive radius ρ = ρ′/α. At α=1 the shape will then be a tangent ogive. Under 1it's a sharp secant of the form discussed here, becoming conical as α approaches zero. Over 1 it's a bulging secant, becoming increasingly spherical as α approaches 2*l/d. E.g., I vaguely recall an Honest John nosecone being in part a secant ogive with α = ~1.78 (IIRC there's also a conic transition below the ogive). For the nosecone in discussion, where l = 4d, α = 8 produces a sphere.
Given the documented 4:1 fineness ratio, I believe the α that models the Arcturus secant ogive is 0.7. There is also a small spherical blunting. Here's a comparison of such a nosecone (yellow, modeled in OpenSCAD) against the best scale drawings I've found (black outline), published in the Jan/Feb 2019
Total Impulse newsletter of the Jackson Model Rocket Club (JMRC) by Roy Houchin II and Chris Timm:
Looks like a good match to me.
An STL of that model is attached, a half scale Arcturus nosecone according to the OP's specs based around LOC 2.26 tube. It has 1.6mm walls (approximately, the shape of the cavity permits more at the shoulder junction), somewhat arbitrarily picked as that's 4 perimeters using a 0.4mm nozzle. Happy to generate versions w/ other wall dimensions, anchors, etc..
