Tangent, but lacking continuity?

Before I go into a third dimension with this, Can anyone help me refine that curve at the red mark? The lines are all tangent, but there’s definitely a bump. (the inner and outer curves above the red mark are parallel)

Turn on the control points for that curve (F10), and use Nudge to tweak the shape.
Having CurvatureGraph turned on for both curves might help tune it up too.

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Thanks John! Hadn’t thought of turning on curvature graph while working…
Nor have I ever tried the nudge command.
But I’m getting results:

Edit: Also notice I moved the Gumball to the join point. Before asking I had tried rebuilding with 5 points instead of 3 but only added complexity.
Another edit. I’ve been searching around the previous questions re: continuity, Kyle Houchens (sp) covered it in our Skype class, but now I’m trying to make it happen I realize I’ll “know it” when I get it, but it ain’t there yet.

And while I was trying to figure that out I incidentally discovered that holding Alt while picking saves me from the tedious hassle of looking to the corner of my screen to turn on/off the appropriate snaps.
It’s the little things.

Technically this issue is resolved, but I still don’t know how to draw a pair of arcs the connect G3. In researching I also discovered that “acceleration” is a concept, and I was trying to do that although I had no name for it. If it helps here’s a screen shot from a different help page:

TLAR: that looks about right. Is there not a more exact science than that?

Draw a single, multispan degree 4 curve. The spans will have G3 continuity between them. Use ConvertToBezier if you want/need a pair of single span curves.

For two degree=2 arcs to have better than G2 tangent continuity, they will have to have the same radius so they have the same rate of curvature change.
At that point you might as well replace them with a single arc.

David thanks, could you specify the command I’m looking for? I tried fairing the curve, starting with a parabola, warping a spiral, … are you referring to a freeform curve?

I’m picturing a whip, I’m getting two distinct arcs.
UPDATE: Found it, I can specify the degree of curvature on _interpcrv. Today I learned.

A degree 4 curve created with the Curve command will automatically have G3 continuity between spans.

Back to your question:

Do you mean circular arcs? Circular arcs have constant curvature. Two circular arcs which are adjacent to each other can have G0, posiiton or continuity; G1, tangency. It is not possible for the arcs to have a higher level of continuity than G1…

G3 continuity requires continuity of the rate of change of curvature.

EXactly, I say with the confidence of a man who just discovered this a few minutes ago. Now that I see how it works the trick is to locate the points so that the finished G3 curve conforms to my imagination, but that’s just work. Thanks again.