Math help needed to calculate 3D curve

[jim2W82A7]

The project is to design a material handling chute.  Imagine an airplane taking off.  It rises in a straight line for some distance climbing at 30 degrees.  Then it executes a 90 degree right turn of a specific radius (as viewed from above) while steadily increasing its rate of climb to 60 degrees.  After completing the turn it continues to climb in a straight line at 60 degrees for some distance.

At this stage these numbers are approximate, so I would like to develop the math to calculate points along the turn, with initial climb angle, turn radius, degrees of turn, and final climb rate as inputs.  Then I'll use these points to create a 3D interpolation spline to define the path of the curve, add the start and finish straight lines,  and create a sweep of the chute profile.

Can anyone here shed light on how to calculate the points?  Or is there an easier way to create the curve?  I might be able to manage it if I could calculate the elevation at which the turn will end and the 60 degree straight climb commence, but that has eluded me too.

Thanks for any help.

[jim2W82A7]

Maybe the Smooth (G2) function will give a suitable result.  The resulting turn isn't a constant radius as viewed from above, but that may not be a firm requirement.  Testing will be required to determine that.  In the mean time if anyone can calculate the points please chime in.

Thanks!

[blandb]

Something like below?

[WHolzwarth]

Something like that (2019 IPT)?

☹️ Will we ever get Inventor file attachments back here in the forums?

[blandb]

I see now, makes more sense....Had my moment there for a sec.....I agree with @WHolzwarth!

[jim2W82A7]

This doesn't appear to finish at the 6o degree up angle.  Does it?

[jim2W82A7]

This looks like a solution.  I've downloaded the .zip but need to update my copy of I 2018 to use it.  I'll get back when that's finished.  Thanks!

[jim2W82A7]

Ich habe Probleme mit dem Update. Können Sie diesen Teil möglicherweise im Format 2018 veröffentlichen? Vielen Dank!

[WHolzwarth · Accepted solution]

Now I'm back with 2018. I didn't test parameter changes, but it should be possible.

Anybody here, who likes zipping of Inventor files?

[blandb]

For the longest time I thought I was doing something wrong, until @johnsonshiue pointed out that I needed to .zip it. Must have been a change in the website update??

[WHolzwarth]

😊 Perhaps a new productivity aspect ..

[jim2W82A7]

Das hat es geschafft! Vielen Dank!

That did it! Thanks very much!