Difficulties with Equation Curves

[Anonymous]

I'm having difficulties constructing a Haack series nose cone profile in Inventor. 

To give a brief background, Haack series nose cones are profiles closely related to airfoils which are described by equations. A basic overview of the equations is here, and I'm attempting to construct the von Karman variety where C = 0.

I'm attempting to construct a profile with a base radius of 12.5 mm and a length of 30 mm, so my equation was as follows:

y(x): (12.5/sqrt(PI))*sqrt((acos(1-((2*x)/30))-(0.5*sin(2*(acos(1-((2*x)/30)))))) 

iterated from x_min to x_max over 0 to 30 mm.

Checking this in a online graphing calculator gives the correct profile and behavior that I'm trying to use. This is the correct version of the curve:

However, Inventor responds with the following:

This is obviously incorrect for a number of reasons:

1.  Some weird offset is being applied to the zero point (8.51 mm).
2.  The height of the curve (the difference between the thickest point and thinnest point) is not 12.5 mm.
3.  The curve is in the wrong quadrant (-x,-y as opposed to positive x and y quadrant). 

I've attempted to:

•  Double-check the equation. I know that I may not have coalesced the multiple equations into a single line correctly, and then entering it into a text-based, non-pretty-printed format opens up the possibility for errors. However, I cannot find something readily apparent with the equation that appears wrong, and permuting it in a calculator shows that numerous single errors (omitting a coefficient, etc.) would still create a curve in the ballpark of being correct. 
•  Toggle the degrees/radians unit preference in Document Preferences, just in case Inventor was interpreting the trigonometric functions incorrectly. No effect in either case.

I haven't tried to offset the curve by the odd amount (8.51 mm), because that wouldn't address the other two issues. I have no idea where that value is coming from - it appears to just be a peculiar number. I do have the feeling that there is an obvious mistake here, however, so I'm not ruling out that all this was a novice error.

Finally, for future reference, how do I "spot" the equation curve, as in define its start point? In this project I'm going to be using multiple equation curves with precise "landing points". How do I define a specific reference for where the curve begins? The equation curve tool, while useful, doesn't appear to have many configuration options.

[Xun.Zhang]

Hello @Anonymous ,

Thanks for reporting this case, I need more time to investigate it.

[Anonymous]

Hi @Xun.Zhang,

In the meantime I was able to find a solution - I was simply browsing for equation curve information and stumbled across someone trying to construct the same profile as I am. It was from 2013 and not labeled as such, so doubtful that it would appear in search results on the subject. I only identified the curve based on the form of the equation; it appears to be typed directly as the posted reference in my OP.

The thread can be found here, with the solution on page 2. The solution given, after adjustment to my numbers, was:

(12.5/sqrt(PI))*sqrt(acos(1 ul-2 ul *x/30) / 1 rad-sin(2 rad*(acos(1 ul-2 ul *x/30)/1 rad))/2 ul)

The quadrant error still persists, although I have managed to fix that through rotation of the curve about the origin. I've looked at the working equation and nothing comes to mind for the cause of the error other than Inventor being needlessly particular about how units are described.

If you can come up with a variety of the equation that works, certainly let me know - while the above solution may work for this equation, it may not for a future one, and I'd like to understand how the Equation Curves tool works to avoid this error in the future.

[johnsonshiue]

Hi Guys,

This may have something to do with the return value of acos(). Normally, acos() returns the angle in radian. But, in Inventor, acos() returns degree.

Many thanks!

[Xun.Zhang]

Hello @Anonymous ,

Try set -

x(t): 30 mm * t
y(t): 12.5 mm / sqrt(PI) * sqrt(( acos(1 ul - 2 ul * 30 ul * t / 30 mm * t / 180 ul * PI) - ( 0.5 mm * sin(2 mm * ( acos(1 ul - 2 ul * 30 ul * t / 30 mm * t / 180 ul * PI) )) ) ))

Check out the example from enclosed file.

Hope it helps!

[WHolzwarth]

It's not really the needed shape, Xun.

After some bad attempts I got it now. (2019 IPT)

[Xun.Zhang]

Awesome!

[WHolzwarth]

Not like that, Xun. Only some trial and error ..