Creo drawing datum curve from equation inaccurately

Question

I'm modelling a Haack Series Nose cone. The nose cone equation for the curve is:

This is the equation for the datum curve that I have in Creo thanks to the people who helped me in a previous thread where I could not get the equation to draw near the bounds:
R = 49L = 560z = ty = ( R / sqrt ( PI ) ) * sqrt ( ( acos ( 1 - ( 2 * t / L ) ) ) * pi / 180 - sin ( 2 * acos ( 1 - ( 2 * t / L ) ) ) / 2 )x = 0.0
So here is the problem: zooming in where the observed segment of the curve spans about 10 mm of length, there appears to be a small concave segment and the tip seems to blunt abruptly:

The gradient should always be decreasing, yet by visual inspection and the curvature analysis tool, we can see this is not the case.
 
This is how the shape should look:

I've attached an excel plot of what the values should be for the length of the cone. Creo more or less agrees with the numbers until it gets within less than 20 mm of the tip where the concavity and weirdness starts happening.
Why is this happening 😞   ?

KenFarley · Accepted Answer

There are a couple of settings that I have in my config.pro file that might help:

accuracy_lower_bound
default_abs_accuracy

I don't know what the default for these is, but maybe that's what is causing your troubles. I have both set to 0.00001 in my config.pro file and it works fine, don't know if there is some sort of hard-coded limit built into the software.

If you're using inches for your model, 0.001 is probably not precise enough.

tbraxton · Answer

Try defining the curve using these relations. Using this I do not see the inflection in the curve shown above.

C=0
R=49
L=560

x=t

/*convert deg to rad
theta=acos(1-(2*x/L))

/* define terms used in Y equation
q1=R/sqrt(pi)
q2=sin(2*theta)/2
q3=(sin(theta))^3

y=q1*(sqrt(theta*pi/180-q2))

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