Nose Cone Generator

Utility to generate 3D printer G-code files for common nose cone shapes

Usage

This console mode utility accepts a JSON formatted parameters file and produces the resulting G-code as output which can be optionally written to a file or produced as output to the console.

ImpulseRocketry.NoseConeGenerator -p=paramtersFile -o=outputFile

Argument	Description
parametersFile	JSON formatted parameters file
outputFile	Optional file to write G-code output to instead of writing to the console.

Parameters File

The JSON formatted parameters file accepts the following parameters:

Parameter	Description	Default Value
Shape	The name of the nose cone shape to generate as detailed below	Haack
ShapeParameter	The additional shape specific parameter where applicable	0
Diameter	The external diameter of the base of the nose cone	26.6 mm
Ratio	The ratio of the height of the nose code to the base diameter	5.5
WallThickness	The thickness of the nose cone wall	1 mm
BaseHeight	The height of the base cylinder	5 mm
LayerHeight	The height of each layer of the print	0.2 mm
Resolution	The length of each straight line segment that makes up the circumference of the nose cone	0.6 mm
BedTemperature	Temperature of the 3D printer bed	60 C
ExtruderTemperature	Temperature of the 3D printer extruder	230 C
FilamentDiameter	The diameter of the filament	1.75 mm
BuildPlateWidth	The width (max x coordinate) of the build plate	220 mm
BuildPlateDepth	The depth (max y coordinate) of the build plate	220 mm
Brim	The width of the brim to attach to the base. A skirt will be generate when this is set to zero	0mm

Example

{
    "shape": "PowerSeries",
    "diameter": {
        "value": 26.6,
        "unit": "mm"
    },
    "ratio": 5,
    "shapeParameter": 0.5
}

Available Shapes

Conic

A simple cone shape defined by the formula:

$$ y = { x R \over L} $$

Where $L$ is the length of the nose cone and $R$ is the radius of the base. The shapeParameter is ignored for this shape.

Haack

Defined by the formula:

$$ \theta = {\arccos \left( 1 - {2x \over L} \right)}$$

$$ y = { R \over \sqrt \pi} \sqrt { \theta - {\sin \left(2\theta \right) \over 2} + C \sin^3\left(\theta \right)} $$

Where $L$ is the length of the nose cone, $R$ is the radius of the base, and $C$ is the shapeParameter value.

Haack Series Type	$C$ Value
LD-Haack (Von Kármán)	$0$
LV-Haack	$1/3$
Tangent	$2/3$

Tangent Ogive

This is the segment of a circle aligned so that the rocket body is tangent to the curve of the nose cone at its base, and the base is on the radius of the circle.

$$ \rho = {{R^2 + L^2} \over 2R } $$

$$ y = { \sqrt { \rho^2 - \left(L - x \right)^2 } + R - \rho} $$

Where $L$ is the length of the nose cone and $R$ is the radius of the base. The shapeParameter is ignored for this shape.

Parabolic

Similar to the tangent ogive, except that the shape is defined by a parabola rather than a circle.

$$ y = {R \left( {{ 2 \left({x \over L}\right) - K \left({x \over L} \right)^2 } \over 2-K } \right)} $$

Where $L$ is the length of the nose cone, $R$ is the radius of the base, and $K$ is the shapeParameter in the range $ 0 \leq K \leq 1 $

Elliptical

This shape is formed from one-half of an ellipse, with the major axis as the center line and the minor axis aligned to the base of the nose cone. The shape is defined by this formula:

$$ y = { R \sqrt { 1 - { x^2 \over L^2 } } } $$

Where $L$ is the length of the nose cone, and $R$ is the radius of the base, The shapeParameter is ignored.

Power Series

Defined by the following formula:

$$ y = R { \left( { x \over L } \right)^n } $$

Where $L$ is the length of the nose cone, $R$ is the radius of the base, and $n$ is the shapeParameter in the range $ 0 \leq n \leq 1 $ which determines how blunt the tip is.

Power Series Type	$x$ Value
Cylinder	$0$
Parabola	$1/2$
Three Quarter	$1/3$
Cone	$1$