Model Rocket Nose Cone Geometry Calculator
Choose a nose-cone profile and enter the dimensions to generate coordinate stations plus geometry estimates for volume, surface area, shell mass, and center of mass. The output is meant for layout, CAD setup, and material planning before you verify the final part.
Estimated nose assembly mass (g)14.19
- Fineness ratio
- 2.86
- Tangent-ogive generating radius (mm)
- 294.46
- Base tangent angle (degrees)
- 0
- Outer enclosed volume (cm3)
- 51.76
- Wetted surface area (cm2)
- 74.64
- Internal cavity volume (cm3)
- 62.35
- Estimated material volume (cm3)
- 11.45
- Estimated assembly center of mass from tip (mm)
- 76.15
Profile coordinate table
| Station | x from tip (mm) | radius y (mm) |
|---|---|---|
| 0% | 0 | 0 |
| 5% | 5 | 1.75 |
| 10% | 10 | 3.41 |
| 15% | 15 | 4.97 |
| 20% | 20 | 6.42 |
| 25% | 25 | 7.79 |
| 30% | 30 | 9.06 |
| 35% | 35 | 10.24 |
| 40% | 40 | 11.32 |
| 45% | 45 | 12.32 |
| 50% | 50 | 13.22 |
| 55% | 55 | 14.04 |
| 60% | 60 | 14.77 |
| 65% | 65 | 15.41 |
| 70% | 70 | 15.97 |
| 75% | 75 | 16.44 |
| 80% | 80 | 16.82 |
| 85% | 85 | 17.12 |
| 90% | 90 | 17.33 |
| 95% | 95 | 17.46 |
| 100% | 100 | 17.5 |
All length inputs and coordinate outputs use millimeters; areas are square centimeters, volumes are cubic centimeters, and mass is grams.
The hollow nose uses a radial wall-thickness subtraction, not a true normal offset from the outside surface.
How to use this calculator
- Choose the profile that matches the nose cone you want to draw or compare.
- Enter the nose length, base diameter, wall thickness, and shoulder dimensions in millimeters.
- Enter an effective material density that reflects the printed, molded, or filled part.
- Use the coordinate table for CAD points, then compare the mass and center of mass with the finished hardware.
How the nose cone geometry is calculated
The calculator treats the nose cone as a surface of revolution around its centerline. Let L be nose length, D be base diameter, R = D / 2, x be distance from the tip, and u = x / L. The selected profile supplies the outside radius y(x).
For a conical nose, y = R * u. For a tangent ogive, rho = (R^2 + L^2) / (2R) and y = sqrt(rho^2 - (L - x)^2) + R - rho. For an elliptical nose, y = R * sqrt(2u - u^2). Parabolic profiles use y = R(2u - K u^2) / (2 - K), with K = 0.5 for the 1/2 parabola and K = 1 for the full parabola. Power profiles use y = R * u^n, with n = 0.5 or 0.75.
For Haack-series profiles, theta = acos(1 - 2u) and y = R / sqrt(pi) * sqrt(theta - sin(2theta) / 2 + C sin(theta)^3). Von Karman uses C = 0, and LV-Haack uses C = 1/3. Very small negative values inside the square root can happen from floating-point rounding near the ends, so the calculator clamps those to zero.
The fineness ratio is F = L / D. The outside volume is Vo = pi * integral(y^2 dx), and wetted area is A = 2pi * integral(y * sqrt(1 + y'^2) dx). Those integrals are evaluated numerically with adaptive Simpson quadrature. For profiles with singular tip slope, the surface-area integration starts just aft of the tip and adds the tiny tip segment as a straight frustum so the derivative is not evaluated at x = 0.
Wall thickness, mass, and center of mass
The hollow nose uses a radial wall-thickness model: yi = max(y - t, 0). The inner nose volume is Vi = pi * integral(yi^2 dx). The shoulder is modeled as a hollow cylinder with material volume Vs = pi * Ls * (Rs^2 - Ri^2), where Ri = max(Rs - ts, 0). Total material volume is Vm = Vo - Vi + Vs, then mass is Vm converted to cubic centimeters times the entered density.
The center of mass is the first moment of the shell and shoulder divided by material volume: xcg = (pi * integral(x(y^2 - yi^2) dx) + Vs(L + Ls / 2)) / Vm. It is reported from the nose tip.
What moves the result most
Base diameter drives volume strongly because radius is squared in the volume integral. Wall thickness and effective density usually dominate the mass estimate for printed parts. Profile choice changes the volume distribution and base tangent angle, which can matter when you are matching a body tube, sanding a plug, or placing nose weight.
What this calculator leaves out
This is geometry and material planning, not an aerodynamic, structural, or flight-readiness analysis. It does not include bulkheads, eye bolts, ballast, glue, paint, printer over-extrusion, support material, surface finish, shrinkage, or recovery hardware. A radial wall is also not the same as a true normal offset, especially near the tip of steep profiles.
Worked example
With the default tangent-ogive nose, L = 100 mm and D = 35 mm, so R = 17.5 mm and the fineness ratio is 100 / 35 = 2.86. The tangent-ogive generating radius is (17.5^2 + 100^2) / (2 * 17.5) = 294.46 mm, and the base tangent angle is 0 degrees.
Using a 1.2 mm nose wall, a 25 mm shoulder with 33.5 mm outside diameter, 1.2 mm shoulder wall, and 1.24 g/cm3 material density, the calculator gives an outside nose volume of about 51.76 cm3, wetted area of about 74.64 cm2, internal cavity volume of about 62.35 cm3, material volume of about 11.45 cm3, mass of about 14.19 g, and assembly center of mass about 76.15 mm from the tip.
Common questions
What is a tangent-ogive nose cone?
A tangent-ogive nose cone is generated from a circular arc that meets the body tube tangent at the base. That means the side slope is zero where the nose meets the tube, which gives a smooth transition for a cylindrical body.
How is nose-cone fineness ratio calculated?
Fineness ratio is nose length divided by base diameter. A 100 mm nose on a 35 mm tube has a fineness ratio of 2.86. It is a shape descriptor, not a complete aerodynamic prediction.
Which nose-cone shape should I choose for a subsonic model rocket?
For many subsonic model rockets, a smooth ogive, elliptical, or parabolic nose is usually practical, and differences are often smaller than build quality, surface finish, and stability choices. Use this calculator to compare dimensions and mass, then use simulation software when performance matters.
How can I use the coordinate table in CAD?
The table lists axial distance from the tip and profile radius at 5% length intervals. Enter the points as a sketch curve, spline, or reference table, then revolve the profile around the centerline. Add your own shoulder details, tip treatment, and manufacturing clearances as needed.
What is the difference between Von Karman and LV-Haack profiles?
Both are Haack-series profiles. Von Karman uses the zero-drag-area form with the Haack constant set to zero, while LV-Haack uses a constant of one third. In this calculator that changes the radius distribution, volume, surface area, and center of mass for the same length and base diameter.
Does the estimated center of mass include recovery hardware or nose weight?
No. The center of mass includes only the modeled nose shell and hollow shoulder. Bulkheads, eye bolts, shock-cord anchors, ballast, paint, glue, and recovery hardware must be measured or added separately.