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Nose Cone Trade Study

Aerodynamics Team

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Overview

Objective: Explore nose cone options and determine appropriate nose cone for the FAR 10k Competition Rocket

Topics:

  • Conical
  • Bi-Conic
  • Haack Series
  • Tangent Ogive/Secant Ogive
  • Elliptical
  • Parabolic
  • Power Series

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Speed

In order to determine the most aerodynamic nose cone, speed must be considered. Nose cone profiles perform differently at different speeds. For our purposes, hypersonic speed will still be analyzed for completeness, but not taken into consideration because our rocket will not reach such speeds. Our rocket will stay strictly in the subsonic region.

Mach Number provided by NASA Glenn Research Center [1]

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General Dimensions

L = overall length

R = radius of base

y = radius at x

x = any point along L (x = 0 at nose cone tip)

C/L = centerline

​

Image by G. Crowell Sr., “The Descriptive Geometry of Nose Cones” [2]

*All Equations are from G. Crowell Sr., “The Descriptive Geometry of Nose Cones”

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Conical

  • Equations:

​

  • Advantages:
    • Simple profile compared to others
    • Easy to perform calculations and manufacture
    • Tip can be rounded to decrease drag at subsonic speeds [3]
  • Disadvantages:
    • Although drag reduction is very high at hypersonic speeds, sharp cones do not perform well in subsonic/transonic [3]
    • Highly susceptible to heat at hypersonic speeds [3]
  • Longer nose cones have less drag but are more fragile [4]
  • Shorter nose cones have more drag but are sturdier [4]
  • OpenRocket estimated apogee: 3045 m

Coefficient of Drag vs Mach Number from RASAero

Render from SolidWorks

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Bi-Conic

  • Equations for :

​

  • Equations for :

​

  • Advantages
    • Same advantages of conical but sturdier and lower drag [6]
  • Disadvantages
    • Still has high drag for subsonic/transonic speed
    • Slightly more complicated to manufacture than Conical, but still easier than round cones

Image by Wikipedia, “Nose Cone Design” [7]

Image by G. Crowell Sr., “The Descriptive Geometry of Nose Cones” [2]

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HAACK Series

  • Equations:
  • Shape is designed for less drag
    • Is constructed not from geometric shapes, but derived mathematically for the purpose minimizing drag for a given Length and Diameter [5]
  • Base is not perfectly tangent to the body
    • Is so slight that it is not noticeable [5]
    • Except when C=⅔
  • Types
    • LD-Hacc (Von Kármán)
      • C=0
      • Gives minimum drag for the given length and diameter [5]
      • Performs well at transonic speeds (around Mach 0.8) [8]
    • LV-Hacc
      • C=⅓
      • Gives minimum drag for the given length and volume [5]
    • Tangent
      • C=⅔
      • Base is perfectly tangent to the body [5]

LD-Haack (Von Kármán) (C = 0)

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Tangent Ogive/Secant Ogive

Tangent Eq:

Secant Eq:

* with

* with

and

Secant Advantages & Disadvantages:

  • Can be preferable over conic for hypersonic because more volume for given base and length [7]
  • Harder to model mathematically [7]

Tangent Advantages & Disadvantages:

  • Compromise between structural integrity and drag and weight [7]
  • Easier to model than power series and secant ogive [7]
  • Good performance for hypersonic speeds [9]
  • Blunted ogive makes it more appealing for lower speeds
  • OpenRocket estimated apogee for tangent: 3386 m

tangent

secant

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Elliptical

Equation:

​

Advantages & Disadvantages:

  • good for subsonic flight [2]
  • popular in low-powered model rocketry due to good aerodynamics at low speeds [8]
  • not ideal for transonic or hypersonic flight [2]
  • OpenRocket estimate: 3159 m

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Parabolic

  • Equation:

where

  • Advantages
    • Performs well in subsonic/transonic (K’ = ¾ ) [8]
  • Disadvantages
    • Produces a sharp tip that will need to be blunted [4]
    • Not tangent to body [2]
    • Above factors contribute to difficult manufacturability
  • Parabolic shape is preferable over ogive for subsonic [9]
  • According to OpenRocket, best K’ for our rocket is ½ (3419 m).

Render from SolidWorks

Coefficient of Drag vs Mach Number from RASAero

K’ = ½

K’ = ¾

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Power

  • Equation:

where

  • Advantages
    • n = ½ and n = ¾ perform well in transonic [2]
    • Blunt tip if n < ~0.7 [2]
    • Relatively simple calculation and manufacturing
  • Disadvantages
    • Not tangent to body [2]
  • n will need to be calculated to determine what works best for our rocket.
  • According to OpenRocket, the best n for our rocket is n = 0.7 (3413 m).

Top: Render from SolidWorks

Bottom: Coefficient of Drag vs Mach Number from RASAero

n = ½

n = ¾

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References

[1] https://www.grc.nasa.gov/www/k-12/airplane/mach.html

[2] http://servidor.demec.ufpr.br/CFD/bibliografia/aerodinamica/Crowell_1996.pdf

[3] https://aviation.stackexchange.com/questions/24414/why-when-is-the-blunt-nose-better

[4] https://www.astro.rug.nl/~hoek/geometric-aerodynamics.pdf

[5] https://en.m.wikipedia.org/wiki/Nose_cone_design

[6] https://www.rrs.org/2022/06/25/biconic-nosecone-geometry-and-sizing/

[7] https://www.irjet.net/archives/V7/i8/IRJET-V7I8605.pdf

[8] https://themodelrocket.com/the-essential-guide-to-model-rocket-nose-cones/

[9] http://www.aerospaceweb.org/question/aerodynamics/q0151.shtml

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