METHODOLOGY

Stability Analysis

The Barrowman Method for calculating Center of Pressure (CP) and determining rocket stability margin.

01

Static Stability

Rocket stability is determined by the relative positions of the Center of Pressure (CP) and Center of Gravity (CG). A stable rocket has its CG forward of its CP, creating a restoring moment when disturbed.

CG— must be forward (closer to nose)
CP— must be aft (closer to tail)

When a stable rocket is disturbed (e.g., by a gust), aerodynamic forces at the CP create a moment that rotates the rocket back toward its original trajectory.

02

Stability Margin

The stability margin is the distance between CG and CP, typically expressed in calibers (body diameters):

Eq. 1
Stability Margin=CPposition−CGpositionDbody\text{Stability Margin} = \frac{CP_{position} - CG_{position}}{D_{body}}
Margin (cal)StatusRecommendation
≥ 1.5STABLERecommended for most rockets
1.0 – 1.5MARGINALMay be acceptable with care
< 1.0UNSTABLERocket will tumble, needs redesign

Overstability

A stability margin greater than 3 calibers can cause weathercocking in windy conditions, where the rocket turns into the wind instead of flying straight up.
03

The Barrowman Method

The Barrowman Method, developed by James S. Barrowman in 1967, calculates CP by summing the contributions of individual rocket components. Each component contributes:

Normal Force

CN

How much lift it generates

CP Location

X_CP

Where that force acts

The total CP is a weighted average of all component contributions:

Eq. 2
CPtotal=∑(CNi×CPi)∑CNiCP_{total} = \frac{\sum (CN_i \times CP_i)}{\sum CN_i}
04

Component Contributions

Nose Cone

The nose cone is the primary destabilizing component — its CP is far forward.

Normal Force
CNnose=2×sin⁡(α)CN_{nose} = 2 \times \sin(\alpha)
Nose TypeCP Position
Ogive0.466 × L_nose
Conical0.667 × L_nose
Parabolic0.500 × L_nose
Von Karman0.466 × L_nose

Fins

The fins are the primary stabilizing component — their CP is far aft.

Fin Normal Force
CNα,fins=Kfb×4n(s/D)21+1+(2s/(cr+ct))2CN_{\alpha,fins} = K_{fb} \times \frac{4n(s/D)^2}{1 + \sqrt{1 + (2s/(c_r+c_t))^2}}
KfbK_{fb}Body-fin interference factornnNumber of finsssFin semi-spanDDBody diametercrc_rRoot chordctc_tTip chord

The body-fin interference factor accounts for the interaction between the body tube and fins:

Interference Factor
Kfb=1+rs+rK_{fb} = 1 + \frac{r}{s + r}
05

Angle of Attack Effects

CP position varies with angle of attack (AoA):

At 0° AoA

Geometry

CP from shape only

As AoA ↑

Forward

Body contribution grows

At 90° AoA

Center

Approaches geometric center

Full AoA Sweep

This is why our stability calculator computes CP from 0° to 90° in 1° steps, not just at 0°. The full sweep shows how stability changes under various flight conditions.
CP vs AoA
CP(α)=CNnose×CPnose+CNbody×CPbody+CNfins×CPfinsCNtotalCP(\alpha) = \frac{CN_{nose} \times CP_{nose} + CN_{body} \times CP_{body} + CN_{fins} \times CP_{fins}}{CN_{total}}
06

Design Guidelines

To Increase Stability (Move CP Aft)

  • Larger fins — increase span and/or chord
  • More fins — 4 fins more stable than 3
  • Move fins aft — maximize moment arm
  • Add sweep — moves fin CP aft
  • Add nose weight — moves CG forward

To Decrease Stability (Move CP Forward)

  • Smaller fins
  • Add tail weight — moves CG aft
  • Shorter body tube

Unstable Rocket

If your rocket has a stability margin below 1.0 calibers, it will tumble during flight. Add nose weight or increase fin size before flying.

SOURCES

References

Academic Papers

  • The Practical Calculation of the Aerodynamic Characteristics of Slender Finned Vehicles — Barrowman, J.S. (1967)

    The original Barrowman Method thesis - foundational for all CP calculations

  • The Theoretical Prediction of the Center of Pressure — Barrowman, J.S. & Barrowman, J.A. (1966)

    Earlier paper establishing CP calculation theory

Textbooks

  • Topics in Advanced Model Rocketry — Mandell, G., Caporaso, G., & Bengen, W. (1973)

    Classic reference covering stability, drag, and trajectory analysis

  • Handbook of Model Rocketry — Stine, G.H. (2004)

    7th Edition - Standard hobbyist reference with stability guidelines

Tools & Calculators

Try the Calculator

Put this methodology into practice with the interactive calculator.

Open Stability Calculator