Model Rocket Stability & Fin Sizing Calculator

How the stability margin is calculated

This calculator uses the simplified Barrowman method for a slender, axisymmetric rocket with three or four conventional trapezoidal fins. It treats the nose and fin set as normal-force contributors, finds each component center of pressure, and combines them with a normal-force-weighted average.

Use one length unit throughout. Let d be body diameter, R = d / 2, Ln be nose length, N be fin count, Cr be root chord, Ct be tip chord, s be span, Xs be leading-edge sweep, Xf0 be the fin root leading-edge position, and Xcg be the loaded center of gravity from the nose tip.

The nose normal-force slope is CNa_n = 2. The nose CP is Xn = k * Ln, where k is 2/3 for a conical nose, 0.466 for a tangent ogive, 1/2 for a parabolic nose, and 1/3 for an elliptical nose.

The fin mid-chord line is lm = sqrt(s^2 + (Xs + (Ct - Cr) / 2)^2). The fin normal-force slope is CNa_f = (1 + R / (R + s)) * (4N(s / d)^2 / (1 + sqrt(1 + (2lm / (Cr + Ct))^2))). The fin CP is Xf = Xf0 + Xs(Cr + 2Ct) / (3(Cr + Ct)) + (Cr + Ct - CrCt / (Cr + Ct)) / 6.

The total center of pressure is Xcp = (CNa_n * Xn + CNa_f * Xf) / (CNa_n + CNa_f). The static stability margin is SM = (Xcp - Xcg) / d, expressed in calibers. A margin at or below zero is unstable, below one caliber is marginal, one to two calibers is a common design range, and a much larger value can make the rocket turn into the wind more strongly.

What moves the result most

Moving the loaded CG forward increases the margin. Larger fin span generally increases the fin normal force and pulls the combined CP aft toward the fin CP. Moving the fin set aft also helps. Nose shape matters, but the fin position and launch-ready balance usually dominate the practical decision.

Reverse fin sizing and ballast

For fin sizing, the calculator varies only s and uses bisection to find the smallest span that makes (Xcp - Xcg) / d meet the target. Root chord, tip chord, sweep, fin count, and fin location stay fixed. If the fin CP is not far enough aft, or the needed span is beyond the search bound, the result reports no span solution.

For ballast, the target CG is Xtarget = Xcp - T * d. The required mass is mb = M(Xcg - Xtarget) / (Xtarget - Xb), clamped to zero when the current CG already meets the target. Positive ballast only works when the ballast location is forward of the target CG.

What this calculator leaves out

The estimate omits body lift corrections, boattails, transitions, canards, tube fins, ring fins, fin thickness, fin flexibility, launch lugs, motor thrust alignment, wind, and dynamic stability. It is a small-angle static estimate, not a six-degree-of-freedom flight simulation.

Worked example

For the default rocket, the tangent-ogive nose is 100 mm long and the body diameter is 41.6 mm. Three fins have a 100 mm root chord, 50 mm tip chord, 60 mm span, 35 mm sweep, and root leading edge 350 mm from the nose tip. With the loaded CG at 290 mm, the Barrowman calculation gives a CP at about 341.95 mm.

The CG-to-CP distance is about 51.95 mm, so the static margin is 51.95 / 41.6 = 1.25 calibers. To reach a target of 1.5 calibers by fin span alone, the same planform needs about 72.91 mm of span. Nose ballast at 30 mm from the tip would need about 12.56 g, moving the CG to about 279.55 mm.