Center of Pressure vs Center of Gravity Stability Calculator

Stability margin is the distance from the center of gravity (CG) to the center of pressure (CP), expressed as a multiple of the body diameter. A margin of 1.5 calibers means CP is 1.5 body diameters behind CG. The caliber unit normalizes margin for rockets of different sizes, so a 1.5-caliber margin is equally stable for a 29 mm tube and a 150 mm tube.

Most rocketry organizations recommend 1 to 2 calibers of static stability margin for typical model and high-power rockets. Below 1 caliber, the rocket is sensitive to crosswind gusts and small CG shifts from motor burn-through. Above 3 calibers, the rocket may weathercock aggressively into the wind and fly a curved path. Competition rockets targeting maximum altitude often fly at 1.0 to 1.3 calibers to minimize weathercocking drag.

The center of pressure is the point along the rocket body where the net aerodynamic side force acts when the rocket flies at a small angle of attack. It is determined by the shape of every surface exposed to airflow: nosecone, fins, and body transitions. CP is not fixed; it shifts forward at transonic speeds and changes slightly with angle of attack. The Barrowman equations give the linear, subsonic CP position used for design and stability checking.

The center of gravity is the point along the rocket's axis where the entire mass of the vehicle is effectively concentrated. It shifts during flight as propellant is consumed, typically moving aft (rearward) on solid-motor rockets as the dense motor casing empties forward of the fins. Always check CG at both the loaded (full propellant) and burnout states. The worst-case stability margin usually occurs at burnout when CG has shifted aft the most.

The Barrowman equations are a set of closed-form aerodynamic equations published by James Barrowman in 1966 for estimating the subsonic center of pressure of slender fin-stabilized rockets. They treat each component separately: nosecone contributes CN = 2.0 with CP at a fraction of its length from the tip; fins contribute CN and CP based on fin count, span, chord lengths, and sweep. The total CP is the weighted average of all component CPs. Barrowman's method is the foundation of all major model rocketry simulation tools including OpenRocket and RASAero.

In rocketry, one caliber equals one body diameter at the maximum diameter of the rocket. If a rocket has a 66 mm airframe, one caliber is 66 mm. Stability margin in calibers equals (X_CP - X_CG) divided by body diameter. Using calibers instead of absolute length makes the margin comparable across rocket sizes: both a 24 mm sport rocket and a 98 mm high-power rocket are considered stable at 1.5 calibers despite having very different physical CP-to-CG separations.

When a stable rocket tilts slightly off course, aerodynamic forces act at the CP and create a restoring torque about the CG that pushes the nose back toward the flight direction. If CP were ahead of CG, the same aerodynamic forces would create a destabilizing torque that would push the nose further off-axis, causing the rocket to tumble. This is the same principle that makes a dart or shuttlecock stable: heavy forward tip (CG) and lightweight feathered tail (CP near the back).

Larger fins increase the fin normal force coefficient CN_fins, which moves the total CP backward toward the fin group. The CP shift is proportional to the square of the fin semi-span divided by body diameter: larger span or smaller body diameter moves CP backward faster. Doubling the fin span roughly quadruples the fin CN contribution. Adding more fins (3 vs 4) also increases CN proportionally but does not change the per-fin CP location.

Over-stability occurs when the stability margin exceeds about 2.5 to 3 calibers. An over-stable rocket is very sensitive to crosswind: any side gust produces a large restoring torque that turns the nose aggressively into the wind. Instead of flying a straight path, the rocket weathercocks and flies an arcing trajectory that reduces apogee altitude and makes landing prediction difficult. Competition altimeter rockets are deliberately designed near the 1 to 1.5 caliber range to minimize weathercocking.

The simplified Barrowman equations are accurate to within 5 to 10 percent for typical sport rockets at subsonic speeds below Mach 0.6. Accuracy decreases for: body fineness ratios below 5 (stubby rockets), large body-to-fin diameter transitions, thick fins with rounded leading edges, and flights above Mach 0.8 where transonic effects shift CP forward. For high-performance rockets above Mach 0.6, use OpenRocket or RASAero with full Barrowman plus transonic corrections.

Yes, sweep changes both the fin normal force coefficient and the CP position. A swept fin with the same span and chord has a slightly lower CN than an unswept fin of the same planform area because the effective aspect ratio is lower. The CP of a swept fin is also further aft than an unswept fin of the same root chord length. Net effect: moderate sweep (15 to 30 degrees) tends to move the fin CP backward, which improves stability margin, but with diminishing returns at higher sweep angles.

Run the Barrowman Estimator for each stage independently using the mass and geometry of that stage at ignition (with the upper stage still attached for the lower stage, detached for the upper stage). The lower stage stability must be checked with the full rocket mass above it, since the upper stage shifts CG forward. The upper stage is typically analyzed separately at its own ignition point after stage separation. Both stages must individually satisfy the 1 to 2 caliber stability target.