Why thickness is the only lever that really works
The expression has thickness over root chord raised to the cube inside a square root, so the flutter speed goes as thickness to the power of 1.5. Take the defaults — a 4.7 by 2.4 in fin with a 2.4 in semispan, 0.125 in thick, from a sheet whose datasheet gives 350,000 psi of shear modulus, at 14.7 psi and 59 F — and the flutter speed comes out at 2,188 ft/s, which is Mach 1.96.
Go to 1/16 in stock instead and it collapses to 774 ft/s. That is not a small change for halving one dimension; it is a factor of 2.83, which is 2 to the power of 1.5, exactly as the exponent says. Go the other way to 3/16 and it is 4,020 ft/s.
Now compare that with the other terms. Twenty percent more shear modulus buys 9.5 percent on the speed, because stiffness only enters under the square root. Ten percent more semispan costs 12 percent, because the aspect ratio is cubed in the denominator and semispan drives it. And thirty percent less air pressure buys 20 percent. The rank order is stable: thickness first, planform second, material third.
The trap in the pressure term
Flutter speed goes as one over the square root of the local air pressure, which means a fin is hardest to flutter where the air is thinnest. People read that and conclude that the fast part of the flight is fine because it happens high up. It is the wrong way round for most rockets: the highest speed of a hobby flight arrives at burnout, which is low, in thick air, at the worst pressure of the whole trajectory.
So the number to put in is the pressure at burnout altitude, not at apogee. At 14.7 psi this fin flutters at 2,188 ft/s. Drop the pressure to 10 psi, which is a few thousand feet up, and it is 2,653 — but the rocket is going slower by then, so it never gets near either figure. The ratio to watch is speed over flutter speed at the same instant, and it peaks near burnout.
What the expression cannot know about your fin
It wants one shear modulus for an isotropic panel. Plywood and glass laminate are not isotropic, so there is no single correct value and the number you put in is a decision about which loading direction concerns you. Datasheet figures for sheet goods also vary by maker and by batch more than most people assume, and the page treats yours as an input for that reason rather than carrying a table of materials.
It also wants a flat panel of even thickness. A bevelled fin is 0.125 in in the middle and much less over the bevel, which the expression cannot see, and the direction of that error is unhelpful: the real speed is below the computed one. A fin attached by a fillet alone rather than through the wall is a softer panel than the expression assumes, and again flutters lower. And a fin that has been knocked on a previous landing is not the fin you calculated.
None of that makes the number useless. It makes it a comparison rather than a threshold. Run two fin designs through it and the ratio between them is meaningful. Read the absolute figure as a limit that something is safe below and you have used it for the one thing it cannot do.
The thing that gets designed out
The uncomfortable interaction is with stability. Fin area is what puts the centre of pressure aft, and semispan is the most efficient way to get it. But semispan is also what drives the aspect ratio, and the aspect ratio is cubed in the flutter denominator — so the change that most efficiently buys stability margin is the change that most efficiently costs flutter speed. Ten percent on the semispan is worth about a fifth of a calibre of margin on the airframe in the stability page and costs 12 percent of the flutter speed.
There is no way around that except thickness, which costs mass and drag and moves the balance point aft. Anyone who tells you fin design is straightforward has not run both pages on the same rocket.
Questions people ask
How thick do rocket fins need to be?
This page will not give you a number, because the answer depends on your material, your planform, the speed you expect and the margin your club works to — and because a thickness quoted without those is worthless. What it does instead is invert the arithmetic: give it a speed and a ratio you want, and it reports the thickness that reaches it for your fin and your material. At the defaults, wanting 1.5 times a 700 ft/s flight needs 0.077 in, against the 0.125 in in the field.
What is the difference between flutter and just breaking a fin?
A fin that breaks has been overloaded by a force. A fin that flutters has been fed energy by the airflow at its own natural frequency until the amplitude grows past what the material takes, and the force that finally breaks it can be far larger than the steady aerodynamic load. That is why flutter has a speed rather than a load, why it can happen suddenly with nothing else changed, and why stiffness matters more than strength for it.
What shear modulus should I use for plywood or fibreglass?
Whatever the datasheet for the sheet you bought says, in the direction you are worried about. There is no single right value, because neither plywood nor a glass laminate is isotropic and the expression assumes one that is. Sheet goods also vary by maker and batch. The 350,000 psi in the field is a placeholder to replace, not a statement about any product, which is why the page asks rather than looks it up.
Does the bevel on my fins change the answer?
Yes, and downward. The expression sees one thickness across the whole panel; a bevelled fin is at full stock only over the middle and thinner across the bevelled edges, so it is softer than the calculation assumes and flutters lower. There is no honest correction for it in this expression. If you bevel deeply, treat the computed speed as an optimistic bound rather than a figure.
Why does the flutter speed go up with altitude?
Because the aerodynamic energy feeding the oscillation scales with air pressure, and there is less of it up high. Flutter speed goes as one over the square root of pressure, so thin air is friendly. The catch is that the fastest part of a hobby flight is usually right after burnout, which is the lowest and thickest part of the fast section. Put in the pressure where the rocket is actually going fast, not the pressure at apogee.