Overview
Flutter is a self-excited vibration: a fin’s bending and twisting modes couple with the airflow and draw energy from it until the fin breaks, often in a fraction of a second. Martin’s 1958 NACA note distilled flight and wind-tunnel experience into a working estimate of the speed at which it starts. Bennett (2023) re-derived the amateur-rocketry form of it, corrected a factor of two that earlier newsletter articles introduced, and showed how the fin’s centroid changes a constant Martin had fixed.
The calculator evaluates the flutter speed at every point of your flight (or at the point of maximum velocity), finds the worst point, compares it with your speed and tells you what to change. It is an estimate for preliminary design, not a guarantee.
The flutter speed
where a is the speed of sound and p the pressure at the altitude considered, p_0=14.696 psi, G the shear modulus of the fin, \kappa=1.4. With \varepsilon=0.25, DN=39.294 psi, which Martin rounded to 39.3. Any consistent units can be used; G, p_0 and DN must share the pressure unit.
The widely copied “1.337” form is not used. 1.337 is 39.3/14.696/2, but those articles divided by two once more, which overstates V_f by \sqrt2 (Bennett). This matters because the overstated speed is unsafe.
Panel geometry
for one exposed panel, with b the semi-span (RockSim) or height (OpenRocket). The thickness ratio uses the root chord (Bennett, and altimetercloud.com). For an elliptical fin use the trapezoid of the same root chord, span and area: tip chord c_T=2S/b-c_R. If the thickness tapers, use its average or the value at mid-span.
Centroid correction
Martin’s 39.3 assumes the fin’s centroid is half a chord behind the leading edge, i.e. \varepsilon=0.25 chord behind the quarter chord. For a swept trapezoid with sweep length m (root leading edge to tip leading edge, along the body), Bennett gives
A swept fin has \varepsilon>0.25, a larger DN and a lower flutter speed (Bennett’s example: \varepsilon=0.349, DN=54.88 psi, 40 % above 39.3). A centroid ahead of mid-chord would give \varepsilon<0.25 and a higher speed; the calculator does not credit that and uses 0.25.
Atmosphere
Bennett’s standard atmosphere for the troposphere: temperature falls 0.00356 °F per foot from the sea-level value,
with h above sea level. The calculator ties the lapse line to your launch-site temperature, T_{SL}=T_0+0.00356\,h_0, so a standard site gives exactly T_{SL}=59 °F. Above 36 089 ft, where Bennett’s equations stop, the standard isothermal layer continues the pressure. Hot days lower the flutter speed (higher speed of sound, but much higher pressure); the calculator reports the safety factor on a day 20 °F hotter.
Bennett’s own hot-day numbers (1580 and 2077 ft/s) put the site temperature in as the sea-level value and use the altitude above ground, i.e. they treat the site as if it were at sea level; that is a little more pessimistic than the lapse-line method above.
Shear modulus
The shear modulus dominates the answer, and is the least certain input. Bennett’s suggested working values, chosen with margin (psi): balsa 33 359; birch aircraft plywood 89 000; G10/G12 fibreglass 600 000; carbon-fibre epoxy 600 000; 6061-T6 aluminium 3 800 000; 6Al-4V titanium 6 200 000; 4130 steel 12 000 000. Measured values for G10 range from 425 000 to 1 700 000 psi; in-plane shear of a laminate depends mostly on the epoxy, so carbon and glass behave alike. From Young’s modulus and Poisson’s ratio, G=E/(2(1+\nu)), which overestimates G for composites. For tip-to-tip reinforcement Bennett suggests doubling G as a rough allowance.
The calculator also offers the bulk materials of OpenRocket’s database with their in-plane shear modulus (OpenRocket core Databases.java, the commit that added the shear modulus; its comments cite MatWeb, designerdata.nl, Peak of Flight 615 and wood-handbook ratios). Those values are listed as given there, not independently checked here. The woods, plywood, fibreglass and balsa agree with Bennett’s working values. The 3D-printed plastics (PLA, PETG, ABS, ASA at 100 % infill) are indicative only: a printed fin’s stiffness depends on orientation, layer bonding and temperature, and the calculator warns about it.
The flight
Flutter is most likely low in dense air at high speed — usually at motor burnout. Give either the maximum velocity and its altitude above the launch site, or a flight profile (altitude above ground and speed at several points); the calculator evaluates every point and reports the worst. “Fill from the Trajectory Simulation” runs that calculator with your saved inputs and takes its speed and altitude history.
Safety factor and verdict
| Verdict | Condition | Source |
|---|---|---|
| UNSAFE | SF<1.2 | Bennett: a margin under 20 % is “potentially unsafe”; altimetercloud.com: below 1.2 “danger”. |
| MARGINAL | 1.2\le SF< target | Bennett: under 25 % is “a poor risk”. |
| SAFE | SF\ge target | Target default 1.5 — altimetercloud.com’s minimum recommendation; raised to 2 when the flight is supersonic (altimetercloud.com). |
The target can be raised; it is never lowered below 2 for a supersonic flight. These thresholds are judgement from the two sources, not from Martin.
What to change
Because V_f\propto t^{3/2} and V_f\propto\sqrt G exactly, the thickness and shear modulus that reach a target safety factor at the worst point are
The semi-span enters through the aspect ratio and the area, so the longest span is found by bisection (the safety factor falls monotonically as the span grows). The Explore section also ranks the inputs by how much ±10 % of each moves the safety factor; thickness and span usually dominate, then the material.
Cross-checks
- Bennett’s worked example (7.5 in root, 2.5 in tip, 3 in span, 4.285 in sweep, G10, 1500 ft/s at 18 500 ft ASL): the tests reproduce C_x=4.49 in, \varepsilon=0.349, DN=54.88, −6.86 °F, 1043.36 ft/s, 7.2 psi, and V_f= 1425, 1991.7 and 2618.1 ft/s for 1/8, 5/32 and 3/16 in, and his hot-day figures with his method.
- altimetercloud.com (formula read from its page code on 25 October 2026): V_f=a\sqrt{G(t/c)^3/(1.337\,A^3p\,(\lambda+1)/2)}. It has no (A+2) term and no centroid correction, so it equals Martin’s form times \sqrt{2/(A+2)} for a symmetric fin (lower by 12 % at A=0.6, 29 % at A=2). The tests reproduce its code for three designs; the calculator shows its value in Explore. The tool could not be queried interactively, so its code is the reference.
- FLUTTER MARGIN1 (Hoult’s workbook): t/c on the chord at 75 % span and DN=39.3, which is less conservative for tapered or swept fins; reproduced to 12 digits and shown in Explore.
Assumptions and limits
- An estimate for preliminary design (Martin’s stated purpose), not a guarantee: keep a margin.
- Flat plates of constant thickness, trapezoidal (or equivalent) planform, cantilevered rigidly from the body. Fin–body flexibility, attachment, fin cans and tip-to-tip layups are not modelled.
- Validated to about Mach 1.5 (Bennett); beyond is extrapolation.
- Bennett’s atmosphere is tropospheric (below about 36 000 ft); the calculator continues it isothermally.
- Each panel is independent; the number of fins does not enter.
- Not verified in this build: Martin’s NACA TN 4197 itself was not available; its form and constants are taken from Bennett’s restatement. (Bennett’s reference list prints “TN 4917”; the note is TN 4197.)
References
- J. K. Bennett, “Fin Flutter Analysis Revisited (Again),” Peak of Flight newsletter 615, Apogee Components, 19 December 2023. PDF ↗
- Altimeter Cloud, “Rocket Fin Flutter Calculator,” altimetercloud.com (formula and thresholds read 25 October 2026). Page ↗
- D. J. Martin, “Summary of Flutter Experiences as a Guide to the Preliminary Design of Lifting Surfaces on Missiles,” NACA TN 4197, 1958 — through Bennett.
- C. P. Hoult, FLUTTER MARGIN1 workbook (RS&T) — the previous version of this calculator.