Envelope expansion at 250 KEAS: 2.2% damping
A twin turboprop with a design dive speed VD of 250 KEAS at 15,000 ft is in flutter envelope expansion. The agreed go/no-go criterion is that damping of the wing/aileron mode must stay at or above 3% of critical with no rapidly worsening trend; if the criterion is violated, expansion stops and the aeroelastic model is revisited. Burst-pulse responses were obtained at 230, 240 and 250 KEAS at FL150, mid CG, clean configuration. Analysis gives 3.5%, 3.0% and, at 250 KEAS, a 6.15 Hz response whose peak of 0.42 g decays to 0.21 g after five complete cycles. The certification basis requires flutter-free flight to 1.15 VD at all altitudes and weights. The flight test team argues that 2% damping is normal at the edge of the envelope and wants to fly the 260 KEAS point tomorrow morning to complete the block. The chief engineer asks you for a written recommendation before the brief.
1. Reduce the 250 KEAS response to a damping ratio and say whether the agreed criterion is met. What checks would you make on the measurement itself?
Read the worked answer
Reduction. Peak-to-peak ratio over n = 5 cycles: A₀/A₅ = 0.42/0.21 = 2.00. Logarithmic decrement δ = (1/5) ln 2 = 0.693/5 = 0.1386. Damping ratio ζ = δ/√(4π² + δ²) ≈ δ/(2π) = 0.1386/6.283 = 0.0221, i.e. 2.2% of critical. (The exact expression gives 2.205% - no practical difference.)
Verdict: 2.2% is below the agreed 3% floor. On the agreed rule, expansion has already stopped at 250 KEAS, which is VD at this altitude.
Measurement checks before acting on it: the trace must be a clean single decaying sinusoid with no beating (beating means two close modes and invalidates a single-degree-of-freedom log-decrement reduction); confirm the pulse did not drive the actuator into a rate limit or clip; confirm the accelerometer is on primary structure, not a flexible panel; confirm the trigger amplitude was large enough to be above noise but small enough to stay linear.
Model cross-check: the frequency is essentially unchanged from the lower points, which is more consistent with a stiffness-coupled control-surface coalescence than with simple aerodynamic damping loss. If the model predicts, say, 4% at 250 KEAS and the aircraft delivers 2.2%, the model is non-conservative and must be corrected before further flight.
2. Use the trend in the three damping values to estimate where damping reaches zero, and assess the proposal to fly 260 KEAS against the required 1.15 VD clearance.
Read the worked answer
Successive slopes. 230→240 KEAS: (3.0 − 3.5)/10 = −0.05 %/kt. 240→250 KEAS: (3.0 − 2.2)/10 = −0.08 %/kt. The decline is accelerating, which is the classic signature of approaching a flutter boundary - damping falls faster than linearly as mode coalescence is neared.
Extrapolation on the last slope: zero damping at ≈ 250 + 2.2/0.08 = 277 KEAS. Required clearance is 1.15 × 250 = 287.5 KEAS. Even this optimistic straight-line projection places the boundary 10 kt inside the speed range that must be shown flutter-free, with no margin at all rather than a positive one. Using the average slope (−0.065 %/kt) gives ≈ 284 KEAS, still short.
260 KEAS: predicted damping 2.2 − 0.08 × 10 = 1.4%, roughly half the criterion, with the boundary only ~17 kt away. The point buys no certification credit and adds risk, so the answer is no.
Why the truth may be worse than the line: the extrapolation assumes the same mode and mechanism persist, that no nonlinearity (freeplay, actuator rate limit, separation) enters, and that 15,000 ft is the critical altitude. None of the three is yet demonstrated.
3. What technical and procedural actions do you recommend before any further flight, and what evidence would change your conclusion?
Read the worked answer
Immediate. Do not fly the 260 KEAS point. Declare a temporary limitation - VMO reduced to a speed with demonstrated damping of 3% or better, e.g. 240 KEAS - and put it in writing before the morning brief. Notify the head of airworthiness and the certification authority or ODA under the agreed test-readiness procedure. The agreed rule says expansion stops on criterion violation; the schedule does not override it.
Engineering. A ground vibration test in the flight configuration (control surfaces installed, representative fuel and stores) to update the stiffness and mass idealisation; check aileron mass balance and control-circuit freeplay against drawing limits; reconcile the model's predicted trend with the three measured points. A fix (mass balance, ballast, local stiffness, or added damping) is then required, followed by an updated analysis and a repeat GVT.
Resumption. Restart from a speed with at least 3% damping in 5-kt increments, and repeat across the altitude envelope, at forward and aft CG, and with any external stores - the 15,000 ft clean point is unlikely to be the critical case.
Evidence that would change the conclusion: a validated measurement artefact (beating, rate limit, instrumented panel) that invalidates the 2.2% value; a GVT-based model that reproduces 3.5–3.0% at 230–240 KEAS and explains 2.2% at 250 by a mechanism that does not lead to coalescence; or a demonstrated boundary above 287.5 KEAS with positive damping throughout.