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Flight-by-flight fatigue spectrum of a four-engine transport from the VGH gust and maneuver counts of NASA Memorandum 1-17-59L

Tool	Fatigue Spectrum Generation
Source	Engel, J. N., and Copp, M. R. (1959). Analysis of Acceleration, Airspeed, and Gust-Velocity Data From a Four-Engine Transport Airplane Operating Over a Northwestern United States–Alaska Route. NASA Memorandum 1-17-59L, National Aeronautics and Space Administration, Washington, DC. Tables I and II(a); Gallagher, J. P., Giessler, F. J., Berens, A. P., and Engle, R. M. (1984). USAF Damage Tolerant Design Handbook. AFWAL-TR-82-3073, section 5.4.2, Table 5.4.1 and Example 5.4.1.
Level	Professional

Problem

A transport's VGH records over 263 flights (672.9 hours) give the gust accelerations above 0.3 g by flight condition (climb 161 in 57.5 h, en route 909 in 490.8 h, descent 944 in 124.6 h, in 0.1 g classes) and the operational maneuvers (13,339 in 672.9 h, positive and negative). Taking a wing lower-skin point whose stress is proportional to the load factor with 1-g stresses of 13, 12 and 11 ksi in the three segments, a ground stress of −2 ksi, 10 taxi cycles of ±1 ksi per flight and a landing impact of −4 ksi, build the flight-by-flight stress sequence of a 100-flight block with 0.3 g gust omission, 0.8 g clipping, 0.2 g maneuver omission and 0.5 g maneuver clipping, check that its peaks reproduce the exceedance table, and rainflow count it.

Inputs to Enter

Segments: Climb 0.2186 h, 136 kt, S_1g 13 ksi, curve A; En route 1.8662 h, 164 kt, 12 ksi, curve B; Descent 0.4738 h, 168 kt, 11 ksi, curve C; maneuver curve M on every segment; stress per g = S_1g
Curves A, B, C: Table I class counts ÷ hours as exceedances per 1,000 flight hours, positive and negative peaks combined (A: 0.3 g 2,800, 0.4 g 608.7, 0.5 g 313.0, 0.6 g 86.96, 0.7 g 34.78, 0.8 g 0; B: 1,852 … 2.04 at 0.8 g; C: 7,576 … 16.05 at 0.8 g); curve M: Table II(a) per 1,000 h, +0.1 g 9,257 … +0.5 g 4.46, −0.1 g 10,566 … −0.4 g 1.49
Levels: equal 0.1 g steps, gust omission 0.3 g, clipping 0.8 g, maneuver omission 0.2 g, clipping 0.5 g; ground −2 ksi, 10 taxi cycles of 1 ksi amplitude, landing −4 ksi; 100 flights per block, seed 1, random order within a segment

Open the Fatigue Spectrum Generation tool (loaded with this example)

Answers

Occurrences by differencing (Table 5.4.1): en route band 0.3–0.4 g carries (1,852.08 − 273.02) per 1,000 h × 1.8662 h ÷ 2 = 1.473 cycles per flight; expected gust and maneuver cycles per flight 6.529, omitted below the omission levels 48.0 per flight
100-flight block (cumulative rounding from the top): climb gusts 24/4/2/1/0, en route 148/18/5/1/1/0, descent 147/23/7/1/1/0 cycles at 0.35 … 0.80 g; 653 gust and maneuver cycles, 1,000 taxi cycles
Sequence: 3,238 reversals, largest stress 21.45 ksi (a 0.75 g climb gust at 13 ksi), smallest −4 ksi (landing), 100 ground-air-ground cycles of mean range 20.89 ksi; the sequence's peaks per segment equal the block table (43 / 276 / 205)
Rainflow of the block (ASTM E1049 §5.4.5): 1,619 cycles = half the reversals; 442 cycles with range ≥ 4 ksi, 116 ≥ 10 ksi, 86 ≥ 20 ksi, 16 ≥ 22 ksi; the 100 largest are the ground-air-ground cycles from the flight peaks to −4 ksi
Regenerating the Memorandum's own 263 flights from the same curves returns its printed class counts exactly (1,676 / 237 / 78 / 12 / 8 / 3 gusts, 13,339 maneuvers) when the curves are counted as cycles

Notes

The tool's default inputs are this mission; press Submit. The exceedance data are the Memorandum's; the stresses and ground loads are illustrative. Every number above is reproduced by test_fatigue_spectrum_generation.php (186 checks) and by an independent numpy implementation of the generator (References/Fatigue-Spectrum/checks/specgen_check.py), which gives the same 3,238-point sequence from seed 1.