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From the Rolls-Royce experimental archive: a quarter of a million communications from Rolls-Royce, 1906 to 1960's. Documents from the Sir Henry Royce Memorial Foundation (SHRMF).
Technical table of coefficients for calculating torsional vibrations in V-engines with 60, 65, 80, and 90 degree bank angles.

Identifier  ExFiles\Box 179\2\  img219
Date  10th February 1932 guessed
  
VEE ENGINES — TORSIONAL VIBRATIONS
Sin nπ/B

60° 65° 80° 90°
n ω *θ/N *Z n ω *θ/N *Z n ω *θ/N *Z n ω *θ/N *Z
1.414 1.77 82.5 1.5 1.89 60 1.730 2.18 45 1.78 2.24
1.0 .16 17.5 1.98 .84 200 .318 .06 180 0 0 0
1.932 1.32 0 .26 1.35 340 1.97 1.34 315 1.78 1.21
0 0 165 .26 1.12 120 1.0 4.33 90 1.42 6.15
1.932 1.32 312.5 1.84 1.26 260 1.284 .88 225 .77 .52
1.0 .16 100 1.28 .20 40 1.88 .30 0 2 .32
1.414 1.78 247.5 1.11 1.39 180 0 0 135 .77 .97
1.732 .25 35 .77 .12 320 .684 .11 270 1.42 .23
.517 .35 182.5 .04 .03 100 1.284 .87 45 1.78 1.21
2.0 8.66 330 1.94 8.40 240 1.0 4.33 180 0 0
.517 .35 117.5 1.04 .71 20 1.970 1.34 315 1.78 1.22
1.732 .28 265 1.76 .28 160 .348 .05 90 1.42 .23
1.414 1.77 52.5 1.80 2.28 300 1.732 2.16 225 .77 .97
1.0 .16 200 1.76 .03 80 1.42 .23 0 2 .32
1.932 1.32 347.5 1.99 1.36 220 .684 .46 135 .77 .52
0 0 135 .76 3.30 0 2 8.66 220 1.42 6.14
1.932 1.32 282.5 1.58 .11 140 .684 .46 45 1.78 1.21
1.0 .16 70 1.84 .30 280 1.42 .22 180 0 0
1.414 1.77 217.5 .65 .82 60 1.732 .216 315 1.78 .224
1.732 .28 5 2 .32 200 .348 .05 90 1.42 .22
.517 .35 152.5 .48 .33 340 1.970 1.34 225 .77 .53
2.0 8.66 300 1.732 7.50 120 1.0 4.33 0 2 8.66

THE COLUMNS MARKED * WOULD IF MULTIPLIED BY THE MAGNITUDE OF THE APPROPRIATE HARMONIC OF THE GAS AND INERTIA TORQUE BE AN EXACT CRITERION OF THE SEVERITY OF THE TORSIONAL PERIODS. AS THEY STAND THEY ARE DIRECTLY COMPARABLE ALONG THE HORIZONTAL LINES BUT NOT ALONG THE VERTICAL COLUMNS. THIS TABLE SHOWS THEREFORE THE RELATIVE IMPORTANCE OF ONE PARTICULAR VIBRATION WHEN THE VEE ANGLE OF THE ENGINE IS VARIED. THE IMPORTANT VIBRATIONS ARE UNDERLINED.

nφ/B IS A NON-DIMENSIONAL COEFFICIENT DEPENDING ON THE DEFLECTION CURVE OF THE CRANKSHAFT.
φ/B IS THE ANGLE OF LAG OF ONE BANK OF CYLINDERS BEHIND THE OTHER.
Z IS THE COMBINED EFFECT OF BOTH BANKS.
  
  


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