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NOTICE: When government or other drawings, specifications or other data are used for any purpose other than In connection vlth a definitely related government procurement operation, the U. S. Government thereby incurs no responsibility, nor any obligation whatsoever; and the fact that the Government may have formulated, furnished, or In any way supplied the said drawings, specifications, or other data Is not to be regarded by implication or otherwise as in any manner licensing the holder or any other person or corporation, or conveying any rights or permission to manufacture, use or sell any patented invention that may in any way be related thereto.. ! 7? 61-3-3 \l .7 MNnS _.

Introduct ion 13 Analysis 23 Assumptions Non-dimensionalizat ion 25 Equations of motion 26 Evaluation of stability derivatives Static derivatives Dynamic derivatives Evaluation of coefficients to stability quartic Characteristic equation in hovering Calculation of roots to the quartic and cubic equations for various flight configurations Approximate factorization of quartic Discussion Variation of quartic roots with tilt angle Effect of physical parameters Conclus ions Recommendations for further study 90 References Page A. Inflow ratio and induced velocity derivatives 137 B. Values of parameters and assumed lift-curve slope for Vertol 76 139 C. Determination of value for K from experimental data 141 D. Calculated values for all parameters 153 4 LIST OF FIGURES Page 1. Sketch showing velocity vectors at wing and definition of various angles 2. Forces acting on aircraft 95 3. Center of gravity movement with wing tilt 4. Graph of Z and 70as function of Lw 5. Charts of R and derivatives 6. Charts of () and derivatives 106 7, Forces acting at flapping hinge 113 8. Sketch showing velocity change at rotor due to pitching 114 9. Sketch defining velocity vectors and angles at tail 113 10. Aircraft in steady pull-up 115 11. Charts of trim conditions L16 12. Variation of roots of characteristic equation with wing tilt angle 122 13. Comparison of exact roots with approximations 123

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