THE DETERMINATION OF AERODYNAMIC STABILITY COEFFICIENTS FROM SOUNDING ROCKET FLIGHT DATA

More demanding requirements f o r sounding rocket accuracy aiid flight stability, and an increasing number of flight failures have caused a recent re-examination of actual rocket flight performance. The twin t e r ro r s of Magnus Instability'and Catastrophic Yaw, which plague conventional ordnance, also stalk rockets. Investigations of the non-linear dynamic behavior of sounding rockets have been undertaken by using'a computer program for numerically integrating the six-degree-of-freedom equations of motion. The use of this computer program has made possible the comparison of experimental and analytical determinations of the flight performance of sounding rockets. A l s o , it has provided a better understanding of noli-linear effects and, most important, it has provided new methods for the analysis of flight data. Accurate angular orientation data obtained from the free flight telemetry records of two Tomahawk sounding rockets has k e n "fitted" by the Quadracyclic Theory using a special formulation of the \lethod of Differential Corrections. The exact motion of the rockets and thcir associated aerodynamic stability coefficients, CLw , C v q + GuCi and CM c! have been determined. coefficients obtained from the flight data a r e compared with wind tunnel values. the earth's atmosphere. In the othercase, the rocket was re-entering the earth's atmosphere. In both cases , the Magnus Moment is shown to play a major role in the clynamic stability of the sounding rocket. able f o r detailed analysis of (:atastropliic Yaw, special dynamic wind tunnel tests were carr ied out which demonstrate that Roll Lock-In can occur in P K' Where possible the aerodynamic stability In onc case , the Tomahawk rocket was exiting If'hjle no sounding rocket flight data was availIhc>cke'i t i c supersonic spmk . INI'KODUCTION By the end of World War 11, a considerable su r plus of rocket motors had accumulated. Thus, it was possible to initiate a program for the scientific sounding of the earth 's upper atmosphere. a s today, was to place a scientific instrument to a s high an altitude as possible. The aim was high altitude, not high accuracy. A wobbling motion of the payload was relatively unimportant. For a given rocket motor, maximum altitude was reached by minimizing the total weight of the sounding rocket. Over reducing the weight of the motor case resulted in dramatic explosions. However reduction of the weight of the stabilizing f ins , by reducing their a rea , caused no such dramatic consequences, unless, of course, the static m a r gin was decreased to zero, thereby causing the rocket to tumble. These minimum fins, however, often caused the rocket to fail to reach the desired altitude due to the drag from the resulting wobbling motion and ' also caused the rocket to be quite inaccurate. poor launchings would have been classed a s flight failures, however, the scientific investigators were not unduly concerned since their experiments did yield data on the upper atmosphere and, also, the accuracy of the trajectory was quite unimportant;except , when the rocket returned to inhabited areas , which was not infrequent. Xerodyiiamically speaking, the usual sounding rocket static margins were an order of magnitude smaller than the minimums permitted on conventional ordnance. Ordnance static margins run between 20% to XP) of missile length. Sounding rockt static margins a re often a s small a s 2% or 3%. This same situation exists even today. perform a s well a s they do. l 'he primary reason for this unnatural success, in spite of the poor a e r o d ~ ~ ~ a m i c s , is due to 111e fact that the acccleration of the souiiding rocket during burning i d quite Jyiiaiiiically stabilizing. However ~ as the c;ounding rocket leaves the cai-ths atmosphere thc nutotioiin~ motion often builds up t u a large conilig to the decreasing density of the atmosphere. inore sophisticated and large wobbling mrttio have become unacceptable. Also, soundiiig rockets ha\re become larger and more expensive. E ,astly, The primary purpose of these early launchings, In normal ordnance practice these particular In this light, it is amazing that sounding rockets In recent years scientific payloads hnoc become