- Joined
- Jun 7, 2011
- Messages
- 260
- Reaction score
- 264
Attached below are RASAero II predictions for Subsonic, Transonic, and Supersonic Center of Pressure (CP) compared to wind tunnel data for two configurations of the ARCAS sounding rocket (ARCAS Short and ARCAS Long). The Supersonic wind tunnel data is up to Mach 4.63, approaching Hypersonic (Mach 5). The wind tunnel data is from NASA TN D-4013 and TN D-4014.
Slides 2-4 present the wind tunnel model configurations, and Slide 5-6 show the two ARCAS configurations entered into RASAero II.
The RASAero II CP (and CD) predictions are compared to the Subsonic, Transonic, and low Supersonic wind tunnel data for the ARCAS Short and ARCAS Long configurations on Slides 8 and 9. With the boattail only on part of the fin root, the exact way to implement the Barrowman Method is somewhat up to debate. The method used in RASAero II is to calculate the volume of the cylinder and the part of the boattail that are under the fin root, and then calculate the diameter of a cylinder of the same length that has the same volume. The diameter of this cylinder is now the diameter of the rocket body under the fins, and the fins are projected toward the centerline of the rocket until they intersect that cylinder. Thus the RASAero II Barrowman Method results are labeled on the graphs on Slide 8 and 9 as RASAero II Implementation of the Barrowman Method.
Note on Slides 8 and 9 that the Rogers Modified Barrowman Method and the Barrowman Method (as implemented in RASAero II) give similar results, very similar results in the case of the ARCAS Long configuration. Generally the Rogers Modified Barrowman Method is more accurate than the Barrowman Method, but in many cases the Rogers Modified Barrowman and Barrowman Methods will produce similar results, as shown here. This is because Barrowman left off additional normal force at the nose and the tail, but since he missed additional normal force at both the nose and tail, more accurate methods will in many cases produce surprisingly small changes in the CP. For these particular two cases (ARCAS Short and ARCAS Long), the Barrowman Method was more accurate, although the two predictions were close, very close for the ARCAS Long configuration. Both methods got very close to the Subsonic CP for the ARCAS Long configuration.
Note for the ARCAS Long configuration wind tunnel data on Slide 9 the unusual forward movement of the CP at Transonic, and then the CP moves aft again going into low Supersonic. The ARCAS Short configuration wind tunnel data on Slide 8 shows a more typical looking CP curve with Mach number, where the CP moves aft Transonic, and then for Supersonic the CP starts moving forward with increasing Mach number. This illustrates why you want to have an additional 1.0 calibers stability margin on top of the bare minimum 1.0 calibers stability margin, for a total stability margin of 2.0 calibers, at Supersonic Mach numbers to cover for possible CP mispredictions like shown on Slide 9. Hence the 2.0 calibers stability warning message for Supersonic Mach numbers built into RASAero II.
Slides 10 and 11 show the RASAero II predictions for the Supersonic CP compared to the wind tunnel data for the ARCAS Short and ARCAS Long configurations. RASAero II produced very accurate predictions for the Supersonic CP from Mach 1.5 to Mach 3, the area of interest for the forward movement of the CP for high power rockets. Again, this is a comparison with actual wind tunnel data for a sounding rocket configuration for Supersonic CP.
The warning message in RASAero II when the stability margin falls below 2.0 calibers for supersonic Mach numbers is there because if the stability margin falls below 1.0 calibers coning, pitch-roll coupling, and other effects seen on some of the prior flights mentioned in this thread can occur. With even the best supersonic CP prediction methods there can be errors, and the unusual CP shift for the ARCAS Long Configuration for Transonic Mach numbers shows why you want to have an additional 1.0 calibers stability margin on top of the bare minimum 1.0 calibers stability margin, for a total stability margin of 2.0 calibers at Supersonic Mach numbers. Thus the warning message included in RASAero II.
Chuck Rogers
Rogers Aeroscience
View attachment RASAero II Comparisons with ARCAS CP and CD Data.pdf
Slides 2-4 present the wind tunnel model configurations, and Slide 5-6 show the two ARCAS configurations entered into RASAero II.
The RASAero II CP (and CD) predictions are compared to the Subsonic, Transonic, and low Supersonic wind tunnel data for the ARCAS Short and ARCAS Long configurations on Slides 8 and 9. With the boattail only on part of the fin root, the exact way to implement the Barrowman Method is somewhat up to debate. The method used in RASAero II is to calculate the volume of the cylinder and the part of the boattail that are under the fin root, and then calculate the diameter of a cylinder of the same length that has the same volume. The diameter of this cylinder is now the diameter of the rocket body under the fins, and the fins are projected toward the centerline of the rocket until they intersect that cylinder. Thus the RASAero II Barrowman Method results are labeled on the graphs on Slide 8 and 9 as RASAero II Implementation of the Barrowman Method.
Note on Slides 8 and 9 that the Rogers Modified Barrowman Method and the Barrowman Method (as implemented in RASAero II) give similar results, very similar results in the case of the ARCAS Long configuration. Generally the Rogers Modified Barrowman Method is more accurate than the Barrowman Method, but in many cases the Rogers Modified Barrowman and Barrowman Methods will produce similar results, as shown here. This is because Barrowman left off additional normal force at the nose and the tail, but since he missed additional normal force at both the nose and tail, more accurate methods will in many cases produce surprisingly small changes in the CP. For these particular two cases (ARCAS Short and ARCAS Long), the Barrowman Method was more accurate, although the two predictions were close, very close for the ARCAS Long configuration. Both methods got very close to the Subsonic CP for the ARCAS Long configuration.
Note for the ARCAS Long configuration wind tunnel data on Slide 9 the unusual forward movement of the CP at Transonic, and then the CP moves aft again going into low Supersonic. The ARCAS Short configuration wind tunnel data on Slide 8 shows a more typical looking CP curve with Mach number, where the CP moves aft Transonic, and then for Supersonic the CP starts moving forward with increasing Mach number. This illustrates why you want to have an additional 1.0 calibers stability margin on top of the bare minimum 1.0 calibers stability margin, for a total stability margin of 2.0 calibers, at Supersonic Mach numbers to cover for possible CP mispredictions like shown on Slide 9. Hence the 2.0 calibers stability warning message for Supersonic Mach numbers built into RASAero II.
Slides 10 and 11 show the RASAero II predictions for the Supersonic CP compared to the wind tunnel data for the ARCAS Short and ARCAS Long configurations. RASAero II produced very accurate predictions for the Supersonic CP from Mach 1.5 to Mach 3, the area of interest for the forward movement of the CP for high power rockets. Again, this is a comparison with actual wind tunnel data for a sounding rocket configuration for Supersonic CP.
The warning message in RASAero II when the stability margin falls below 2.0 calibers for supersonic Mach numbers is there because if the stability margin falls below 1.0 calibers coning, pitch-roll coupling, and other effects seen on some of the prior flights mentioned in this thread can occur. With even the best supersonic CP prediction methods there can be errors, and the unusual CP shift for the ARCAS Long Configuration for Transonic Mach numbers shows why you want to have an additional 1.0 calibers stability margin on top of the bare minimum 1.0 calibers stability margin, for a total stability margin of 2.0 calibers at Supersonic Mach numbers. Thus the warning message included in RASAero II.
Chuck Rogers
Rogers Aeroscience
View attachment RASAero II Comparisons with ARCAS CP and CD Data.pdf