The AeroRocket wind tunnel has been used to determine center of pressure location (XCp) and zero-degree drag coefficient (Cd) of spool rocket models having various plate-separation to plate-diameter ratios (L/D). Five spool rocket wind tunnel models were tested having L/D ratios of 1, 1.33, 1.67, 2 and 3. The ratio of the separation distance (L) to plate diameter (D) is the value of L/D used to correlate Cd and XCp for data presentation. To avoid wind tunnel wall interference effects the diameter (D) of the spool rocket end-plates are 1.5 inches and fabricated using 1/32" thick aircraft plywood to more accurately simulate the plate-diameter to plate-thickness ratio used to fabricate most practical spool rockets. The end-plates are supported by a single 3/8" diameter (d) wooden dowel or cylindrical body having lengths of 1.5", 2", 2.5", 3" and 4.5" for each of the five models tested in the AeroRocket wind tunnel. Figure-1 schematically displays the force balance system used to determine Cd of the spool rocket models in the AeroRocket wind tunnel. Figure-5 displays the various spool rocket models tested to determine drag and center of pressure location.

Displacement in the axial (drag) and vertical (lift) directions are measured using the two load cells labeled DRAG and LIFT respectively in Figure-1 and then converted to drag and lift forces in Newtons using the Vernier CBL-2 computerized data acquisition system. The force balance system pictured above is designed to separate the aerodynamic forces and the associated displacements in the axial and vertical directions when the weight on the force-balance plate causes the model to be freely suspended. Spool rocket drag coefficient (Cd) has been plotted in the form presented in Figure-2a and Figure-2b as a function of L/D. The AeroRocket wind tunnel Cd data (red dots) in Figure-2a are plotted with Cd data (blue line) from an independant source referenced in the report dealing with drag of circular plates. The report also introduces a curve-fit approximation of spool rocket Cd verses L/D over the range of L/D=0.5 to L/D =3.5. Figure-2b presents a representation of the curve-fit data for spool rocket Cd verses L/D. The actual report labels all axes.

Center of pressure measurements are performed using a special XCp-Caliper that secures the model in the wind tunnel test section using two opposing low friction points. Figure-5 displays the spool rocket models tested (L/D = 3 not pictured) and the XCp-Caliper used to secure the spool models during center of pressure measurement. The models are secured by the cylindrical sting placed behind the rear plate. Figure-6 illustrates the L/D = 2 spool rocket model being tested in the AeroRocket wind tunnel. The model in this configuration is stable because the support point is ahead of the actual center of pressure. The actual center of pressure location (XCp) is determined by moving the sting support location rearward until the model becomes unstable and "noses over" to one side or the other when the wind tunnel is operating. Figure-6 further illustrates how the spool rocket model is secured in place during center of pressure location testing. Please notice the pitot tube used to measure the difference between static pressure and dynamic pressure for determining flow velocity in the wind tunnel. An analog velocity meter is used to convert the resulting pressure differential to test section flow velocity in feet per minute.

Figure-7 displays the AeroRocket wind tunnel results for center of pressure (XCp/D) location verses L/D for the five spool rocket models tested. The center of pressure (XCp) is normalized by the plate diameter, (D). Normalization is performed to generalize the results to any size spool rocket design. The AeroRocket wind tunnel XCp/D data (red dots) in Figure-7 are plotted along with a logarithmic curve-fit approximation of spool rocket XCp/D verses L/D over the range of L/D = 0.5 to L/D = 3.5.

For a spool rocket the center of pressure (XCp) is located behind the rear plate of the model. Therefore, it is necessary to support the spool rocket behind the back plate when attempting to determine center of pressure location. To support the model for center of pressure measurement a support sting was added to the rear of each spool rocket model. The following discussion describes why the presence of the cylindrical support sting does not affect the center of pressure location of the model being tested.

For angles of attack less than 10 degrees the normal forces acting on any cylindrical body are small and the effect of a support sting on center of pressure location can be neglected as stated in TIR-33. In other words, the normal forces acting on a cylindrical body, that could contribute to center of pressure movement, are seen to disappear for angles of attack less than 10 degrees. Therefore, the presence of a cylindrical support sting inserted behind the model does not alter the center of pressure location of a model being tested in the wind tunnel. Therefore, the effect of a cylindrical support sting attached to the rear of any wind tunnel model on center of pressure location is very small because the normal forces acting on a cylindrical body are small for angles of attack less than 10 degrees. This discussion is important because the measurement of center of pressure location (XCp) relies on the placement of a cylindrical support sting behind the rear plate of the spool rocket model. The support sting and spool rocket model combination are held securely in place during center of pressure measurement by the two opposing points of the XCP-Caliper illustrated in Figure-5 and Figure-6. Figure-6 illustrates the L/D = 2 spool rocket model being tested in the AeroRocket wind tunnel. The model in this configuration is stable because the support point is ahead of the actual center of pressure. The actual center of pressure location (XCp) is determined by moving the sting support location rearward until the model becomes unstable and "noses over" to one side or the other when the wind tunnel is operating. Figure-5 and Figure-6 further illustrate how the spool rocket model is secured in place during center of pressure location testing. Please notice the pitot tube used to measure the difference between static pressure and dynamic pressure for determining flow velocity in the wind tunnel. An analog velocity meter is used to convert the resulting pressure differential to test section flow velocity in feet per minute.

By the principal of similitude a wind tunnel model needs to be similar in shape and have the same Reynolds number (U*D/v) to accurately model the flight characteristics of any "similar" full size rocket. In addition, the correlation of circular plate wind tunnel measurements to other full size spool rocket configurations using circular plates is enhanced by the fact that above Reynolds number 1,000 and up to Reynolds number 1.0E7 the drag coefficient of disks and plates is practically constant and approximately equal to 1.17 for a single circular plate in normal flow. In other words for a circular plate the transition from laminar flow to turbulent flow occurs above Reynolds number 1,000 and the associated drag coefficient (Cd) for a flat circular plate in turbulent flow remains constant up to the highest Reynolds number ever tested, approximately 1.0E7. The spool rocket wind tunnel models tested in the AeroRocket wind tunnel had an average Reynolds number of 50,550. Because Reynolds numbers are well above 1,000 and below 1.0E7 the results are representative of the region of spool rocket air flow where Cd is constant and predictable over a wide range of velocity. This relationship between Cd and Reynolds number makes possible the extension of these wind tunnel test results to any spool rocket that has Reynolds number and shape similar to the spool rocket models tested.

SPECIAL NOTICE
NO PART OF THIS REPORT MAY BE COPIED OR TRANSFERRED TO ANOTHER USER WITHOUT THE WRITTEN CONSENT OF JOHN CIPOLLA/AEROROCKET. ALSO, WHEN PURCHASING AEROROCKET SOFTWARE AND REPORTS THE USER IS AGREEING THE SOFTWARE/REPORT IS SOLD AS IS AND NO WARRANTY IS EXPRESSED OR IMPLIED. THE USER TAKES COMPLETE RESPONSIBILITY FOR USING THE SOFTWARE/REPORT AND PROPERLY INTERPRETING THE RESULTS.