McCormick 



Though somewhat inconsistent, the data: namely, the time history of the 

 velocity, did point to the fact that laminar flow was still not being achieved with 

 TRI-B even though the slots were now modified. However, the tilt traces and 

 visual observations of its surfacing confirmed the fact that the body was under- 

 going violent excursions during its rise to the surface. This had been experi- 

 enced to a lesser degree during the first series of tests and had apparently been 

 cured by adding 10 lbs of lead in the tail. For the second series of tests the CG 

 was even slightly behind that of the configuration with the lead. At this point, it 

 was realized that the contribution of the hydrodynamic forces on the tail to the 

 slope of the pitching moment curve completely overshadows that due to the dis- 

 placement between the CG and the center-of-buoyancy above about 10 fps. Hence 

 on a buoyant, vertically-rising body, moving the CG aft improves the stability at 

 low speeds but, due to the shortening of the tail moment arm, is detrimental at 

 higher speeds. 



At this point in the program wind tunnel tests of a model of TRI-B showed it 

 to be statically unstable, contrary to calculations of its dynamic stability made 

 early in its design. These same tests indicated that an increase in the chord of 

 the tail from 4 inches to 6 inches would provide static stability. Hence a new 

 tail was made and shipped to the field. Successive runs with the new tail showed 

 the stability problems to be solved. The body repeatably rose with no indication 

 on the tilt traces of any deviations from the vertical. 



Unfortunately, solving the stability problem did not result in a reduction in 

 the drag according to the terminal velocity. Thus in the latter part of May, the 

 body was returned to ORL for additional laboratory studies. It is planned to test 

 this body in the Garfield Thomas Water Tunnel at the design Reynolds number. 

 However, these tests must await the installation of a honeycomb in the tunnel 

 designed to reduce the turbulence in the test section to a level acceptable for 

 such tests. 



ANALYSIS BASED ON KARMAN-POHLHAUSEN METHOD 



The analysis on which the design was based was felt to be inadequate for 

 several reasons. The assumed velocity profile was too approximate. In addi- 

 tion the stability limit having a fixed value did not consider the dependence of 

 the stability of a laminar layer on the shape of velocity profile. Also there was 

 no means to calculate the change in velocity profile across the slot. 



An exact prediction of the stability of laminar boundary layers involves the 

 solution of the eigen-value problem defined by the Orr-Sommerfeld equation. 

 Fortunately, enough cases, with and without suction have been investigated so 

 that one is able to specify a stability limit, Rscrit» ^^ ^ function of some meas- 

 ure of the shape of the velocity profile. Figure 5 taken from Ref. 2, presents 

 Rs*^jj as a function of the shape parameter H, the ratio of displacement thick- 

 ness to momentum thickness. More recently Tollmein in Ref. 3, presented the 

 curve shown in Fig. 6. Here, the shape parameter used is related to the curva- 

 ture at the wall measured in terms of displacement thickness. Qualitatively 

 both criteria are in agreement. A profile having a relatively higher velocity at 

 the wall will have a greater value of K and a smaller value of H . 



1008 



