Theory of Stability of Laminar Flow 467 
[7] Schlichting, H., and Ulrich, A., “Zur Berechnung des Umschlungs Laminar-Turbulent,” 
Jahrbuch d. dt Luftfahrtforshung 18, 1942 
[8] Schubauer, G.B., and Shramstad, H.K., “Laminar Boundary Layer Oscillations and 
Stability of Laminar Flow,” National Bureau of Standards Research Paper 1772 
[9] Max O. Kramer, Communication Jour. Aero-Space Sciences, June 1957 
[10] Max O. Kramer, Communication Jour. Aero-Space Sciences, May 1959 
[11] Max O. Kramer, “Boundary Layer Stabilization by Distributed Damping,” Jour. Amer. 
Soc. of Naval Engineers 72:25 (1960) 
DISCUSSION 
T. G. Lang (U.S. Naval Ordnance Test Station) 
I would like to mention that I have observed Dr. Kramer’s experiments on models utiliz- 
ing compliant surfaces in Long Beach Harbor in California and consider his test apparatus ° 
to be well designed and his reported results to be accurate. When the theory of distributed 
damping using compliant surfaces was first proposed by Dr. Kramer, it was mentioned that 
sea mammals such asporpoises and whales utilize this phenomena to reduce their drag. Re- 
ports by many observers of fish and sea mammals indicate high performance. I would like 
to describe a study which was recently conducted by the U.S. Naval Ordnance Test Station 
(NOTS) on the performance characteristics of a live porpoise. These results which I shall 
present are still preliminary since additional analysis is planned. 
The performance tests were conducted by a group of NOTS personnel in the towing tank 
at Convair, San Diego. This tank is 315 feet long, 12 feet wide, and 6-1/2 feet deep. It 
was filled to a depth of 4-1/2 feet on June 3, 4, and 5 and to 6 feet on June 15 with sea 
water. This water was continuously filtered except during tests, and chemicals were added 
to prevent growth of plankton and bacteria. The tests were composed of two types. One 
type was a peak-effort run down the tank, and the other was a motionless glide through a 
series of large underwater hoops. The porpoise was tested both in its natural condition and 
with a ring, whose thickness varies from 1/16 to 1 inch, placed around its head section. 
The purpose of the thinnest ring was to induce turbulence on the body. The thicker rings 
were used to significantly increase the drag of the porpoise by a fixed amount and thereby 
aid in determining its horsepower output when the top speed with each ring is known. 
Figure D1 shows a porpoise with such a ring placed around its head section. This is a 
porpoise similar to the one used in these tests, except it was trained to support itself in the 
position shown in the figure for several seconds. Figure D2 shows the dimensions of the 
porpoise (Pacific white-sided dolphin) which was tested in this program. It is 6.7 feet long, 
has a maximum diameter of 1.2 feet, and weighs 200 pounds. The distance versus time data 
were primarily measured by overhead cameras. Two cameras were mounted at the beginning 
of the runs behind underwater windows, but much of their data was lost due to camera mal- 
function. 
Figure D3 shows that portion of the horsepower which was required on the peak effort 
runs to produce the recorded acceleration. It is noted that horsepowers up to 1.8 were 
