done while the weight is in motion) the tunnel can operate at resonance 

 at any period. The theory and operation of the active counterweight 

 system are discussed in Section III. 



The drive system includes a timing mechanism which, at 45° intervals 

 in the angle o£ the driving arms or phase, can time a single rotation of 

 the worm shaft. One rotation of the worm shaft occupies only 1/48 of a 

 cycle of the driving arms, or 7.5° of phase; therefore, separate timings 

 provide a quasi-instantaneous rate of rotation of the driving arms as a 

 function of phase and a check on the steady operation of the drive sys- 

 tem. 



The flow out of the cylinders and reservoirs is turned from verti- 

 cal to horizontal by curved conduits and continues into the test section 

 through horizontal removable "spools" with constant rectangular cross 

 section. 



III. COUNTERWEIGHT ANALYSIS 



A schematic diagram in Figure 3 shows the tunnel with the cylinders 

 and drive system at the right and the reservoirs at the left. The sche- 

 matic is presented to assist only in the analysis; true proportions are 

 provided in Figures 1 and 2. In Figure 3, Jl is the distance from the 

 zero position of the pistons measured along the centroid of the water 

 conduit. Except in the test section and in the adjacent spools the con- 

 duit is divided and the centroid falls in the area between. The cross- 

 sectional area of the conduit, including both branches where there are 

 two, is denoted A(Jl) . Special values of A(Jl) are: Ac, the combined 

 cross-sectional area of the two cylinders; A, the cross-sectional area 

 of the test section, without divider, above the sand bed; and A^, the 

 combined cross-sectional area of the two reservoirs which, by circum- 

 stance, is slightly less than Ac. The combined mass of the pistons and 

 their yoke is denoted by Mp, which is also the mass of the passive count- 

 erweight (actually hung as two separate halves), and the mass of the 

 active counterweight is denoted by Ma. 



The purpose of the following analysis is, for any given rate of 

 rotation a, to determine y, the elevation (which can be positive or 

 negative) of the active counterweight when s = o, such that the power 

 input from the motor is a minimum. Under this condition the motor is 

 required to work only against the dissipative forces of fluid and piston 

 friction and not to lift or to accelerate masses of metal or water. 



The power input in excess of the rate of dissipation due to fric- 

 tion is equal to the time rate of change of the total energy of the 

 system. Thus, the power input is minimized if the total energy is held 

 constant with time. That is, ideally. 



12 



