291 



DIRECTION 



OF MEASURED 

 FORCE 



SUPPORT FLEXURE (4) 

 0.750 IN. X 0.035 IN. 

 ( I .90 CM X 0.084 CM) 



MEASUREMENT FLEXURE 

 0.500 IN. X 0.005 IN 

 ( 1.27 CM X 0.0127 CM.) 



FIGURE 6. Schematic diagram of flexure arrangement. 



For simplicity and economy, the flexure consisted 

 of conventional steel shim stock clamped between 

 the half body and the afterbody by sets of wedges. 

 The flexures were pinned and epoxied to the wedges 

 prior to insertion into the dynamometer plate. 

 Before assembly, eight strain gages were mounted 

 and waterproofed, with one gage placed at each 

 corner of the two large faces of the flexure. The 

 gages were electrically compensated for tension 

 (or compression) and torsion. In order to check 

 vertical alignment to the flow, two of the support 

 flexures were also strain-gaged. 



Calculations indicated that the measured strain 

 in the flexure due to dynamic forces would be 135 

 percent of the strain due to a static force with 

 the same amplitude, assuming small damping. Also, 

 the phase angle of the strain relative to the applied 

 force would be affected by the large ratio of 

 excitation frequency to the natural frequency. 

 Consequently, the experiment incorporated an inter- 

 nally mounted electromagnetic voice coil to calibrate 

 the measurement flexure as a function of force 

 amplitude, frequency, and forward speed. Initally, 

 with a series of known static forces applied to the 

 body, a current was applied to the coil to return 

 the body to its unloaded position, as indicated by 

 the strain output from the measurement flexure. 

 These static calibrations revealed that the coil 

 current varied linearly with applied force and that 

 the flexure strain was virtually independent (less 

 than 2 percent variation) of the axial location of 

 the applied force. 



Dynamic calibrations of the dynamometer were 

 performed using a frequency generator and amplifier 

 with the known sinusoidal current directly input to 

 the coil. (It is assumed that in the low frequency 

 range of interest, to 60 Hz, the applied force 

 is independent of frequency) . The response amplitude 

 (relative to the applied current or force) was 

 found to vary linearly with the applied force. By 

 averaging the data, the transfer function for each 

 frequency and forward speed was determined as shown 

 in Figure 7. These results revealed anomalous 

 behaviour for frequencies of 20 Hz and 50-60 Hz, 

 which were later identified as resonant frequencies 

 associated with the towing structure. 



Instrumentation and Data Acquisition 



During each data run the following physical quanti- 

 ties were measured (see Figure 8) : the force on 

 the half body, the surface pressure at two locations 

 on the body, the distance between the body and the 

 propeller (tip clearance) , propeller blade angular 

 position and rotation speed, the forward speed of 

 the towing carriage, and the horizontal accelerations 

 of the afterbody. 



Pressures were measured by metal diaphragm solid- 

 state gages (KULITE XTMS-1-190) flush mounted to 



the half body surface. The propeller tip clearance 

 which varied slightly with forward speed, was 

 determined by measuring the distance between the 

 35-horsepower dynamometer body and the test after- 

 body at two axial positions using linear variable 

 differential transformers (Schaevitz 1000 HCD) . 

 These low friction devices recorded relative move- 

 ment without transmitting mechanical vibration. 



The propeller blade angular position and rotation 

 speed were measured by a Baldwin Shaft Position 

 Encoder mounted on the 35-horsepower dynamometer 

 tachometer shaft, generating one interrupt per 

 degree of revolution and another interrupt once per 

 revolution. During the experiments each data channel 

 was sampled for each six degree increment of propel- 

 ler rotation, thus providing 20 samples per cycle 

 for blade frequency quantities. (The time lag 

 between successively sampled channels and the delay 

 between the encoder interrupt and capture of the 

 sample, together amounting to several degrees of 

 rotation, were later accounted for in the data 

 reduction) . Analog data output from the measurement 

 tranducer was digitized and stored on magnetic tape. 

 Data for each angular position of the propeller 

 were summed and averaged over several hundred 

 revolutions in an attempt to reinforce the signal 

 of interest while self-cancelling random noise. 



In order to determine the blade-frequency com- 

 ponents of the unsteady force (and pressure) on 

 the half body, a Fourier analysis was applied to 

 the averaged data to yield the coefficients of the 

 series g 



F{e) = -::: — I- ) a cos m6 + b sin m6,-iT £ 6 iTT 

 2 / m m 



m=l 

 9 



r- 



c COS (m9 - Y ) 

 m m 



(60) 



m=l 



in which 6 (t) is the blade position angle (Figure 

 8). For the three-bladed propellers, the nondimen- 



0.6 

 0.4 



0.2 

 0.6 



0.4 



0.2 



0,6 



4 KNOTS (4.lm/s) 

 o Co* 



it 2 0.4- 



0.2 

 0.6 



5 0.4 



0.2 



6 KNOTS (3.lm/s) 



O o O 



O O o 



8 KNOTS (4.1 m/s) 

 o 



o o 



10 20 30 40 50 60 70 

 FREQUENCY, Hi 



FIGURE 7. Force dynamometer amplitude response as a 

 function of -frequency for several forward speeds. 



