Experimental Determination of Unsteady Propeller Forces 



DIGITAL ANALYSIS 



A digital analysis of the recorded data is performed using an IBM-7090 

 computer. Each of the data channels is digitized at intervals corresponding to 

 6 degrees of shaft rotation for 200 shaft revolutions. These values are then 

 averaged to obtain an average cycle for one revolution and calibration signals 

 on the tape are used to scale these average values to represent the input to the 

 recorder in volts. The photographic record made from the oscilloscope can be 

 compared directly with this output from the computer. These average values 

 are then divided by the gain of the amplifiers, which has to be entered into the 

 computer program for each test. The result is the output of each strain-gage 

 bridge in millivolts. Each set of six voltage values, for each 6° increment of 

 shaft rotation is now multiplied by the 6x6 calibration matrix to obtain the pro- 

 peller forces and moments in pounds and pound-feet. Since the gages are rotat- 

 ing with the propeller, the side forces and bending moments are relative to a 

 rotating reference frame. To obtain vertical and horizontal forces and mo- 

 ments, they are resolved by using trigonometric relationships. A harmonic 

 analysis of these results gives the amplitudes and phase angles of any desired 

 number of harmonics of the shaft rotation frequency. 



TYPICAL TEST RESULTS 



The unsteady forces produced by a propeller have frequencies determined 

 by the blade frequency and the frequency components in the wake. Unsteady 

 thrust and torque are present only if the wake has frequency components equal 

 to the blade frequency or any of its harmonics. Unsteady side forces and bend- 

 ing moments are present only if the wake has frequency components equal to the 

 blade frequency or a harmonic plus or minus one. The forces relative to the ro- 

 tating shaft will have this frequency. However, when resolved into vertical and 

 horizontal forces relative to a fixed reference frame, these frequencies become 

 equal to the blade frequency or its harmonics. 



Figures 14 and 15 show the outputs of the thrust and moment gages for a 

 three-bladed propeller in a three- and four-cycle wake. These wakes were ap- 

 proximately sinusoidal with only a little harmonic content. Figure 14 shows that 

 in the three-cycle wake a strong three-cycle thrust signal was produced, but the 

 moment signal was rather complex and actually much weaker than indicated by 

 the photographs, since the gain of this channel was greater. Figure 15 shows 

 that in the four-cycle wake the thrust was complex and weak, while the moment 

 shows a strong four-cycle component. When resolved into vertical and horizon- 

 tal moments, they will become three-cycle or blade frequency signals. These 

 are the unfiltered electrical signals and must be corrected for the gain of each 

 channel and multiplied by the calibration matrix to obtain values in the mechani- 

 cal units of force and moment. The pulses seen on each record represent shaft 

 revolutions and are used as the phase reference for both the digital and the on- 

 the-spot analysis. 



The three- and four-cycle wakes were produced by screens using the method 

 developed by McCarthy (10). Figure 16 shows a drawing of the three-cycle 

 screen. Figures 17 and 18 show the harmonic analysis of the longitudinal veloc- 

 ity component in the propeller plane as measured with a pitot rake. 



267 



