Static Testing Dissertation

by Calvin A. Gongwer


Acceptance testing of thrusters involves static thrust measurements.  Various static thrust measuring systems are shown. Thrust balance types include: parallelogram, bell crank, vertical beam, direct hanging, direct weighing, floating lateral, rolling lateral, and sliding lateral. The principle of null positioning to insure accuracy is discussed. Methods of detecting the onset of cavitation are presented.  Common errors in thrust measurements are shown.  The paper also includes the general extrapolation relationships for thrusters and a relationship between net thrust and forward speed.


An  underwater  thruster as used on an ROV ( remote operated vehicle ) or  manned  vehicle,  is usually comprised of a motor driven propeller in a duct. Open propellers are used less often. This paper is directed towards the ducted thruster systems although most of it applies to the open propellers as well. A thruster operates in the static or near static regime. This means that the ratio of vehicle speed to the relative exit velocity from the duct varies from zero to about one third. Static or stationary testing is usually done since it is much simpler than testing while simulating vehicle forward speed.


For each particular thruster at static conditions, there are general relationships between thrust( T ), rotational speed( N ) , and shaft horsepower( SHP ), which are useful in extrapolating from a particular test point to other operating points. At large Reynolds numbers these relationships are accurate to within one percent over a wide range of conditions. The principal relationships are:

T = K1N2


SHP = K2N3


from which

T = K3SHP2/3


from which

T / SHP  =  K1 / K2N


Where K1, K2, and K3 are constants for a particular thruster or class of identical thrusters of the same size. The effect of size can be included but is beyond the scope of this paper.  For any particular test point the values of T, N and SHP can be substituted in the above equations and the Ks solved for.

Equation IV gives thrust per shaft horsepower and is obtained by dividing I by II.  Equation IV shows that for any particular thruster, the thrust per shaft horsepower can be made as large as desired by reducing the rpm( N ). However, equation I shows that the thrust diminishes at a rapid rate as N decreases. Thus it is desirable to use a more correct figure of merit for the static performance of thrusters than the thrust per shaft horsepower.


Rather than using thrust per horsepower, a correct figure of merit will now be derived. It is based on the expression for the kinetic power of a jet of water such as that provided by a thruster. The factors involved are A, the cross sectional area of the jet or “rod” of water, the thrust( T ), W, the specific weight of the water and G, the acceleration of gravity. This relationship is:

Jet Kinetic Horsepower = (T3/2 / 1100 )(G / WA)


A, the jet cross sectional area is usually the exit area of the duct. The assumption is made that the jet velocity is uniform across the area, A. This is the minimum kinetic power condition for a given thrust. Thus, equation V credits the thruster with only the jet power of the best possible velocity distribution across the jet.

To evaluate equation V one need only measure the static thrust and to know A, the duct exit area and W the specific weight of the water. The thruster figure of merit is then the ratio of the equation V to the shaft horsepower input:

h = Kinetic Jet  Horsepower (from V) / SHP


Shaft horsepower would ordinarily be obtained by measuring the torque and rpm of the motor and applying the equation

SHP = 2p N Torque / 33,000


However, torque and rpm are difficult to measure in the field but can be determined, in the case of electric motors, from voltage and current measurements which are used with a calibration curve of the motor. For hydraulic motor drives the oil horsepower can be determined by measuring the pressure drop across the motor and the oil flow rate. This is related to the shaft horsepower by the motor efficiency.  hmotor, which is determined by tests in the hydraulic laboratory or from the figures supplied by the motor manufacturer. Thus:

Oil Horsepower = ( gpm (US) x 231 x  Dp ) / ( 12 x 33,000 )



Shaft Horsepower = Oil Horsepower x hmotor


The friction of the shaft seals should be taken into account in the shaft horsepower delivered to the thruster. Often an air run in which the prop absorbs negligible power can be used to determine the seal friction.

The effect of fluid density, fresh versus salt water, can be determined from equation V. Solving V for thrust and lumping the other factors into a factor K, we obtain:

T = KW1/3


This shows that thrust at constant power varies as the cube root of the water density. Thus, for sea water at a specific gravity of 1.025, the thrust increase over fresh water is .025/3 or .008 or about 1%.


A caution should be expressed under this heading in that the jet issuing from the thruster should not impingeon the frame supporting the thruster or the reading will be in error. This goes for the placement in the ROV as well in that the jet should clear the vehicle without obstruction. As a help in design, the jet diverges from the thruster exit at between 3 and 6 degrees half angle. Also, all spring scales and load cells must be calibrated by comparison of weights with a platform scale.

Mistakes are common in the measurement of static thrust. One of these involves managing the tare due to gravitational forces. The problem for a vertical beam thrust balance is shown in Fig. 1.  If the beam is allowed to displace thru an angle due to deflection of a spring balance as the thrust is applied, the weight of the system moves as the c.g. moves and a tare is introduced.

This tare can be avoided if:

1) A null reading dynamometer such as an electric load cell is used in stead of the spring balance.
2) The spring scale is pulled so the lever or beam is returned to its zero position and hence x and o are zero. This is called nulling the system.
3) The c.g. and c.b. are located at the pivot of the beam. This is occasionally done by using adjustable weights.

Failure to null a system of this type often introduces an error due to flexure of the hydraulic or electrical lines leading to the thruster.

The exact location of the thrust axis. I2, in Fig. 1, is determined by assuming that it coincides with the geometrical axis of the thruster. This may not be the case if asymmetry of any kind exists.

The parallelogram, sliding, and rolling cart thrust balances eliminate this type of tare since they don’t tilt under the thrust deflection. Also, the thrust axis need not be located precisely.

Direct hanging on a scale with the thrust force directed downward is one of the best methods of measuring thrust. This is shown in Fig. 2.

However, most thrusters, without downstream guide vanes have a torque on them, approximately equal to the motor torque. This is countered as in the sketch by a long light rod extending laterally which touches some supporting structure or the side of the tank.  In Fig. 2 the jet is shown directed upward and not impinging on a cross member of the supporting frame. If a frame cross member in the jet is unavoidable such as in deep water tests, it should be as far from the thruster as possible and have a streamlined shape in the direction of the thrust. If the hanging thrust system is in deep water as for the AMETEK/STRAZA tests at Lake Vincent, it is easy to increase the test depth to large values to test for cavitation performance. The frame is extended by adding extension members to accomplish this.

Tests involving the complete ROV floating at pier side are usually made as shown in Fig. 3. If the scale is held high on the pier with the tow line sloping into the water some of the cable weight is included in the thrust reading. To avoid this a pully or sheave at the water line is often used. The error due to friction in the pulley is eliminated by “dithering” the system by periodically and rhythmically striking the line. Often there is enough fluctuation in the thrust reading to produce an automatic “dither”.

In variable depth tests made in a pressurized tank at PERRY the arrangement was as shown in Fig. 4. The tank is so large that the return flow is stagnant and doesn’t contribute to any error. The thrust balance was of the rolling cart type and the thrust was exerted on a hydraulic cylinder, and read on a pressure gage. The hydraulic motor driving the thruster produced enough “dither” to eliminate the effects of friction on the balance and in the hydraulic cylinder.

The complete cavitation performance of the Mod 1002 thruster shown in Figure 5 was determined in this facility.

The determination of cavitation onset can be done by plotting thrust versus pressure drop across the hydraulic motor as In Fig. 5, or thrust versus current in the case of DC motors with permanent magnets. The linearity is destroyed when cavitation occurs, disrupting the flow as in Fig. 5.  Also, if a good rpm measurement is available a plot of thrust versus T/N2 shows the onset of cavitation as the value falls abruptly from a constant value which is a characteristic of the thruster.

Cavitation is accompanied by internal under-pressures on the suction sides of the prop blades where the pressure (absolute) falls below the vapor pressure of the water. At incipient cavitation, a few vapor bubbles appear and as the thrust is increased or the unit is brought shallower, free jet cavitation occurs which corresponds to the horizontal lines of Fig. 5.  As the figure shows, about 70 feet of submergence is sufficient to eliminate thrust loss due to cavitation on the model 1002 at the 600 lbf thrust level. The cavitation limiting thrust is proportional to the absolute submergence meaning depth plus the atmospheric head of 34 feet.


Ideally, N is determined by a magnetic pick-up indicating off a rotating part, such as a blade tip, in which a magnetic insert has been placed.  An electronic counter then gives precise rpm. However, in water in a field location this is difficult to arrange. Mechanical counters can also be used if a shaft end can be reached. This is often difficult as well.

For hydraulic motor driven thrusters the oil flow rate can be measured with a standard flow meter which has been calibrated. The rpm, N, is then calculated from:

N = ( gpm( US ) x 231 / d ) x hV


where: gpm = the flow rate in gallons per minute
      d= the motor displacement in cubic inches per rev.
hV= the volumetric efficiency of the motor.

hV can be determined from the manufacturer’s curves and, for good motors, lies between .96 and .99. This if it is taken at .975 it is within 1 1/2 percent of the possible values and thus the max error is 1 1/2 percent in the speed determination. Usually the value of hV can be estimated more closely from knowledge of the particular motor.

For DC motor driven thrusters the rpm can be determined from the motor calibration curve. A typical example of which is shown in Fig 6. The voltage and armature current are measured from which the rpm can be read off the chart


Testing at forward speed is beyond the scope of this paper. However, for open water results, meaning none of the wake of the vehicle is inducted into the thruster, results can be derived from static tests. A set of these curves are shown in Fig. 7. In deriving these curves the assumption is made that the internal efficiency of the thruster remains the same at all conditions. The inducted water has a negative momentum rate and this is subtracted from the exiting momentum rate to obtain net thrust. The effect of ram pressure on the inlet is allowed for. The external drag of the duct is neglected. This is justifiable since the unit is assumed to be streamlined like a jet engine nacelle and also because of the relatively low ratio of forward speed to exit jet velocities at which these thrusters normally operate.


If the main propulsion thrusters operate in the wake of the vehicle, the negative momentum rate inducted in open water is reduced because the water velocity the duct sees at its inlet is reduced. This has a favorable effect on net thrust and the thrust deduction shown in Fig. 7 can be greatly reduced. This can be a dividend for the designer or “ace up the sleeve” in meeting performance specs.