Lab. v.
ScheepsbouvAunde
Technische Hogeschool
Delit
Notes on a Course delivered at
A.E.W. Haslar, April 21st-23rd, 1969
70,x4
UNIVERSITY COLLEGE, LONDON
ADMIRALTY EXPERIMENT WORKS.
1111
P1969-1
ainimiePART
2
THE PLANAR MOTION MECHANISM
TIM 1= FOR TI E P M
by T.B. Booth
The preceeding lectures have described what the PlLM does and what results are produced by it. We now consider briefly the use to which these results will be put, and the merits of the PMM relative to other techniques.
Five types of problem arise, and are amenable to a 'derivative' approach,
Stability on a straight course for a small disturbance (for which the lengitudinal, vertical and lateral motions are uncoupled and the analysis is linear)
Stability on a curved course for a small disturbance (for which the motions are coupled, but the analysis in terms of the disturbances is linear)
Stability for large disturbances
(for which the motions are coupled, and the analysis is non linear)
Computation of trajectories in response to a series of control movements and engine orders
(which requires a mathematical model in terms of velocity components rather than velocity disturbances from a steady
state)
Design of auto-control systems.
Problems of type (a) and (b) above can be treated by carrying out the standard manoeuvres of turning circles, zig zags and spirals, but thp type of problem we face at LEW, notably in the field of submarine safety, cannot be treated in such a manner, and we therefore adopted the 'deriva-tive' approach some years ago. More recently problems concerning surface
ships have arisen which require the 'derivative' approach. There is an obvious advantage in having a common treatment of both submarines and surface ships and it is likely that the 'derivative' approach will become the standard method of dealing with these problems at AEW. An indirect benefit of this approach is that derivatives provide 'fingerprints' of the vessel's behaviour, and it is easier to relate cause and effect via
derivatives than directly, e.g. the effea.ts of a change of geometry, or loss of engine power, or Reynolds Number are more easily envisaged and computed by first establishing their effect on the derivatives.
LLT' N' y' + Nt.vi + N'rr' +
If a 'derivative' approach is to be made the -problem becomes one of finding their values. The most general problem which has arisen at AE177 is that of developing the mathematical model of the submarine. This involves all six equations of motion and covers all possible sub-marine motions, control movements and propeller RPM. The inforwation required includes all that is needed for any of the other types of
problem. Strictly the 'derivatives' are in this case more correctly described as coefficients, but this distinction does not affect the techniques for measuring them. The mathematical model includes in the equations of motion a large number of non-linear and coupling terms and so far all effort has gone into measuring their coefficients on a quasi-static basis. So far as I am aware no attempt has yet been made to construct a mathematical model which allows for frequency dependence of
the coefficients. This is usually justified on the grounds of the low frequencies in actual motions5 but if frequency is important in a
particular problem then the preceeding lectures will have made clear the importance of the PMM in handling such problems.
Assuming that a quasi-static treatment is adequate, the following
methods are available for finding the values of the derivatives
-Computation
Model test - Static tow
Model test - Dynamic tow (PMM) Model test - Rotating arm Full scale trials.
Full scale trials are expensive and difficult to conduct.
Although they are essential to the testing of the validity of the whole derivative technique and provide valuable case history they do not pra-vide information in the design stage andour attention must therefore be concentrated on computation and tank testing.
We now examine the application of these methods to the case of
stability on a straight course, and then to the mathematical model.
Por the basic case of stability of a ship on a straight course,
the expressions for the forces and moments
are:-Y' .Y" Y'r' + + Y1
All these derivatives can be estimated by computation but not with sufficient acaaracy to rely solely on computation. ( In a later lecture Mr Burcher will illustrate why it is necessary to achieve fair accuracy in the important derivatives.) Ultimately there is a good prospect of improving the accuracy, either by interpolation of data or by improved direct calculation. It is likely to be some years before this is achieved, and meanwhile tank experiment is the best method available. This is particularly true of AEW work, since we are frequently dealing with designs which are radically different from those existing.
In a static tow r = = . o and the equations reduce to
Yrvr+
vLN'
IT'+ N! 6
By towing at varying drift angle and rudder amidships and measuring Y and
N, values are obtained for
Yv and Nv Similar tows at zero drift angle and varying rudder angle gives Y, and These are direct5 reliable measurements.
Alternatively Yy and Ny can be obtained from the PI/1M dynamic tow as described in the preceeding lectares. This is an indirect, less reliable measurement, which has the advantage of time saving since it is made in the course of dynamic tows which would be made in any case.
The derivatives
Yr and Nr require yawing to be introduced into the experiment. This is achieved by the rotating arm and by the PlAhl. The
rotating arm has the advantage of putting v = ir = = o and thus giving direct measurement. It has the disadvantages of being a very expensive item of equipment, and of being unable to achieve the low values of r.
(Er. Burcher will illustrate the difficulty this can produce in a later lecture lecture.) The PTEM gives a less direct measurement, but it is capable
of giving lov: values of r, and on balance will usually be the better method.
The remaining derivatives Y., Y.. N.. N. reauire acceleration in v- r' v' r
sway or yawing to be introduced into the experiment, and this is best done
by the PlIDT. Other methods introduce acceleration in the axial direction
also and thereby produce most undesirable complications.
For the stability of a ship on a straight course therefore, the whole of the information needed can be obtained from static and trnamic
tows on the PlUM, only one setting up and calibration being needed.
Everything that has been said of the ship applies to the submarine also, but with negligible variations due to Froude Number. Strut
inter-ference is always present to some extent in submerged submarine model experiments and is worst for the rotating arm experiments. This is an additional reason in favour of the PMM for measuring the rotary
derivatives Yr9 Nr. Everything that has been said of the Y and N
equations applies to the Z (heave) and 31 (pitching) equations also. (The additional term in the pitching equation due to hydrostatic buoyancy
pre-sents no problem.) However, the roll motion produces an extra equation which must be considered and also introduces extra terms into the sway
and yawing equations. In order to measure these it is necessary to introduce roll and acceleration in roll intc the experiment.
The PMM
incorporates a facility for oscillating the model in roll througha smallangle and hence measuring these derivatives. So far the mechanical problems have not been overcome satisfactorily9 but there seems no reason
why this Should not be achieved. (Ideally a rig to give steady rolling would be desirable - the equivalent of the rotating arm - but this
presents extreme mechanical problems and is unlikely to be practical.
Alternatively, the roll derivatives can be estimated. The accuracy is no more than fair, but may be adequate.)
aubject to overcoming the mechanical problems of measuring roll derivatives, the PMM can give all the information required for the stability of a submarine on a straight course.
We now consider the mathematical model of the submarine. The
difference from the stability case discussed above lies in the addition of a multitude of non-linear terms and in the wide range of speed and RPM to be covered. The rstandardi equations used for submarine
simulation at NSRDC are given in Ref. 19 and as an example the lateral
equation is given in Appendix 1. (Note that althuugh the derivative notation is used for convenience the Yv etc. are more correctly described
as coefficients since Y no longer equals A disaussion of the
meaning and importance of the extra terms is outside the scope of the
1)resent lecture, but will be touched on later by Mr. Chislett. However, it is important to note that the form of the non-linear terms is mere
empirical than theoretical. Other authors use other terms9 e.g. Strom-Tojsen in Ref. 2 uses terms such as Y9 Yvr29 Yv2r9 instead of
vvvYIt
is therefore advantaous to have a method of v/v/, Yv/r/.
measurement which gives the form of the term as well as the value of the coefficient. On the other hand the non-linearities do not need to be known as accurately as the linear terms and, if necessary, it is better. to assume a form for a non-linearity which may be imperfect rather than to omit it completely. (In any case the measurement of non-linearities is more seriously affected by strut interference.)
Terms which do not involve angular velocities or accelerations, in this case
Y* Yvw Yv/v/' are obtained in both form and value directly from static tow.
Terms which involve angular velocities other than roll, in this
case Ylrq Yvir Yqr Y/r/ Yv/r/, are obtained in both form and value
directly from rotating arm experiment. Mr. Chislett will later discuss methods of obtaining this type of term from the PAIL The use of the PMMfor this purpose is less direct than the rotating arm since
accele-ration terms are always present in PlIM oscillations, and the analysis is less certain. In particular use of the PMM may depend on assuming the correct form of the non-linearity. All in all the rotating arm is
preferable if available, but the PMM may well prove to be usable.
Terms which involve roll are particularly difficult to measure.
Ywp can be measured by the P1UM running with the table tilted to give an
incidence to the model. Yip/p/ requires the roll velocity to be high relative to the forward speed. This can be achieved by the PMM roll
facility, but it presents problems in distinguishing the non-linear effect from frequency effects. YPq requires an experiment involving roll and pitching simultaneously. This could be achieved by adding a
roll mechanism to the rotating arm, but I am not aware of this having been done. Conceivably the FiCLI could be modified to oscillate in pitch and roll simultaneously, but the subsequent analysis would be so indirect that one would require practical proof of its validity. At the moment therefore YPq can only be estimated by computation.
The only remaining terms are those involving y, and arise when the forward component of velocity differs from the steady straight course velocity corresponding to the propeller RPM. These are obtained by repeating the corresponding test OV02 a range of propeller RPM.
The equations do not contain any non-linear terms involving
acceleration. It can be shown that such terms do not arise inpotential flow, and this is usually quoted as justification for the omission, but I am not aware of this having been verified in practice.
This brief disaussion of tho Y equation does not claim to be exh2ustive, and indeed there are many questions
which
have not yet been answered, but it is hoped that what has been said will put into perspective the roles of the PMM and rotating arm. These maybe summed up asfollows-The PMM is particularly suited to obtaining linear derivatives and to measuring their dependence on frequency. It is also capable of
measuring roll derivatives.
The rotating arm is particularly suited to obtaining both the form and value of non-linear terms which involve rotations, including cross
couplings. It is not able to measure roll derivatives or acceleration derivatives.
*
References
Standard Equations of Motion for Submarine Simulation
Mbrton Gertler and Grant R. Hagan. NSRDC Report 2510, Juno 1967.
A Digital Computer Technique for Prediction of Standard
Manoeuvres of Surface Ships. J. Strom-Tejson DTNB Report 2130
Dec.
1965.
ri APPEUD IX 1 LATERAL FORCE, Y from DTMB 2510
LATERAL FORCE y
r.
mi v - wp + ur(r2 + p2) +
ZG (qr p) (qp + r) j+e-L [Y Y.' r i Y.' p. + Y pip,' pipl + Y
pq
pq +Yqr'
cirri2 r P r-+
-2- 43
1 +Yvq'
vq + Y ' wp + Y ' wr 2 L v 1wp
+ L
P3 ry
+Y up+Y
.16r + y
1 v i (v2 ? t u P ir/or V ri IVIIe
u2 +
Yv uv +
Yvivl
i(v2 +
-+-P 2 ¡I'vw+Y6r'a2 ori
vw
+ B) cose
sin 4) r (i1)-uv +Y
'v.! (1/.2 +
w2)+ y6rni e)r u2
1)+In
where Uc is ' commanded speed'
THE MECHANICAL SYS1.121 AHD ITS USE
by R. S. Tee
Preliminary Remarks on the Ship Tank
The LEW PlAM for vertical plane oscillations was designed and
built by Nydronautics Incorporated, of Maryland, U.S.A. and is a direct descendant of the eauipment used by N.S.R.D.C. (Taylor Ebdel Basin), Washington, D.C. It is tailored to the requirements of No. 2 Ship Tank at AEW both as regards dimensions and instrumnntation.
Before studying the detail of the PMLlit is worthwhile to des-cribe Ho. 2 Ship Tank briefly and to consider the general experiment technique for such a facility. No. 2 Ship Tank, shown in fig. 2, is 890 feet long, 40 feet wide and 1S feet deep. The channel contains fresh water which is dosed with chlorine to minimise the growth of aquatic life in the tank. Yodels are towed along the tank by a
carriage straddling the tank and running on a pair of well levelled rails. The carriage accelerates to a pre-set speed which is held for
the maximum distance compatible with safe stopping at the end of the pass. The steady speed is adjustable at present up to a maximum of 1500 feet/minute. As the running speed is increased the length of
tank available for constant speed is reduced and hence time at constant speed is doubly reduced.
We shall here be concerned only with experiments on submerged bodies, i.e. bodies which are sufficiently far below the water surface for there to be no surface disturbance and sufficiently far from any solid surface for there to be no interference from that surface. Under these conditions experiments may be run at speeds other than those required by equality of Fraude Number. In this case the model speed may be chosen to minimise the effects of disparity of Reynolds Humber between model and full size. This requirement calls for high model speed which must be tempered by the conflicting problems,
The higher the speed the ETeater the power to be supplied from inside the model, and
The higher the speed the shorter the time available for measurement and integTation.
The conditions of complete absence of Fraude Number effect are of course ideal and as model tests must be made in the limited depth of
a ship tank some minor aurface effects are to bc found. Additionally with a self propelled model i.e. a captive model in uhich the forces in
the X direction are balanced by thrust from some propulsor, it is difficult to determine the exact propulsion conditions with the PTJM
equipment. If the model is then ran at a number of speeds some
variation in flow conditions from those of the true propulsion condition
could occur between the different speeds. This random error in deter-mining the propulsion condition, together with a free surface effect which
will charge rapidly with speed changes, will provide a scattering effect in correlating data from tests involving variations in model speed. If either of these effects is gradual uver the speed range used for a series of tests it is possible for them to add to a Reynolds Number effect which itself introduces a steady .change in force coefficient of the form
Force/ p12v2 with change of upeed.
The problem of speed effects upsetting the results of model tests
is overcome at /.ET:7. by running at a single upeed, generally 600 feet per minute for a 16 foot model. This speed also gives a satisfactory model propulsion power requirement and a convenient time at constant speed.
This device does not however eliminate or even estimate the differences between model and full size which must be.dealt with by a correlation
constant from previous experience. The Reynolds number effect will be most marked in the derivatives due to control =face angle variations. In this case some improvement may be made by fitting turbulence
stimu-lating pins or wires to ensure that the flow is fully turbulent over the control surfaces.
Descrilytion of the 11-,dronautics
In essence the functions of the PDLM are threefold: It must measure the forces acting on the model.
It is the mechanical connection between model and carriage. It is the reference frame for model attitude and motions. For our present purposes it is convenient to describe the mechanism in terms of these functions and in the order shown above, starting at the
attached model. Fig. 1 shows the general arrangement of the PNEK.
Forces are measured by modular force gauges assembled into what
is effectively a six component balance. Groups, each of three gauges, are mounted at two points separated longitudinally in the model. The
three Gauges in each group are arranged such that one will measure the X component, one will measure the Y component and the other will measure
the Z component of the applied force. Each group of gauges forms a
cantilever rigidly attached to the model and pin jointed to the supporting
swords.
The modular force gauge, which is described in another chapter, measures shear force hence each gauge in the cantilever is measuring the
force component, corresponding to its measuring axis, acting at the pin
joint. This arrangement of gauges gives enough information to determine the forces X, Y5 Z and the moments, 11 and N. To complete the six
component balance a torque gauge is introduced into the after gauge cantilaver with its axis in the x direction to measure moment L. The longitudinal axis of the full balance is carefully aligned in the model to coincide with the longitudinal (x axis) axis of the model. The longitudinal axis of the gauges is arranged to pass through the point in the model corresponding to the vertical mass centre of the ship, the longitudinal position of the gauges being arranged so that the ship mass
centre is midway between the pin joints of each gauge group.
The model is supported outside the gauges by a pair of streamlined struts or swords. To minimise the interaction between the swords and model the section of the swords is reduced to 3 inch chord length for
some 12 to 18 inches distance from the model. This small section length of sword telescopes into the larger sword section so giving a means of adjusting sword length and also maximum depth of immersion. The connection between the swords and gauge gToups is by a series of pin joints designed to give freedom of movement for the forced motions as well as a point of zero bending moment in the gauge assemblies to determine the points of action of the applied (measured) forces. The swords are hung from carriers fixed to the driving mechanism. The carrier-to-sword joint is in the form of a horizontal slide which allows the sword spacing to be varied from 3 feet 9 inches to 7 feet 7 inches. If the mechanism is to be used to impart rolling motions to the model the minimum sword spacing is then 6 ft 0 inches, this limitation being necessary to allow the rolling push-rod to be connected to the mechanism. The upper part of each sword carrier forms a piston which engages in a vertical.cylinder in the tilt table. The tilt table forms the main
frame Of the mechanism and has sufficient stiffness for this to be lifted by crane complete with swords and model. The tilt table is supported by bearings, at its mid length, which enable the table to be tilted about a
transverse horizontal axis, to set the model at steady angles of attack. The tilt table bearings are supported by split pillow blocks fixed to
the 'A' frame. The 'A' frame is a tubular construction space frame with a pair of machined vertical slides (which clamp onto vertical support rails fixed to the carriage structure) and a pair of braced horizontal arms to support the tilt table bearing blocks. The vertical face of the
'A' frame also houses ajacking screw with a link from the travelling nut to the forward end of the tilt table. This jacking system is used to adjust the angle of the tilt table.
In the description of the tilt table support system we have seen the way in which static angles of datum inclination are applied. Oscil-latory motions in the vertical plane, i.e. pitching and heaving, are
imparted to the model by oscillating the swords with a vertical motion. The type of motion is defined by the phase difference between the motions of the swords. In this PILM the motions are produced by slider-crank mechanisms, one for each sword and both driven from a common shaft. The pistons of the sword carriersare the sliders for the slider crank mechanisms. The cranks are infinitely adjustable from 0 to 2 inches, and when at the normal setting of 1 inch one 1/20 of the length of the connecting rod. With this arrangement, the equipment designers claim that the motions are satisfactory approximations to simple harmonic motion for this application. Between the forward sword crosshead and the main driver pulley there is a phase changer. This is a sliding flanged coupling that is so adjustable as to provide any phase difference between the motions of the two swords. The main drive shaft is turned by a belt drive from a constant speed motor. The belt drive is arranged with a choice of five ratios to Eive main main drive frequencies of
0.2079 0.344 O.
A separate fixed radius crank may be attached -Là the main drive shaft if the other cranks are at zero eccentricity. This crank drives a small piston which imposes a linear S.H.M. on a push-rod that is fitted
to the after, sword; this provides a means of rolling the model to a fixed amplitude of ± 2.6 degrees.
The final important feature on the tilt table is a fixe channel sine-cosine potentiometer which is fitted to the forward end of the main
drive shaft . This potentiometer is used to provide a datum by means
of which measured forces and moments may be separated into in-phase and
quadrature Components.
Experiments for deeply submerged bodies
The theory relating the model to the full scale ship embodies data which refers to a body that is completely free in water. It is essential that this condition is approached as closely as possible with the model in the ship tank. In particular all efforts must be made to minimise any interference between the swords and any major appendange,
such as the bridge fin. It is aarrent practice for deeply submerged bodies5 to mount the model upside down to remove the bridge fin from
the viscinity of the swords.
For many experiments the model is tested with some appendages removed or replaced by others of alternative form. As it is difficult to ensure that weight and buoyancy changes will be equal when the
appendages are changed it is usual tc choose some suitable appendage condition in which the model will be ballasted to neutral buoyancy before being fitted to the PDILL The amount by which the model is
out of neutral buoyancy may be determined for each model appendage condition by a tilt test once the PLIA1 and model are rigged on the carriage. For this test the model is always fully submerged in water with the carriage stationary. The tilt table is inclined in 2 degree increments to ± 10 degrees. At each step X and Z components of force
are measured. The "out of buoyancy" force is determined from the
slope of a curve in which the sum of the two X-gauge readings is plotted against pitch angle. The model mass (which must include the mass of water in those spaces uhich uould be free flooding in the dhip) is
defined as
+ B
envelope volume of model density of water
excess buoyancy as measured by the X gauges.
This is the model mass uhich has to be accelerated (in part) by forces transmitted and measured by the X gauges. It rffust be augmented
by the mass of twice (i X gauge + XY gauge connector + Y gauge) for the Y gauges, uith similar modifications for the Z gauges. The out of 'buoyancy moment' is found by plotting the difference in Z gauge readings against angle of inclination. The buoyancy moment per unit angle of trim is then
moment = 3 sT1.7trd spacing (Z2 - Z1) / anglo of inclination.
5
m =
where V =
=
Althaugh similarity of external form is preserved it is unlikely that the model will have the same inertia characteristics as the full scale ship. This is because the instrumentation, propulsion motors etc. all place limitations on the way space is emplo:Tod within the model. The moments of inertia may be determined by oscillation tests iperformed in air; alternatively they may be estimated by empirical formulae, depending on the accuracy required and the existence of suitable data for similar models. Por the inertia tests performed in air, all aper-tures in the external surface are sealed and those spaces within the model which will subsequently be free flooding (i.e. in the towing tests)
are filled with water. The phase changer is set to give 180 degrees phase difference between the sword motions and the crank radii are set
at 1 inch. The mechanism is run at each of the five frequencies and the in-phase components of the forces measured by the Z gauges are
recorded for each frequency used. The moment of inertia may be deter-mined from the slope of the curve obtained by plotting difference in Z force components against pitching acceleration.
A similar series of tests for roll will determine the moment of
inertia for roll. In each case the moments of inertia will be about the gauge axes which have been aligned with the axes corresponding to the centre of gravity of the full scale ship and not those corresponding
to the model centre of gravity.
The tank tests for a fully submerged body can give data for both
vertical and horizontal plane motions. The limitations of the P1411 require that the model be turned on its side for the horizontal motions and this divides the tests into two
series:-Firstly, with the model mounted upright,
Control surfaces at zero deflection; vary datum inclination of body
Datum inclination of body zero; each set of
hydroplanes is deflected independently
Control surfaces at zero deflection; the model is oscillated in pure heave
Control surfaces at zero deflection; the model is oscillated in pure pitch
Control surfaces at zero deflection and body
inclination zero; the model is oscillated
Secondly, with the model mounted on its side, the tests autlined above are repeated for the hydrodynamic forces and moments associated with horizontal (i.e. antisymmetric) motion.
..Por each measurement two readings are made with a reversal of gauge connection between them. This is so that any small zero error may be removed from the results. These two readingn are referred to as normal (N) and reverse (R) gauge connection.
For static forces one measurement is made for each datum
inclination or control surface deflection. Fc,r dynamic tests (pitching and heaving) the in-phase and quadrature components of force are avail-able, although they mcy not be read simultaneously.
It is usual for several readings to be made in one pass along the tank and it is always arranged for the N and R readings to be made in the same pass.
The force component readings are recorded by line printer in the format shown in figure 3. The data is manually spaced on the carriage
so that one block of numbers refers to a single pass along the tank. Carriage speed and control surface deflections are recorded manually and logged by the experimenter.
Having studied the detail of the mechanism and the various tests to be made with the mechanism we can now conveniently tie the motions of the mechanism to the motions required in testing the model.
Let us assume that the motions of the swords along their vertical axies is simple harmonic motion.
Then if
Z1 is the displacement of the forward sword
from its mean position
and Z2 is the displacement of the after sword
from its mean position
in the case of a general motion for this mechanism these motions may be expressed as
= a sin wt =' a sin(wt - 1)
The amplitude of the motions are limited to being equal for equal uuord
spacing from the ship centre of gravity.
As these displacements are about a mean position t . o
corres-ponds to the mechanism being so positioned that the forward crosshead is
level and about to move in a direction corresponding to + ve Z for the model axes.
In the case of pure heaving the model mast remain level,
therefore z1 z2 and so S = o. Also the mechanism motion is in-phase with the model motion so that the sine-cosine potentiometer zero may be
set at the mechanism zero defined above.
In the case of pure pitching we want the model axis origin
(corresponding to the ship centre of gravity) to move along a sinusoidal path in the vertical plane with the model x-axis remaining tangential to
the path.
In the limited case of equal sword spacing and equal sword motion amplitudes, the displacement of the model axis origin will be
Z +Z
Zo . 1 2
2
Substituting the expressions for Zl + Z2 and expanding we get
a
Zo = - sin wt (1 + cos
I)
-
cos wt sin c/2
Differentiating this w.r.t. t for the vertical velocity of
the origin,
Zo+ cos )) cos wt + sin
S sin wti (1)2 t
pae to the phase angle between the swords the model x axis will be inclined to the pitch angle
e
given by,9
Z2 - Zl(2)
where b is the sword spacing
Substituting for Z1 and Z2 and expanding we get,
- cos
S)
sin wt + sin i cos IA I ..(3)
b ; 4
Now the vertical velocity with respect to the model axes is,
Zo = 7-cos -
sinS
(4)
The definition of the required motion leads to-"= o
and for small angles sin
e
so that equation(4)
reduces toSubstituting from equations (1) and (3) into equation
(5)
--,et
U
'1 + cos
4
cos wt + sin ç1 sin wtb
1 cos y) sin wt + sin 9S cos wt2
Equating sine and cosine terms in wt
+ cos
4
- -
sin (6) , 2 bw.
U -- sin p,- cos
90
(7)
2Solving equations (6) and
(7)
for cos we get the following relationship for the phase angle between the sword motions for pure pitching 1 _(M2
cos=bw
1+ç
bw) Returning to equation (3)- (1 - cos
4
sin wt + sin cos w ,b
this can be restated as
= af"3. Sin Ç! / COS (Vit
-'2
Since = o for pitching the Ditch angle ì = o when
2
cos (wt Lm 0
2
for our purposes when wt
= 90 +
k from
our defined mechanism zero. 2This is the angle the forward crosshead must make with the mechanism zero when the sine-cosine potentiometer is at zero in order that the in-phase and quadratare components of the forces will be referred to the model motion.
Experiments with Surface Effect
Uhen a submerged body is made ta run close ta the surface, the waves that are created modify the derivatives that relate to deep sdb-mersion. It is necessary, sometimes, to investigate this modification. It is possible to reduce the model immersion with the AEW PM.21 by a
case the model must be upright to present the correct form to the surface.) A series of shallow depths may be examined, each one by a set ofexperiments. As wavemaking is an important feature the carriage speed must now be that required by equality of Froude Number and the data will no longer by applicable to all speeds. Under these conditions the data must be corrected to account for disparity of Reynolds Number between model and
ship.
Requirements for Models
To suit the facility as regards operating speeds and freedom from tank boundary effects, the models used one normally 15 to 18 feet long. Within this length the division of space is largely dictated by the
requirements of the PZUM gauges. As rolling motion is generally required the sword spacing must be at least 6 feet.
As the model must be run upside down and on its side it is essential that the change from the one configuration to the other be easily accomplished without disturbing the gauges or cables. It is usual practice therefore to make a body of revolution for the centre
portion of the model which carries the gauges and to add suitable append-ages to provide necessary departures from the axial symmetry - generally a bow unit, casing, bridge fin and a stern unit incorporating the
propulsion motor. These appendages may be screwed to the main body in the positions required for the different configurations.
STAT IC PITCH ANGLE ± CARRIAGE .--SUPPORT RAIL 8 FT. O IN, 4 Ft 5IN. ' FFkAME SINE/COSINE POT ! FWD. SWORD CROSSHEAD _FORCE \GAGES PHASE CHANGER SWORD T R UNN I ON BRG. 7 FT. 7 IN. ..- --MAXIMUM MAIN MOTOR 3 FT MIN IMUM F REFERENCE POINT BELT DRIVE / X Y Z AFTER SWORD / CROSSHEAD -ROLL CFk ANK - TILT TABLE CYLINDER ---ROLL MECHANISM SWORD CARRIER _ SWORD 22 N COLLAPSIBLE
L ROLL BALANCE K' SIX COMPONENT
BALANCE
FIG. I. GENERAL ARRANGEMENT OF THE HYDRONAUTICS PLANAR MOTION MECHANIShi F'OR
I 1 121
314(1516118(9110111112113114i
013+00 +0059+000 +0033+0055-221 -2166+0393-0000 0002-0000 1 1 012+00 +0059+0000+0033+0055-2216-2167+0392-0000 0002-0000 1 1 011+00 +0049+0000+0027+0045-2203-2185+0316-0000 0002-0000 1 1 010+00 +0049+0000+0027+0045-2203-2185+0316-0000 0002-0000 1 1 009+00 +0041+0000+0013+0035-2186-2202+0244-0000 0002-0000 1 1 J08+00 +0041+0000+0018+0035-2187-2202+0244-0000 0002-0000 1 1 007+00 +0040+0000+0013+0025-2167-2220+0172-0000 0002-0000 1 1 006+00 +0040+0001+0014+0025-2169-2222+0172-0000 0002-0000 1 1 COLUMN CODING 1 Run Number2 Tilt Table Angle
3-12
10 sets of Force Components13 Timor Control Unit mode - Code 1 - Static Mode 4 second Integration Time 2 - Static Modo 10 second Integration Time 3 - Dynamic at Standard Calibration
4 - Dynamic at 10 times Standard Calibration
14 Force Component Separator Codo 1 - Calibrate
2 - In-Phase Component 3 - Quadrature Component
15 N + R Code N +
-16 Total Integration Time
17 Number of Qycles for Evnamic Sample Pass Number added in Ilhnuscript
151
161171
Pass No. - 04000 00 ) + 04000 00 ) 5-
04000 00 ) + 04000 GO ) - 04000 00 ) + 04000 00 ) - 04000 00 ) 6 + 04000 00 )GITGES AND DTSTRUMENTATION
by B. K. Simmon.ds
Modular Force Gauge (Fig. 1)
1. Mechanical
The modular force gauge used in the AEWPMM is a
4"
cube machined out of a solid4"
cube of stainless steel. The stainless steel, ARNr0 STEEL CORP.17-4
PH., was chosen for therfollowingreasons:-excellent flexural properties, corrosion resistant,
can be machined and heat treated without distortion, iv. has practically zero mechanical hysteresis.
Each gauge has three pairs of faces known as flexures, mounting gurfaccs and open ends and the dimensions are guch that all gauges are interchangeable..
The inside ofthe gauge is formed by machining away as little material from the aube as is practical and providing two major parts. These parts arc the pedestals which support and maintain the relative position of the transducer coil and core. The coil pedestal (which is very stiff) is integral with, and moves with one mounting face, and the core pedestal (which is also very stiff) is integral with, and moves with the opposite mounting face. This arrangement is guch that the transducer senses the
deflection of the flexures as a parallel movement of one mounting face with another. The relative deflection of the mounting faces is about
0.01 inch for a load of 500 lb. The natural frequency of the rig with
a 2000 lb. model attached (this includes the added mass of the model) is about 16 Hz for each gauge compared with a maximum forced motion frequency
of 0.66 Hz. The static calibration therefore applies to the oscillatory forces meagured. The spring constant of the flexure boxes is in fact
chosen hish anaush to obtain a natural frequency which does not result in magnification of oscillatory forces due to either carriage vibrations or forced mechanism motions, and is yet low enough to give good
sensitivity and resolution.
Interaction between gauges is stated to be of the order of 0.05 per
cent. Por Practical purposes they meagure one pure component of force each, in the X. Y9 and Z directions. See Fig. 3.
2. Electrical
The transducer used with the force gauges is of the variable reluctance type.
The signal output of the transducer changes when its core is dis-placed axially relative to its coil. This is because of changes inthe length of air gaps between the poles. The sensitivity and the range of linearity of the transducer is governed by the ratio of maximum core movement to length of air gap. It is 8:1 for a 500 lb gauge.
Roll Gau,-e (Fig. 2)
This gauge is designed to meagure pure torque about one axis. It
is not affected by forces and moments exerted in other directions. The primary elements of the gauge are the shaft assembly and coil. The shaft assembly is further subdivided inte a flexure section and an
armature. The shaft is made of K monel because of its low mechanical hysteresis and non-magnetic properties. The flexural element is located about midway along the length of the shaft. Magnetic stainless steel is used for the armature which consists of three rings fastened over the
shaft, one at each end and one at the middle of the flexural element. These rings are supT)orted by a slotted cylinder which is attached to the
shaft and transforms an angular twist into a longitudinal displacement. The configuration of the rings is such that two longitudinal air
gaps
are formed at each side of the centre ring. When a torque in a given direction is applied to the shaft, .the air gap on one side decreases and the one on the other side increases by an equal amount. The differential changes inmagnetic path cause the signal changes in the transducer.The torsional spring constant of this gauge is 650 lb-feet per 30
minutes of twist. The air gaps in the armature are 0.02 inches to obtain the desired sensitivity and linearity.
The coil unit used in conjunction with the armature constitutes the transducer and is excited in the same manner as the modular force gauges.
The roll gauge is fastened into a block and is so mounted in the
model that it has freedom about the pitch and yaw axes but is restrained
about the roll axis. Thus when a roll moment is applied, there is essentially no rotation of the coil or the fixed end of the shaft.
Instrumentation (Fig. 4)
The instrumentation used with the AEW PLIM comprises the data acquisition system for both static and dynamic tests.
It consists of 10 channels of signal conditioning and digital read out equipment, and 0 channels for dynamic measurements. All channels and
components are designed to be completely interchangeable and each channel is independent of the others. The output is recorded by a line printer which can record data from all 10 channels, run number and switch positions
simultaneously.
Each channel consists
ofg-A signal conditioner. (SCU)
A force component separator.
(ros)
An integrating digital voltmeter. (TTNTI)
The SCU has the following facilities:-gauge balance,
choice of polarity (according to a chosen sign convention), amplifier balance,
choice of sensitivity based on gauge calibration by means of the 'CAL' and 'SPAN adjustments.
A timer control unit
(Tau)
controls the integrating time of all IDVM's in the static modo. In the dynamic mode, the integrating time is controlled by both the TCU and micro switch pulser. ( see later note)Static Mode of Operation
In this mode the amplified gauge signal (maximum + 10v) is passed through the POS and into the ADVM, the TCU providing a fixedtimebase of either C.19 4 or 10 seconds. In this mode, the system integrates and displays a reading which is the mean force imposed on the gauge. For
the same gauge force, the readout is the same in the 0.19 4 or 10 seconds integrating period, since a time base factor is incorporated in the IDVM's.
The outputs of all the IDVM's are fed to the in line printer uhich records information on command. The visual display on the IDVM's is retained until the next command for readout is given.
lynalide of Operation
This system is made up of 8 channels (only 8 FCS's being available). The sinusoidally varying signal, imposed on the gaige by the PIVII is
fed into the SCU. The product of the output signal from the SCU with
either the sine or cosine signal generated by the sin-cos potentiometer (which is driven by the PMM at drive frequency) is fed into the IDVM.
The time base for the IDVM in this mode is controlled by the TCU and micro-switch pulse. (This micro-switch is geared to the sin-cos
potentiometer and operates once per revolution of the potentiometer). The number of cycles of oscillation of the model by the PMM is selected
on the TCU, the IDVM starts counting at the first cloaure of the micro-switch and stops after the selected number of cycles are completed. The
time of integration is displayed by the electronic clock on the TCU. The integral ofthe signal is therefore the reading displayed on the IDVM divided by the selected time of integration. These readings are recorded as before upon completion of the integration cycle.
Instrumentation Units
1.
Sic-n1
ConditionerThis is basically a two channel unit providing a 45 volt 400 Hz excitation to two differential variable reluctance gauges and converts
the ac output of each to a dc. I.e. a demodulator. There are five of these units.
Facilities:-Switches
a) Function
i. Int.Bal.
This connects the transformer primaries in parallel so that their voltages are equal, regardless of gauge position.
The demodulator portion can then be balanced using the Int.Bal. potentiometer. This adjustment will not normally require resetting after initial set-up.
Amp.Zero
This-shorts the operational amplifier input to earth enabling it to be balanced using the Amp.Trim. potentiometer.
Operate
This sets the unit into operational mode. Cal
This provides a step change in output equivalent to a known and repeatable gauge loading.
b) Polarity
This reverses connections to the outer legs of the gauge
winding. It allows a signal polarity to be selected to agree with a loading convention.
Potention¡eter Controls
i. Gauge Zero
This balances the gauge electrically. Offsets up to about full scale can be balanced out by this potentiometer. Large amounts of pro-load offset, however, dhould be corrected by re-positioning the gauge slug.
ii. Offset
This permits zeroing the
signal
output at any initial load condition.apan
This adjusts operational amplifier gain to standardise the output voltage in terms of load onthe gauge le 500 lbs 5.0 volts.
Force Component Saparator
This unit accommodates F, channels of static and dynamic information, the static or dynamic mode of each channel being selected.
In addition the unit provides a dynamic mode selector switch which is identified as follows: LIGHT NO CAL N 1 CAL R 1 IN- N 2 IN R 2
WAD N
3WAD R
3where N and R mean normal and reverse respectively, CAL is calibration, IU is in phase and WAD is quadrature.
Integrating Digital Voltmeter
This Integrates the POS output and provides in phase, quadrature and calibration components. There are 10 of these units.
In Line Printer
This prints out the following data Run number,
Tilt table angle,
8 blocks of model information (10
static),
Mode,Signal
definition (in phase, quadrature or calibration), Polarity,Time,
Mhthematical Operations performed by the Instrumentation System
STATIC NODE
In this mode of operation the gauge autput is fed via the S.C.U. to the F.C.S. directly.
Denoting the force on the gauge by PG, then the uutput of the F.C.S. is F(FCS) FG.
This is fed directly to the IDVN and integrated over a period T where T 0.1 sec., 4 sec. or 10 sec., depending on the setting of the modo switch on the T.C.U. Including a static scale factor Ks the output of the IDVM is
F IDVM) . Ks FGdt o
=F
7GT
F(Immi) F G XsT DYNANIC NODE HEAVINGThe gauge signal may be expressed as F gauge . F* + FIN sinwt + Four, cos wt
where P3. a bias' 2,N and FOUT are in-phase and quadrature
components respezbtively, w is the oscillation frequency and t is zero where the heave is zero, moving downwards.
This signal is applied to the sin/cosine potentiometer which multiplies it by sin wt or cos wt and also halves it. The
output from the sine/cos potentiometer is
therefore:-In7Rhase (FCS switch to IN)
sin wt 1/
F(FCS),N _ TkF*sin wt +E.
i2
nF
wt + FOUT sinwt coswt)
O;uadrature
(ros
switch to WAD)7(7CS)
OUT F gauge x cos wt = 1(F*cos wt + FIn sin wt cos wt +FOUTxos2w
2 2
Alternatively, with the PCS switch set to CAL the sima/coz potentiometer is 'oypassed, but the signal is still halved,
giving:-1 1 /
F
=p
b
.-auge x - =
a +
F sin wt + FOU1 cos wt)2 2 * IN
Whichever of these signals is selected is applied to the IDVM and
integrated over a selected number of cycles, n say, each of period T secs where T This integration does not commence at t= o, bit is controlled by the pulsar which operates at t = VA-T, t'+ 2T, etc. .
Including also a calibration factor Kim. the outyut from the IDVM
is:-Hence Inshase
t,+ nT, (F10V7A1)N - K
I - DYN
I'
(-ELIO'S) ardtt,
t,+ nT,
f/
= 1?sin wt + F sin2wt + F sin wt cos wt) dt
2
.f
IN OUTt,
-t,+nT
1- t
= P:DYNj -F* cos wt + FIN(t - sin2wt) - FOUT cos 2 vrt
2 !
-
2w --- it,L w 2 4w
= KDTnTPT
4
since cos w(to-nT) = cos(wt,+2nil) = cos wt, sin au(t,+nT)= sin 2 wt,
cos 2w(t,+nT) = cos 2 wt,
FM
= 4 IDVM')flTn T
Quadrative
A similar integration gives
:-T, (F IDVN)OUT = K
nTF
DYN OUT HenceThe dynamic scale factor KI,JyN is related to the static scale factor K as follows
For TCU switch set to DYN 10 XD.=
= As
" FIN 1 Y
4
= . (F IIA711)
CUT OUT .
CAL
With the POS S switch set to CAL the I DVM output is t-t1+ nT
(p1) CAL
= Kim/ F0.02 dtt, +nT
--
Km.
( F* + FIN sinwt + coswt) dtFOUT 2 t, Km. n T F 2 Hence F* (I?IDVM) CAL YN PITCHING
identical results are obtained for pitching as for heaving.
In pitching the time t at which the pitch is zero differs from that at which heave is zero. To compensate for this the sin/cos potentiometer spindle is rotated rela,tive to the drive shaft so that sine = o, cosine= 1,
when pitch is zero. If now time t is measured from the time of zero pitch
pitching downwards the analysis is identical with that for heave. The phase relationships are Shown in Fig. 5.
In the heave mode zero heave occurs when the struts are at half travel, i.e. they are both in their mean vertical position. In the pitch mode zero pitch occurs when the struts are near the top dead centre; the forward strut is advanced from t.d.c. by an angle 2 and the after strut is retarded from t.d.c. by the same angle. Pig.5 shows that if the forward strut is advanced by en angle Os on the after strut, the potentiometer spindle must be advanced by a further angle 90°
2
relativo to the forward strut. (Alternatively the potentiometer autput may be set to zero and 1800 out of phase with the pitch by retarding the
spindle 500
+ Os
relative to the forward strut. In that case the2
polarity of the out-out is reversed for both in-phase and quadrative components. This can be corrected by appropriate settings of the
polarity selector switches.)
pulser micro switch (fixed) pulser (on potr'spindle)r , pulser
potspindle
' phase chamgeafter strut forward strut
...----2
Pitching mode
Angular positions at zero pitch.
FIG. 5
/ potentiometer zero (sine= o, cosine= 1) fixed to frame
potentiometer spindle
\\
potentiometer phase changer\
\ 4. forward strut after strut Heaving modeAngular positions at zero heave.
\microswitch
OPEN END
PLEXURE ArNS
ROLL
ShAFT
AIR GAP
AIR GAP
TpA NS IDUC E
COI LS
1\\N,
N
T AN SOU C ER
CO! LS
CABLE
ROLL GAUGE ASSEMBLY (simpLIFIED)
To 59t-L.ER,S-CIL ASS `f F oR R L.L. ,?Ss'r` ( F 147-T
/
111/
/ /
/
/
//
GUSSETED AN GL F_
BRACK ET
,I.ExuR ESf3ED PLAT E
MODULAR FORCE GAUGE ASSEMBLY
CHANNE LED PLATE
t 0 VAC
50/0
E) --- C. REGULATOR GA U GE Fr C"u
_
TILT TABLE CONTROL POI SIN-COS-POT ACK LI SCON NE CT BOX RE MOTE oNTROL SER (t1-0. coNT ROL LT TABLE CONTROL sto COND. C. POWER C(13) P 3 SCOPE AkiP SCAN vER1IC A L A NO HORIZONTAL CO,IT ROL Ns.,-)L-TPi
E NTAT ION
F MAT I C
c(3)TSU
LI NE
PRINTER
WON NO INDEX CONTROL4
REMOTE sTART TABLE TI LT. # t Mt, ,114,..111.1 114 fi0
11.404Atiot,' t , , I ,,j11111 1,10,mw,e044.4,,,,Syk 'Ark4. ',,r1,16.40,43164141,11,1,4, ' V441. i;
DATA REDUCTION
by A.Driscoll
This lecture is a brief description of the data recorded by the AEU PLET and the mathematical reduction needed to obtain the derivatives.
Data Recordin
Figure 1 shows the format of the seventy two character line printer which records output, and gives the relative print out positions of the data from the gauges and other instruments. Every experiment conducted
on the model involves two lines of print out data, one line each for the normal and reverse modes. The tilt-table angle in degTees, giving the
attitude of the model, is shown in columns
4-6,
the gauge readings in counts are shown in columns II-42, the time of the experiment in seconds in columns65-69.
The print out from the timer control unit, incolumn 59,
gives a value of 1 for static experiments, the DVM's integrating over a 4 second interval, a value of 2 for static experiments integralingover a 10 second interval, a value of 3 for dynamic experiments
integrating over the time of the selected number of cycles and a vnlue of 4 for dynamic experiments with the gain increased by a factor of 10.
The model, and PMM operating conditions, consisting of the model length, the distance between the swords, the position of the gauges in relation to the centre of gravity, the amplitude of roll oscillation, the length of the oscillating crank, the carriage speed and the rudder and hydroplane angles are recorded in the experimenters red book.
The Model inverted (a) Tare Tests
A static tare test with the model at the experiment depth of submersion, and at as near neutral buvancy as possible, is conducted
toevaluatethemodeltassc
mm, and the model hydrostatic moment (10- ) .m The submerged model is pitched in regular steps from 100 bow rise to
10° bow dive. The sum of the readings from the forward
and after "X" gauges are plotted against their respective pitch angles. The slope of the resulting curve gives the amount by which the model is heavy or light. (Figure
3.)
This amount is taen added to or gubtracted from the calculated form displacement. The gauges in the An PMM are arranged such that encroaching into the form displacement are half the weight of the "X" gauges, the total weight of the ftY" gauges and half the weight of the "Z" gauges, together with the weight of the strongbacks and anglo brackets.difference of the "Z," gauge readings is plotted against pitch angle9 the slope of this curve multiplied by x (half the distance between the pivots) being the value of (%)m. (Figure
3.)
Pure pitching in air experiments are conducted to evaluate the model longitudinal moment of inertia (Iy)m, the model being completely filled with water the "in phase" component of "Z" force being measured. The
slope of the plot of
X(ZAFT-ZFr,,D)
against
3
2
2 ,2
gives the value of (Iy)m; To reduce the amount of calculation involved in this tare test (ZAFT -ZFWD) is plotted
against49
the slopesubsequently being non-dimensionalised. (Figure
4.)
The transverse moment of inertia (Ix)m is evaluated by pure rolling in air experiments, the "in phase" components of roll forces being
plotted as for (Iy)ni
Stati* Experiments
These experiments are conducted on the model with variations of pitch angle Ef with constant hydroplane angles9 and also with variations
in hydroplane angle with constant pitch angle. The experiments are conducted with the Timer Control Unit (T.C.U.) in the calibration
4 second or 10 second operating mode. The values of the non-dimensional lift forces Z' and pitch moments for each experiment are calculated
from equations 1. The values of Z1 are plotted against their respective pitch gles (figure 5) the Z' value at G, 0 being the Z derivative, the slope at G. . 0 multiplied by
57.3
being the Z derivative and the average difference between the fllax values of slope and 6xperiment plot\
divided by 6/e/ multiplied by
(57.3)2
being the Z'/, // derivative.
VT IV
These derivatives give the equation Z' + Zjvw + Z6/w/w/ as the fit to the curve.
Similarly from the plots of M' against pitch angle, and Z' and M'
against hydroplane angle9 the derivatesMI, / /9 Z! Z1 / /9
"'
W'M
W/ W/ 45 5/ g 5/ 'M
and Mt / / are evaluated.bs SS/ S/
Dynamic Experiments
These experiments are conducted on the model with constant pitch
angle and constant hydroplane angle. The experiments are conducted with the T.C.U. in the olynamic moder. The values of the non-dimensional lift forces Z' and M' are calaulated from equations 29 the roll moment K1
calaalated from equation
5,
the experiments being conducted for "quadrature" and "in phase", normal and reverse modes of operation.For the pure heave experiments the component of velocity, w'o, of the origin of the body axis along the "z" axis relative to the fluid and the component of acceleration, 1Y are calculated from equations 3.
The Z' and MI vnlues calculated from the "quadrature phase" experiment are divided by their corresponding values of w' , the resulting slopes
2 °
being plotted against their corresponding-% values. The plots of Z'/
IV 0
and Mt/ , give straight lines, the values of the intercepts at
w o
equal to zero being the derivatives Z' and (Mt + I'ym) giving a check on the static experiment derivatives.
The Z1 and M' values calculated from the "in phase" experiments are related to *'o as above to obtain the derivates (Z' - m'm) and M.'.
For the pure pitching eameriments the angular velocity component q'o relative to the "y" axis and the angular acceleration component cro are calculated from equation 4.
The reduction of the pitching data is as for the heave experiments relating Z' q'o and ? to give the derivates (Zq' + mini) and
WAD'
WAD'
2
and relating Z'
4'o
and to give the derivatives Z' and(M'
- Itym).For the pure rolling experiments the angular velocity component p'o relative to the "x" axis and the angular acceleration component
L'o
are calculated from oquations 6.The 1(.1 values calculated from the "quadrature phase" experiments are plotted against pto the resulting slope being the derivative Kp'.
Similarly the plot of the "in phase" X' values against 15.'o gives the derivative KL'.
3. The Model on Side Tare Tests
Tare tests are conducted as for the model inverted to evaluate the longitudinal moment of inertia
(Iz)m the analysis being similar. Static tomeriments
Also the same as for model invented.
Dynamic laxperiments
Data reduction of the experiment results obtained from the model on side is conducted as for the model inverted, the lift forces Z' and pitch moments M' becoming yaw force Y' and yaw moments N'. The velocity
and acceleration components vro, Tic) and 1.-To being calculated from
equations 3 and 49 the reaulting evaluated derivates being
Y;' 'v/v/' 11*' N-;' 14117/v/
STATIC
Y!,2! Ys11/62/5
N6
and N6R/h/Note:- ,H is the rudder angle.
Y', (Y + Iz1m) V.'
(Y.'
-
m' ) and N.m"
(Y'- m,)
N' r m r' I'zm) rOwing to the amount of time involved in the lengthy calculation and plotting required to define the derivatives an AEW computer
programme has been developed. The values of the non-dimensional forces and moments, the frequencies, and velocity and acceleration components are calaulated from equations 1 to 6.
The static derivatives are evaluated by best fit mathematical equations to the plots of forces and moments against pitch angae, hydroplane angle, etc., the mathematical equationsbeing derived from
aX2
o- bXo
-cl
=aminimum
(Figure 6)Jlathematical equations have been derived to Lit the plots of the dynamic experiment results agsinst,a2, and K' against p'oando
to give directly the values of the dynamic derivatives.
4
HEAVE
EQUATIONS 1
ST..LTIC =ERIN=
s
Z1 or Y' = 005 (Normal gauge reading Reverse gauge reading)
Gauge constant /Z.12. U .
xrY1
o r_ N' = - Z'FWD or L FWD - AjFT
1 I:2T 1
where 1 = model length in feet U = model speed in ft/sec.
X = distance between CG and gauge in feet . density between water in slugs/ft3.
EQUATIONS 2
DYNAMIC EaPEREMTTS
Zt y t 2. (Normal gauge readin _fLaug
Gauge constant. Time. ()/2.12.U2.
IV or N' as static experiments. ,EQUATIONS 3 wro, v'o U A021 PP
al a
where a = length of oscillating crank in feet.
EQUATIONS 4 q'o, rio where cos
ti
o 2a 7"b
1 2 2a. '2"2 . sin 2 t...2.2.0 2 1 + EQUATIONS 5K = 0.5 (Normal gauge reading + Reverse gauge reading)
Gauge constant. /2. . H 2 . EQUATIONS 6 o
22
6where amplitude of roll oscillation in degrees
* Note:-
The values of the reverse gauge readingn used inequations i and 5 although recorded in reverse mode are not in fact reversed.
1/4)0100
I124
!lac 131ilf
14. I TILT TABLE ANGLE0011111111k 1222r
222 233: :333344 4
3901 3456'0390 12,34 56.190
436T ,90122 +XXX. +XXX.X*XXX:r4tX.X.X.XiXX API' 7.1D AFT .17,rD X GAUGES 1 Y GAUGESiavs
ftiA1S 1 14.0,,,,,,1..--OtAt Loo:i(t 1/171 rilki340
40(.41 *003 -oc..51 1 H/45 ie/3 13
! i
4 o c. (14 40.411.4-00 in, i- /oil 4.01:ill r-Csot.45
4-ocx>i 4-ot-22, i o(5 4/00i 1--0(pli1 -oco ci
I ! I . , 1 1 A I rile OA( t)
if 64 5.
.of?
1 c, JE-/ELikrE.
iterit2
f..\ Lxxxx xxxx
An I ROLL
I Z GAUGES 1- GAUGE'4444455555555
4567390123456
xxx+xxxx+xxxl
¡EXTRA GAUGES IF rEQUI RED '36666 , 756'89i1
urs..x.: x: TIME OF OSC I LL.A.TIONS 141 gA:1.53 3 C,52S5 3 4 04;)s-, 314
2 Tf: 2FIGURE 3
Q:P!TCH ANGLE
>< NJ;<
X N
`1.STATIC TARE TEST
o
z
2)0 0
GRE-:ESFIGURE 4
PITCHiNG N AIR
Ci La..12
[b
o
rt
(
N t,y65,c)YE
EQUATiON
Y0= QXØ + b X, + C
"t.
(.1 Xt.,2
b X0+ C -YE
EiFST FIT IS WHEN :
(E)2 is A MINIMUM
i.e. r YE
-
a. x-
bxo- c12 -
A MIMMUM
0
FIGURE 6
RESULTS OBTAINED FROM P.M.M. by R.K.Burcher.
1. Introduction
Before discussing the results so far obtained from the ?LEW Planar Mbtion hhchanism, it is wcrth considering the object of the experiments. The use of the derivative approach in the designbf submarines may be
described under two main headings:
The investigation into the directional stability and control effectiveness of a new design5 in comparision with previous successful designs,
The fcrmulation of an equation of motion so that manoeuvres,
particularly those under emergency conditions, can be investigated.
Item (a) needs to be undertaken at an early stage in the design so that madifications to form or control aurfaces can be introduced if
necessary. Such investigations require a knowledge of the linear steady or slow motion derivatives and these can most readily be obtained from the P.M.M.
Item (b) follows when the design has hardened and there is less chance of subsequent changes in design. The results provide safety margins and handling information to the Commanding Officer of the
submarine. This investigation requires more knowledge of the fluid forces and moments than (a), particularly of the non-linear derivatives
(or coefficients). In addition to the data that can be obtained from the P.M.M. it demands the use of the Rotating Arm Facility.
Before the P.M.M. arrived, the facilities available at AEVI for the measurement of derivatives were the towing carriage in the Ship Tank and the Rotating Arm in the Manoeuvring Tank. The towing carriage in the Ship Tank can only provide information on the derivatives for straight line steady motion. By towing the model down the tank at various drift angles either in the vertical'or horizontal plane, the derivatives with resect to away or heave can be obtained. Similarly by towing the model with various control angle settings the control derivatives can be
obtained. The Rotating Arm provides the ability to investigate the hydrodynamic forces on a model in a curved path. From a series of experiments with various radii and drift angles it is possible to obtain a mathematical fit to the measured forces in terms of the steady motion parameters with higher order and cross coupling terms. The coefficients
of these terms are loosely called derivatives but should not be regarded as anything more than coefficients of an approximate representation of
the hydrodynamic force which is convenient for the computation of a trajectory in a complex manoeuvre.
These two facilities therefore provide a considerable amount of information 'out by no means all that is required. They provide no in-formation at all on the acceleration derivatives and in the past these have had to be estimated from the theory for a simple ellipsoidal body
of the same volume and length to diameter ratio. Lt first sight these facilities do provide the necessary motions -Lo obtain the first order derivatives with respect to sway (v), heave (w)9 pitching (q) and yawing (r) but there is a practical problem. The experiments in the Ship Tank can be devised to give aufficient data to define the slope of the force curve at the origin in away and heave. However the Rotating Lam facility has a limited range of radii, so that9 with the smallest size cf model that we would be prepared to use, the range of values of r' or q' is about 0.2 to 0.6. Within this range we can conduct as many
experiments as necessary to define the force function but to obtain the derivatives 7e 9 N' 9 Z', M' we need to know the slope of the force curve
at the origin, i.e. at r' or q' = O. In this region we can only obtain values of the force at r' = 0.2 from Rotating Llm and at r' = 0 from
Ship Tanl: experiments. With the non-linearity of the curves and some experimental scatter the determination of the yawing and pitching derivatives can never be very accurate; indeed in some cases they are almost indetelLiinate (see Figure 1). This question of accuracy in the determination of the first order derivatives is very important when assessing directional stability.
The criterion for directional stability in the horizontal
plane is
Y N
- N (Y -m) --, 0vr
vWritten in this form the product terms are of unknown value depending on the particular vessel. However the criterion may be re-writtan as
r NNy 0
Y-m
r
Moment in which form the fractions are in the nature of a lever arm, i.e.
Force and for all vessels is of the order of 0.5. Thus the stability
criterion is the difference of two quantities of the same order of magnitude and is very dependent on the accuracy of determination of the
derivatives. ks a simple example, if a vessel is in fact marginally
stable, i.e. Nr Nv
Y -m
Yv
Y
v and the individual derivatives have been
c2iterion could lead to 0.95 Nr 1.05(Yr-m) 1.05 Ny 1.1 Nr 111. . 0.9 r
0.95
Yy Yr-m Yv Yvi.e. unstable or alternatively to +0.2 NV i.e. stable.
The use of estimated derivatives at an early stage in design is attended by this diffiaulty. By itself, an estimated derivative may
appear to agree reasonably well with a measured value but on combining dervaties as above to assess stability it is faund that they can be very misleading.
Results of EX7periments
In the short time the P1Mhas been in operation at AEW, teething troubles have restricted the number of experiments we have conducted, and there are many moreproving experiments that we wish to conduct before we shall be satisfied with the data produced. The work we have done has posed problems, not all of which can be answered at this time; but those problems may be of interest here.
Our initial experiment was in the nature of a "scarfing" test where we used a model for which relevant data had previously been obtained. The experiments using the PTJM included both static and dynamic modes of operation. The static runs with variaus fixed angles of drift should
compare directly with previous experiments conducted in the Ship Tank. For the dynamic experiments we adopted the recommendation of the
manufacturer to use constant carriage speed and amplitude of oscillation and obtain the vnriation in the motion parameter by daanges of frequency. The equipment only provides for 5 different frequencies so that our plottinEs of measured force against motion parameter were limited to 5
values. This should be sufficient if a straight line plot is obtained
together with relevant comparitive data is shown in Table 1.
Before discussing the comparison of the data obtained there are some problems involved in the analysis of P1411 data in order to arrive at the values of the derivatives which should be considered. Previous
lectures have given the basis of the analysis and the step by step
procedure. Our first sets of experiments were analysed using this
method and plotting the results to obtain the derivatives from the slopes. However it soon became obvious that the Ping is capable of producing data
