The use of reversed propellers to stop bodies moving in a fluid

ARCHIEF

Lab.

y.

Scheepsbouwkunde

Technische Hogeschool

THE USE OF KE VER SED PROPELLERS To

STOP BODIES MOVING ¡N A FLUID

+

LLOYD TREFFHEN

+

Repnted from

NAVAL

ENGINEERS JOURNAL

+

NOVEMBER, 1962 PRINTED IN U.SA.

THE USE OF

REVERSED PROPELLERS TO

STOP BODIES MOVING IN A FLUID

THE AUTHOR

is a graduate of Webb Institute, class of 1940. He was a Society of Naval

Architects Scholar, obtaining an M.S. degree in Marine Engineering at M.I.T. in 1942. In 1950 he obtained a Ph.D. degree at Cambridge University. He has

worked with: the General Electric Company as a test engineer and u.s a ma-rine applications engineer; the Bureau of Ships in World War II as a Naval Reserve officer; the Naval Attache in London as a consultant; the Office of

Naval Research as Technical Aide to the Chief Scientist and Executive

Secre-tary of the Naval Research Advisory Committee; the National Science Foundation as Executive Secretary of the National Science Board; and Har-vard University as a faculty member. At present he is Professor and Chair-man of Mechanical Engineering at Tufts University, and Vice President of

Electronics Research Group, Inc.

RATHER cOMPLICATED process of the stopping

of a ship can be approximated by a model that does

not involve several of the variables which, at first glance, would seem to be important. This simple

model may have general applicability to the braking

of bodies in a fluid. Ships, helicopters,

reversed-propeller airplanes, and fish act in a manner similar to the proposed model.

This study is an otugrowth of tests on a model propeller which, when running astern, seemed to achieve only the astern thrust expected of an im-penetrable disc. This occurred over a large speed

range, from about 20 per cent to about 200 per

cent of the idling speed. The same percentage range

(which corresponds to 120 per cent to 300

per

cent slip)

occurred when the idling speed was

changed by changing the water velocity in the

pro-peller tunnel. At astern slips beyond 300 per cent,

the astern thrust became much larger than for a

disc, often after a transition region in which it was briefly smaller.

Examination of data for other propellers showed that the propeller I had experimented with was not unusual. I also found that full-scale trial data

times (not always) indicated the same tendency for

the astern thrust to hang at about the disc drag

value until a propeller slip of about 300 per cent

was finally achieved. I concluded that a forward jet

does not establish itself until a slip of about 300

per cent is reached. At lower speeds, however, the propeller prevents all but a small flow through itself,

and therefore achieves a drag roughly equal to that

of an impenetrable disc. Since, during crashback,

ship propellers spend most of their time in the range

of 120 per cent to 300 per cent slip, the

observa-tion suggested a simple approach to the predicobserva-tion of ship movement during crashback.

If this observation is substantially valid for crash-backs, the only important propeller parameters are

A, the total disc area, and PN, the pitch times the

astern rpm achieved just before the ship stops.

Other important parameters would then be expected

to be: the ship's mass, M, and its initial velocity, V0; the density of the fluid, p; and the variable to be predicted, either the time to stop the body, T,

or the reach, R. From these parameters the

Pi theorem in dimensional analysis suggests the rela-tionship for time to stop:

pAV0T 1PN pA3'1

2M V0' M

and, for reach, the relationship:

pAR (PN pA3/2

M

V0'

M

A further idealization of the crashback maneuver permits direct calculation of the system. Assume:

The mass to be decelerated is that of the ship. The decelerating force throughout the

maneu-ver is that of an impenetrable, propeller-sized disc, i.e. pAV2/2.

When the slip reaches 300 per cent, the

de-celerating force becomes infinite,

and the

maneuver is over.

The equation for time to stop then easily follows.

The differential equation is:

M

pAV2

dT 2 (3)

Integration from time zero until the ship's speed is reduced to PN/2:

fPN _dV

M

ST--Jvo

gives the solution:

pAV0T

1+ 2 (5)

2M PN/V0

The reach can be similarly obtained. Substituting dr=VdT in Equation 3 gives the differential equa-tion:

M

=dR

(6)

(4)

Integration from position zero until V is reduced to PN/2 gives:

pAR1

2

M

2PN/V0

Crashback data for

several naval ships and

models are plotted in Figures 1 and 2. These points represent: destroyers, cruisers, submarines, and several types of carriers; two and four propellers;

ahead and astern crashbacks from fractional as well

as full powers; full-scale and model tests; and

pump-jet as well as orthodox propellers. Rather

surprisingly, the quantitative predictions, Equations 5 and 7, shown as curves in Figures 1 and 2, are of

the right order of magnitude. On the time-to-stop graph, Figure 1, half of the points are within 9 per cent of the curve given by Equation 3. The data, however, are selected, in that they represent naval

ships only.

Some information does exist on non-naval vessels,

and it suggests an appreciably greater scatter than naval ships demonstrate. This is probably due in

part to less accurate instrumentation. Another pos-sibility is suggested by a tendency for ships with a large value for the dimensionless group, (pA3/2/M),

to lie above the curves of Figures 1 and 2, and for

6 5 2 o o 0.2 0.4 0.6 0.8 1.0 PN Vo 1.4 '.6

Figure 2. Reach during crashback. 18

Figure 1. Time to stop during crashback.

6 5 4 pAR M CURVE pAR FOR EQUATION 7, 2

-

2 2

REVERSED PROPELLERS TREFETHEN

4

p A\4T CURVE FOR EQUATION 5

2M pAVI 2

i:'

-o O 0,2 0.4 as 0.8 1.0 1.2 1.4 1.6 PN Vo (1) (2)

those with low values to lie below. This group did not arise in the quantitative predictions, Equations 5 and 7, which were based on assumptions that

ig-nored such factors as wake and thrust deduction,

entrained mass, and ship resistance. The dimension-al andimension-alysis that led to Equations 1 and 2, however, would tend to allow for such details, provided one

didn't stray too far from geometric similarity. The group, (pA2/M), did arise in those equations. One

would, therefore, expect that Equation 5 and 7 might

fit one type of situation only, that in which all the ignored factors cancelled each other. One would

not expect them to fit those cases where the ignored

factors did not cancel. The nature of the analysis

leading to Equations 5 and 7 is such that there is no

a priori reason to expect that any real ships would correspond to it. For example, there is nothing in the analysis to indicate that the hull resistance of

real ships would not outweigh all the other factors

that the analysis ignores. It is therefore a

coinci-dence that, in fact, real ships do approximate those equations.

The ships and models that are closest to Equation

5 have, statistically, a value of about 0.02 for the

dimensionless group, (pA3/2/M). Cruisers have

about that value. Therefore, one is inclined to

con-clude that, for such ships, all the factors ignored

in the derivation of Equation 5 tend to cancel. Ships that have a larger value for the group, such as tugs (which swing a large propeller for their bulk), tend to lie above the prediction of Equation 5. Those with

smaller values, such as tankers, tend to lie below.

The following equation for time-to-stop is therefore suggested (on a best-fit, empirical basis rather than

on analytical grounds) as more representative of reality than Equation 5:

pAV T 2 pA3/2

2M

(_1+PNIv)

(50 M ) (8)

The tanker Esso Suez (Reference 1)

stopped

about 25 per cent more quickly than Equation 5 predicts. (Her data are not included in Figures 1 and 2, which report naval vessels only.) Since the

Esso Suez has a value of about 1/200 for the

(pA2/M) dimensionless group, Equation 8 pre-dicts a stopping time appreciably closer to her

ex-perimental values than Equation 5 predicts. The fact that the Esso Suez was a single-screw ship, yet fits closely into the trends of the multiple-screw naval ships plotted in Figures 1 and 2, would suggest that the foregoing analysis is applicable to single-screw

vessels. There are other single-screw ships,

how-ever, which do not fit so neatly. Perhaps they were not so well instrumented, but, lacking further data,

it would seem advisable to apply Equation 8 to

single-screw ships with more reservation than to

multiple-screw ships, if only because one would expect appreciably larger hull-propeller

interac-tions with single-screw ships.

In Figure 2, it will be seen that the reach data

tend to lie about 15 per cent below the prediction of Equation 7. They are also affected by the (pA3'2/M) group in a way similar to the time-to-stop points of

Figure 1. An empirically adjusted form of

Equa-tion 7:

pAR 2 pAV2 1/5

M

=1.7 (lnN/)

(50 M

)

(9)

might therefore be expected to predict reach more accurately than Equation 7.

A number of generalizations can be drawn from the foregoing comments:

The only factors of primary importance in

de-termining the crashback reach, or time-to-stop, of a ship are: the ship's mass; the ship's speed;

the disc area of the propellers; and the astern

rpm-times-pitch achieved near the end of the

maneuver.

It is unimportant, for a rough approximation, whether the propellers are fore or aft, pump-jet or conventional. Even the ability of the engines to reverse the propellers quickly is not of great

importance.

The crash-back maneuver is dominated by pro-pellers acting as impenetrable discs.

A simple model, deceleration of a mass by a constant force until slip is 300 per cent, leads

to equations that predict reach and time-to-stop. The dimensionless group, (pA312/M), appears

to incorporate to some extent such secondary

factors in the crashback maneuver as: thrust

de-duction factors; wake factors; entrained mass;

and hull resistance.

An examination of detailed thrust data shows a

somewhat more complicated picture than the model

assumes. The astern thrust curve is only approxi-mately fiat. The increase that occurs in the region

of 300 per cent slip is of course not infinite, and, in fact, there is some indication that the thrust re-duces briefly before it increases. This may be due to a vortex-ring circulation established when the

propeller does manage to push fluid forward. When recirculating the same fluid, there would be no mo-mentum interaction with the bulk of the fluid, and

therefore practically no thrust. Also, there would be practically no torque, a condition that would

cause the engine, particularly a piston steam engine, to accelerate. This suggests that attributing "racing" to cavitation or to "sucking air" may sometimes be an error. In the final stage, when the propeller does

succeed in establishing a forward jet that doesn't

recirculate, the propeller becomes efficient as a stop-ping mechanism, and completes the stopstop-ping process quickly.

The value of 300 per cent slip for establishment

of a forward jet does not appear to be supported by

any basic reasoning. A value of 200 per cent

REVERSED PROPELLERS TREFETHEN

would have such support, for, at that slip, an ideal

impeller disc would emit fluid with a velocity equal

to and opposite to that of the oncoming fluid, and therefore with enough momentum to penetrate it. Perhaps it is because propellers are far from ideal impeller discs that slips nearer 300 per cent are

required.

The predictions in this paper are rough

predic-tions. In many cases they would fit to within 5 per

cent to 10 per cent, but there are also cases where

they might be in error by 50 per cent or more. The

parameters considered are too few to assure

re-liability in all cases. If detailed and accurate knowl-edge is available for the ship, the propeller, and the engine characteristics, then a more reliable predic-tion for reach and time-to-stop could be computed

by a detailed integration of the maneuver.

Refer-ences i and 2 describe how this can be done. They also cite other sources of information on crashback

data. The data in Figures 1 and 2 of this paper are

not available in the literature; I appreciate the

Navy's allowing me to abstract them from its test

data.

Since I have no reversed-propeller braking data

for airplanes, I have no knowledge of whether they operate quantitatively in a fashion similar to ships.

They appear to be qualitatively similar.

Further-more, descending helicopters show analogous vortex and counter-jet flows. When a helicopter descends rapidly, its downward jet may be converted to vor-tex-ring recirculation. If this happens, much of the lift disappears, and descent becomes uncomfortably rapid. One other swimming device is also similar in sorne ways to a ship. A large fish, when it stops, does

so by shutting off its ahead propulsion system (its tail) and extending a "barn door" fin on each side until its speed is a fraction of its normal speed. It then completes the stopping maneuver quickly by forward sweeps of these fins. Perhaps fish, like

ships, use "parachute" braking until the speed be-comes so low that the reverse propulsion muscles

have the capability of establishing forward jets.

REFERENCES

E. F. Hewins, H. J. Chase, A. L. Ruiz, "The Backing

Power of Geared-Turbine Driven Vessel," Trans. Soc. Naval Architects and Marine Engineers, Vol. 58, 1950, pp. 261-328.

H. J. Chase, A. L. Ruiz, "A Theoretical Study of the Stopping of Ships," Trans. Soc. Naval Architects and

Marine Engineers, Vol. 59. 1951, pp. 811-834.

R&D

A high gravity centrifuge will be installed this summer at the Naval Ordnance Lab for use in the study of undersea nuclear explosion. By exerting a 300-G pull on water contained in a tank attached to the centrifuge, and detonationg small charges under the wafer NOL scientists expect fo simulate nuclear explosion characteristics in deep

wafer.

GUIDANCE

As important advances in the POLARIS program is the development of the smallest,

lightest missile inertial guidance system designated the Mark 2. Developed at jhs

M.I.T. Laboratory, in conjunction with the Raytheon Corp. and General Eectric Co.'s

Ordnance Dept., the system is less than half the size of ifs predecessor, the

now-opera-tional Mark I. The Mark 2 is planned for use in the 2500-mile range POLARIS A-3