Transcript Speed and Revolutions

Speed and Revolutions
(Revised 09 May 2007)
The Development of a Slip Table
for the SS Titanic
RPMs
50
55
60
65
70
75
80
85
Speed
15.6
16.9
18.2
19.5
20.7
22.0
23.2
24.4
%Slip
8.4
9.8
11.0
12.0
13.0
13.9
14.8
15.6
by Samuel Halpern
"As I told you, sir, we were
working at our slip table, and that
is a table based upon so many
revolutions of engines and so
much per cent slip; and you work
that out, and that gives you so
many miles per hour." - Titanic's
5th Officer Harold Godfrey Lowe.
PRESENTATION OVERVIEW
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Titanic's power plant and propelling machinery
Titanic's propellers
What do we know about speed and revolutions?
Developing a model
Speed Vs. revolutions - full ahead
Speed Vs. revolutions - half ahead and less
Calculating propeller slip and angle of attack
A slip table for Titanic
Some maiden voyage speeds
Titanic’s Power Plant and Propelling
Machinery




24 double-ended boilers with 6 furnaces each
5 single-ended auxiliary boilers with 3 furnaces each
144,000 square feet of total heating surface
Coal bunker capacity of over 6,600 long tons
— about 8 days of steaming at full speed
Titanic’s Power Plant and Propelling Machinery
 Two triple-bladed wing propellers each driven by 4cylinder triple-expansion reciprocating engine
— 15,000 IHP each at 75 rpm
 Single 4-bladed central propeller driven directly by a single
low-pressure Parson's turbine
— 16,000 SHP at 165 rpm
Reference: The Shipbuilder, Vol. VI, Special Number, Midsummer 1911
Power Plant Schematic
Crank Sequence on Reciprocating Engines
Port engine phasing was mirror image of starboard engine.
Titanic's Propellers
Looking forward from astern
Central prop and Starboardside Wing prop rotated
clockwise going ahead
Port-side Wing prop rotated
counter-clockwise going ahead
Location
Blades
Material
Diameter
Pitch
Area
Wing
Props
3
manganese
bronze
23 ft 6 in
34 ft 6 in
160
sq ft
Central
Prop
4
manganese
bronze
17 ft 0 in
14 ft 6 in
125
sq ft
Titanic Vs. Olympic
• The wing propellers installed on the Olympic in 1911 had a pitch of 33
feet 0 inches.
• The pitch of Olympic's wing blades increased to 34 ft 6 in January 1912.*
• The diameter of Olympic's center propeller was 16 feet 6 inches with a
surface area of 120 square feet.
• Titanic was drydocked on 03 February 1912 for the fitting of her three
propellers.
Olympic and Titanic had almost identical propelling machinery in 1912.
* Wing propeller blades were fastened to a cast steel boss by high-strength studs and
nuts to allow pitch changes without having to replace the entire assembly. Central
propeller was of solid construction with fixed pitch blades that did not allow
adjustment.
References:
1.
Harland & Wolff (H&W) Office Drawing Notebook.
2.
H&W Archives listing particulars of ships 400 and 401.
3.
M. McCaughan, The Birth of the Titanic, 1998.
Developing a Speed Table for Titanic
What Do We Know About Full Ahead Speeds?
• From trial data of the Olympic taken after the disaster
– 18 knots at 60 revolution (BI 25295)
– 21½ knots at 74 revolutions (BI 25292)
• From Duncan Haw's Merchant Fleets: White Star Line
– 22.82 knots at 79 revolutions
• From British Inquiry Day 16 (BI 18372)
– 21¾ to 22 knots at 75 revolutions
• Maximum speed with all 29 boilers connected up (BI 25292)
– 23 ¼ knots
Developing a Speed Table for Titanic
What Do We Know About Half Ahead or Less?
After the Hawke collision in 1911, Captain Smith was asked about
the various speeds made by the Olympic in coastal waters. His
reply was:*
Capt. E. J. Smith: "Half speed 50 [revolutions] would be about 15
[knots], slow 30 [revolutions] would be 8 to 9 knots...[making] easy
steam, coming in and out of port."
* Source: Mark Chirnside.
Disengaging the Turbine Engine
Turbine engine engaged only for ahead speeds greater
the 50 revolutions on reciprocating engines. (Information
from an Olympic engineer.*)
Power reduced by 35% when turbine disengaged.**
Power required goes up as the cube of the speed
If power reduced by 35%, speed is reduced by 13%
(1 - 0.35 )1/3 = 0.866
Therefore if speed was 15 knots with turbine
engaged, it would drop to 13 knots with turbine
disengaged.
* Source: Mark Chirnside.
** 16,000 HP/46,000 HP = 35% reduction
Speed Vs. Revolutions
A Non-Linear Model for Titanic
V = K1Rq
for R  50
with turbine engaged
V = 0.866 K1Rq for R < 50
with turbine
disengaged
V = the speed of the ship through the water (knots)
R = the revolutions on the reciprocating engines (rpm)
K1 = constant
K2 = constant
q = exponent
Values for K1 and q can be derived using 1912 trial
data from Olympic.
Value for K2 obtained from from data provided by Capt. Smith
and disengagement of turbine engine.
How Good is the Model?
Application to USS Saipan
USS Saipan
V = 0.247 R 0.893 for rpm > 99
V = 15 R/99 for RPM < 99
Ahead Values on Telegraph
knots
rpm
1
7
3
22
5
36 AHEAD 1/3
7
48
10
68 AHEAD 2/3
11
74
15
99 AHEAD STNDRD
17
113
20
136 AHEAD FULL
22
152
24
168 AHEAD FLANK
25 max
176
Speed Vs. Revolutions
Solution for Olympic/Titanic with Turbine Engaged
V = 0.563 R 0.8472
for R ≥ 50 rpm
Revolutions of the Turbine Engine
Olympic’s Senior Second
Engineer John Therle, the
turbine would make between
175 and 180 rpm when the
reciprocating engines were
making 80 rpm, and the
maximum number of
revolutions on the turbine
was 190 rpm when the
reciprocating engines ran at
their highest possible speed
Speed Vs. Revolutions
Solution for Olympic/Titanic with Turbine Disengaged
V = 0.488 R 0.8472
for R  50 rpm
Propeller Pitch and Angle of Attack
direction of
ship travel
direction of
propeller
rotation
angle of attack ( )
relative direction
of water flow
pitch angle ( )
•
•
Propeller Pitch is the distance that a propeller would move in one
revolution if it were moving through a soft solid medium not allowing for
any slip.
Angle of attack is the angle between the chord of the propeller blade and a
line representing the relative water flow.
Propeller Slip
theoretical
path of blade
slip
actual path
of blade
direction of
ship travel
actual distance traveled
in one revolution
theoretical travel distance
for one revolution
• Propeller Slip is the difference between the theoretical distance
the propeller should travel in one revolution and the actual
distance the vessel travels.
% slip =
1—
actual distance traveled
in one revolution
theoretical travel distance
for one revolution
× 100%
Calculating Propeller Pitch, Slip and
Angle of Attack for the Titanic
Taking 75 revolutions on
the wing propellers and
the corresponding 167
revolutions on the central
propeller with the ship
steaming at 21.8 knots.
A Slip Table For Titanic
RPM
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
Knots
15.5
15.7
16.0
16.3
16.5
16.8
17.0
17.3
17.6
17.8
18.1
18.3
18.6
18.8
19.1
19.3
19.6
19.8
20.1
20.3
20.6
20.8
21.1
21.3
21.6
21.8
22.1
22.3
22.6
22.8
23.1
23.3
23.5
23.8
24.0
24.3
%-Slip
9.1
9.4
9.6
9.9
10.2
10.4
10.7
10.9
11.1
11.4
11.6
11.8
12.0
12.2
12.5
12.7
12.9
13.1
13.3
13.5
13.6
13.8
14.0
14.2
14.4
14.6
14.7
14.9
15.1
15.2
15.4
15.6
15.7
15.9
16.0
16.2
Pitch Angle, Slip, and Angle of Attack
Titanic’s Wing Propellers
Propeller Pitch = 34.5 ft per revolution
Propeller Diameter D = 23.5 ft
Circumference C =D=73.8 ft
Standard 7/10 radius travel C’=0.7xC = 51.7 ft
Propeller Pitch angle() = tan-1 Pitch/C’ = 33.73°
Titanic’s Center Propeller
Propeller Pitch = 14.5 ft per revolution
Propeller Diameter D = 17.0 ft
Circumference C =D = 53.4 ft
Standard 7/10 radius travel C’=0.7xC = 37.4 ft
Propeller Pitch angle() = tan-1 Pitch/C’ = 21.2°
At 75 rpm = 1.25 rps
V = 21.8 knots = 36.8 ft/sec
At 167 rpm = 2.8 rps
V=21.8 knots = 36.8 ft/sec
But 7/10 radius travel in 1 sec is 1.25 x 51.7 = 64.6 ft
Pitch travel in 1 sec is 1.25 x 34.5 = 43.1 ft
Slip distance = 43.1 – 36.8 = 6.3 ft in 1 sec, or
But 7/10 radius travel in 1 sec is 2.8 x 37.4 = 103.9 ft
Pitch travel in 1 sec is 2.8 x 14.5 = 40.3ft
Slip distance = 40.31– 36.8 = 3.5 ft in 1 sec, or
14.7% Slip at 75 revolutions
8.7% Slip at 167 revolutions
 –  = tan-1 36.8/64.6 = 29.7°
 –  = tan-1 36.8/103.9 = 19.5°
Angle of attack () = 33.7 – 29.7 = 4° at 75 revolutions
Angle of attack () = 21.2 – 19.5 = 1.7° at 167 revolutions
References:
1.
http://www.mercurymarine.com/chapter_4_-_propeller_technology?makePrintable=1
2.
http://www.mh-aerotools.de/airfoils/propuls4.htm
3.
http://www.encyclopedia-titanica.org/discus/messages/5919/5974.html?1006435046
Titanic's Maiden Voyage
The Atlantic Crossing
Distances
Day 1 484 NMs
Day 2 519 NMs
Day 3 546 NMs
to C.P. 258 NMs
total 1807 NMs
Probable Maiden Voyage Engine
Revolutions and Maximum Speeds
SUMMARY AND CONCLUSIONS
 A relationship between reciprocating engine
revolutions and speed through the water has been
developed for the Titanic
 ahead speeds with central turbine engaged (> 50 rpm)
 ahead speeds with central turbine disengaged (< 50 rpm)
 Percentages of slip and angles of attack for Titanic's
wing and center propellers has been derived for a
running speed of 75 revolutions (~22 knots)
 Probable revolutions carried and maximum throughthe-water speeds for Titanic's maiden voyage have
been derived