1. Speed and Revolutions (Revised 09 May 2007)
The Development of a Slip Table
for the SS Titanic
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.

2. PRESENTATION OVERVIEW
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

3. 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

4. Titanic’s Power Plant and Propelling Machinery
Two triple-bladed wing propellers each driven by 4-cylinder 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

5. Power Plant Schematic

6. Crank Sequence on Reciprocating Engines
Port engine phasing was mirror image of starboard engine.

7. Titanic's Propellers 3 4 Location Blades Material Diameter Pitch Area
Looking forward from astern
Central prop and Starboard-side 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
17 ft 0 in
14 ft 6 in
125

8. Olympic and Titanic had almost identical propelling machinery in 1912.
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:
Harland & Wolff (H&W) Office Drawing Notebook.
H&W Archives listing particulars of ships 400 and 401.
M. McCaughan, The Birth of the Titanic, 1998.

9. 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

10. 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.

11. 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%
( )1/3 =
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

12. Speed Vs. Revolutions A Non-Linear Model for Titanic
V = K1Rq for R  with turbine engaged
V = 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.

13. How Good is the Model? Application to USS Saipan
Ahead Values on Telegraph
knots rpm
1 7
3 22
5 36 AHEAD 1/3
7 48
AHEAD 2/3
11 74
AHEAD STNDRD
17 113
AHEAD FULL
22 152
AHEAD FLANK
25 max 176
V = R for rpm > 99
V = 15 R/99 for RPM < 99

14. Speed Vs. Revolutions Solution for Olympic/Titanic with Turbine Engaged
V = R for R ≥ 50 rpm

15. 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

16. Speed Vs. Revolutions Solution for Olympic/Titanic with Turbine Disengaged
V = R for R  50 rpm

17. Propeller Pitch and Angle of Attack
relative direction of water flow
pitch angle ( )
angle of attack ( )
direction of propeller rotation
direction of ship travel
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.

18. actual distance traveled theoretical travel distance
Propeller Slip
actual distance traveled
in one revolution
theoretical travel distance
for one revolution
actual path of blade
theoretical
path of blade
direction of ship travel
slip
Propeller Slip is the difference between the theoretical distance
the propeller should travel in one revolution and the actual
distance the vessel travels.
% slip =
actual distance traveled
in one revolution
theoretical travel distance
for one revolution
× 100%
1 —

19. 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.

20. A Slip Table For Titanic

21. 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°
At 75 rpm = 1.25 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
14.7% Slip at 75 revolutions
 –  = tan /64.6 = 29.7°
Angle of attack () = 33.7 – 29.7 = 4° at 75 revolutions
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 167 rpm = 2.8 rps
V=21.8 knots = 36.8 ft/sec
But 7/10 radius travel in 1 sec is 2.8 x 37.4 = 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
8.7% Slip at 167 revolutions
 –  = tan / = 19.5°
Angle of attack () = 21.2 – 19.5 = 1.7° at 167 revolutions
References:

22. Titanic's Maiden Voyage The Atlantic Crossing
Distances
Day NMs
Day NMs
Day NMs
to C.P. 258 NMs
total NMs

23. Probable Maiden Voyage Engine Revolutions and Maximum Speeds

24. 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 through-the-water speeds for Titanic's maiden voyage have been derived