Sideswipe or Grounding?Sideswipe or Grounding?

Titanic's Impact With the Ice and Its Immediate Aftermath

PART 1 OF 2

by Samuel Halpernby Samuel Halpern

Drawing done by S. P. Skidmore, April 15, 1912, aboard S.S.Carpathia.

Revised, Wednesday, 22 August 2007

PRESENTATION OVERVIEWPRESENTATION OVERVIEW

Some observations Ice in the well deck Center of Buoyancy, Center of Gravity, and Metacenter

The impact force vector Sideswipe or grounding? Underwater contact sequence Calculating maximum impact forces The initial list to starboard Down by the head - a sequence in time

A Titanic Myth A Titanic Myth

"The vessel took the blow of a deadly, underwater, projecting shelf of ice, on her starboard bow near the bridge, and before she swung clear, the mighty ram of the iceberg had torn its way through plating and frames as far aft as amidships, opening up compartment after compartment to the sea." - Scientific American, April 27, 1912.

Grounding on a Submerged Shelf of Ice?Grounding on a Submerged Shelf of Ice?Article From The Sphere 27 April 1912

Passenger Jack Thayer"I wound my watch-it was 11:45 PM-and was just about to step into bed, when I seemed to sway slightly. I immediately realized that the ship had veered to port as though she had been gently pushed. If I had had a brimful glass of water in my hand not a drop would have been spilled, the shock was so slight."

Leading Fireman Frederick Barrett"The water came through the ship's side...about 2 feet above the floor plates, starboard side...She was torn through No. 6 and also through 2 feet abaft the bulkhead in the bunker at the forward head of No.5 section."

Fireman George Beauchamp "Water was coming in on the plates when we were drawing the fires...coming through the bunker door and over the plates...coming through the bunker like."

Some ObservationsSome Observations

A 25 ft pressure head would produce a stream that reached as far as 15 ft across before falling on stokehold plates 2 ft below. Drawing shown is to scale.

Lookout Reginald Lee"The ship seemed to heel slightly over to port as she struck the berg...Very slightly over to port, as she struck along the starboard side."

Lookout Frederick Fleet"She listed to port right afterwards...a slight list...just afterwards [of striking the berg]...[Did it seem that the blow came beneath the surface of the water that caused her to shift over to port?] Yes."

A Few More ObservationsA Few More Observations

AB Seaman William Lucas"I had just left the mess room...It very nearly sent me off my feet."

Passenger Major Peuchen"I had only reached my room and was starting to undress when I felt as though a heavy wave had struck our ship. She quivered under it somewhat. If there had been a sea running I would simply have thought it was an unusual wave which had struck the boat."

Fourth Officer Joseph Boxhall"She was doing Full Speed and it didn’t break my step."

Lookout Reginald Lee"As she struck on the starboard bow there was a certain amount of ice that came on board the ship. That was the forewell deck. It seemed as if she struck just before the foremast."

Ice in the Well DeckIce in the Well Deck

Deriving Distance From Center of Buoyancy To MetacenterDeriving Distance From Center of Buoyancy To MetacenterFor Rectanguiar Cross-Section HullFor Rectanguiar Cross-Section Hull

Deriving Heights of Center of Buoyancy, Center of Gravity, Deriving Heights of Center of Buoyancy, Center of Gravity, and Metacenter on and Metacenter on TitanicTitanic for April 14, 1912 for April 14, 1912

Six Degrees of FreedomSix Degrees of Freedom

• Three translations of the ship’s center of gravity (G) in the direction of the x-, y-, and z-axes:

– SURGE in the longitudinal x-direction, positive forwards– SWAY in the lateral y-direction, positive to port side– HEAVE in the vertical z-direction, positive upwards

• Three rotations about these axes:– ROLL about the x-axis, positive right turning– PITCH about the y-axis, positive right turning– YAW about the z-axis, positive right turning

The Impact Force VectorsThe Impact Force VectorsHeave, Sway, and Negative Surge

Impact Forces Just Aft of Bulkhead Impact Forces Just Aft of Bulkhead BB

Impact Forces Alongside Bulkhead Impact Forces Alongside Bulkhead CC

The resultant force of impacting ice must be on a line that passes over the Center of Gravity longitudinal axis (+) to cause the ship to heel to port. A sideswipe only impact ~25 ft below the waterline would produce a heel to starboard.

Resultant force shown acting perpendicular to side plating in bilge area.

For resultant contact force vector shown, heave component is about 1.7 times sway component.

Calculating Maximum Impact Forces Due To Calculating Maximum Impact Forces Due To Side Impact ComponentSide Impact ComponentContacting an Immovable, Smooth, Unbreakable Object

Calculation Assumptions• Approach speed 38 ft/s (22.5 knots); Heading 0°• Impact at t = 22.5 sec after "Hard-starboard" order• Speed at impact 33 ft/sec; Heading -11°• Angle of impact relative to centerline = 12°• Titanic's displacement 14 Apr = 48,300 tons• Impact kinetic energy = 1,830,000,000 ft-lbs• Point of max impact force taken abeam bulkhead B• Center of gravity (CG) of ship taken at amidships• Coefficient of friction steel-on-ice 0.03; set to 0• Coefficient of restitution 0 (hull deformation only)• Mass of iceberg

Calculation Results• Energy loss from collision = 27,530,000 ft-lbs• Percent of energy lost = 1.5%• Impact impulse = 8,100,000 lbs-sec 3,600 ton-sec• Average sway force over 6 sec = 600 tons*• Added rotational velocity imparted = 0.93° per sec• Velocity of ship after collision = 32.3 ft/sec• Sway velocity after collision = 1.3 ft/sec• Center of percussion (CP) ~ 569 ft aft of bow

* Average force = impulse/time; peak forces can be much greater. Highest forces probably across Holds 1, 2, and 3.

[Ref: S. Zhang, "The Mechanics of Ship Collisions," Dept. of Naval Architecture and Offshore Engineering, Tech. University of Denmark, 1999.]

Model For Side Pressure Vs. TimeModel For Side Pressure Vs. TimeAssume side component contact with berg over area of 8 ft X 40 ft = 320 sq-ft. Force impulse is 3600 ton-sec; Pressure impulse = 11.25 ton-sec/sq-ft

Assume a Rayleigh contact distribution over time with peak force at t=2 sec.

Sway Force = 3600*t/4*exp{-1/2*t2/4} tons

Pressure = Force/320 sq-ft

Peak sway force = 1092 tonsPeak sway pressure = 1092/320 = 3.4 tons/sq-ft

Sway Force Vs. Time

0

200

400

600

800

1000

1200

0 1 2 3 4 5 6 7

time (sec)

Fo

rce (

ton

s)

Estimating How Far She Heeled to Port Estimating How Far She Heeled to Port During ContactDuring Contact

4/12 displacement = 48,300 tons (B&H)4/12 draft = 32' 3'' (B&H)GM = 2.63' (B&H)sway component = 600 tons average over 6 secondsheave 1.7 sway = 1020 tonsResultant force F = 1180 tons (sqrt [600^2 + 1020^2])

sin = F x L = 1180 x 4 = 0.037 2° Disp. x GM 48300 x 2.63

From impulse analysis considering side impact only, we found an average sway component ~ 600 tons. To cause observed heel to port, heave component was shown to be ~1.7 times sway near bulkhead C. Assuming resultant force as shown, moment arm L 4 ft. Heel angle would be given by formula shown below.

F=1180 tonsresultant

600 tonssway

1020 tonsheave

G

moment armL 4 ft

32.25'35.4'

M

38'

waterline

Underwater Contact Underwater Contact — Sideswipe or Grounding?— Sideswipe or Grounding?

Some Observations

• A pure sideswipe (sway component force) would cause the ship to heel to starboard, not to port, during the allision.

• A pure grounding (heave component force) just along the bottom of the hull would not likely produce what was observed in the forward boiler rooms as the ship's double bottom extended around the turn of the bilge in those spaces.

The most probable contact appears to be an allision along the bilge area on the forward starboard side of the ship producing heave, sway and slight negative surge components to the forces of impact.

+

+

+

-

-

-

CONTINUED IN PART 2CONTINUED IN PART 2