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MS Herald of Free Enterprise
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Herald of Free Enterprise in Dover's Eastern Docks, 1984
History
United Kingdom
Name:
Herald of Free Enterprise (1980–1987)
Flushing Range (1987–1988)
Owner:
Townsend Thoresen (1980–1987)
Compania Naviera S.A. (1987–1988)
Operator: Townsend Thoresen (1980–1987)
Port of registry:
Dover, UK
Kingstown, Saint Vincent
Builder: Schichau Unterweser, Bremerhaven, Germany
Launched: 1980
Identification: IMO number: 7820485
Fate:
Capsized 6 March 1987
Raised April 1987
Scrapped in 1988
General characteristics
Class and type: RORO car and passenger ferry
Tonnage: 13,601 brt
Length: 131.91 m (432 ft 9 in)
Beam: 23.19 m (76 ft 1 in)
Draught: 5.72 m (18 ft 9 in)
Installed power: 23,967bhp
Propulsion: 3 x Sulzer 12ZV 40/48 diesel engines
Speed: 22 knots (41 km/h; 25 mph)
Capacity: 1,400
MS Herald of Free Enterprise was a roll-on/roll-off (RORO) ferry which capsized moments after leaving the Belgian port of Zeebrugge on the night of 6 March 1987, killing 193 passengers and crew.[1]
The modern 8-deck car and passenger ferry, owned by Townsend Thoresen, had been designed for rapid loading and unloading on the competitive cross-channel route, and there were no watertight compartments. When the ship left harbour with its bow-door open, the sea immediately flooded the decks, and within minutes it was lying on its side in shallow water.
Although the immediate cause of the sinking was found to be negligence by the assistant boatswain, who was asleep in his cabin when he should have been closing the bow-door, the official inquiry placed more blame on his supervisors and a general culture of poor communication in Townsend Thoresen.
The vessel was salvaged and put up for sale, and on September 30, 1987, was sold to Naviera SA Kingstown, and was renamed Flushing Range. Then on March 22, 1988, she was taken to Taiwan to be broken up.
Since the disaster, improvements have been made to the design of RORO vessels, with watertight ramps, indicators showing the position of the bow-doors, and the banning of undivided decks.
Contents
[hide]
1 Design and construction
2 Capsizing
2.1 Background
2.2 Sinking
2.3 Investigation and inquiry
3 Inquest
4 Aftermath
4.1 Immediate
4.2 Long term
4.3 Disaster Action
4.4 Gallantry awards
5 See also
5.1 Sister ships
6 References
7 External links
Design and construction[edit]
In the late 1970s, Townsend Thoresen commissioned the design and construction of three new identical ships for its Dover–Calais route for delivery from 1980. The ships were branded the Spirit-class and were named Herald of Free Enterprise, Pride of Free Enterprise and Spirit of Free Enterprise.[2] The name "Free Enterprise" dates from Townsend Car Ferries' pioneering private sector roll on/roll off ferries, introduced in 1962.[3] The Herald began active service on 29 May 1980.[4]
To remain competitive with other ferry operators on the route, Townsend Thoresen required ships designed to permit fast loading and unloading and quick acceleration. The ships comprised eight decks numbered A to H from top to bottom which contained the following:[5]
A-deck: Crew accommodation and radio room
B-deck: Crew accommodation and galley
C-deck: Passenger areas and galley
D-deck: Suspended vehicle deck within E deck
E-deck: Upper vehicle deck
F-deck: Mezzanine level
G-deck: Main vehicle deck
H-deck: Engine rooms, stores and passenger accommodation
Loading of vehicles onto G deck was through watertight doors at the bow and stern.[6] The wheel house was positioned towards the stern, making it difficult to see the bow doors.[7] Loading of vehicles onto E deck and F deck was through a weathertight door at the bow and an open portal at the stern. Vehicles could be loaded and unloaded onto E and G deck simultaneously using double-deck linkspans in use at Dover and Calais.[8]
The ships were constructed by Schichau-Unterweser AG in Bremerhaven, Germany. Propulsive power was by means of three 8000bhp 12-cylinder Sulzer medium-speed diesel engines driving variable-pitch propellers.[9] The vehicle deck bow doors were constructed by Cargospeed, Glasgow, Scotland.[4]
Capsizing[edit]
Background[edit]
On the day the ferry capsized, Herald of Free Enterprise was working the route between Dover and the Belgian port of Zeebrugge. This was not her normal route and the linkspan at Zeebrugge had not been designed specifically for the Spirit-class vessels: she used a single deck, preventing the simultaneous loading of both E and G decks, and the ramp could not be raised high enough to reach E deck.[10][11] To compensate for this, the vessel's bow ballast tanks were filled.[10] However, the ship's natural trim was not restored after loading.[10] Had Herald of Free Enterprise survived, she would have been modified to obviate the need for this procedure.[11]
It was normal practice for the assistant boatswain to close the doors before moorings were dropped. However, the assistant boatswain, Mark Stanley, had returned to his cabin for a short break after cleaning the car deck upon arrival, and was still asleep when the harbour-stations call sounded and the ship dropped her moorings.[12] The first officer, Leslie Sabel, was required to stay on deck to make sure the doors were closed.[13] Sabel said he thought he saw Stanley approaching. He was seriously injured in the disaster and the court concluded that his evidence was inaccurate.[13] It is believed that, under pressure to get to his harbour station on the bridge, he had left G deck with the bow doors open in the expectation that Stanley would arrive shortly.[13] The court also described the attitude of boatswain Terence Ayling, believed to have been the last person on G deck, as most unfortunate.[13] Asked why he did not close the doors given there was no one else there to do it, he said it was not his duty.[13] However the court praised his work in the rescue.[13]
Captain David Lewry assumed that the doors had been closed since he could not see them from the wheelhouse owing to the ship's design, and had no indicator lights in the wheelhouse.[14]
Sinking[edit]
The ship on her side half-submerged
The ship left her berth in Zeebrugge inner harbour at 18:05 (GMT) with a crew of 80 and carrying 459 passengers, 81 cars, 3 buses and 47 trucks. She passed the outer mole at 18:24 (GMT) and capsized about four minutes later.[15]
When the ferry reached 18.9 knots (35.0 km/h; 21.7 mph) 90 seconds after leaving the harbour, water began to enter the car deck in large quantities. The resulting free surface effect destroyed her stability.[16]
In a matter of seconds, the ship began to list 30 degrees to port.[17] The ship briefly righted herself before listing to port once more, this time capsizing.[17] The entire event took place within 90 seconds.[18] The water quickly reached the ship's electrical systems, destroying both main and emergency power and leaving the ship in darkness.[16]
The ship ended on her side half-submerged in shallow water 1 kilometre (0.5 nmi; 0.6 mi) from the shore. Only a fortuitous turn to starboard in her last moments, and then capsizing on a sandbar, prevented the ship from sinking entirely in much deeper water.[16]
Crew aboard a nearby dredger noticed Herald of Free Enterprise's lights disappear, and notified the port authorities. The alarm was raised at 19:37 local time (18:37 GMT).[19] Rescue helicopters were quickly dispatched, shortly followed by assistance from the Belgian Navy, who were undertaking an exercise within the area.[20] Wolfgang Schröder (de), the German captain of a nearby ferry,[21] was commended by Prime Minister Margaret Thatcher and received a medal from King Baudouin of Belgium for his heroic efforts in rescuing passengers.[22]
The disaster resulted in the deaths of 193 people. Many of those on board had taken advantage of a promotion in The Sun newspaper offering cheap trips to the continent.[23] Most of the victims were trapped inside the ship and succumbed to hypothermia because of the frigid water.[24] The rescue efforts of the Belgian Navy limited the death toll. Recoverable bodies were removed in the days following the accident. During the rescue the tide started to rise and the rescue team was forced to stop all efforts until morning. The last of the people left on board died of hypothermia.[25]
Investigation and inquiry[edit]
A public Court of Inquiry into the incident was held under British judge Lord Justice Barry Sheen in 1987.[26] It found the sinking was caused by three main factors—Stanley's failure to close the bow doors, Sabel's failure to make sure the bow doors were closed, and Lewry leaving port without knowing whether the bow doors were closed. While the court determined the immediate cause of the sinking was Stanley's failure to close the bow doors, it was very critical of Sabel for not being in a position to prevent the disaster, calling his actions "the most immediate" cause of the sinking.[13]
The fact that Stanley was asleep at the time of departure led Sheen to examine the working practices of Townsend Thoresen, from which he concluded that the poor workplace communication and stand-off relationship between ship operators and shore-based managers was the root cause of the sinking,[12] and identified a "disease of sloppiness" and negligence at every level of the corporation's hierarchy.[27] Issues relating to the breaking of waves high on the bow doors while under way and requests to have an indicator installed on the bridge showing the position of the doors were dismissed; the former because of the attitude that ships' masters would come and "bang on the desk" if an issue was truly important, and the latter because it was thought frivolous to spend money on equipment to indicate if employees had failed to do their job correctly.[14]
The design of Herald of Free Enterprise was also found to be a contributory cause of the sinking.[12] Unlike other ships, which are subdivided into watertight compartments, the vehicle decks of RORO vessels are normally contiguous: any flooding on these decks would allow the water to flow the length of the ship.[10] This issue had been identified as early as 1980, following the losses of Seaspeed Dora and Hero in June and November 1977 respectively.[28] The need to adjust the ship's bow trim to use the port facilities at Zeebrugge and failure to readjust before departure was another factor in the sinking.[18]
In October 1983, Herald of Free Enterprise's sister ship Pride of Free Enterprise had sailed from Dover to Zeebrugge with the bow doors open, after her assistant boatswain fell asleep.[13] It was therefore believed that leaving the bow doors open alone should not have caused the ship to capsize. However, tests by the Danish Maritime Institute after the accident found that once water began to enter the vehicle deck of a RORO, it was likely that the vessel would capsize within 30 minutes, while other tests showed that the lack of watertight subdivision common on other vessels allowed the weight of water to flow freely and increase the likelihood of capsizing.[18]
Another factor that contributed to the capsizing was the "squat effect". When a vessel is under way, the movement under it creates low pressure, which has the effect of increasing the vessel's draught. In deep water the effect is small but in shallow water it is greater, because as the water passes underneath it moves faster and causes the draught to increase. This reduced the clearance between the bow doors and water line to between 1.5 metres (4.9 ft) and 1.9 metres (6.2 ft). After extensive tests, the investigators found that when the ship travelled at a speed of 18 knots (33 km/h), the wave was enough to engulf the bow doors. This caused a "step change": if the ship had been sailing at less than 18 knots and not in shallow water, people on the car deck would probably have had time to notice the bow doors were open and close them.[29]
Inquest[edit]
In October 1987, a coroner's inquest jury into the capsizing returned verdicts of unlawful killing. Seven people involved at the company were charged with gross negligence manslaughter, and the operating company, P&O European Ferries (Dover) Ltd, was charged with corporate manslaughter, but the case collapsed after Justice Turner directed the jury to acquit the company and the five most senior individual defendants.[30] It did, however, set a precedent that corporate manslaughter is legally admissible in English courts. The disaster was one of a number that influenced thinking leading to the Public Interest Disclosure Act 1998.[31]
Aftermath[edit]
Immediate[edit]
MS Herald of Free Enterprise towed into the harbour at Vlissingen after salvage, May 1987
A salvage operation, conducted by Dutch company Smit-Tak Towage and Salvage (part of Smit International), was embarked upon almost immediately to refloat the ship. The operation was successfully concluded in late April 1987, allowing the remaining bodies trapped underwater to be removed. The ship was towed to Zeebrugge, and then across the Western Scheldt to the yard of De Schelde in Flushing, where her fate was decided. It had originally been assumed that she could be repaired and continue sailing. However, no buyer was found; she was sold to Compania Naviera SA of Kingstown, Saint Vincent and the Grenadines, for scrapping. She was renamed Flushing Range and the Townsend Thoresen branding painted over before her final sailing to Kaohsiung, Taiwan, for scrapping.[32] She began her final voyage on 5 October 1987, together with MV Gaelic, towed by the Dutch tug Markusturm.[33] The voyage was interrupted for four days when the ships encountered the Great Storm of 1987 off Cape Finisterre, where Herald of Free Enterprise was cast adrift after its tow rope parted,[34] resuming on 19 October 1987. The hulk began to disintegrate while off the coast of South Africa on 27 December 1987, and had to be towed into Port Elizabeth on 2 January 1988 to undergo temporary repairs to allow her to continue her voyage. She finally arrived in Taiwan on 22 March 1988.[35]
Owing to the incident, the Townsend Thoresen name had inevitably been broadcast on television and in newspapers around the world. P&O quickly decided to rebrand the company as P&O European Ferries, repaint their fleet's red hulls in navy blue and remove the TT logo from the funnels.[36]
Long term[edit]
The sinking of the Herald of Free Enterprise caused the highest death-count of any peacetime maritime disaster involving a British ship since the sinking of HMY Iolaire on 1 January 1919 near Stornoway, Isle of Lewis, where at least 205 perished of the 280 aboard.[37]
Since the accident several improvements to the design of this type of vessel have been made. These include indicators that display the state of the bow doors on the bridge, watertight ramps being fitted to the bow sections of the front of the ship, and "freeing flaps" to allow water to escape from a vehicle deck in the event of flooding. The International Convention for the Safety of Life at Sea regulations were changed in 1990 to require 125 centimetres (49 in) of freeboard (in the case of RORO vessels, defined as the height between the vehicle deck and the water line) for all new ROROs, instead of the previous 76 centimetres (30 in).[18] Some vessels omit the bow door configuration altogether and vehicles enter and exit from rear doors only. New International Maritime Organization (IMO) regulations are in place that prohibit an open (undivided) deck of this length on a passenger RORO vessel.[citation needed]
The divers and rescuers who entered the capsized vessel to retrieve corpses received psychosocial support designed and delivered by Belgian Army psychologist Luc Quintyn. This was the first step to the establishment of a Crisis Psychology Unit within the Belgian Army Hospital.
Neither of Herald of Free Enterprise's two sister ships are still operational; the former Spirit of Free Enterprise was extended to increase her cargo capacity during her time under the P&O flag in a stretch and total rebuild operation and scrapped in 2012. Pride of Free Enterprise was still more or less as built; she was scrapped in 2015.[38]
A few scenes of the disaster videotaped live by the media were used by film director Krzysztof Kieślowski as part of the conclusion of his film Three Colours: Red that bound together the Three Colours trilogy.
In Britain, a group named Ferry Aid released a charity record of the song "Let It Be" by The Beatles.
Nicholas Ridley, a government minister at the time, was criticised for alluding to the accident (while speaking on another subject) on 10 March 1987. He was quoted as saying that "although he is the pilot of the [parliamentary] Bill, he has not got his bow doors open". He apologised for the remark.[39]
In 2007 Belgian singer Jonathan Vandenbroeck, more commonly known as Milow, released a song to mark the 20th anniversary of the tragedy. Titled "Herald of Free Enterprise", the song echoes the tragic events of the evening and was featured on his 2009 album Milow.
The disaster was the subject of an episode from Series 2 of Seconds From Disaster.
On 1 July 2014, The History Press released a book called Ninety Seconds At Zeebrugge: The Herald of Free Enterprise Story, telling the story of the disaster and its aftermath.
St Mary's Church, Dover houses a permanent memorial to the disaster.[40]
Disaster Action[edit]
Australian businessman Maurice de Rohan, who lost his daughter and son-in-law in the tragedy, founded Disaster Action, a charity which assists people affected by similar events.[41]
Gallantry awards[edit]
The following British awards for gallantry on the night of the sinking were gazetted on 30 December 1987:[42]
Herald of Free Enterprise crew
Michael Ian Skippen, Head Waiter, George Medal (posthumous)
Leigh Cornelius, Seaman, Queen's Gallantry Medal
Stephen Robert Homewood, Assistant Purser, Queen's Gallantry Medal
William Sean Walker, Seaman, Queen's Gallantry Medal
Thomas Hume Wilson, Quartermaster, Queen's Gallantry Medal
Herald of Free Enterprise passenger
Andrew Clifford Parker, Assistant Bank Manager, Nippon Credit International, George Medal
Belgian Navy
Lieutenant-Ter-Zee 1ste Klas Guido A. Couwenbergh, Queen's Gallantry Medal
Lieutenant-Ter-Zee 1ste Klas Alfons M. A. C. Daems, Queen's Gallantry Medal
Royal Navy
Lieutenant Simon Nicholas Bound, Queen's Gallantry Medal
Able Seaman Eamon Christopher McKinley Fullen, Queen's Gallantry Medal
Chief Petty Officer Edward Gene Kerr, Queen's Commendation for Brave Conduct
Chief Petty Officer Peter Frank Still, Queen's Commendation for Brave Conduct
Tijdelijke Vereniging Bergingswerken
Piet Lagast, Diver, Queen's Gallantry Medal
Dirk van Mullem, Diver, Queen's Gallantry Medal
See also[edit]
Belgium portal
United Kingdom portal
Nautical portal
Disasters portal
List of RORO vessel accidents
List of maritime disasters
MV Tricolor, an automobile cargo ship which sank nearby in 2002
List of United Kingdom disasters by death toll
Why–because analysis
Ferry Aid
Coordinates: 51°22′28.5″N 3°11′26″E / 51.374583°N 3.19056°E / 51.374583; 3.19056[43]
Sister ships[edit]
Fate of the three sister ships:
the Herald, renamed Flushing Range, was scrapped in 1988
the Spirit of Free Enterprise sailed under a range of names on the English Channel and between the Greek islands. She was scrapped in September 2012 as MS Anthi Marina.
The Pride of Free Enterprise sailed as MF Sherbatskiy between Spain and Morocco. She was scrapped in 2015.
References[edit]
Citations
Jump up ^ MV Herald of Free Enterprise Report of Court N0. 8074, Formal Investigation. UK Department of Transportation
Jump up ^ Yardley 2014, p. 13.
Jump up ^ Yardley 2014, p. 6.
^ Jump up to: a b Yardley 2014, p. 14.
Jump up ^ Yardley 2014, pp. 11–12.
Jump up ^ Yardley 2014, p. 12.
Jump up ^ Hiles, Andrew (2004). Business Continuity: Best Practices : World-class Business Continuity Management. Rothstein Associates Inc. p. 20. ISBN 978-1-931332-22-4.
Jump up ^ Yardley 2014, p. 23.
Jump up ^ Yardley 2014, p. 10.
^ Jump up to: a b c d Wittingham, The Blame Machine, p. 121
^ Jump up to: a b Robins, Nick (1995) The evolution of the British ferry, Kilgetty : Ferry, ISBN 1-871947-31-6, p. 89
^ Jump up to: a b c Wittingham, The Blame Machine, p. 120
^ Jump up to: a b c d e f g h "mv HERALD OF FREE ENTERPRISE Report of Court No. 8074 Chap 10 The immediate cause of the disaster" (PDF). DTI. Retrieved 2010-12-31.
^ Jump up to: a b Wittingham, The Blame Machine, p. 120–1
Jump up ^ http://www.maib.gov.uk/cms_resources.cfm?file=/HofFE%20part%201.pdf court report
^ Jump up to: a b c Bell, Bethan (6 March 2017). "Zeebrugge Herald of Free Enterprise disaster remembered". BBC News. Retrieved 6 March 2017.
^ Jump up to: a b Holmes, Geoffrey (4 March 2017). "Zeebrugge Ferry Disaster 30 Years On". The Independent. Retrieved 6 March 2017.
^ Jump up to: a b c d Wittingham, The Blame Machine, p. 122
Jump up ^ Yardley 2014, p. 113.
Jump up ^ Yardley 2014, p. 114-116.
Jump up ^ Maitland, Clay (26 August 2010). "Tragic death of Wolfgang Schroeder". ClayMaitland.com. Retrieved 4 February 2016.
Jump up ^ "Zim Mexico III accident in Mobile, AL" (PDF). Sidelights. The Council of American Master Mariners, Inc. 36 (4). Winter 2006. Archived from the original (PDF) on 28 October 2016. Retrieved 28 October 2016. Captain Schröder was a hero of the MV Herald of Free Enterprise Disaster some years back, when he and his ship saved a large number of the passengers. For his heroic actions, he received a letter of commendation from the Prime Minister of the United Kingdom (Margaret Thatcher) and a medal from the King of Belgium.
Jump up ^ Yardley 2014, p. 29.
Jump up ^ Yardley 2014, pp. 86,100.
Jump up ^ Yardley 2014, pp. 137–8.
Jump up ^ Wittingham, The Blame Machine, p. 119
Jump up ^ "mv HERALD OF FREE ENTERPRISE Report of Court No. 8074 Chap 14 The management" (PDF). DTI. Retrieved 2010-12-31.
Jump up ^ "Roll on, roll off freight ships with open garage decks potential death traps, naval men believe". The Times (61529). London. 20 January 1981. col A, p. 2.
Jump up ^ "The "Squat" effect and the sinking of the "Herald of Free Enterprise"". ExpoNav. Retrieved 6 March 2017.
Jump up ^ [(1990) 93 Cr App R 72]
Jump up ^ Foundation, Internet Memory. "[ARCHIVED CONTENT] UK Government Web Archive – The National Archives". Retrieved 7 March 2017.
Jump up ^ Micke Asklander. "M/S Herald of Free Enterprise". Fakta om Fartyg. Retrieved 2008-02-23.
Jump up ^ History and photos of Gaelic Ferry Archived 12 May 2012 at the Wayback Machine., visited 5 November 2011
Jump up ^ Gripper, Ann (25 October 2013). "UK weather: A look back at the devastating Great Storm of 1987 that nobody predicted". Daily Mirror. Retrieved 30 May 2015.
Jump up ^ History of the Herald of Free Enterprise, visited 6 November 2011
Jump up ^ Burtles, Jim (2014). Emergency Evacuation Planning for Your Workplace: From Chaos to Life-Saving Solution. Rothstein Publishing. p. 2. ISBN 978-1-931332-56-9.
Jump up ^ "A BBC drama-documentary will delve into one of the biggest disasters in Dover history". Kent Live. 14 February 2017. Archived from the original on 14 February 2017. Retrieved 6 March 2017.
Jump up ^ Koefoed-Hansen, Michael (2007) M/F Oleander, The ferry site, www page, accessed 22 June 2007
Jump up ^ "House of Commons PQs - Margaret Thatcher Foundation". Retrieved 7 March 2017.
Jump up ^ "Zeebrugge disaster marked by memorial service 25 years on". BBC News. 6 March 2012. Retrieved 9 October 2015.
Jump up ^ "Disaster Action". Retrieved 7 March 2017.
Jump up ^ "No. 51183". The London Gazette (Supplement). 30 December 1987. p. 61.
Jump up ^ mv Herald of Free Enterprise: Report of Court No. 8074 Formal Investigation (PDF), Crown Department of Transport, 1987, ISBN 0-11-550828-7, Archived from the original on 6 October 2007, retrieved 2008-04-08 CS1 maint: BOT: original-url status unknown (link)
Sources
Whittingham, Robert B. (2004). "Organizational and management errors". The Blame Machine: why human error causes accidents. Oxford: Elsevier Butterworth-Heinemann. ISBN 0-7506-5510-0.
Yardley, Iain (2014). Ninety Seconds at Zeebrugge: The Herald of Free Enterprise Story. The History Press. ISBN 978-0-7509-5736-6.
External links[edit]
Hundreds trapped as car ferry capsizes (BBC News)
Zeebrugge disaster was no accident (BBC News)
Disaster Action website
Herald of Free Enterprise accident 3D simulation
The time line from the Heralds launch to her eventual breaking up
[show]
v
t
e
Shipwrecks and maritime incidents in 1987
Shipwrecks
20 Feb: USS Accokeek
4 Mar: HMAS Colac
6 Mar: Herald of Free Enterprise
15 Jun: ARA Comodoro Py
16 Jun: HMS Yarmouth
16 Jul: Havel
17 Jul: USS Bausell
July (unknown date): USS McKean
26 Sep: Iran Ajr
27 Nov: USCGC Duane
28 Nov: USCGC Bibb
5 Dec: Cason
12 Dec: Rainbow Warrior, Samson
20 Dec: Doña Paz
Other incidents
7 Apr: USS Daniel Boone
1 May: Saint Eloi
24 Jul: Bridgeton
16 Oct: Hengist, Sea Isle City
20 Dec: Vector
1986 1988
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Phase (waves)
From Wikipedia, the free encyclopedia
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The relationship between period, frequency, and amplitude for a sine wave is illustrated in this image[1]
Phase is the position of a point in time (an instant) on a waveform cycle. A complete cycle is defined as the interval required for the waveform to return to its arbitrary initial value. The graph to the right shows how one cycle constitutes 360° of phase. The graph also shows how phase is sometimes expressed in radians, where one radian of phase equals approximately 57.3°.'
Phase can also be an expression of relative displacement between two corresponding features (for example, peaks or zero crossings) of two waveforms having the same frequency.[1]
In sinusoidal functions or in waves "phase" has two different, but closely related, meanings. One is the initial angle of a sinusoidal function at its origin and is sometimes called phase offset or phase difference. Another usage is the fraction of the wave cycle that has elapsed relative to the origin.[2]
Contents
[hide]
1 Phase shift
2 Phase difference
2.1 Phase comparison
3 Formula for phase of an oscillation or a wave
4 See also
5 References
6 External links
Phase shift[edit]
Illustration of phase shift. The horizontal axis represents an angle (phase) that is increasing with time.
Phase shift is any change that occurs in the phase of one quantity, or in the phase difference between two or more quantities.[2]
This symbol: φ {\displaystyle \varphi \,} is sometimes referred to as a phase shift or phase offset because it represents a "shift" from zero phase.
For infinitely long sinusoids, a change in φ {\displaystyle \varphi \,} is the same as a shift in time, such as a time delay. If x ( t ) {\displaystyle \scriptstyle x(t)\,} is delayed (time-shifted) by 1 4 {\displaystyle \scriptstyle {\frac {1}{4}}\,} of its cycle, it becomes:
x ( t − 1 4 T ) = A ⋅ cos  ( 2 π f ( t − 1 4 T ) + φ ) = A ⋅ cos  ( 2 π f t − π 2 + φ ) {\displaystyle {\begin{aligned}x\left(t-{\tfrac {1}{4}}T\right)&=A\cdot \cos \left(2\pi f\left(t-{\tfrac {1}{4}}T\right)+\varphi \right)\\&=A\cdot \cos \left(2\pi ft-{\tfrac {\pi }{2}}+\varphi \right)\end{aligned}}}
whose "phase" is now φ − π 2 {\displaystyle \scriptstyle \varphi \,-\,{\frac {\pi }{2}}} . It has been shifted by π 2 {\displaystyle \scriptstyle {\frac {\pi }{2}}} radians (the variable A {\displaystyle A} here just represents the amplitude of the wave).
Phase difference [edit]
In-phase waves
Out-of-phase waves
Representation of phase comparison.[1]
Left: the real part of a plane wave moving from top to bottom. Right: the same wave after a central section underwent a phase shift, for example, by passing through a glass of different thickness than the other parts.
Phase difference is the difference, expressed in degrees or time, between two waves having the same frequency and referenced to the same point in time.[2] Two oscillators that have the same frequency and no phase difference are said to be in phase. Two oscillators that have the same frequency and different phases have a phase difference, and the oscillators are said to be out of phase with each other.
The amount by which such oscillators are out of phase with each other can be expressed in degrees from 0° to 360°, or in radians from 0 to 2π. If the phase difference is 180 degrees (π radians), then the two oscillators are said to be in antiphase. If two interacting waves meet at a point where they are in antiphase, then destructive interference will occur. It is common for waves of electromagnetic (light, RF), acoustic (sound) or other energy to become superposed in their transmission medium. When that happens, the phase difference determines whether they reinforce or weaken each other. Complete cancellation is possible for waves with equal amplitudes.
Time is sometimes used (instead of angle) to express position within the cycle of an oscillation. A phase difference is analogous to two athletes running around a race track at the same speed and direction but starting at different positions on the track. They pass a point at different instants in time. But the time difference (phase difference) between them is a constant - same for every pass since they are at the same speed and in the same direction. If they were at different speeds (different frequencies), the phase difference is undefined and would only reflect different starting positions. Technically, phase difference between two entities at various frequencies is undefined and does not exist.
Time zones are also analogous to phase differences.
A real-world example of a sonic phase difference occurs in the warble of a Native American flute. The amplitude of different harmonic components of same long-held note on the flute come into dominance at different points in the phase cycle. The phase difference between the different harmonics can be observed on a spectrogram of the sound of a warbling flute.[3]
Phase comparison[edit]
Phase comparison is a comparison of the phase of two waveforms, usually of the same nominal frequency. In time and frequency, the purpose of a phase comparison is generally to determine the frequency offset (difference between wave cycles) with respect to a reference.[1]
A phase comparison can be made by connecting two signals to a two-channel oscilloscope. The oscilloscope will display two sine waves, as shown in the graphic to the right. In the adjacent image, the top sine wave is the test frequency, and the bottom sine wave represents a signal from the reference.
If the two frequencies were exactly the same, their phase relationship would not change and both would appear to be stationary on the oscilloscope display. Since the two frequencies are not exactly the same, the reference appears to be stationary and the test signal moves. By measuring the rate of motion of the test signal the offset between frequencies can be determined.
Vertical lines have been drawn through the points where each sine wave passes through zero. The bottom of the figure shows bars whose width represents the phase difference between the signals. In this case the phase difference is increasing, indicating that the test signal is lower in frequency than the reference.[1]
Formula for phase of an oscillation or a wave[edit]
The phase of an oscillation or wave refers to a sinusoidal function such as the following:
x ( t ) = A ⋅ cos  ( 2 π f t + φ ) y ( t ) = A ⋅ sin  ( 2 π f t + φ ) = A ⋅ cos  ( 2 π f t + φ − π 2 ) {\displaystyle {\begin{aligned}x(t)&=A\cdot \cos(2\pi ft+\varphi )\\y(t)&=A\cdot \sin(2\pi ft+\varphi )=A\cdot \cos \left(2\pi ft+\varphi -{\tfrac {\pi }{2}}\right)\end{aligned}}}
where A {\displaystyle \scriptstyle A\,} , f {\displaystyle \scriptstyle f\,} , and φ {\displaystyle \scriptstyle \varphi \,} are constant parameters called the amplitude, frequency, and phase of the sinusoid. These functions are periodic with period T = 1 f {\displaystyle \scriptstyle T={\frac {1}{f}}\,} , and they are identical except for a displacement of T 4 {\displaystyle \scriptstyle {\frac {T}{4}}\,} along the t {\displaystyle \scriptstyle t\,} axis. The term phase can refer to several different things:
It can refer to a specified reference, such as cos  ( 2 π f t ) {\displaystyle \scriptstyle \cos(2\pi ft)\,} , in which case we would say the phase of x ( t ) {\displaystyle \scriptstyle x(t)\,} is φ {\displaystyle \scriptstyle \varphi \,} , and the phase of y ( t ) {\displaystyle \scriptstyle y(t)\,} is φ − π 2 {\displaystyle \scriptstyle \varphi \,-\,{\frac {\pi }{2}}\,} .
It can refer to φ {\displaystyle \scriptstyle \varphi \,} , in which case we would say x ( t ) {\displaystyle \scriptstyle x(t)\,} and y ( t ) {\displaystyle \scriptstyle y(t)\,} have the same phase but are relative to their own specific references.
In the context of communication waveforms, the time-variant angle 2 π f t + φ {\displaystyle \scriptstyle 2\pi ft\,+\,\varphi } , or its principal value, is referred to as instantaneous phase, often just phase.
See also[edit]
In-phase and quadrature components
Instantaneous phase
Lissajous curve
Phase angle
Phase cancellation
Phase problem
Phase velocity
Phasor
Polarity
Polarization
Coherence, the quality of a wave to display a well defined phase relationship in different regions of its domain of definition
Absolute phase
References[edit]
^ Jump up to: a b c d e "Time and Frequency from A to Z". "Phase". National Institute of Standards and Technology (NIST). Retrieved 12 June 2016. This content has been copied and pasted from an NIST web page and is in the public domain.
^ Jump up to: a b c Ballou, Glen (2005). Handbook for sound engineers (3 ed.). Focal Press, Gulf Professional Publishing. p. 1499. ISBN 0-240-80758-8.
Jump up ^ Clint Goss; Barry Higgins (2013). "The Warble". Flutopedia. Retrieved 2013-03-06.
External links[edit]
Wikimedia Commons has media related to Phase (waves).
"What is a phase?". Prof. Jeffrey Hass. "An Acoustics Primer", Section 8. Indiana University. © 2003. See also: (pages 1 thru 3. © 2013)
Phase angle, phase difference, time delay, and frequency
ECE 209: Sources of Phase Shift — Discusses the time-domain sources of phase shift in simple linear time-invariant circuits.
Phase Difference Java Applet
Retrieved from "https://en.wikipedia.org/w/index.php?title=Phase_(waves)&oldid=804987684"
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