Trials In Tainted Space Deck 92

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Graphs of probability P of not observing independent events each of probability p after n Bernoulli trials vs np for various p. Three examples are shown:
Blue curve: Throwing a 6-sided die 6 times gives 33.5% chance that 6 (or any other given number) never turns up; it can be observed that as n increases, the probability of a 1/n-chance event never appearing after n tries rapidly converges to 0.
Grey curve: To get 50-50 chance of throwing a Yahtzee (5 cubic dice all showing the same number) requires 0.69 × 1296 ~ 898 throws.
Green curve: Drawing a card from a deck of playing cards without jokers 100 (1.92 × 52) times with replacement gives 85.7% chance of drawing the ace of spades at least once.

In the theory of probability and statistics, a Bernoulli trial (or binomial trial) is a random experiment with exactly two possible outcomes, 'success' and 'failure', in which the probability of success is the same every time the experiment is conducted.^[1] It is named after Jacob Bernoulli, a 17th-century Swiss mathematician, who analyzed them in his Ars Conjectandi (1713).^[2]

The mathematical formalisation of the Bernoulli trial is known as the Bernoulli process. This article offers an elementary introduction to the concept, whereas the article on the Bernoulli process offers a more advanced treatment.

Since a Bernoulli trial has only two possible outcomes, it can be framed as some 'yes or no' question. For example:

Is the top card of a shuffled deck an ace?
Was the newborn child a girl? (See human sex ratio.)

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Therefore, success and failure are merely labels for the two outcomes, and should not be construed literally. The term 'success' in this sense consists in the result meeting specified conditions, not in any moral judgement. More generally, given any probability space, for any event (set of outcomes), one can define a Bernoulli trial, corresponding to whether the event occurred or not (event or complementary event). Examples of Bernoulli trials include:

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This floor is related to the Fools Rush In mission. In The Merchant Deck if you go to the red light zone,there will be an event, in it will be present mysterious figures, and then there will be two options, follow and ignore, choosing follow Steele will do automatic actions, but will not be able to catch the mysterious.

Flipping a coin. In this context, obverse ('heads') conventionally denotes success and reverse ('tails') denotes failure. A fair coin has the probability of success 0.5 by definition. In this case there are exactly two possible outcomes.
Rolling a die, where a six is 'success' and everything else a 'failure'. In this case there are six possible outcomes, and the event is a six; the complementary event 'not a six' corresponds to the other five possible outcomes.
In conducting a political opinion poll, choosing a voter at random to ascertain whether that voter will vote 'yes' in an upcoming referendum.

Definition[edit]

Independent repeated trials of an experiment with exactly two possible outcomes are called Bernoulli trials. Call one of the outcomes 'success' and the other outcome 'failure'. Let ${displaystyle p}$ be the probability of success in a Bernoulli trial, and ${displaystyle q}$ be the probability of failure. Then the probability of success and the probability of failure sum to one, since these are complementary events: 'success' and 'failure' are mutually exclusive and exhaustive. Thus one has the following relations:

{displaystyle p=1-q,quad quad q=1-p,quad quad p+q=1.}

Alternatively, these can be stated in terms of odds: given probability p of success and q of failure, the odds for are ${displaystyle p:q}$ and the odds against are ${displaystyle q:p.}$ These can also be expressed as numbers, by dividing, yielding the odds for, ${displaystyle o_{f}}$ , and the odds against, ${displaystyle o_{a}:}$ ,

{displaystyle {begin{aligned}o_{f}&=p/q=p/(1-p)=(1-q)/qo_{a}&=q/p=(1-p)/p=q/(1-q)end{aligned}}}

These are multiplicative inverses, so they multiply to 1, with the following relations:

{displaystyle o_{f}=1/o_{a},quad o_{a}=1/o_{f},quad o_{f}cdot o_{a}=1.}

In the case that a Bernoulli trial is representing an event from finitely many equally likely outcomes, where S of the outcomes are success and F of the outcomes are failure, the odds for are ${displaystyle S:F}$ and the odds against are ${displaystyle F:S.}$ This yields the following formulas for probability and odds:

{displaystyle {begin{aligned}p&=S/(S+F)q&=F/(S+F)o_{f}&=S/Fo_{a}&=F/Send{aligned}}}

Note that here the odds are computed by dividing the number of outcomes, not the probabilities, but the proportion is the same, since these ratios only differ by multiplying both terms by the same constant factor.

Trials In Tainted Space Deck 92 Episode

Random variables describing Bernoulli trials are often encoded using the convention that 1 = 'success', 0 = 'failure'.

Closely related to a Bernoulli trial is a binomial experiment, which consists of a fixed number ${displaystyle n}$ of statistically independent Bernoulli trials, each with a probability of success ${displaystyle p}$ , and counts the number of successes. A random variable corresponding to a binomial is denoted by ${displaystyle B(n,p)}$ , and is said to have a binomial distribution.The probability of exactly ${displaystyle k}$ successes in the experiment ${displaystyle B(n,p)}$ is given by:

{displaystyle P(k)={n choose k}p^{k}q^{n-k}}

where ${displaystyle {n choose k}}$ is a binomial coefficient.

Bernoulli trials may also lead to negative binomial distributions (which count the number of successes in a series of repeated Bernoulli trials until a specified number of failures are seen), as well as various other distributions.

When multiple Bernoulli trials are performed, each with its own probability of success, these are sometimes referred to as Poisson trials.^[3]

Example: tossing coins[edit]

Consider the simple experiment where a fair coin is tossed four times. Find the probability that exactly two of the tosses result in heads.

Solution[edit]

For this experiment, let a heads be defined as a success and a tails as a failure. Because the coin is assumed to be fair, the probability of success is ${displaystyle p={tfrac {1}{2}}}$ . Thus the probability of failure, ${displaystyle q}$ , is given by

{displaystyle q=1-p=1-{tfrac {1}{2}}={tfrac {1}{2}}}

Using the equation above, the probability of exactly two tosses out of four total tosses resulting in a heads is given by:

{displaystyle {begin{aligned}P(2)&={4 choose 2}p^{2}q^{4-2}&=6times left({tfrac {1}{2}}right)^{2}times left({tfrac {1}{2}}right)^{2}&={dfrac {3}{8}}.end{aligned}}}

References[edit]

Trials In Tainted Space Deck 92 Series

^Papoulis, A. (1984). 'Bernoulli Trials'. Probability, Random Variables, and Stochastic Processes (2nd ed.). New York: McGraw-Hill. pp. 57–63.
^James Victor Uspensky: Introduction to Mathematical Probability, McGraw-Hill, New York 1937, page 45
^Rajeev Motwani and P. Raghavan. Randomized Algorithms. Cambridge University Press, New York (NY), 1995, p.67-68

External links[edit]

Wikimedia Commons has media related to Bernoulli trial.

'Bernoulli trials', Encyclopedia of Mathematics, EMS Press, 2001 [1994]
'Simulation of n Bernoulli trials'. math.uah.edu. Retrieved 2014-01-21.

Retrieved from 'https://en.wikipedia.org/w/index.php?title=Bernoulli_trial&oldid=985798435'

S-92 HELIBUS™

Background

The S-92 Helibus was designed and developed during the 1990 decade to serve as both a commercial passenger carrier and as a military troop/cargo carrier. Its initial design was intended to take advantage of the both the proven technologies of the Black Hawk models as well as the four million flight hours accumulated on the H-60 series at that point in their history. The H-60 dynamic system in particular had reached a proven high level of durability as a result of this extensive operating service experience. However, the initial design of the S-92 using the then existing H-60 propulsion and dynamic systems mated to an enlarged fuselage proved to be too limited in useful load capability. This limitation was created by a combination of the higher weight of a new airframe designed to carry 19 passengers and to the structural limitation of a 22,000 pound gross weight imposed by the existing H-60 dynamic system.
Because these limitations imposed too great a penalty on speed and range performance, the decision was made to redesign and upgrade the basic H-60 dynamic system where needed to achieve a mission gross weight closer to 25,000 pounds while at the same time designing the dynamic components to meet newly issued FAA requirements regarding damage tolerance for commercial helicopters. That effort was so successful that Sikorsky was awarded the 2002 Collier Trophy by the National Aeronautics Association acknowledging its achievements in safety, operating cost and traveling comfort. The S-92 design benefited from many new technologies that together represented a new helicopter generation. Chief among these were the advanced rotor blade that employed improved airfoil design and blade tip configuration as well as a fully composite material spar and a fully damage tolerant main rotor head design. In addition, Sikorsky's new Active Vibration Control System provided much reduced vibration levels throughout the operation aircraft and rotor speed ranges. Significant cockpit display system improvements helped improve aircraft safety and reduced pilot workload. The reader should note that the S-92 and its derivative models were still in production at the time that this model history was prepared. As a result, changes to the design, equipment, features, weights and performance described herein are likely to take place as this model becomes further developed and improved. For current information on the S-92 Program, go to the Sikorsky web site at http://www.sikorsky.com/Index

S-92 Development Timeline

June 1995: Sikorsky and five international partners introduced the S-92 during the Paris Air Show.
August 1998: The ground test vehicle, Aircraft No. 1, made its first run.
November 20, 1998: The first flight worthy version, Aircraft No. 2 was delivered to the Sikorsky Development Flight Center in West Palm Beach, Florida.
December 23, 1998: The S-92 took to the air for the first time in West Palm Beach. The No. 2 helicopter made eight takeoffs and landings during its 50-minute inaugural flight.
October 19, 1999: Aircraft No. 3, the second S-92 to fly, joined the flight test program.
January 25, 2000: Sikorsky signed the S-92's launch customer, Halifax, Nova Scotia based Cougar Helicopters, and offshore oil support operator.
October 10, 2000: The S-92's engine, the General Electric CT7-8 turboshaft, received FAA certification.
February 8, 2001: The first S–92 to incorporate customer inspired design changes made its first flight at West Palm Beach.
October 5, 2001: The first S–92 in the final production configuration, which included the Rockwell Collins glass cockpit, made its first flight at Sikorsky headquarters in Stratford, Connecticut.
April 9, 2002: The military variant, incorporating major structural enhancements and systems upgrades, flew for the first time at West Palm Beach.
December 19, 2002: Sikorsky received FAA type certification for the S-92 after compiling 1,570 test flight hours.
August 2003: Full-aircraft HIRF testing for JAA Certification began at Patuxent River ,Maryland
June 8, 2004 Sikorsky received European Joint Aviation Authorities JAR Part 29 certification
September 27, 2004: Initial delivery was at Heli-Expo 2004 show in Las Vegas

The Sikorsky S-92 commercial model was unveiled at Heli-Expo '92 in Las Vegas, Nevada on March 22, 1992. The mockup had a 19 passenger airline style interior and a five-tube (each eight by seven inches) Honeywell Electronic Flight Information Systems (EFIS) flight deck. The mockup was fitted with a new rotor that was based on the UH-60 BLACK HAWK. Offshore oil exploration was the primary target for the S-92. Scheduled airlines and general utility duties were also being targeted. A 23 seat military version of the proposed helicopter, a growth derivative of Sikorsky's H-60 family, was also being shown to potential customers in full size model form.

S-92Debut at Heli-Expo'92 in Las Vegas

.
S-92 Military Derivative Full Scale mockup

A decision on the future of the S-92 would be made by the end of this year. The required Customer interest did not develop and in 1993 Sikorsky postponed launching the S-92 due to the international helicopter market downturn and instead began searching for international risk sharing partners.

Team S-92

A new era began June12th 1995 at the Paris Air Show with the formal launch announcement of the full scale development of the Sikorsky S-92 HELIBUS™ with six international team members. Full scale development of the S-92 commenced.

Serving as the leader of Team S-92, Sikorsky designed and manufactures the aircraft's dynamic systems and carried out final assembly, flight test, and certification. Each international partner performed the detail design work for its section of the aircraft based on basic data supplied by Sikorsky. Partners were responsible for all tooling planning and tooling, and provided 5 prototype shipsets, specific test pieces, and all required spare parts to support the flight test program. Members included the following risk sharing partners:

Japan's Mitsubishi Heavy Industries (7.5% - main cabin)
Spain's Gamesa Aeronautica (7% - main rotor pylon, tailcone/transition section and composite interiors),
Peoples Republic of China's Jingdezhen Helicopter Group (2% - tail pylon and horizontal stabilizer)
Taiwan's Aero Industrial Development Corporation (AIDC) (6.5% - Cockpit Structure)
Brazil's Embraer (4% - sponsons complete with fuel system and landing gear).

.S-92 Build Components

Telecommunications between partners played a vital role for Team S-92. A satellite communications network linked all partners. Three-dimensional electronic models were posted by the Sikorsky drawing release system over the network. All drawings were digital CATIA (Computer Aided Three-dimensional Interactive Application) drawings with real time interface with all partners. To assist in the development and manufacturing processes for the separate sections of the helicopter, Sikorsky personnel were stationed with each of the international partners. Each team was assigned an On-Site Partner Manager plus quality assurance, operations, logistics, manufacturing engineering, and various engineering design and analysis staff members as required. Complementing the international efforts of our partners were the Integrated Product Development (IPD) Teams based at the Sikorsky Stratford, Connecticut Facility. The IPD Teams were responsible for the aircraft's dynamic systems, electrical/electronic systems, systems engineering, systems integration and test.

The major subcontractors were General Electric (CT7-8D turboshaft engines), Rockwell Collins (Avionics Management System (AMS)), and Hamilton Sundstrand (Automatic Flight Control System (AFCS)).

Sikorsky built five prototype S-92s, one for ground testing and four flight test aircraft.

#1 aircraft, the ground test vehicle, was scheduled for 350 hours including 200 hours to certify the main gearbox.
#2 aircraft, the first flight aircraft, was scheduled for 340 hours of flying
#3 aircraft was closest to the production aircraft and focused on the aircraft's operating systems. These systems included the auxiliary power unit, the engines Full Authority Digital Electronic Controls (FADEC), Automatic Flight Control System (AFCS) and engine development.
#4 aircraft was the acoustics and options development platform and scheduled for 124 hours of flying.
#5 aircraft, a utility configured aircraft was scheduled for 480 hours of flying at maximum gross weight and external load testing

The first flight was on December 23 1998 at the Sikorsky Development Flight Center in West Palm Beach, Florida. The 50 minute maiden flight consisted of 8 takeoffs and landings including hover, forward, and sideward flight maneuvers.

S-92 First flight December23, 1998

As originally envisioned the S-92 was to combine upgraded dynamic system components of the H-60/S-70 series with a larger cabin. However, in order to provide competitive performance in the commercial market, the S-92 is essentially an all new helicopter, with larger, composite construction, swept, tapered and anhedral tipped main rotor blades, new tail rotor, and a new four stage transmission based on the three stage S-70 unit.

The flaw-tolerant hub and yoke design provided unlimited life and improved safety, and the main gearbox incorporated advanced corrosion-resistant materials and coatings

Unlimited life main rotor blades incorporate composite spar technology and utilize a swept, tapered anhedral tip. This design provided improved lift and maneuverability

Anti-torque control was provided by unlimited life tail rotor blades with bearingless composite flexbeam. Pitch control links used elastomeric bearings

The S-92 main transmission featured a unique planetary gear system, and
utilizes advanced materials for long life

Some 40% of the aircraft was of composite construction. The S-92's main cabin was wider and longer than the S-70's and featured a rear loading freight ramp, while the cockpit featured a Rockwell Collins EFIS system with four color liquid crystal displays, with provision for a fifth. Power was from two FADEC equipped General Electric CT7-8D turboshaft engines.

Design changes announced in July 2000 in response to customer requests included a 16 inch increase in cabin length aft of the cockpit to permit installation of a 50 inch wide cabin door to improve hoisting capability and to accommodate a Stokes litter during SAR operations; reduction in the length of tail rotor pylon by about 41 inches to offset additional weight of cabin extension; and the horizontal stabilizer was repositioned from the left side opposite the tail rotor to the right side at the base of the tail rotor pylon. These changes provided additional benefits in creating an improved fold configuration for shipboard operations, increased bird strike protection deriving from the relocation of tail rotor drive shaft and controls aft of the tail spar, and a flatter hover attitude arising from a forward shift of the helicopter center of gravity, improving visibility for confined space and shipboard landing, and increasing aft fuselage ground clearance. The revised configuration was incorporated from the third prototype and on all production aircraft.

Configuration Features

Airframe

Cabin: 6 ft high, 6.58 ft wide, 20 ft long
Hydraulic cargo ramp (140 cuft/3.9cum)
10 cabin windows
Air conditioning system
Active vibration control system
Retractable, energy-absorbing, tricycle landing gear

Cockpit

Health and Usage Monitoring System (HUMS)
Four-axis, fully-coupled autopilot
Enhanced Ground Proximity Warning System (EGPWS)
Traffic Collision Avoidance System (TCAS1)
Weather radar
Four 6 x 8 inch multi-function displays
Nav Management System
Collins Proline IV avionics
Cockpit Voice Recorder/Flight Data Recorder

Powerplant and fuel system

Integral inlet particle separator
Two GE CT7-8A turboshaft engines
Honeywell 30-150 APU for ground power, engine start, and in-flight emergency / supplemental power.
Pressure refueling system
Dual crashworthy fuel cells located in sponsons(380 gal / 1,440 l each)

Rotor and drive system

Four blade fully articulated main rotor system
Rotor brake system

Electrical

Two 60/75 KVA, oil spray cooled, 12,600 R.P.M. three phase generators
One APU driven, 30/35 KVA, air-cooled, 12,000 R.P.M. three-phase generator
Two generator control units
Two 400 amp, 28VDC regulated transformer rectifiers
One 125 amp, 28 VDC backup regulated transformer rectifier
One 15 amp-hour (cont. rating) 19-cell nickel-cadmium battery charged by DC converter
External power receptacles, one 28 VDC and 115 VAC
Two fixed landing lights
One controllable landing light
Provisions for Rotor Ice Protection System (RIPS)

Advanced Cockpit and Onboard Systems

S-92 Instrument Panel

The S-92cockpit features a Rockwell Collins avionics package that displays flight-critical data on six-inch by eight-inch, color, liquid-crystal, multifunction displays and includes dual flight-management systems with integrated control of the flight director. The instrument panel was reduced in width, compared with earlier designs, to improve the pilots' field of view. Situational awareness also can be enhanced through the addition of weather radar data with a flight path overlay, a forward-looking infrared (FLIR) system and a digital moving map. The cockpit is night-vision-goggle-compatible and can simulate one engine-inoperative conditions for training purposes. Other key cockpit systems include an Engine Indicating Caution Advisory System (EICAS) and a Honeywell Enhanced Ground-Proximity Warning System (EGPWS).

General Arrangement Drawing

S-92 3-view Drawing

Mission Systems

S-92 OPTIONAL EQUIPMENT

Airframe and Rotors

Overhead cockpit windows
Full sliding door
Sliding upper cabin door, right side
Sliding cabin window, left-side, forward
Jettisonable cabin windows
200 psf cabin floor
Tail pylon pullout steps
Air conditioning system
Cold weather heat system
Main and tail rotor blade ice protection system

Furnishings

Jumpseat (cockpit observer)
Utility type soft cabin interior
Crashworthy, side-facing, fold-up utility seats (up to 22)

Propulsion/Fuel Systems

Electrical Systems/Lighting

High intensity search light
Helicopter Emergency Egress Lighting (HEEL) for emergency exits and optional pushout windows
Lower anti-collision light
Logo lights
Recognition lights
Rotor head inspection light
Emergency floor lighting

Avionics

Trials In Tainted Space Deck 92 Full

Fifth color display 6' x 8' LCD (center position on instrument panel)
SAR AFCS upgrade with coupled search patterns AFCS Crew Hover
Universal flight management system (UNS-1ESP) with GPS
TCAS I (Traffic Collision Avoidance System)
Enhanced Ground Proximity Warning System (EGPWS)
SATCOM (Satellite Communications
FLIR (Forward Looking Infra-Red)
Loudhailer

Special Mission Equipment

Cargo hook (10,000 lb capacity)
Up to 16 litter medical evacuation kit
Floor roller system
Ramp roller system
Ramp cargo flippers
Cargo loading winch
Single rescue hoist
(1-full capability 600 lb, 320 fpm)
Dual rescue hoists (2-full capability, 600 lb, 320 fpm)
Deployable emergency locator beacon
Jettisonable forward sponson mounted life rafts (14/21 person)
Cabin cargo tiedown rings
Wire strike protection

General Characteristics and Performance

PERFORMANCE
Standard Day, Sea Level at 26,150 lb/11,861 kg gross weight

Maximum speed (Vne)		165 kts 306 km/hr
Maximum continuous cruise speed		153 kts 284 km/hr
Long range cruise speed		139 kts 258 km/hr
Range: offshore configuration (3,000 ft, ISA plus 10°C.)
- with 19 passengers and 30-minutes reserve plus 10%		444 nm 823 km
- with 19 passengers and no reserve		544 nm 1,008 km
Maximum range with internal auxiliary fuel (370 gallons)		726 nm 1,345 km
Service ceiling		15,000 ft 4,572 m
Hover ceiling out-of-ground effect		7,125 ft 2,172 m
Hover ceiling in-ground effect		11,320 ft 3,450 m

WEIGHTS

Maximum takeoff gross weight, civil configuration
- internal load	26,150 lb 11,861 kg
- external load	28,300 lb 12,837 kg
Maximum external load	10,000 lb 4,536 kg
Weight empty, offshore oil	15,900 lb 7,212 kg
Weight empty, airline	15,600 lb 7,076 kg
Weight empty, search and rescue	16,200 lb 7,348 kg
Weight empty, 10-place executive transport	17,200 lb 7,801 kg
Maximum fuel load, (internal, standard)	5,130 lb 2,327 kg

GENERAL DATA

Crew seating capacity	2
Seating capacity, airline-style seating	19-24 passengers
Seating capacity, utility side facing seating	22 passengers
Baggage compartment volume	140 cu ft 4.0 cu m
Fuel capacity (internal, standard)	760 US gal 2,877 L

POWERPLANT RATINGS
per engine, Standard Day at Sea Level

Engine quantity and type Two General Electric CT7-8A
Twin engine takeoff, 5 minutes	2,520 shp 1,879 kw
Twin engine, 30 minutes	2,336 shp 1,742 kw
Maximum continuous	2,043 shp 1,524 kw
OEI, 30 seconds	2,600 shp 1,912 kw
OEI, 2 minutes	2,520 shp 1,879 kw
OEI, 30 minutes	2,498 shp 1,863 kw

AIRCRAFT DIMENSIONS

Main rotor diameter (blade tip circle)	56' 4' 17.17 m
Tail rotor diameter (blade tip circle)	11' 0' 3.35 m
Fuselage length	56' 2' 17.10 m
Fuselage width Nemu installer mac.	14' 2' 4.32 m
Length over-all (including rotors)	68' 6' 20.88 m
Height over-all
- to tip of tail rotor, positioned vertically	17' 11' 5.47 m
- to tip of tail rotor, positioned diagonally	16' 10' 5.12 m
Width (including horizontal stabilizer)	17' 3' 5.26 m
Width (blades parked at 45° to fuselage)	40' 0' 12.36 m
Main landing gear tread	10' 5' 3.18 m
Wheel base	20' 4' 6.20 m
Passenger cabin length (with bulkhead)	20' 0' 6.10 m
Passenger cabin width	6' 7' 2.01 m
Passenger cabin height	6' 0' 1.83 m

Production History

The first S-92A was delivered to PHI, Inc. of Lafayette Louisiana on September, 27, 2004. By early 2012 over 150 S-92A helicopters have been delivered to customers worldwide with 400,000 total flight hours. Production is ongoing. For current information on the S-92 Program, go to the Sikorsky web site at http://www.sikorsky.com/Index

S-92A First Production Delivery September 2004

Prepared by Vinny Devine
March 2012

for additional reading see NEWSLETTER JULY 2012 AND NEWSLETTER JULY 2013

last update MARCH 25, 2014