Reblog: The Math That Saved Apollo 13

GCDXY here presents images from the Apollo 13 flight checklist. This is itself a re-representing of images that Gizmodo posted when Apollo 13 Commander James Lovell sold the checklist last year, but I’m just coming across this now. And it nicely combines the mathematics and the space history interests I so enjoy.

The particular calculations done here were shown in one of many, many, outstanding scenes in the movie Apollo 13. However, the movie presents the calculations as being done on slide rule, when the computations needed are mostly addition and subtraction. It is possible to use slide rules to do addition and subtraction, but that’s really the hard way to do it; slide rules are for multiplication, division, and raising numbers to powers.

But considerable calculation for Apollo (and Gemini, and Mercury) was done without electronic computers, and the movie would have missed out on presenting an important point if it didn’t have the scene. So the movie achieved that strange state of conveying something true about what happened by showing it in a way it all but certainly did not.

gcdxy

Two hours after a service module’s oxygen tank explosion on Apollo 13, Commander James Lovell did calculations that helped put the ship back on course so that they could return back to Earth. They needed to establish the right course to use the Moon’s gravity to get back home. Check out the article on Gizmodo from November 2011.

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Wednesday, June 6, 1962 – Food Contract, Boilerplate Purchase

The Manned Spacecraft Center has awarded to the Whirlpool Corporation Research Laboratories of Saint Joseph, Michigan, a contract to provide the food and waste management systems for Project Gemini. Whirlpool is to provide the water dispenser, food storage, and waste storage devices. The food and the zero-gravity feeding devices, however, are to be provided by the United States Army Quartermaster Corps Food and Container Institute, of Chicago. The Life Systems Division of the Manned Spacecraft Center is responsible for directing the program.

Monday, June 4, 1962 – Gemini Mission Begins In Simulation

At the Brooks Air Force Base in Texas two men have begun a simulation of a long-duration Gemini Mission. This program, run by the Air Force School of Aviation Medicine, will have them live for fourteen days in an atmosphere simulating that proposed for the Gemini spacecraft. This will be a 100 percent oxygen atmosphere maintained at five pounds per square inch of pressure.

Friday, June 1, 1962 – Operations Coordination Meeting, Astronaut Applications Close

Today’s was the first spacecraft operations coordination meeting. Presented at it was a list of all the aerospace ground equipment required for Gemini spacecraft handling and checkout before flight.

June 1 was also the nominal closing date for applications to be a new astronaut. Applications were opened April 18. The plan is to select between five and ten new astronauts to augment the Mercury 7.

Tuesday, May 29, 1962 – Ejection Seat Plans

The development testing plans for the Gemini spacecraft ejection seat were settled in a meeting between representatives of McDonnell, Weber Aircraft, the Gemini Procurement Office, Life Systems Division, Gemini Project Office, and the US Naval Ordnance Test Station at China Lake, California.

Thursday, May 24, 1962 – Parachute testing starts

At the Naval Parachute Facility in El Centro, California, North American completed a successful drop test of the emergency parachute recovery system, using a half-scale test vehicle.

Wednesday, May 23, 1962 – Paraglider Wing Wind Tunnel Test

The Ames Research Center has begun the first wind tunnel test of the inflatable paraglider wing, using a half-scale model of the wing intended to bring Gemini flights (after the first one) to a touchdown on the ground. This is the first large-scale paraglider wing in the full-scale test facility. The objective of the test program, to run over two months, are to understand the basic aerodynamic and loads data for the wing and spacecraft system, and to identify potential aerodynamic and design problems.

Monday, May 21, 1962 – Launch Pad 19 For Gemini; Pulse Code Modulation for Telemetry

The pulse code modulation method is to be used for transmitting Project Gemini telemetry. McDonnell has awarded an $8 million subcontract to Electro-Mechanical Research, Inc, of Sarasota, Florida, for this digital transmission system. The system will use a pulse code modulation subsystem, an onboard tape recorder, and a pair of VHF transmitters, and be capable of transmitting data in real or delayed time.

Friday, May 18, 1962 – Parachute Landing System

McDonnell has subcontracted the parachute landing system to be used for the first Gemini flight to Northrop Ventura. The cost is estimated at $1,829,272. The design for this flight is to use a single parachute system, a ring-sail parachute with diameter 84.2 feet. Later flights are to use the paraglider system under development. Earlier meetings have worked out a provisional schedule of events for the parachute landing.

Thursday, May 17, 1962 – Retrorocket and Parachute Decisions

The meeting about the retrograde rocket motors has concluded the design should be changed to provide about three times the thrust level. This will allow retrorocket aborts at altitudes as low as between 72,000 and 75,000 feet. The meeting was between representatives of McDonnell and the Gemini Project Office.

Wednesday, May 16, 1962 – Retrorockets, Parachutes, and Interface Group

Representatives of the Gemini Project Office and of McDonnell are meeting to discuss retrograde rockets for the Gemini spacecraft. These rockets are currently to be provided by Thiokol.

Tuesday, May 15, 1962 – Ejection seat in review; rocket catapult contract; new liaison

The first ejection seat design review has been completed. The two-day conference at McDonnell in Saint Louis was attended by representatives of McDonnell, Northrop Ventura (formerly Radioplane), Weber Aircraft, and the Manned Spacecraft Center. This is the first of a series of ejection seat design meetings planned from March 29.

Monday, May 14, 1962 – Titan II Statement of Work Given

The Manned Spacecraft Center has issued its final Statement of Work for the Air Force Space Systems Division. Space Systems Division is, in this context, contractor to NASA procuring Titan II launch vehicles, as modified for the manned program’s needs. The statement, itemizing the tasks Space Systems Division is expected to do or provide, and on what schedule, and how acceptable performance will be measured, and so on, began being prepared by the Manned Spacecraft Center on January 3. The initial budgeting and planning were completed by the end of March. Though final the plan is subject to amendment.

Saturday, May 12, 1962 – Project Gemini Cost Estimates Growing

A current estimate of Project Gemini costs shows considerable increases from the projections of December 1961. The spacecraft cost, estimated at $240.5 million, is now projected at $391.6 million. Titan II costs, expected five months ago to be about $113.0 million, have risen to $161.8 million. The Atlas-Agena budget has risen from $88.0 million to $106.3 million, despite this part of the program’s slowing down. Support development, including the paraglider program, has increased from $29.0 to $36.8 million. There is a bright spot on the budgetary front: the estimate of operations cost has declined from $59.0 to $47.8 million.

Friday, May 11, 1962 – Survival kit, biological measurements, spacewalk requirements

A two-day meeting on Gemini crew support systems has identified seven parameters to be measured for determining crew conditions during the Gemini flights. The instruments needed for the highest priority items — blood pressure, electrocardiogram, phonocardiogram, electroencephalogram, respiration, galvanic skin response, and body temperature — would require about three and a half pounds per pilot, require two watt-hours of power, and demand the shared use of six telemetry channels. Approved for development, then, are measurements of the electrocardiogram, respiration rate and depth, oral temperature, blood pressure, phonocardiogram, and nuclear radiation dose.

Friday, May 4, 1962 – Threats to First Gemini Spacecraft Schedules Identified

The Manned Spacecraft Center has issued its third analysis of the schedule of the Gemini program. The new plan calls for two additional boilerplate spacecraft, in order to help ground testing. Test hardware has begun construction, and plans for the spacecraft ground tests are formed.

Tuesday, May 1, 1962 – Digital coding, Gemini rendezvous and radar schemes

A working group made of representatives from Goddard Space Flight Center and the Manned Spacecraft Center has formed to study making Project Gemini telemetry be transmitted fully by Pulse Code Modulation (PCM) systems. This follows a briefing from Lockheed on the system. Pulse Code Modulation is a method of numerical representations of samplings of an original analog signal. Human speech has been transmitted on such systems in experimental equipment as long ago as 1926, and was used — in conjunction with a vocoder, developed by Bell Labs, and with randomized thermal noise recorded by the Muzak Corporation — to provide secure high-level Allied communications during the Second World War.

Friday, April 27, 1962 – Paraglider Meeting Produces 21 Changes

Following a review of the design and testing philosophy for the Half-Scale Test Vehicle, part of Phase II-A of the Paraglider Development Program, the Half Scale Test Vehicle Design Review Board has recommended to North American 21 changes in the test vehicle design and the test procedures.

Thursday, April 26, 1962 – Agena Launch Vehicle, Paraglider Plans

Lockheed today presents its proposed propulsion development plans for the Gemini-Agena target vehicle. The description includes studies on propulsion system optimization, a program to develop multiple-restart capabilities for the primary propulsion system, and the development program for the secondary propulsion system.

Wednesday, April 25, 1962 – Studebaker to build heat shields

The CTL Division of the Studebaker Corporation, Cincinnati, Ohio, has received a subcontract form McDonnell to provide a pair of backup heatshields for the Gemini spacecraft. The contract is for $457,875.

Monday, April 23, 1962 – Malfunction Detection System plan

Martin-Baltimore has submitted to the Air Force Space Systems Divisions a descriptive study and a proposed configuration for the Malfunction Detection System.

Thursday, April 19, 1962 – IBM Awarded Computer Contract

McDonnell has awarded IBM’s Space Guidance Center, of Owego, New York, a $26.6 million subcontract for the Gemini spacecraft computer system. IBM is also responsible for integrating this digital computer with the spacecraft’s systems and the components electrically connected to it. These components are to include the inertial platform, the rendezvous radar, the time reference system, the digital command system, the data acquisition system, the electronics for attitude control and maneuvers, the autopilot for the launch vehicle, console controls, displays, and aerospace ground equipment.

Wednesday, April 18, 1962 – Astronaut Applications Open

NASA is accepting applications for additional astronauts and will be doing so through June 1, 1962. The plan is to select between five and ten new astronauts to augment the existing corps of seven. The new astronauts will support Project Mercury operations, and go on to join the Mercury astronauts in piloting the Gemini spacecraft.

Friday, April 13, 1962

A report is being presented today to the Gemini Project Office regarding the abort criteria for the malfunction detection system. The report is presented by Martin-Baltimore and the Air Force Space Systems Division.

Thursday, April 12, 1962

The Manned Spacecraft Center has confirmed that for the currently planned missions the Agena target satellite’s planned orbital lifetime of five days will be sufficient.

Monday, April 9, 1962

The Gemini Project Office has received the “Gemini Manufacturing Plan” prepared by McDonnell. The plan calls for the construction of four static articles to be used in ground testing. According to the plan, dated April 6, and presented by Earl Whitlock of McDonnell, production spacecraft Number 1 is to be followed by static article Number 1.

Saturday, April 7, 1962

McDonnell has awarded a $1 million subcontract to the ACF Electronics Division of ACF Industries (Riverdale, California). The subcontract is to provide C-band and S-band radar beacons for the Gemini craft. The beacons are to be part of the tracking system for the spacecraft.

The C-band radar would transmit at 5765 MHz and receive at 5690. The S-band radar would transmit at 2910 MHz and receive at 2840.

Wednesday, April 4, 1962

The Defense Products Division of B F Goodrich Company of Akron, Ohio, has been awarded a cost-plus-fixed-free contract by the Manned Spacecraft Center. The contract, for $209,701, is to design, develop, and fabricate prototype pressure suits. Goodrich has been at work on contract-related materials since the 10th of January.

Tuesday, April 3, 1962

NASA’s Ames Research Center looks to have a place in the development of Project Gemini. Representatives of Ames, and the Manned Spacecraft Center, and Martin, and McDonnell meet today to discuss the Gemini wind tunnel program and the role Ames will have in it.

Saturday, March 31, 1962

The configuration of the Gemini spacecraft is formally frozen. McDonnell has been defining the spacecraft since the basic configuration was firmed up on December 22, 1961. Since then McDonnell has been writing detailed specifications for the entire vehicle, its major subsystems, and its performance.

Friday, March 30, 1962

Martin-Baltimore has submitted to the Air Force Space Systems Division the document Description of the Launch Vehicle for the Gemini Spacecraft. This defines the concept and the philosophy for each proposed subsystem as well as laid out the design for the Gemini launch vehicle.

Thursday, March 29, 1962

McDonnell awards an $18 million subcontract to the Saint Petersburg, Florida, Aeronautical Division of Minneapolis-Honeywell. This subcontract is to provide the Inertial Maneuvering Unit of the Gemini spacecraft.

Wednesday, March 28, 1962

McDonnell awards a subcontract worth $2.5 million to the Collins Radio Company of Cedar Rapids, Iowa. The subcontract is to provide the voice communications system for the Gemini spacecraft.

Friday, March 23, 1962

Air Force Space Systems Division has published the Development Plan for the Gemini Launch Vehicle System. Using experience drawn from the Titan II and the Mercury development programs it is estimated the development of the launch vehicle will require a budget of $164.4 million. This includes a contingency fund of 50 percent to cover cost increases and unforeseen changes.

Wednesday, March 21, 1962

McDonnell awards a $4.475 million subcontract to the Western Military Division of Motorola, Inc, of Scottsdale, Arizona. Western Military Division is to design and build the Digital Command System for the Gemini spacecraft. This is to receive in digital format commands from ground stations, to decode them, and to send the commands to the appropriate spacecraft systems. Two types of commands are anticipated: real-time commands for spacecraft functions, and stored program commands to update data on the spacecraft’s digital computer. The Digital Command System is to consist of a receiver/decoder package and three relay packages.

Air Force Space Systems Division awards a letter contract to the Aerojet-General Corporation of Azusa, California. This is to research, develop, and procure fifteen propulsion systems for the Gemini launch vehicle, and also for the design and development of related ground equipment. Aerojet was authorized to work on the engines on February 14th. Final engine delivery is scheduled by April 1965.