The Earth's Rotation Rate
One might believe without further reading that this discussion is about the rotation rate of the Earth. However, the real purpose is to emphasize the importance of critical examination of assumptions and communications for a project. Therefore, you need the discipline to read my entire elaboration.
I had offered my services to implement a free idiot check of the CAIB Final Report prior to its official release. My proposal was declined, but that didn’t stop me from performing a critical examination. Why is this document important? Well, I guess you might try asking the nice people at NASA’s Return to Flight Team since somebody is supposed to learn from mistakes.
For this lesson you will need a copy of Volume 3, Part 4 of the CAIB Final Report and know something about the geometry of a circle. The CAIB Final Report section can be downloaded by following Columbia Accident Investigation Board link at http://caib.nasa.gov/news/report/pdf/vol3/part04.pdf if you don’t already have a hard copy of the document.
Turn to section 4.3.1. "Trajectory and Footprints Summary and Methodology" of the document.
You will find two items:
The first item is the statement:
"JSC MOD-DM has presented the methods and assumptions used in this investigation to several NASA peer-reviews and in international and U. S. forums for feedback, and continuously refined the methodology presented here."
The second item is the phrase:
"...Earth rotation rate of 7.292115146 x 10-5 deg/sec."
An average person might not challenge the second item given the vanity of the first item. However, I wasn’t intimidated from making simple calculations as follows:1 hour = 60 minutes = 60 minutes x 60 seconds / minute = 3600 seconds
Therefore, the ratio of 1 hr / 3600 sec is established.Some may argue that actual sunlight for a day on planet Earth can vary due to location, date of the year, the leap year, or even the notion that days are getting longer since the Earth’s rotation rate is thought to be slowing down. However, I shall use the definition that a day consists of approximately 24 hours.
Now, the Earth’s geometry is best described as a sphere. This sphere rotates about its axis every 24 hours to make the day. This rotation forms a circular path of 360 degrees so a day consists of a 360-degree rotation.Therefore, the ratio of 360 deg / day is established.
(360 deg / day) x (day / 24 hr) x (1 hr / 3600 sec) = 4.1666667 x 10-3 deg/sec
Alternatively,
(4.1666667 x 10-3 deg/sec) x ( pi radians / 180 deg) = 7.2722052 x 10-5 radians/sec
Therefore, based on my calculations using the 24 hour assumption, the Earth rotates at 4.1666667 x 10-3 deg/sec or 7.2722052 x 10-5 radians/sec.
Now, let’s compare NASA’s value of 7.292115146 x 10-5 deg/sec. By the way, why do I state NASA’s value? Contrary to some opinions, preparation of the supposedly independent CAIB Final Report had assistance from NASA. Well, the "JSC MOD-DM" designation in the first item implies ingenuity from a department at NASA’s Johnson Space Center.
7.292115146 x 10-5 deg/sec converts to 1 sec / (7.292115146 x 10-5 ) degand
( 360 deg / day ) x ( 1 sec / ( 7.292115146 x 10-5 deg ) ) x ( 1 hr / 3600 sec ) = 1371.3 hr / day
Hint:
pi radians = 180 degrees
with pi approximately = 3.141592654
At this point I remembered a similar problem that cost NASA or the American taxpayer over 327 million dollars referred to as the Mars Climate Orbiter Measurement Fiasco. The fiasco resulted in a spacecraft destroyed as it entered the atmosphere of Mars at a lower orbit than conceived. The navigational software was based on a prior model and insufficiently utilized pre-flight testing and data checking during flight. Lockheed Martin, the NASA contractor, elected to use the imperial measurement system while the JPL division of NASA elected to use the metric measurement system. Inconsistent utilization of the measurement units was obviously due to poor communications at several management levels.
Considering that billion dollar fiascos with the loss of lives have occurred with similar discrepancies, I decided to improve my analysis and lecture NASA via email communications with Jefferson Davis Howell, Jr., JSC Director.
Transcripts of these communications are as follows:
Sunday, November 09, 2003 2:21 PM
From: Weldon K. Chafin, Jr.
To: JSC Director
Subject: CAIB report discrepancy for earth's rotation rate
Mr. Howell:
I think I discovered the nature of the CAIB report discrepancy for earth's rotation rate as described:
http://boss.streamos.com/download/caib/report/lowres/vol3/part04.pdf
4.3.1. Trajectory and Footprints Summary and Methodology
"JSC MOD-DM has presented the methods and assumptions used in this investigation to several NASA peer-reviews and in international and U. S. forums for feedback, and continuously refined the methodology presented here."
"...Earth rotation rate of 7.292115146 x 10-5 deg/sec."
It seems that some lessons are not learned very well. This embarrassing oversight could be analogous to the English/Metric system conversion error that caused the demise of the Mars Climate Orbiter on September 23, 1999. It is too bad that I was excluded from these reviews. The error is the use of degrees as units rather than radians. The value of 7.292115146 x 10-5 radians/sec would be correct since it is consistent with the following calculation:
4.1780746 x 10-3 degrees/sec x (pi radians / 180 degrees) = 7.292115816 x 10-5 radians/sec neglecting a slight precision error. It looks like someone screwed up either with typographical error, misinterpretation, etc. The question remains on how the JSC MOD-DM used this value in calculations.
I really wasn't too concerned about more complex precision issues since the absence of radians to degrees conversion had much greater magnitude in discrepancy. Anyway, I had sufficiently articulated the problem to the Director of Johnson Space Center.
However, I must have raised a serious question because I received the following reply mentioning an audit:
Monday, November 10, 2003 5:51 PM
From: JSC Director
To: Weldon K. Chafin, Jr.
cc: STONE, BROCK R. (RANDY) (JSC-AB) (NASA) ; Bill Readdy (Bill Readdy) ; Sean O'Keefe (Sean O'Keefe)
Subject: RE: CAIB report discrepancy for earth's rotation rate
Thank you for your note as well as your careful and alert reading of the CAIB Report. The JSC Mission Operations Directorate has performed a careful audit of all the programs which use that parameter and have assured me that the correct units are incorporated. The discrepancy you found in the CAIB Report was a typographical error in the report itself and was not used incorrectly in any of the investigation analysis.
Once more, thank you for your interest and concern.
Best Wishes, JD Howell, Jr.
I surely thought that somebody else caught this problem before me. After all, I would not receive the hard copies of the CAIB Final Report already available to NASA. I had actually tried to convey the problem to a few other NASA organizations prior to contacting Howell, but those entities never responded to me for whatever reason. So, I decided on the following reply:
Monday, November 10, 2003 9:40 PM
From: Weldon K. Chafin, Jr.
To: JSC Director
Subject: RE: CAIB report discrepancy for earth's rotation rate
Mr. Howell:
I thank you for your prompt response in this matter.
Please inform me of how and when you and the JSC Mission Operations Directorate were initially apprised of this discrepancy.
NASA’s clarification stating "the first indication" set me apart from the rest:
Wednesday, November 12, 2003 12:14 PM
From: JSC Director
To: Weldon K. Chafin, Jr.
cc:
Bill Readdy (Bill Readdy) ; STONE, BROCK R. (RANDY) (JSC-AB) (NASA) ; HARPOLD, JON C. (JSC-DA) (NASA)Subject: RE: CAIB report discrepancy for earth's rotation rate
To the best of my knowledge, your inquiry was the first indication we had that there was a possible discrepancy. As stated previously, after receiving your e-mail I directed our Mission Operations Directorate to audit all programs that use these measurements to ensure that the correct units of measurement were being used.
Best regards, JD Howell, Jr.The fact that the discrepancy required an audit of calculations meant that the issue extended beyond the report itself. Imagine what would be going through the minds of NASA management if space vehicle launches, EVAs, etc. were imminent while a calculation vital to success of these activities was being audited due to the possibility of a parameter error. Would NASA apply similar judgment precedents such as confusion, indecision or improper decisions on the merits of the 'Crater' tile damage assessment program during a critical time? Would the problem seemingly disappear in a stove pipe management scenario relegating the 'One NASA' concept to a facade? I commend Mr. Howell for being responsible and not taking an unnecessary gamble on this issue.
End of lesson.
School’s out.