NavList:
A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
Did a precessing gyro lead to the loss of Earhart?
From: Gary LaPook
Date: 2010 Sep 11, 20:08 -0700
Jackie posted this on a different thread and I thought this should have a new title.
Jackie wrote:
"On 9/10/2010 1:13 PM, Jackie Ferrari wrote:
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"I responded:
I've not read Lodeesen's book but I have some problems with his theory.
First, airplanes do not have gyro-compasses, they have a much simpler "directional gyro," DG. The difference is that a gyro-compass seeks north while a DG does not and just maintains its orientation in inertial space, it just stays pointed in the same direction as it was set. Because of this, the DG is set by referral to the magnetic compass and is not relied on, by itself, for heading. The reason the DG is used is that it is steadier than the compass and so makes it easier to maintain your heading.
Pilots know that DGs precess. Gyroscopic precession is the normal tendency of a gyroscope to change its orientation when pushed by an outside force and the direction of the movement is as though the external force had been applied 90 degrees later in the rotation of the spinning gyroscope. However, what pilots are told is precession is NOT gyroscopic precession, it is "apparent precession." What makes a DG appear to precess is simply the gyroscope maintaining its orientation in inertial space while the earth turns under it. It behaves just like the Foucault pendulum in Paris which appears to change the plane of its swing during the day, but the pendulum is actually maintaining its orientation while the earth turns under it. The name for this is "earth rate precession." The earth turns 15.04 degrees per hour in inertial space so earth rate precession could make the DG appear to precess at this rate. But, just like the Foucault pendulum, a DG would only precess this fast if it were at the north or south pole. At any lower latitude it will appear to precess at a slower rate equal to 15.04 degrees per hour times the sine of the latitude. The Foucault pendulum hanging in the Pantheon in Paris at 48° 51' north appears to change its orientation by just 11.3 degrees per hour. Earhart's flight was made along the equator. The sine of zero degrees is zero. 15.04 degrees per hour times a sine of zero is zero so there should have been no earth rate apparent precession.
Another source of apparent precession is "transport precession" which is caused by the airplane transporting the DG across lines of longitude which appears to the DG as though the earth were spinning at a different rate. For a plane flying eastward, the number of degrees of longitude crossed would be added to the 15.04 degree per hour rotation of the earth and cause a faster apparent precession while a plane flying westward would subtract it movement from the rotation of the earth. Earhart was flying about two degrees per hour eastward so would increase the rate of apparent precession but since this is also limited by the sine of the latitude the total apparent precession would still be zero.
Since pilots spend most of their time NOT flying near the equator they expect to see their DGs precess so check them regularly against the compass and reset it to agree with the compass approximately every ten minutes so it is unlikely that Lodeeson's theory explains the disappearance.
gl"
From: Gary LaPook
Date: 2010 Sep 11, 20:08 -0700
Jackie posted this on a different thread and I thought this should have a new title.
Jackie wrote:
"On 9/10/2010 1:13 PM, Jackie Ferrari wrote:
Captain Marius Lodeesen a friend and student of Noonan discusses this on p 113 of his book 'Captain Lodi Speaking ' addressing what could have gone wrong on the Lae to Howland leg. He says that Noonan was probably well to the north of the track owing to procession of the gyrocompass. If , unable to get a fix he then aimed off North putting him even further away from Howland.I once got to wondering just how far north he would have had to have been off track and things like optimal distances from the destination and angles for aiming off, to minimise the danger arising from this, but gave up not being of a mathematical bent! I would be very interested therefore in anything you come up with and will be following this thread closely.Jackie."
-----------------------------------------------------------------------------------------------------------------------------------------
"I responded:
I've not read Lodeesen's book but I have some problems with his theory.
First, airplanes do not have gyro-compasses, they have a much simpler "directional gyro," DG. The difference is that a gyro-compass seeks north while a DG does not and just maintains its orientation in inertial space, it just stays pointed in the same direction as it was set. Because of this, the DG is set by referral to the magnetic compass and is not relied on, by itself, for heading. The reason the DG is used is that it is steadier than the compass and so makes it easier to maintain your heading.
Pilots know that DGs precess. Gyroscopic precession is the normal tendency of a gyroscope to change its orientation when pushed by an outside force and the direction of the movement is as though the external force had been applied 90 degrees later in the rotation of the spinning gyroscope. However, what pilots are told is precession is NOT gyroscopic precession, it is "apparent precession." What makes a DG appear to precess is simply the gyroscope maintaining its orientation in inertial space while the earth turns under it. It behaves just like the Foucault pendulum in Paris which appears to change the plane of its swing during the day, but the pendulum is actually maintaining its orientation while the earth turns under it. The name for this is "earth rate precession." The earth turns 15.04 degrees per hour in inertial space so earth rate precession could make the DG appear to precess at this rate. But, just like the Foucault pendulum, a DG would only precess this fast if it were at the north or south pole. At any lower latitude it will appear to precess at a slower rate equal to 15.04 degrees per hour times the sine of the latitude. The Foucault pendulum hanging in the Pantheon in Paris at 48° 51' north appears to change its orientation by just 11.3 degrees per hour. Earhart's flight was made along the equator. The sine of zero degrees is zero. 15.04 degrees per hour times a sine of zero is zero so there should have been no earth rate apparent precession.
Another source of apparent precession is "transport precession" which is caused by the airplane transporting the DG across lines of longitude which appears to the DG as though the earth were spinning at a different rate. For a plane flying eastward, the number of degrees of longitude crossed would be added to the 15.04 degree per hour rotation of the earth and cause a faster apparent precession while a plane flying westward would subtract it movement from the rotation of the earth. Earhart was flying about two degrees per hour eastward so would increase the rate of apparent precession but since this is also limited by the sine of the latitude the total apparent precession would still be zero.
Since pilots spend most of their time NOT flying near the equator they expect to see their DGs precess so check them regularly against the compass and reset it to agree with the compass approximately every ten minutes so it is unlikely that Lodeeson's theory explains the disappearance.
gl"
