A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Position-Finding
From: Jeremy C
Date: 2010 May 14, 20:04 EDT
I have tested Byron's method on two different occasions when steady at anchor and have compared the results with azimuths of the sun shot very soon after (within 5 minutes or so). My comments about the method and the general idea of compass error are below.
First the general information so others can repeat the experiment. I found position via GPS to 3 decimal places of minutes. Given the accuracy of GPS and the location of the GPS antenna in relationship to the gyro repeater used, I gave myself a position accuracy of 15 yards.
From this gyro repeater, I took a bearing of a water tower with a center pipe with a 5x Alidade and hairline sight. The distance from the charted position to this water tower was 3.148nm (interpolating the last 0.1 second of arc of Latitude which was the accuracy of the scales on the chart) or 6375.7 yds. If I follow Byron's math correctly, I get an ambiguity of reading of 0.141 degrees.
With this in mind, i determined the error of that gyro repeater to be between 0.36 and 0.64 degrees west. While the normal method yielded an error of 0.5 degrees West.
With the same Alidade I shot an azimuth of the sun and determined the error to be 0.9 degrees West.
The second iteration of the experiment saw a range of 6288.7 yds with the same position ambiguity, which yielded a 0.143 gyro error ambiguity. Again with the repeater I found a gyro error of 0.4 deg West or 0.26 to 0.54 degrees West.
The azimuth this time yielded an error of 0.8 degrees West.
So we have two iterations that gave us repeater errors within 0.1 of a degree of each other and the exact same offset between the two methods. Now the question in my mind is which is more accurate? Am I to believe the azimuth or the terrestrial bearing? That 0.5 degree difference could certainly affect my fixes on the harbor chart I am using.
Also a thing to consider: in either method, this is a measure of the error of a specific gyro repeater, and is not the error of the master gyro unless the two are aligned exactly. To make this method useful for actual piloting, it must be performed on each repeater that will be used and each ambiguity recorded. It can be argued that each repeater should be matched exactly to the master gyro, when we are talking about accuracies of 0.1 degree, this may very well be impossible on some equipment which leads me to my second point.
Given the position ambiguity ranges we can now easily obtain by GPS or DGPS (especially on military ships which have the ultra-accurate GPS signals), our measures of bearing ambiguity far exceed in accuracy the tools we are apt to be using in gathering and plotting the data.
Perhaps there are new gyro repeaters out there on new ships that have accuracies of 0.1 degrees, but all gyros that I've sailed with have 1 degree marks on the master so i am only confident to eyeball interpolate to 0.25 degrees at best. The repeaters, where the bearing is actually being taken as opposed to the digital repeater, are also only marked to 1 degree.
Secondly, regular azimuth circles and even high powered alidades such as mine can offer incredible accuracy if kept level, but you are still reading on a scale that must be interpolated, and again, i can only confidently go down to 0.25 degree in my readings.
Thirdly, the plotting tools on any of these charts that I have used are also marked in 1 degree increments. Unless computer plotting is being used (and it certainly can be on the Naval ICE system) you are also limited to about 0.25 degrees.
Lastly, the accuracy of the bearing and the fix are also greatly determined by the person shooting the bearing and/or plotting the bearings; and the timing of each. A ship in motion needs expert observers shooting all bearings very close to simultaneously (or if there is a time interval, the lines must be advanced or retarded accordingly) in order to obtain maximum accuracy.
I would love to test the Franklin fix theory with the derived compass error, but i hit against the wall of reality in the merchant marine, there just aren't enough people on the bridge to devot to this method. Perhaps when next there is a cadet, we can attempt it, but with only one bearing shooter of limited experience and skill, I am not expecting much more than i have seen in the past in terms of accuracy.