NavList:

A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding

HOME

Re: When even a Davis Mark 3 is too much
From: Brad Morris
Date: 2017 Jan 15, 11:26 -0500

Gentlemen

In all of the referenced builds in this thread, not one mention has been made of eccentricity or the so called "centering error".

Centering Error is the precision by which the rotation of axis of the index arm is placed in reference to the center of the arc which holds the division markings.

We can compute the centering error as a mathematical function.

AngularError = arctan (displacement/IndexArmLength)

Where the displacement is the offset between the index arm axis of rotation and the center of arc.

Naturally, we can invert the equation

IndexArmLength * tan (AngularError) = displacement

Let us examine how that plays out. It is stated that 1 arc minute of accuracy is achievable. Further, that a 20 inch index arm length is utilized.

20*tan (1/60)=.005817 inches.

That is, for a 20" index arm length, the index arm axis of rotation has to be placed within 6 thousandths of an inch in X and Y, relative to the arc, to yield a homemade sextant with an accuracy of 1'.

Whilst a metal sextant, using modern machine tools, can be manufactured to that level of precision, I find it astonishing that a sextant made of wood can be manufactured to that tolerance. Further, I don't understand how wood, given its proclivities to expand and contract with moisture content, can hold that tolerance.

We can also apply the equation to a manufactured sextant. We will assume that there is no arc error and that the resolution of the sextant is equal to the accuracy of the second. The resolution will be 6 arc seconds. Further, let us assume a 6 inch index arm length

6inches*tan (6 arc seconds/60/60)=displacement

.000174 inches = displacement

A nominal metal sextant, with modern manufacture, must hold the index arm axis of rotation to within 174 millionths of an inch.

Centering Error was considered to be fairly important. So much so that double index arm sextants were manufactured. That is, the index arm has two verniers, 180° apart. With this method of centering and a properly divided arc, the affect of the centering error is halved (according to literature). That is, the displacement error in X and Y can be doubled and still maintain the accuracy error due to centering.

Brad

On Jan 15, 2017 6:05 AM, "Örjan Sandström" <NoReply_Sandstrom@fer3.com> wrote:

It should be possible to do some refinement of tolerances through repetition.
Lets say we use John´s tapemeasure* on the perifery metod to make a 2880mm circumference 1440 tooth marine plywood** hirth indexer (basically a pair of crown wheels with 60 degree teeth interlocking).
this should then be used to make a second set, If no great preassures are involved this second set should be about as good as most plastic sextants***, good enough? this could then be used to engrave the main scale.
What is to come is bit more daunting, the verniere, it will need bit more work as each line need a slight offsetfrom the perfect 1440 div, I thought of making a second set of hirth couplings, but then it dawned on me, I only need to move everything 1 extra line in 121 lines, that means I can likely get away with micrometer adjustment, it needs to move the arm holding the engraving tool mere 2mm ofset along periphery.
*Most 5m tapemeasures are within 1,4mm/m accurate and top class 1 witin 0.6mm/m over whole length so with a 2880 mm perifery accuray is better than 0.9mm along perifery between any two teeth (~1/4 tooth) and adjacent teeth much better than that.
**ok plywood flexes but lets make it say two layers 20mm glued screwed togeter for base with the donut we cut teeth into another 20mm, 60mm marine ply, pretty stiff and as whole donut is holding with all of its 1440 teeth...
***Metal hirth indexers are capable of fractions of arcsecond accuracy and ball indexers on same principle are even better.
Main reason for accuracy is that any errors are, more or less, averaged out.
This is also one of very few measuring devises that get better accuracy for wear (to a point).
Care to guess what is used to index the wormgear of modern drum sextants.

Subject:
Author:
Start date:	(yyyymm dd)
End date:	(yyyymm dd)

NavList:

A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding

Compose Your Message

NavList

What is NavList?

Get a NavList ID Code

Retrieve a NavList ID Code

Email Settings

Custom Index

Add Images & Files
Name or NavList Code:	Email:

Name:
	(please, no nicknames or handles)
Email:

NavList ID Code: