Simple question (I think)

[Bo’sunParticipant @bosun58570]

Good morning All,

Do regular/domestic spirit levels have curved vials?

[Bo’sunParticipant @bosun58570]

Spirit Level vials?

[Thor 🇳🇴Participant @thor]

I think they have a slightly curved inside, the more accurate/sensitive levels have less curvature than a coarser one.

Thor

Edited By Thor 🇳🇴 on 21/04/2023 12:04:46

[Nicholas FarrParticipant @nicholasfarr14254]

Hi Bo'son, if you mean the type from DIY stores, many of them have slightly barrel shaped ones.

Regards Nick.

[SillyOldDufferModerator @sillyoldduffer]

I don't think you can generalise. Most of mine of the rough levelling type are definitely bent, others are straight and probably barrel ground. My collection varies tremendously with vials ranging from dubiously bent plastic to well-made glass. They all work, but the cheap ones are only OK for finding a rough level, untrustworthy if an accurate flat is needed.

Dave

[Bo’sunParticipant @bosun58570]

Thanks Guys,

The reason I ask is: I was reminiscing through some old FMC Trade School log books, and I came across some of my notes from the Standards Room Instructor, who said the curvature on the reference level vial, which I recall as being about 24" long, was equal to the curvature of the earth. It just got me wondering as these things often do.

[mark costello 1Participant @markcostello1]

It must work the earth stays level.

[old martParticipant @oldmart]

Not exactly true, the average flatness of the earth greatly exceeds the requirements of an optical flat.

[Nigel Graham 2Participant @nigelgraham2]

I suspect an old wives', or all old instructors' tale there.

Try measuring the displacement of a couple of inches of glass tube. (Yes, it's calculable, but…)

[Clive HartlandParticipant @clivehartland94829]

Yes, the internal diameter of a precision vial is hand ground to a curve. I seem to remember that a 20" bubble had a radius of 60'.

[NealebParticipant @nealeb]

I think the sums are pretty easy here.

Let's say that 20" of tilt give a 1mm movement of the bubble – about right? So we need to find the radius of the curve in which 20" of rotation is equivalent to 1mm at the circumference. Think of a giant toroidal tube if you like, of which the vial is the tiny bit that you can see. Clearly, rotate the toroidal tube and the bubble will move, giving the numbers we are working with. 20" is equivalent to 1/3', 1/(3*60) deg, 1/(3*60*360) revolutions. So the full circumference is 1mm times (3*60*360), which my calculator makes 64800mm

Radius equals circumference/2*pi, =10313mm.

So approx radius of vial is about 10m. Substantially less than the radius of the earth?

[roy entwistleParticipant @royentwistle24699]

I thought that the earth was flat

And why did they call it earth if over three quarters of it is water

Roy

[SillyOldDufferModerator @sillyoldduffer]

Posted by Nealeb on 22/04/2023 10:09:38:

I think the sums are pretty easy here.

Let's say that 20" of tilt give a 1mm movement of the bubble – about right? So we need to find the radius of the curve in which 20" of rotation is equivalent to 1mm at the circumference. Think of a giant toroidal tube if you like, of which the vial is the tiny bit that you can see. Clearly, rotate the toroidal tube and the bubble will move, giving the numbers we are working with. 20" is equivalent to 1/3', 1/(3*60) deg, 1/(3*60*360) revolutions. So the full circumference is 1mm times (3*60*360), which my calculator makes 64800mm

Radius equals circumference/2*pi, =10313mm.

So approx radius of vial is about 10m. Substantially less than the radius of the earth?

I got a bigger equivalent radius for a Starrett 98-18 Machinists Level, where the graduations measure an angle equivalent to a slope of 0.43mm per metre.

Assuming I did it right, always a big if, this calculator suggests the Starrett vial has a radius of 1162.79081 metres. (Or would be the vial was really a bent tube; actually it's a much easier to make straight tube with a shallow barrel ground inside.)

Still much less than the radius of the earth though, which is about 6700km.

Pedantically, the bubble aligns with the planets centre of mass, and the accuracy of the level relative to a true right angle is limited by the vial mounting.

I don't know what the most accurate way of setting a level is. With a theodolite, two staves, extreme care, many traverses, and much error checking it's possible to survey a level accurate within to about 10mm per kilometre. Though I have an ancient theodolite, I doubt I could achieve that accuracy in practice, though it might be fun to try. Establishing an accurate level over several neighbouring properties does me no good at all – the level can't be used in a workshop!

Dave

[Anonymous]

Precision vials are made by very slightly bending a straight tube in a fixture. A straight hole is the created and honed. When the tube is released the result is a hole on a very large radius.

Andrew

[Grindstone CowboyParticipant @grindstonecowboy]

To answer the original question, yes they do (or at least they used to, they may have been superseded by the barrel type shown by Nick). Precision / engineer's levels are another matter

Theodolites will give you a flat plane, but that may not be what you want – the towers on the Humber bridge are further apart at the top than at the bottom, otherwise they wouldn't be perpendicular to the Earth's surface (other bridges are available).

Rob

[Pete RimmerParticipant @peterimmer30576]

Vials might be ground of bent. The one in my box square is certainly ground as it works inverted.

[SillyOldDufferModerator @sillyoldduffer]

Posted by old mart on 21/04/2023 21:00:22:

Not exactly true, the average flatness of the earth greatly exceeds the requirements of an optical flat.

I'm worried about this one. On average, I think it's true all spheres are flat, but this must be misleading maths, because spheres aren't flat in any direction, ever. This is true all the way down to a geometric point, which has no dimensions, and can't be flat or curved in a human sense. Unlike a line between two points, which is also dimensionless, but is perfectly straight. I think the first truly flat thingy is a dimensionless plane defined by two dimensionless lines at a right-angle. My brain hurts!

Anyway, if optical flat is levelled with a clear view to the horizon, the flat can be shown experimentally to be tangent to the surface. Even a small optical flat 's more than capable of showing the earth isn't flat, whatever the average says.

Interesting that we live in a universe where mathematics can describe almost everything logically and precisely, except several worrying exceptions prove something else deeply contradictory is also going on.

Dave

[Michael GilliganParticipant @michaelgilligan61133]

In answer to the opening question … it would depend upon your interpretation of the term ‘regular/domestic’

Here is a short verbatim quote “from the horse’s mouth”

:

The manufacturing process varies considerably based on the vast range of precision levels, level vials, electronic level sensors, and angle-measuring inclinometers that we produce. However, the general process usually starts at our own dedicated vial-making department. Here, glass tubes are meticulously checked for cracks and deformities before being cut into smaller cylinders and a radius ground into the inner diameter. […]

MichaelG.

.

Ref. __ https://www.leveldevelopments.com/2020/08/the-manufacturing-process-at-level-developments/

Ref. __ https://www.leveldevelopments.com/products/

Edited By Michael Gilligan on 26/04/2023 06:28:15

[Nicholas FarrParticipant @nicholasfarr14254]

Posted by Bo'sun on 21/04/2023 12:47:21:

Thanks Guys,

The reason I ask is: I was reminiscing through some old FMC Trade School log books, and I came across some of my notes from the Standards Room Instructor, who said the curvature on the reference level vial, which I recall as being about 24" long, was equal to the curvature of the earth. It just got me wondering as these things often do.

Hi Bo'son, I think that if a 24" long vial was equal to the curvature of the earth, it would be almost flat, and would probably only measure less than microns, and for practical purposes would be next to useless. The earth anyway is slightly squashed, as it is lager at the equator than at the poles by about 27 miles, due the the rotational forces exerted on it. You may have part of the equation missing, in that the reference vial might be a ratio of the average radius of the earth to its length, which to me would make more sense.

Regards Nick.

[Anonymous]

Posted by SillyOldDuffer on 25/04/2023 11:45:08:

…dimensionless plane defined by two dimensionless lines at a right-angle.

Not true! In Euclidian geometry a plane can be defined by distinct three points, a line and a point that is not on the line, two lines that intersect at a point or two parallel lines. There is no requirement for the two intersecting lines to be at right angles.

Andrew

[SillyOldDufferModerator @sillyoldduffer]

Posted by Andrew Johnston on 26/04/2023 08:34:08:

Posted by SillyOldDuffer on 25/04/2023 11:45:08:

…dimensionless plane defined by two dimensionless lines at a right-angle.

Not true! In Euclidian geometry a plane can be defined by distinct three points, a line and a point that is not on the line, two lines that intersect at a point or two parallel lines. There is no requirement for the two intersecting lines to be at right angles.

Andrew

He's right! I was thinking of a Cartesian Plane, and planes don't have to be Cartesian.

Dave

[Anonymous]

A Cartesian plane is simply a Euclidian plane that happens to use Cartesian co-ordinates, so the geometric definitions for a plane remain the same.

Andrew

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