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

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

It must work the earth stays level.

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…)

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

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

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

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.

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

Dave