Talk:Schuler tuning

request for a diagram

The orbit and the tunnel are clear enough, but the pendulum is hard to follow. In any case, the fact that they all have the same period doesn't explain why it is useful in tuning a navigation system. Brallan 09:37, 14 April 2007 (UTC)

Applicable to Strapdown inertial systems too

The article should note that Schuler tuning is applicable to strapdown inertial systems also. Specifically, the Schuler period shows up in the error equations. — Preceding unsigned comment added by Bilbodad (talk • contribs) 14:34, 15 January 2015 (UTC)

Para 2 - «Principle» is confusing, I believe

2015-01-21 1914 - RD - I am loath to make an edit as this topic is new to me, but in getting to the bottom of it (and thank you for uploading the translated paper) I observe that para 2 says "consider a pendulum ... suspended in a uniform gravitational field", and in the following sentence makes it "suspended from the surface of the Earth". I took that to mean that it was still in the uniform gravitational field, whereas at the surface of the Earth the field is non-uniform, as it always points to the centre. Could I suggest two amendments:

1) "at the center of the earth" <add> "and the field would no longer be uniform, but will always point to that center" </add>; and in the next sentence

2) "the bob tends to remain motionless" <replace by> "the bob will remain motionless".

I think that would help new readers. Thank you.

RobinDaniel (talk) 19:15, 21 January 2015 (UTC)

Principle IS confusing

2019-11-10 - I agree and I would go further to say it's downright confusing and not strictly correct. Bringing in the 84 minute period so early in the explanation is what leads to the confusion; the argument is backwards. I have been trying to understand the Schuler phenomenon for many years and all of the articles I read made the same confusing error. Only today, when I saw his actual paper for the first time did the penny drop. It's not only powerful but amazingly simple. Translating liberally, here is what he says:

Say we have a mass distribution pivoted without friction about a horizontal axis at the earth’s surface. Obviously, if we apply a horizontal acceleration, it will (or maybe not) rotate, depending only on how well balanced it is. If it’s perfectly balanced, (ie centre of mass = centre of rotation) then the acceleration produces no torque and the mass doesn’t rotate. However, if it is NOT balanced, it will experience an angular acceleration proportional to the applied linear acceleration

dw/dt = m dv/dt e/(m L^2) = dv/dt e/L^2, where

m is mass

e is imbalance (distance between c of m and c of pivot)

L is radius of gyration

dv/dt is the acceleration

If e is zero, the mass keeps pointing in the same direction regardless of the acceleration. If e is non-zero, it will rotate.

Frank van Kann 07:41, 10 November 2019 (UTC) --Frank van kann (talk)

Schuler asked this very simple question

We would like this angular motion be such that the initial vertical axis of the mass (eg distinguished by a line painted on it) keeps pointing toward the centre of the earth as the device sweeps along the curved surface of the earth.

What are the conditions on e and L to achieve this?

The answer is remarkably simple.

The horizontal velocity v represents an angular velocity w1 at the centre of the earth:

w1 = v / R

Therefore

dw1/dt= dv/dt / R

This gives dw/dt = e/L^2 R dw1/dt

so the condition for w1 = w is just

dw/dt = dw1/dt

and therefore

R e/L^2 = 1

giving

e = L^2/R

What does this have to do with 84 minutes??

Well, the unbalanced pivoted mass is actually a compound pendulum, whose period is

T = 1/(2 π) sqrt (L^2/(e g)) = 1/(2 π) sqrt (R/g) = 84 min.

That’s surely impossible to achieve with hardware: if L = 100 mm, then e = 1.5 nm.

Frank van Kann 07:43, 10 November 2019 (UTC)