Amplitude calculation formula

[LittleWatchShop]

 

Edited May 28, 2023 by LittleWatchShop
Corrected pi

[JohnR725]

unfortunately I mathematically challenged so I can't help you with the formula sort of. but I can give you a reference here is a manual for a timing machine that I do not have but I do have a collection of timing machine manuals and it has the formula.

B600_english -.pdf

[LittleWatchShop]

Not sure why pi is included in the formula...I will ponder

[Endeavor]

Interesting, two equations for the same calculation. However π* has an asterisks.

• = optional

Sorry, I ponder as well but in this case I couldn't help myself

Edited May 28, 2023 by Endeavor

[tomh207]

1 hour ago, Endeavor said:

Interesting, two equations for the same calculation. However π* has an asterisks.

• = optional

Sorry, I ponder as well but in this case I couldn't help myself

It’s a common thing in computer circles that * is used to denote multiplication 

 

Tom

[praezis]

I

4 hours ago, LittleWatchShop said:

Not sure why pi is included in the formula...I will ponder

It is a sinus swing!

[Endeavor]

1 hour ago, tomh207 said:

It’s a common thing in computer circles that * is used to denote multiplication 

 

Of course I know that, just giving it a twist

 

[LittleWatchShop]

I took a watch and measured the waveform on an oscilloscope to get ta.  In order to get the amplitude reported on the timegrapher, I have to divide by pi.  So, it needs to be there.

I have done the derivation where the rotation of the balance wheel is approximated as a sinusoid [sin(2 * pi * f * t)].  When the argument of a sin() is a small angle, it can be approximated as the angle itself:

sin(theta) ~ theta for small theta.

Thus, in the derivation, sin(2 * pi * f * t) becomes 2*pi*f*t.

So that is where pi enters the expression for Amplitude.

Edited May 28, 2023 by LittleWatchShop

[LittleWatchShop]

------------------------

OK here is the derivation.  Check my work!

[praezis]

BR = beat rate (e.g. 18000)
T = swing period (e.g. 0.4 s)
T = 2 * 3600 / BR
LA = lift angle (@ t1)
A = amplitude angle (@ T/2)
———————————

A = LA / sin( 2 * Pi * t1 / T)

here  sin(x) about equal to x:
A = (LA * T) / (2 * Pi * t1)
   = (LA * 3600) / (Pi * t1 * BR)
   = (LA * 1146) / (t1 * BR)

Frank

Edited May 29, 2023 by praezis

[LittleWatchShop]

On 5/29/2023 at 7:37 AM, praezis said:

LA = lift angle (@ t1)

How are you ascribing LA at a single time point (t1)?

[praezis]

Hi,

t1 is the time to travel through LA.
1st to last pulse of esc. noise.

Frank