Jump to content

Maximum speed of a balance wheel...


Recommended Posts

Hi,

this is just a question out of couriosity... :)

My SEIKO SNK809 has a 7S26C movement. Its balance wheel has roughly a 4.5mm radius (I measured that with a transparent ruler on the transparent
back of the watch...if someone has the exact value I would be the last one, who insists of the value mentioned above....;) ). From that I can calculate the circumference
of the balance wheel. Assuming an amplitude of 260 degree gives me the way a point travels on the balance wheel by multiplying the circumference by 26/36.
Furthermore this way is traveled 21600 times an hour. This gives me the linear speed of that point.
BUT: The speed changes in accordance to a sine function...
And here I got stuck: speed is the derivation of distance by time. The derivation of sine(t) dt gives me a cosine function...and I am again right from where I started..with a 90 degree phase shift.
How can I calculate the maximum speed of a point traveling in accordance to a sine function around a circumference if I know the speed it would need to have, when it would be linear motion? I cannot get my head around it... ;)

HEEEEEELLLLLPPPPP!  :):):)

Cheers!
mcc

 

Link to comment
Share on other sites

Equation of motion is sinesoidal , so it's velocity is derivative of sine function which is cosine function , parameters giving maximaum speed  times it's cosine function gives you istantaneous speed.

S=s max × cos(alpha)     

S max is the speed you explained calculation of. S max occures at alpha=0.

S= 2πr( 26/36) ( frequency) × cos( alpha) 

 

 

Link to comment
Share on other sites

Both velocity and speed vary sinusoidally.  

The fact that velocity is a vector and speed scalar quantity, shouldn,t cause  doubts in your mind that speed is unworthy of following a sinusoidal behaviour, is this where you let doubts get in your visualising the system?

Your understanding of the rest is good, I don,t see what caused your doubts.

Link to comment
Share on other sites

Join the conversation

You can post now and register later. If you have an account, sign in now to post with your account.

Guest
Reply to this topic...

×   Pasted as rich text.   Restore formatting

  Only 75 emoji are allowed.

×   Your link has been automatically embedded.   Display as a link instead

×   Your previous content has been restored.   Clear editor

×   You cannot paste images directly. Upload or insert images from URL.



×
×
  • Create New...