What I am after is a way to create a rule which I can apply in order to determine the time it will take for the needle to reach a point on the lp.
For instance, I can measure from the beginning of the groove, say 1 cm in the radius, and that should let me know that the needle will reach that point in 36 seconds...
Are you playing 78 R.P.M. discs? Since shortly after the introduction of the 33 R.P.M. LP, variable pitch was introduced into vinyl playback. This means the distance between grooves is varied depending upon the musical content. Simply look at the surface of a LP and you will see the more shiny and the duller portions of the disc surface which represent the amount of uncut vinyl between adjacent grooves. Therefore the distance traveled in linear inches is not the same from disc to disc. There cannot be an equation to measure an inconsistent distance. The actual rotational speed of the disc has nothing to do with what you are asking for. Even if the groove were of a constant pitch, you would first have to ascertain the actual speed of the table's platter which is almost never exactly 33.000 R.P.M.
SC - Even if you try to create such a rule, you'll have to use a much smaller increment of measure than a centimeter. Them grooves is pretty tiny little things.
Sorry friend if I used the wrong word. I am not about trying to create a RULE in order to rule anyone or anybody. I was just after a convenient way of evaluating time elapsed on LPs.
Serge Those grooves called pitch Can be precisely measured and or calculated Each revolution is different but in Greek called Delta Theda can also be calculated its deviation so even if the time intervals are different for each time needle complete a revolution. Its rate of change can be included and calculated.
The shinny part in the pitch can be compressed differently in the lacquers when vinyl is mastered but can also be easily calculated. If you need equations I can do so they are all 12th grade math.
If you need help just list all requirement details
My congrats to Nuck for reaching 5000 milestone sorry if I missed it.
How about a dial indicator, firmly mounted, with a point into the groove of an old record, and measure the linear travel of one rotation at the outside of the record, and repeat at the inside, then extrapolate the rest. As a function of radius and pi, maybe that is enough?
I passed grade 12 math, but hell, that was over a week ago!
That's almost impossible Besides Serge was looking for a "way to create a rule which I can apply in order to determine the time it will take for the needle to reach a point on the lp."
Math is not that bad generating the formula is the challenge I certainly can do it but too bad I think he finally gave-up
" ... so even if the time intervals are different for each time needle complete a revolution."
If the disc is spinning at a constant 33.33 R.P.M. (more or less, but always constant), the time it takes to travel one complete revolution is always the same, that is not the problem.
" ... and measure the linear travel of one rotation at the outside of the record, and repeat at the inside ... "
Once again the outside will, within reason, always be the same amount of linear travel. That is not difficult to calculate. If all discs ended with the same amount of lead out groove, the innner dimension would also be a simple calculation. This isn't the case and the amount of linear travel isn't going to tell you where the stylus sits at any one moment. With variable pitch that varies from disc to disc there are no constants to work with. Linear travel has nothing to do with what happens in between the outer and inner groove.
Hello kind contributors with offers to solve the problem I initially posed, with mathematics.
I am afraid that whatever mathematics are used, the results will not be applicable across all LP recordings, each one being, more or less, a special case.
So I have come to the conclusion that at best I can use some kind of averaging time linked to the position on the record. Hence, a groove at the beginning will have a value of 1, whereas that value will progressively change to .8, .7, etc.
The ideal would be a solution where the hardware was smart enough to detect a more rapid change in the displacement of the needle, giving then an accurate positioning of the needle over the space between recordings, which is really the object of this exercise...
But I don't believe there is much chance for hardware manufacturers to devote much time to that, at a time when the record players are history.
Let me make it much easier Speed= 33 rpm radius/Minute Distance= Time x Speed Time= Distance/Speed K= Pitch ceffecient (lets assume=1 for a 40 minute record) So for a 40 minute record DISTANCE=33x40=1320
Note You can keep all units same they cancel out anyway including geometric constant pi
So final formula is Time (minutes)= K x Distance / Speed The only variable will be K (You may use k=1, Distance=1320, Speed= 33) for a standard 40 Minute LP
Robert/ Serge I assume same person since you both from Melrose MA I didn't see your post until it refreshed
Speed of LP is always constant Pitch is also must be constant Regardless the position of the needle revolution is also constant So this is a perfect linear one equation
K=1 it takes 40 minutes k= More than 1 it takes more than 40 minutes K= Less than 1 it takes less than 40 Minutes
So final formula Time(minutes)= Kx40
You have to set K in such a way to control your Total Length
This is a typical case where everthing cancels out all controled by the pitch value K
If the groove was straight or if the determination was how many linear feet the stylus travelled in "X" time, your math would work.
I don't believe that is what the original post requested, however. If I understand the question correctly, the op was trying to determine where along the radius of the disc the stylus will sit after "X" amount of time playing.
Jan I will calculate it Just give me few days (I havn't use a calculator for over 10 years)
All I can tell you Time is constant (per minute) Pitch is constant (k) Inner diameter also constant despite music length They use leads towards the end if one side less than 20 minutes Inner diameter is (4 inch) fixed Outer diameter is also constant (12 inch) Revolution is constant to each circumference 33 rpm
Speed is variable due to distance change per minute Total number of revolutions can be calculated 33.33x20=666.6 you can say 666 per side see I even forgot that 40 minute LP is 20 minute per side
Things you may neglect: - inleads/outleads - Spaces in between songs - motor speed deviations
If requirements in seconds must convert all to seconds otherwise keep everything in minutes and fractions of minutes. Similarly in inches
Distance= 2 x Pi x R (but they may cancel anyway) Total# of R(tot)= 666 You can say R1 to R666 or R0 to R665
Number of revolutions will be like your mortgae payments
circular shift of pitch= delta theta or DT this will be like your mortgae intrest and the only converted length DT= 2 x Pi x Rdt or Rdt= DT/(6.28)
So finally it depends on what you want to calculate Distance with respect to outer diameter or Distance with respect to inner diameter
Just like your compounded mortgae how much do I owe after 6 years or how much did I pay to last 3 years and so on
Everything is Linear. Everything can be calculated Even to Maintain a certain pitch it must be controled by fixed time The only piece of Data that have to rely on is DT and it can be even guestimated
I don't fully understand your math or your logic. It doesn't seem you've compensated for any variability in the groove spacing but rather just "guesstimated" a distance from either the inner or outer limits of the disc. And you still seem to be using "pitch" as a music term and not a mechanical control.
"Speed is variable due to distance change per minute."
Well, not really. The disc is still spinning at a constant 33.33 R.P.M. (though the apparent speed which the stylus encounters is faster as it approaches the inside of the disc). It stil takes the same amount of time for the disc to make one revolution at the outside of the disc as it does at the inside of the disc. I'm not at all sure why this matters to the equation, however. But, if you are measuring from the inner limits of the disc, the variablility of the time/length of each side would seem to make a difference in the equation of distance from the most inner point. Not to mention the variable pitch/spacing of the groove.
"Everything is Linear."
No, I don't think so in this event. Let's say you are the recording engineer who has to master The Firebird Suite onto a disc, the engineer who has to put Fanfare for a Common Man on the same size disc and the engineer who must place a 1980's rock album with about 6dB of dynamic range onto the same size disc. The Suite has its highest dynamic range and deepest bass at the inner groove. The Fanfare has its peaks of level and bass at the front end of the disc side. And the rock album has virtually no dynamics and little bass so the album has very little definition of dull to reflective surfaces and appears as if the grooves are evenly spaced for maximum time per disc side. The amount of variable spacing used for each recording will be quite different from the others and where this variable spacing will occur will be at different location along the disc's radius.
If we are measuring a distance from the lead in or lead out groove, we cannot ignore the variability of time per side and the variable spacing of the grooves for each recording. If, however, we are measuring only the linear travel of the stylus as if the groove had been straightened out into one continuous line, none of that matters (within reason). But in that case, neither does the rest of your math because the stylus will not have changed its location from the edge of the disc.
"Things you may neglect: - inleads/outleads - Spaces in between songs"
I don't understand how these can be ingored if we are measuring distance along the radius of the disc from either the outer edge or label of the disc - if, that is, the measurement is along the radius of the disc.
Let's look at it this way; if we have constant spacing between adjacent groove locations, the equation would be simple. With each rotation the stylus would have moved toward the label by "X" amount. Once variable space is provided for each location along the disc radius, there is an unknown that cannot be defined in the equation. If we take what we consider a conventional recording there is a set distance from the edge of the disc before the music begins. If instead we take a recording with an exceptionally long leead in groove where the music doesn't begin until the stylus has moved one inch along the radius of the disc, the time constant to reach that spot along the radius has changed with variable spacing bewteen grooves. On this imaginary disc the engineer has cut the disc so that the stylus reaches one inch into the disc's radius in two seconds. That is obviously different than our conventional disc where music begins to play toward the outer edge of the disc and it will take several minutes before the stylus is one inch into the disc along the radius.
The thickness of the pitch is constant in length and geometricaly fixed rate due to Pi. (width will have a geometric formation also because of Pi The radius is variable due to delta R meaning for every revolution Circumference= 6.28 x (R-delta R) Expect a lot of cancelations
i.e. everything is linear Even at premastering when they change length to fit more time this has no effect on the pitch these techniques were added on at recent time as a form of compression
I just have to sit down and include everything involved It is not hard. I'm just little lazy and rusty
But it is all 12th grade stuff I JUST WISH NO ONE THROW THIS AT 12th grade SAT test
This is why I asked if he still waiting on one general formula.