Linear Footage Equation

I don't know a formula, but I would use Excel to calculate it using a similar method to my mortgage payments. Starting with your initial diameter (D), the length paid out in one revolution is pi*D, the next revolution the diameter is increased by 2*film thickness, every subsequent revolution the diameter is increased by 2*film thickness and so on until the final diameter is reached. Without knowing any more this will get you to a measurement to within one revolution of the final diameter.

You said any help, there is probably a straightforward formula out there. Someone else can provide that.

here is a quick blast, starting for argument's sake with a diameter of one and a thickness of 0.1 using two columns in Excel, top left B52 which just happened to be a blank area, below are the formulae typed in (I used an apostrophe to make them visible) you can copy and paste this down the sheet until you get the answer you want

The Archimedes Spiral works great in theory - depending on accuracy required, there will a fudge factor - we used to call it a "packing factor" (when rolling flat-rolled steel) based on how tightly the coils really pack space. If you look at it - it boils down to an area calculation - a long thin rectangle vs a donut. But I doubt any material would in reality have a "packing factor" of 1.0.

Dear CSM Engineer,

Good equation, since the net side area of roll Π (R_F²_-R_I²) must be equalized by the length L multiplied by the film thickness d.

But if you mean with the initial radius R_I to be the smaller radius and the final radius R_F is the larger one, in this case, the equation must be written as : L * d = pi(R_F²_-R_I²).

As the OP specified in the question the material was to be "payed out", I wrote the equation for that condition. I'm giving him the benefit of the doubt that he can successfully re-arrange the terms if the conditions change (and to know that a negative result is nonsense).

CSM Engineer is correct if you're looking for a good, ball-park number. The largest variable becomes film thickness variations, and the stretch / grain of the material.

(BTW, this simple method works great when doing inventory of spooled or rolled goods. Mean circumference times number of turns.)

Thanks for everyone's quick response. I guess my calculus is rustier than I thought. My objective was to verify the length of film rolls as supplied by a vendor quoting footage as compared to what we actually see converted in the manufacturing process. I will use the equation on several rolls to see what the order of magnitude is for the difference in values.

Thanks again.

sjp

I will assume you are on a three inch core. Square the outside diameter, multiply by 0.065, subtract 0.8 and divide the number by the thickness of the film. Let us know if it works. If not, I will go to another source since I have not used this in some while. Good luck!

Just a quick question bart@,

where did you find this calculation?

Jeff

No, not even close. Rolls are 60" diameter with reported footage of 7,000 feet. Your equation results to about 925 lineal feet with a film thickness of 0.021".

Hi, sjp!

Boy! So many complications to arrive at an accurate determination of the footage you are purchasing! Do you think you might be getting ripped off? How about if you temporarily purchase from another supplier and compare the results? Just a linear measurement might not give you the answers you are looking for.

Suppose you were to calculate the film by measuring the footage. If you lay it out to measure (assuming that's even a reasonable approach), it will diminish the film's exposure capabilities, so it has to be measured on a spool. In any spooling measurement, there is an air layer that prevents accuracy if the size of the spool itself is calculated or considered as the source for the measurement of length.

If you are buying the film in bulk for still photography, and just wind it into your cassette loader using a dark room or a black bag, you will be shown on an external dial how many shots you can take with it, as calculated from the length wound in; or more accurately by the number of stills that show up on the negative. Or you can just measure the negative rolls after development to determine the accuracy of the winder and use it as a future estimator of film quantity.

Of course, tails on the winding are not used, so they become a waste of the total length, but they can be measured on the negative rolls after developing and added in to the estimation.

Motion picture film length can be verified after shooting by the time it takes to run through the projector using the projection speed as the determiner. If it seems like a reel might be shorter than its label proclaims, change dealers and measure what you get the next time through to verify that you weren't being cheated by the original one. If you are in the motion picture business, you already know the approximate time it should take to run a complete reel of the sizes you normally purchase through the editing suite.

Mark

^{err...if the 'film' you are referring to is not of the photographic variety, the above might not be ...ummm...what you were looking for . In that case, I notice this was written by M..somebody or another, so I wouldn't give it much mind ((*clears throat nervously*))}

Sorry, I was being a little encripted when I posed the question. I am actually looking at large rolls 60" in diameter of both paper products and glass mat webs. Reported footage ranges from 10,000 ft for paper and and 7000 ft for glass mat.

Lets try again. I work within the packaging industry. What is your core size? I will go back to my Guru guy who keeps these formula and see what he develops.

Hi sjp

CSM Engineer has supplied the correct proof of the formula for finding the approximate length of your rolls. The link he gave also shows the full formula.

I have used both to calculate rolls of polyethylene film from 5000 to 8000 feet long and the short formula was accurate to within a few feet which was more than accurate enough for my needs.

L = pi( R²_O - R²_I)÷ T This gives the length of the film currently on the roll.

L= film length

pi= 3.1416

R_O = radius of Outer roll diameter

R_I = radius of Inner core diameter

T = thickness of film

You can use this with confidence especially on tightly wound rolls of paper and plastic film.

Jeff