Thanks for posting it. I am sure a lot of people here do not know why they need to calculate the reciprical spaces. This is why.
If a blank has no taper , all the spaces between the diamonds (or boxes since you may not be doing a diamond pattern inside the box) are the same along the length of the crosswrap and exactly equal to the circumference around the blank if you want a square pattern (in thread art a diamond is usually a square turned 45 degrees.) However , if the blank has a taper, the circumference around the blank is higher towards the butt and shorter towards the tip. In order to keep the boxes square but more importantly , to be able to fit the same number of threads into each box on a closed pattern , The spaces above the center towards the tip will have to be progressively longer towards the tip and progressively smaller towards the butt. Because the required box spacings get smaller where the diameter of the blank is bigger and bigger where the diameter of the blank is smaller , we need to use inverse or rediprical spacing.
Just remember the spacing of the boxes towards the tip get bigger and the spacing of the boxes toward the butt get smaller in order to fit the same number of threads (which is important when doing a closed wrap). The spread sheet TT attached does the calculations for you.
Now before spread sheets (and even now by most people) you could figure the reciprical spacing just using a simple geometry problem. Lets say you will have a center box and 3 boxes above and below that center box. You have 7 center spots and 6 spaces between them. 3 of the spaces have to be smaller towards the butt and 3 must be bigger towards the tip but the total length will be exactly 6 times the average spacing. The average spacing is the circumference of the blank in the middle of the pattern. So decide where you want the center of the pattern and measure the circumference there then multiply that circumference by 6 and you have the total length of the crosswrap.
Anywhere on the blank but roughly where the whole crosswrap will be , make a dot then make a second dot spaced exactly the length of the crosswrap you calculated by 6 times the circumference away. Now you have 2 dots spaced the length of the total crosswrap apart. Measure the circumference of the blank at the dot towards the butt and subtract from it the circumference of the blank at the dot towards the tip. That difference is exactly 6 increments of spacing change so divide it by 6. That number is the incremental increase between the spaces as you go from the butt to the tip or the incremental decrease between the spaces as you go from the tip to the butt.
Now go back to where you marked the center of the length of the crosswrap to be . From that center spot , the first space towrads the tip is the average spacing plus 1 increment. The next dot up is the average spacing plus 2 incremenst and the next dot up is the average spacing plus 3 increments ,etc , etc
The first space going towards the butt from the center spot is the average spacing minus 1 increment , the second spot is the average minus 2 increments and the third dot is the average spacing minus 3 increments , etc , etc.
This is an exact mathematical method (Geometry) and is only limited in accuracy by your ability (accuracy) to measure the circumferences and spacing lengths. The method is absolutely accurate when applied to any number of spaces (for more or less total pattern boxes) as long as the taper of the blank is a straight taper which it almost always is.Remember that there are just 6 spaces for 7 box centers (make any 7 dots in a row and there will always be 6 spaces between them. 9 dots form 8 spaces , etc)
The spreadsheets TT attached illustrate all this if you just know the calculated increment is 1.5 on the top spreadsheet.
Be careful when looking at the location of the diamonds on that pattern 180 degrees around the blank (bottom of blank) shown in row 11 of the top table. Because the spreadsheet is showing only 1 decimal place , the first full spacing from the half space is shifted up by .05 and that error is carried along all the way up the spacing as the spreadsheet adds the 1.5 increment. It won't make any difference in your perception of location since your eyes would never pick up the .05 unit shift of the centers of the bottom pattern but it will mean you will have a .05 unit extra space between the first half pattern and the first full pattern centers on the bottom row of patterns. This means you will have a gap when you pack the threads there because there is room for another thread. When using say A size thread , you will want to change the spreadsheet to use 2 decimal places along that row. I know its picky but if you try to follow my explanation by looking at the spreadsheet numbers , the very first comparison you make on the bottom pattern will be the .05 error and it may confuse you as to what is going on there. The resulting packing space I mention may or may not show up in the thread as a gap. (hell , if your going to be anal you may as well have your head all the way up there
)
Anyway , the spreadsheet is a nice tool to do the work but you still have to be very accurate when you make the measurements of the circumferences at the various points and then again when you measure the lengths. The best bet it to probably use a micrometer and measure the diameters and multiply by Pi to get the circumferences. The use of a vernier caliper will also make the marking of the calculated lengths more accurate.
offset taper spacing
Linear Mode
