Help with equadistant centering
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  1. #1
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    Help with equadistant centering

    TIA for the help, Im sure it's a really simple answer.

    I have a 20 ft length of strap I want to affix to a wall in 14 spots.

    Whats the math behind finding equal spacing of the 14 fixtures and centering them in relation to the 20ft strap from end to end.

    Hope that makes sense.

    Cheers!
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  2. #2
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    Re: Help with equadistant centering

    If you want the attachment points to be on the ends, you just divide your length by 13. The 14th attachment is a zero mark so it's not a part of the sectioning which is why it's 13. If you want the first and last attachment points off the edge, just divide the distance between where you want them by 13.

  3. #3
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    Re: Help with equadistant centering

    I'm sure there's a mathematical formula for that. If you snap 2 parallel lines 15 ' apart. 15 since you want 14 marks . Put your strap on the diagonal so the ends touch the lines. Mark off 1' intervals from the line. It would be much easier on a smaller scale, but the result would be the same.

  4. #4
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    Re: Help with equadistant centering


    SlickmisterN


    Quote Originally Posted by SlickmisterN View Post
    I have a 20 ft length of strap I want to affix to a wall in 14 spots.
    You answered yourself:

    14 x 16" = 224"
    A 20 ft. strip = 240+"
    240" minus 224" = 16". Halving 16" = 8"

    Your 14 holes will [studs] center 8"+ from each end.

    [In practice - strip is always longer then 20', unless
    it is critical - ignore the small over length].

    Speed lay-out with a standard 24' tape:

    strike your off-set-line the length of the strip,
    measure overall length - mark center,
    stretch a standard 24' tape along your-line,
    center 'to your mark' the tapes 16" 'stud centers',
    clamp at center - then clamp both ends of the tape,
    the '16" centers' [diamonds] will be Red.

    Scribe the Red marks - drill - install.

    If you understand this lay-out concept, the math for
    irregular lengths is easier.


    Opus

  5. #5
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    Re: Help with equadistant centering

    If you don't like math:

    Go to a fabric/sewing store and get a good sturdy piece of elastic.

    Put it under a little tension, mark 14 spots equal distance apart.

    Stretch until it's where you want it and transfer the marks.
    Dave J.

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  6. #6
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    Re: Help with equadistant centering

    Quote Originally Posted by TheBFA View Post
    If you want the attachment points to be on the ends, you just divide your length by 13. The 14th attachment is a zero mark so it's not a part of the sectioning which is why it's 13. If you want the first and last attachment points off the edge, just divide the distance between where you want them by 13.
    Using math and numbers, this is the best answer so far. The only issue is: how are you going to measure exactly 18.4615.... inches each time to make them truly equi-distant? If you round to 18.5, then you'll be over the 20' length by 1/2". Depending on you needed accuracy and precision, it is very plausible that this would work for you.

    MinnesotaDave's suggestion is the elastic version of the long-forgotten, hardly taught, geometric constructions of ancient days. I still remember my 9th Grade Geometry teacher teaching this to the class----mind-blown I was, and have not forgotten how to do them to this day. This would be the most accurate, assuming the elastic stretches identically along it's entire length. I would use a modern version of the geometric construction by cheating and using a a straight-edge with markings (a yard stick) and one of those small button-cell laser pointers attached to it. But then again, I'm one clever puppy
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  7. #7
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    Re: Help with equadistant centering

    Quote Originally Posted by Oscar View Post
    Using math and numbers, this is the best answer so far. The only issue is: how are you going to measure exactly 18.4615.... inches each time to make them truly equi-distant? If you round to 18.5, then you'll be over the 20' length by 1/2". Depending on you needed accuracy and precision, it is very plausible that this would work for you.

    MinnesotaDave's suggestion is the elastic version of the long-forgotten, hardly taught, geometric constructions of ancient days. I still remember my 9th Grade Geometry teacher teaching this to the class----mind-blown I was, and have not forgotten how to do them to this day. This would be the most accurate, assuming the elastic stretches identically along it's entire length. I would use a modern version of the geometric construction by cheating and using a a straight-edge with markings (a yard stick) and one of those small button-cell laser pointers attached to it. But then again, I'm one clever puppy
    I have a fondness for Geometric constructions as well. Often they are the foundation for whatever shortcut is currently being used anyway.

    For measuring when presented with decimals, like the .4165 in your example, I teach to multiply (top and bottom) by the accuracy you desire to measure to.

    For example .4165 to the nearest 16th:
    -the numerator would be (.4165)(16) = 6.664
    -the denominator = 16

    Thus round up to 7/16 or down to 6/16 depending on the situation at hand. Naturally 6/16 would be reduced to 3/8
    Last edited by MinnesotaDave; 02-17-2017 at 02:21 PM.
    Dave J.

    Beware of false knowledge; it is more dangerous than ignorance. ~George Bernard Shaw~

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  8. #8
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    Re: Help with equadistant centering

    Not sure what you mean by equidistance. If the 14 fixtures need to be spaced equally apart, then centered or divide 240 inches by 14. If the former , then just play with the difference between the interval you select and the 240 inch strap. Divide the difference by 2 and start measuring from there.

  9. #9

    Re: Help with equadistant centering

    Quote Originally Posted by SlickmisterN View Post
    TIA for the help, Im sure it's a really simple answer.

    I have a 20 ft length of strap I want to affix to a wall in 14 spots.

    Whats the math behind finding equal spacing of the 14 fixtures and centering them in relation to the 20ft strap from end to end.

    Hope that makes sense.

    Cheers!
    A movie is the only way I could conceive, as a way to relay this.



    Sincerely,

    William McCormick
    If I wasn't so.....crazy, I wouldn't try to act normal, and you would be afraid.

  10. #10
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    Re: Help with equadistant centering

    Thanks for the video. 15 spaces not 14, get me every frequently.

  11. #11

    Re: Help with equadistant centering

    Let's say you were on the job and you wanted to lay that out without cadd. I would come up with the 10.4 using that formula and add three inches half the width of the light to the get the center of the first light. And then I would add 16.4" to each one after that to get their centers. I would just do it on a calculator on my phone and just keep adding the 16.4 inches to get the next measurement and the next and the next. It sucks if you lose your place or hit a wrong key, haha.

    13.4
    13.4 + 16.4=29.8
    29.8 + 16.4=46.2
    46.2 + 16.4=62.6
    62.6 + 16.4=79.0
    79 + 16.4=95.4
    95.4 + 16.4=111.8
    111.8+ 16.4=128.2
    128.2+ 16.4=144.6
    144.6+ 16.4=161.0
    161 + 16.4=177.4
    177.4+ 16.4=193.8
    193.8+ 16.4=210.2
    210.2+ 16.4=226.6
    226.6+ 13.4=240

    Each number on the right hand column is the center mark, from one side of the twenty foot length, of a six inch light, with equal spaces on each side of the light and the ends. You just have to get good with converting decimals to fractions. Basically every 0.06 is one sixteenth. So five sixteenths is a quarter 0.250 plus 0.06 which is .310 or 5/16. Seven eighths is 0.875 so 0.8 is about 13/16" After a while they come quick.


    Sincerely,

    William McCormick
    If I wasn't so.....crazy, I wouldn't try to act normal, and you would be afraid.

  12. #12

    Re: Help with equadistant centering

    But that only works for six inch wide lights.

    Sincerely,

    William McCormick
    If I wasn't so.....crazy, I wouldn't try to act normal, and you would be afraid.

  13. #13

    Re: Help with equadistant centering

    Quote Originally Posted by tapwelder View Post
    Thanks for the video. 15 spaces not 14, get me every frequently.
    Yea after I update my movie software, bypass virus programs, get the mic working properly, draw that same picture a couple times while i create errors in calculations, language, order, I go down and put the the coffee pot in the refrigerator or something stupid like that haha. I started trying it with words but it got ridiculous so I made the movie.


    Sincerely,

    William McCormick
    If I wasn't so.....crazy, I wouldn't try to act normal, and you would be afraid.

  14. #14

    Re: Help with equadistant centering

    If you wanted to have a light on each end of the twenty foot run, you would just change the over length from twenty feet to where ever the edge of the lights on the ends come to.

    So if you had six inch lights mounted on both ends you would just take off 12 inches from 240 leaving you with 228 inches to split up, with 12 lights and thirteen spaces.

    Sincerely,

    William McCormick
    If I wasn't so.....crazy, I wouldn't try to act normal, and you would be afraid.

  15. #15
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    Re: Help with equadistant centering

    1st thing always necessary is to determine just where the two attachment points on the ends are going to be. One inch in, two, 1.5 inches?? Untill then there is no length.
    "The things that will destroy America are prosperity at any price, peace at any price, safety first instead of duty first, the love of soft living and the get rich quick theory of life." -Theodore Roosevelt

  16. #16
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    Re: Help with equadistant centering


    SlickmisterN


    I hope your Math Attack recovery goes well . . .

    If you'll chime-back - I will forward: old-school,
    mid-smart, and smartest algorithms
    - to your
    question.


    Opus

  17. #17
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    Re: Help with equadistant centering

    Quote Originally Posted by Oscar View Post
    Using math and numbers, this is the best answer so far. The only issue is: how are you going to measure exactly 18.4615.... inches each time to make them truly equi-distant? If you round to 18.5, then you'll be over the 20' length by 1/2". Depending on you needed accuracy and precision, it is very plausible that this would work for you.

    MinnesotaDave's suggestion is the elastic version of the long-forgotten, hardly taught, geometric constructions of ancient days. I still remember my 9th Grade Geometry teacher teaching this to the class----mind-blown I was, and have not forgotten how to do them to this day. This would be the most accurate, assuming the elastic stretches identically along it's entire length. I would use a modern version of the geometric construction by cheating and using a a straight-edge with markings (a yard stick) and one of those small button-cell laser pointers attached to it. But then again, I'm one clever puppy
    That's true. It could be accounted for with some creative measuring though. I actually haven't done the math so will just take your word for 18.46. With the center point found, go 9.23 as accurately as possible to either side and mark. Then find the center point from those marks to their respective ends. This marks 6 spots, and the rounded lengths can be used to measure away from those being used as references. Not machine accurate, but I think it would look perfect to the eye.
    Last edited by TheBFA; 02-18-2017 at 01:49 AM.

  18. #18
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    Re: Help with equadistant centering

    Quote Originally Posted by TheBFA View Post
    That's true. It could be accounted for with some creative measuring though. I actually haven't done the math so will just take your word for 18.46. With the center point found, go 9.23 as accurately as possible to either side and mark. Then find the center point from those marks to their respective ends. This marks 6 spots, and the rounded lengths can be used to measure away from those being used as references. Not machine accurate, but I think it would look perfect to the eye.
    You can't find the center point and then space things out like that, as you're not guranteed that the midpoint of the total length of the bar will lie in the middle of one of those congruent line set me ts (in general). Using the "divide by one less" approach to get the length of congruent segments, you have to start at either end and make consecutive measurements until you reach the other end. This has to do with if you have even or odd total number of segments.
    Last edited by Oscar; 02-19-2017 at 10:17 AM.
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  19. #19

    Re: Help with equadistant centering

    When I do stairs I use the method of dividing the number of spaces between treads, and the over all length of the stringer. Because I have seen guys use templates, just measure off each step they install and it never comes out right. Some older guys know that you tend to gain, and since the first step down from a landing of a stair case is usually a short step, done on purpose, because of future flooring on the floor the stringer reaches to, it works out for them, most of the time. But they admit it is sometimes hit or miss. Or they cannot get two staircases made at different times the exact same.

    So by using a calculator and coming up with the size of the vertical spacing and the number of spaces and dividing the number of tread spaces into diagonal length of the stringer plus one inch for the top landing. You can get the angular measurement for a really exact placement of each step and just mark it on a stringer.

    You basically just plug in the first number, save it to "memory plus" after making sure the memory is clean by pressing "MC" (memory clean) the first time around, After you store the measurement, you just keep hitting "addition" and "memory recall" to get each and every mark. I write each one down on paper. This way each tread is exactly placed and you can check the last treads placement before you even start.

    But you can see by all the responses that one, we may not even know which way the original poster wants to mount these lights. He may be putting them between two walls, so he will have to leave an equal space on each end as well. Or he may wish to mount two lights on the very end of the strip and then just split up the remaining twelve lights and thirteen spaces in between those.

    But in any situation there are certain rules for each. Which are getting a little skewed.

    Sincerely,

    William McCormick
    Last edited by William McCormick; 02-19-2017 at 11:04 AM.
    If I wasn't so.....crazy, I wouldn't try to act normal, and you would be afraid.

  20. #20
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    Re: Help with equadistant centering

    Some pretty good advise here. I've been building stairs for a long time, and consecutive measurements are key. If you "step off" from one mark to another your inaccuracy is compounded every time. I use the Pythagorean theorem for stairs which helps you find the long side of the triangle A 2 + B 2 = C 2 so just add your total run and rise together, square that then hit the square root button, now you've got your hypotenuse. Divide that up by however many rises you have and make consecutive marks on the top of your stringer, then clamp a guide on your square with the proper run & rise.

    I know I'm off topic, but stairs were brought up.

    Cheers

  21. #21
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    Re: Help with equadistant centering

    Quote Originally Posted by Oscar View Post
    You can't find the center point and then space things out like that, as you're not guranteed that the midpoint of the total length of the bar will lie in the middle of one of those congruent line set me ts (in general). Using the "divide by one less" approach to get the length of congruent segments, you have to start at either end and make consecutive measurements until you reach the other end. This has to do with if you have even or odd total number of segments.
    You find the midpoints by measuring and dividing by half. You can find the position of the center section easily. No matter what distances you start and end, the hard center of that 20' run is 10' exactly. If someone cant use a tape measure to center a 18.46" measurement on the hard center, they don't need to bother trying to measure anything. Thats why I said go 9.23 to either side of that center point. That section is now marked in two points and is prefectly centered. That leaves an even number of sections, 6 to be exact, on either side. The center point of those 6 sections on either side is now another mark for an attachment point. So from this point, you have attachment points 1,4,7,8,11 and 14 marked. Measure 18.46" from point 1 to get 2. Measure from point 4 to get 3 and 5. Measure from 7 to get 6. Measure from 8 to get 9. Measure from 11 to get 10 and 12, and measure from 14 to get 13. You won't visually notice one of the points being off by 0.04" if you just measure at a rounded 18.5". But you can get it even closer by just marking a hair inside 18.5" if it's that important. Of course these numbers are based on having the ends right at the 0 and 20' mark, so the actual dimensions would be different with a different start and end point, but the process would be the same.
    Last edited by TheBFA; 02-24-2017 at 05:35 PM.

  22. #22
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    Re: Help with equadistant centering

    Always start with a sketch

  23. #23

    Re: Help with equadistant centering

    Quote Originally Posted by TheBFA View Post
    You find the midpoints by measuring and dividing by half. You can find the position of the center section easily. No matter what distances you start and end, the hard center of that 20' run is 10' exactly. If someone cant use a tape measure to center a 18.46" measurement on the hard center, they don't need to bother trying to measure anything. Thats why I said go 9.23 to either side of that center point. That section is now marked in two points and is prefectly centered. That leaves an even number of sections, 6 to be exact, on either side. The center point of those 6 sections on either side is now another mark for an attachment point. So from this point, you have attachment points 1,4,7,8,11 and 14 marked. Measure 18.46" from point 1 to get 2. Measure from point 4 to get 3 and 5. Measure from 7 to get 6. Measure from 8 to get 9. Measure from 11 to get 10 and 12, and measure from 14 to get 13. You won't visually notice one of the points being off by 0.04" if you just measure at a rounded 18.5". But you can get it even closer by just marking a hair inside 18.5" if it's that important. Of course these numbers are based on having the ends right at the 0 and 20' mark, so the actual dimensions would be different with a different start and end point, but the process would be the same.

    That is assuming the lights are zero inches in width.

    If the lights are 3/4" inches wide, and you are going to place one at each end of the twenty foot run, you have to take off 3/4" from 20 feet. 3/8" from the ends to the center of the first and last light on the strip. Leaving 239.25" When you divide that by 13 spaces you get 18.40384615384615" just over 18.40 inches center to center between all lights.

    You can start from the center and measure out. However if you are going to be installing lights, I think you would like to just come up with each measurement and place it using a tape measure. I always then go and check each space to make sure they are all the same, incase I have made the old one inch error, reading the tape upside down or if used a new tape that has confused me.

    If you do not do this the two end spaces will be 3/8" too short.

    Sincerely,

    William McCormick
    If I wasn't so.....crazy, I wouldn't try to act normal, and you would be afraid.

  24. #24
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    Re: Help with equadistant centering

    Thank you all. The video was perfect and exactly what I was looking for. I knew in my head I needed 14 standoffs and that's how many I made. But wasn't sure of the math behind what I was doing and why. Thanks again.

    -Slick
    Miller XMT 350 CC/CV
    Miller S74-D
    Hobart Airforce 500i

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