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Thread: Form angles with a combination square

  1. #1
    Supporting Member mklotz's Avatar
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    Form angles with a combination square

    If you have a combination square but didn't spring for the (often expensive) protractor head you can still use it to measure or set angles.

    If you imagine a flat spanning from the end of the head to the end of the beam/scale, you've created a right triangle; the head and beam are always perpendicular.

    The head length is fixed so it can be measured; the beam length is, of course adjustable. The math is simple...

    H = head length
    B = beam length
    A = angle desired

    tan (A) = H / B

    so:

    B = H / tan (A)

    Knowing our desired angle, A, and measuring our head length, H, we can calculate the beam extension, B, to form A.

    In this photo...

    Form angles with a combination square-p1010619.jpg

    I measured H to be 3 & 7/16 in and calculated the beam length needed to form a 30 degree angle...

    B = 3.438 / tan (30) = 3.438 / 0.577 = 5.954 in ~= 3 & 15/16 in.

    I set the beam to that length and then measured the angle formed with an electronic inclinometer...

    Form angles with a combination square-p1010620.jpg

    OK, it's not perfect, but close enough for many applications, especially if the more accurate tools are not to hand.

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    Regards, Marv

    Failure is just success in progress
    That looks about right - Mediocrates

  2. The Following 5 Users Say Thank You to mklotz For This Useful Post:

    emu roo (Jan 25, 2025), Jon (Feb 5, 2025), rdarrylb (Jan 25, 2025), RetiredFAE (Jan 25, 2025), uv8452 (Yesterday)

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    Supporting Member Saltfever's Avatar
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    Quote Originally Posted by mklotz View Post
    edit ... B = 3.438 / tan (30) = 3.438 / 0.577 = 5.954 in ~= 3 & 15/16 in.
    Love the concept, Marv. But you lost me at the end. What does ~=3-15/16 relate to? Isn't beam length 5.954?

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    Supporting Member mklotz's Avatar
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    Quote Originally Posted by Saltfever View Post
    Love the concept, Marv. But you lost me at the end. What does ~=3-15/16 relate to? Isn't beam length 5.954?
    Obviously a finger fumble on my part. That '3' should be a '5'. Specifically, that line should read...

    B = 3.438 / tan (30) = 3.438 / 0.577 = 5.954 in ~= 5 & 15/16 in

    I would fix it in the original post but the time limit on editing has run out so I can't. Thanks for catching that and sorry for the confusion.
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    Supporting Member Saltfever's Avatar
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    Many thanks, Marv. That is a very useful idea. I had never thought of the using the square's head as a side. I'm going to look at it with new eyes from now on!

    I know your thoughts on the imperial system so it was very nice of you to provide the fraction for those that still work with them. Although, now that everyone has a digital caliper now days, I suspect the use of fractions is diminishing. BTW, 61/64ths would be much closer to .954 for those that have a 64ths scale but you were just being kind using 15/16th for those of us with old eyes!
    Last edited by Saltfever; Jan 27, 2025 at 01:28 AM.

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    Supporting Member mklotz's Avatar
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    Quote Originally Posted by Saltfever View Post
    Many thanks, Marv. That is a very useful idea. I had never thought of the using the square's head as a side. I'm going to look at it with new eyes from now on!

    I know your thoughts on the imperial system so it was very nice of you to provide the fraction for those that still work with them. Although, now that everyone has a digital caliper now days, I suspect the use of fractions is diminishing. BTW, 61/64ths would be much closer to .954 for those that have a 64ths scale but you were just being kind using 15/16th for those of us with old eyes!
    Yes, there are closer approximations to .954 than my 15/16. I wrote a program to find the closest rational fraction approximation to any decimal number. It tells me that 83/87 is good to 0.01 %. I really should use numbers like that just to confuse and infuriate the inferial system lovers.

    I stuck with sixteenths because I figure that the old inferial eyesight isn't good enough to read anything smaller on the ruler. Besides, what I'm trying to get across here is the idea that the square can be used for approximate angle setting/measuring when better methods are not to hand. There are much more accurate tools for working with angles.

    The Usonians will never adopt the metric system because, if they did, they would have two measurement systems they don't understand instead of just one. :-)
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    Failure is just success in progress
    That looks about right - Mediocrates

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    Supporting Member Saltfever's Avatar
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    Marv, I'm thinking of drilling a precision hole 1" back from the end so I can center punch more precise angular locations. I think I can keep it within 477/500"!

    I memorized the machinist decimal equivalent chart over 50 years ago and haven't used fractions since. I'm not a woodworker but even when I use a tape I automatically convert without thinking about it. Imperial or metric are seamless to me.

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    Congratulations mklotz - your angle forming method is the Tool Tip of the Month for January 2025!

    This is a simple and easy angle measurement method using a tool that all of us have.

    Some more nice tool tips from January:

    Making Better Drill Press Mortises by Make Things
    Small Stock Center Marking Method by mklotz
    Why Nail Specifications Use "D" by Make Things
    Plane Sole Adjustment by Make Things
    Safe Fuel Tank Welding Method by tonyfoale
    Sled Truing Method by Make Things
    Making Tools Mobile by Make Things
    One Rail Dado Router Track by Make Things

    mklotz - we've added your Tool Tip to our All Tool Tips of the Month winners post.

    And, you'll be receiving a $100 prize, in your choice of Amazon, PayPal, or bitcoin. Please PM me your current email address and prize choice and I'll get it sent over right away.

    Congrats again



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