Is there a good way to lay out a right angle?

Question

Today we set up batter boards and put out marking strings to prepare for constructing a round deck.

We wanted 2 strings that marked the center lines, crossing each other at 90 degrees. We set up batter boards and ran strings between them. Then we measured out a 3/4/5 triangle from the crossing. We looked at the error, adjusted the strings, and repeated until we thought it was good enough.

The strings were not at the same height, so measuring the crossing was tricky. Measuring against the middle of the string is hard, because the string moves so easily.

Each time we adjusted the strings, the crossing point moved, so we had to measure all 3 legs of the triangle each time. If you get measure the hypotenuse and find it's off by some distance d, you have to move the ends of the string by some value that's larger than d, but you don't know how far. You just have to adjust, measure, and repeat.

In this case, the deck is 30' diameter. We started with legs of 6'/8'/10', then realized we had enough room for 12'/16'/20'.

If I was in my workshop building with wood, I would use a carpenter's square or factory corner of a piece of plywood, but at this scale that doesn't work.

I get that 3/4/5 is a good way of checking a right angle, but it's a painful way to create one. Is there a good way to create a right angle with strings, getting it right the first time?

Answer 1

Step #1: Finding the center.

Never built a round deck before, but to find out where you want to put the deck, and to mark the center point, I would drive a stake or nail, tie a string to it that is as long as the desired diameter (30' here), and then walk in a circle with it, keeping it taut, and putting some long nails into the ground, at the end of the string, every 3' or so. Then I'd put a string around all of those nails, wrapping it around each nail a few times. Alternatively, if you are working on concrete, clean it up and use chalk instead of the nails & strings for the outside.

Step #2: Dividing the circle into quadrants.

• Take the string that is attached to the center stake to the edge of the circle and drive a nail/stake there. (On concrete, just make a mark and get someone to hold it there.) Attach a second string to that nail and walk to the opposite side of the circle. PS: The reason you're using the center string here is to MAKE SURE that each mark is 30' from the center, otherwise the math will fall apart.
• Once at the other side of the circle, I would drive another nail/stake, making sure that the string going across the entire circle was both (1) taut and (2) passing directly over the circle. For reference in the next step, we will call these two points Outside Point #1 and #2 (OP1 and OP2.) If you're on concrete, you can pop a chalk line at this point.
• Then, I would use some math. Dividing the circle into quadrants would require 4 points on the outside of the circle that (of which we currently only have 2), if you were to draw lines in between all of them, would form four right triangles (with the right angle in the center, which is what you're asking for.) Knowing that each leg of each right triangle needs to be 30', the hypotenuse of each triangle must be 42' 5 (1/8)" -long (square root of 30^2 + 30^2). Armed with a string of that length, I would attach it to both of nails/stakes/marked points from above, OP1 and OP2, and I would walk to both sides of the circle, near where the other two points, which we'll call OP3 & 4, should be. Make marks where the end of this string crosses over the outside of the circle (to be exact, you should once again have the 30' center string in your hand.) See diagram below. For OP3, make this measurement from both OP1 and OP2, and for OP4, make the measurement once again from both OP1 and OP2. You should have two marks at both the OP3 and OP4 locations, and they should be so close (within 1") that you can just eyeball an average of them. Drive a nail at those locations, and draw a taut string from OP3 to OP4, making sure it passes over the center. Once again, if you're on concrete, pop a chalk line.

I'd imagine that this is the most accurate method outside of buying survey equipment. Good luck!

(Note: Unfortunately, as you swing a string around a nail/stake, it will shorten in length. If you decide to trace out the entire outside of the circle, your distance from the center will decrease as you go. Tying a loop in the string, allowing it to rotate around the nail/stake will prevent this.)

Answer 2

I used to have a pre-made triangle that was made from three lengths of string and three washers, we put a blue one at the 90. It was built using an isosceles triangle instead of a 3/4/5... for this reason I'll warn you that it's easier to build it using metric measurements. You'll also want to make sure the line you're using does NOT have a lot of stretch in it.

If you wanted to layout a square, such as yours the process would be:

1. drive a stake in the "middle", you'll want it just slightly lower than all the others you will drive.
2. drive a nail into the top of the stake
3. put the blue washer on that nail.
4. use the one of the silver washers to place a stake with a nail at another point, pulling the string taut.
5. use the 3rd washer to place a 3rd stake, pulling both taut.
6. use the 3/4/5 trick to check your strings, or a t square held next to the lines, as stretch might have gotten you off slightly. If so, use a cross braced stake and a screw to pull your stake into place.
7. lift the first silver washer you placed off the nail it is on and walk to the second one, trade silver washers
8. place your 4th stake using the recently freed up silver washer
9. repeat the previous three steps to place a 5th stake

You should now have a giant X staked out with roughly 20m diagonals, remove the pre-built strings and washers and ran a string between the 4 outer stakes, they should cross at the center stake, directly above the nail, in a perfect 90.

An alternate method of building a square instead of a cross would be to start with a silver washer on one corner stake, then drive the other silver washer on the diagonally oposite corner stake, finally use the blue washer to drive a third corner stake, then swap the two silvers to setup for using the blue to drive the final corner. This would give a square with roughly 10m sides.