Please check my math

[Salty]

It has been a while since I used the dusty gray matter that was geometry.
I am making my own patio block for an area that currently has 8" x 16" x 1.5" stepping stones. Those do not lay out in this pattern without large gaps between and I am not too keen on cutting that many of them to fit.
However, I do have 12-40# bags of concrete left over from the fence project. Still cannot figure out how I calculated that wrong!
Anyway, the new area was determined to have a 36" radius. The width is 26" and I wanted the first block, the blue area, to have 16" on the outside curve.
Then the math started. What would be the measurement of the inside curve so that I can build the form.
Here's what I figured.
The circumfrence of a 72" diameter is 266". I cheated and used this website!
http://math.about.com/library/blcirclecalculator.htm
Divide that by 16" and you get 16.625, which is the number of 16" sections that would fit in the circumfrence. Now, each section is about 8.5" wide so the next circle toward the center has a diameter of 63.5" and a circumfrence of 199.5". Divide that by the same number of sections and you get 199.5 / 16.625 = 12" for length of the inside arc. I layed it out that way and it looks correct.
How's my math?

[pelligrini]

I didn't try to follow your math very closely, I usually draw all my problems.

Here is a drawing assuming a few items. I don't think I've got the inside radius correct.

[Turaj]

Not sure if I understand your design completely but if you are talking about the outside radius (outside blue section) being 36" then:

Radius = 36, Diameter = 72, Circ. = 226 (not 266!), number of 16" section = 14.14

and for the inside (inside the blue section)

Radius = 27.5, diameter = 55 (not 63.5), Circ. = 172.8 and divided by the same number of sections (14.14) gives you 12.22"!!

An easier way is to go by ratios. Your inside measurement (regardless of number of sections) is equal to: (27.5 * 16) / 36 = 12.22

So your inside measurement is close but you are off on the number of sections (stones?).

All this assuming I understood what you are doing HTH

[crokett]

I would get some cardboard or 1/4" ply and mock it up before I built any forms, just make sure my math was correct. Then I could use the cardboard templates to make the forms.

[Salty]

Not sure if I understand your design completely but if you are talking about the outside radius (outside blue section) being 36" then:

Radius = 36, Diameter = 72, Circ. = 226 (not 266!), number of 16" section = 14.14

and for the inside (inside the blue section)

Radius = 27.5, diameter = 55 (not 63.5), Circ. = 172.8 and divided by the same number of sections (14.14) gives you 12.22"!!

An easier way is to go by ratios. Your inside measurement (regardless of number of sections) is equal to: (27.5 * 16) / 36 = 12.22

So your inside measurement is close but you are off on the number of sections (stones?).

All this assuming I understood what you are doing HTH

Thank you so much Turaj. You understand this madness better than I do. I get brain dead by friday and I see that my math was a bit off.
You are correct. I used 266 even though my calculator said 226. That threw off the number of stones as you noted. Then, I forgot that the next diameter would be reduced by twice the 8.5" width and used the wrong diameter, which gave me too high a number for the circumfrence and, using too large a number for the stones, I just by accident got close to the correct inside arc measurement.
As for laying it out on cardboard, I did use 2 pieces of plywood for the base and struck an arc for the outer circle by using a string and pencil laid out on the floor.

Thanks all for the help.
I'll check my math a little closer for the next inner circle measurements.
I'll also need a good night sleep before getting my head around that formula Turaj.

[chopnhack]

You could also do by eye to whatever is pleasing. You can pour in place each layer and either cut a kerf into the dried cement for joints or use a joint tool. 1/4" ply works well for forms requiring curves. Don't forget to experiment with cement colorants prior to the project, the liquid ones work well and disperse easily into the water for mixing your concrete.

[Salty]

Well, first thing I learned is that in humid weather the block will take a long time to cure.
It set overnight outside and I had plastic lining the form. Tried to remove it and it broke.
I'm sure the plastic kept it from drying very quickly. At this rate it will be months before I have enough blocks made.
Well anyway........
I was rethinking this and wanted to ask 1 more question. The drawing that Pelligrini posted made me realize that maybe I only need 1 pattern for the blocks and just use halves for the ends to stagger the joints.
Is that correct? A block that fits on the outside section would also fit on the inside section?
I think maybe I need some refresher geometry classes!

Salty

EDIT: Never mind...that can't be right.

[dlminehart]

Salty, you need a different pattern for each of the 3 "bands", as the inner and outer radii are unique. I don't know that you need to have each component start in the middle of the adjoining one. If you don't, you may need to make just one extra of each band's elements, dividing it in the mold to give equal sections at each end. Otherwise, to get them to line up on centers, you may have to subdivide the molds and do two separate partial blocks at the ends.

[dlminehart]

Frankly, I think I would pour the concrete into the entire arc and, while it was setting up, deeply emboss the surface (perhaps by impressing two appropriately curved boards with some straight connectors) to give the appearance of separate blocks.

[Salty]

David, your last post is basically what I decided to do.
In fact, after I put the broken one on the area the arc did not seem correct.
A mental review of the data made me realize that I had used 6' as the diameter and it should have been the radius....so...good thing I didn't get too far.
Something is now telling me that deep down I don't want this project!

I found some long pieces of 1/4" x 1.5" wood strips in the garage rafters and so I think what I'll do is about what you said.
I'll pull up the stones in the area to be reworked, bed it with gravel and paver sand and use the strips to form up the outer curved section. I can use thin pieces of stiff plastic to make separate stone sections. I want each one to be separated so that I can put poly sand between them and they can move at will with the weather. After that section is hardened, I'll have the outer form for the next section.
Sounds like a plan. Now I need to get the weather to cooperate.

[Salty]

For those who wanted to know,

..how this project turned out.
It took about 5 sessions of forming and pouring, but it turned out alright.
And there wasn't much math inviolved. I just ran the outside stones at 16" and eyeballed the rest.

[gsmittle]

..how this project turned out.
It took about 5 sessions of forming and pouring, but it turned out alright.
And there wasn't much math inviolved. I just ran the outside stones at 16" and eyeballed the rest.

Looks good--and you used the method I would have. All that math gives me a headache...

g.