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A Helix

Any ideas on how to build a helix?



Take some 1 x 2 lumber and cut it into 4 inch pieces. These will be used for the uprights in order to maintain the proper height of the actual helix.
Get some 1/4 inch plywood.
Cut out a triangle in one corner.
This triangle will be 24 inches long with the angle of 22.5 degrees.
Now in the triangle draw a curve line at 22 inches. Using a router or jig saw cut this line leaving 1 inch not cut at each end. All you need is a slot big enough to use a pencil or pen to mark center lines. You should end up with something like:


This will be a template for drawing the other sections to size and a center line for a track of a 22 inch radius
You could also make a curve cut at 18 and 20 inches for a additional curves. If you do this mark the edges of the triangle at 17 and 19 inches.

You are going to need the pieces to make a octagon circle like:

Cut the enough of the plywood into 5 inch wide sections. You will need 16 pieces for each turn of the helix.
This is where using the template will safe you time. Just line up the section to be marked at the end of the template and draw your cut lines.
Also draw in your track center line
Make your angle cuts

Mark one section in half and cut. This will be used for starting and ending the helix.
Take your pieces to the Helix area.
For the start glue this pieces so that the angle and sides match.
Now glue the top and bottom sections and make your helix. 2 or 3 Clamps should hold them together until the glue dries. You should see something like:


After you get about three quarters the way around the first circle you can start laying your track. It is easier to lay the track as you continue to build the helix.
Place the upright pieces in the inside triangle corners of the helix by gluing and using screws to hold them together.
The minimum area for this helix is a square of 48 inches on each side. Cut the outside triangles where you need to in order to properly place the helix in the area.
Continue to build your helix to the proper number of turns.

Wait about the grade?
Grade of the track is the math of:
Rise / Length (the rise of the track divided by the length of the track)
For example if your length of track is 100 inches and the rise is 1 inch. You get a grade of 1 percent. Okay for those that are real bad at math here are some of the common lengths and rises:
Grade in percent

Length Rise of 1 Rise of 1.5 Rise of 2 Rise of 3 Rise of 3.5 Rise of 4 Rise of 5
100 1.00 1.50 2.00 3.00 3.50 4.00 5.00
96 1.04 1.5625 2.08 3.125 3.6458 4.16 5.21
50 2.00 3.00 4.00 6.00 7.00 8.00 10.00
48 2.08 3.125 4.17 6.25 7.292 8.33 10.42

Okay, that is fine, but how do you get the grade of a helix as it curves?
There is only some minor changes is the math formula that you need to apply for the grade for a helix
Rise / Length (the rise of the track divided by the length of the track)
The hard part is the length of the track. Using:

Using the points A, B, C, D.

If you take the line from A to D and straighten it out you get: You can see that the length of the track from A to D is: Now the level line is just the Circumference of a Circle (the distance around the outside)

2πr

But you have to include that little extra bit from the rise part.
So by using the Pythagorean Theorem. The longest side of a right triangle is always directly across from the 90 degree angle. This side is called the hypotenuse.
So the hypotenuse is the square root of the square of one side plus the square of the other side.
So for a helix you get:
Hypotenuse is the square root of the square of Two times Pi times the Radius plus the rise squared.
                                      
( 2 * π * R )2 + H 2


Again for the math wizards:

Radius Circumfence Rise of 1 Rise of 1.5 Rise of 2 Rise of 3 Rise of 3.5 Rise of 4 Rise of 5
6 37.699 2.6516 3.7548 4.7963 7.9327 9.2443 10.5511 13.1478
9 56.549 1.7681 2.6526 3.5346 5.2977 6.1775 7.0559 8.8076
10 62.832 1.5913 2.3873 3.1815 4.7692 5.5618 6.3533 7.9327
12 75.398 1.3262 1.9890 2.6516 3.9757 3.9932 5.2977 6.6169
15 94.248 1.0610 1.5915 2.1216 3.1815 3.7111 4.2403 5.2977
18 113.097 0.8842 1.3263 1.7681 2.6516 3.0932 3.5346 4.4170
22 138.230 0.7234 1.0851 1.4467 2.1698 2.5312 2.8925 3.6148
36 226.195 0.4421 0.6631 0.8842 1.3262 1.5472 1.7681 2.2099