Ovals | Dictum

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Defining the proportions
Formulas for calculating ovals
Step-by-step explanation

In our last article we described how to calculate polygons. Today, as a continuation of this article, we are going to deal with calculating and constructing ovals.

Defining the proportions

Here you can see the construction of the oval. You can construct ovals using 3, 4, 5 or more circles and changing the proportions.

For this construction, there are also formulas in order to define the right dimensions.

Formulas for calculating ovals:

You can use your calculator or use our online calculator.

Ovals from		3	4	5
Oval length given	Radius(r) =	Oval length/4	Oval length/5	Oval length/6
Calculating Radius(r) when Oval lenght is given close Given Oval lenght? mm How many circles? Radius(r): mm
Oval width given	Radius(r) =	Oval width/ (6-0,866*4)	Oval width/ (8-0,866*6)	Oval width/ (10-0,866*8)
Calculating Radius(r) when Oval width is given close Given Oval length mm How many circles? Radius(r): mm
Calculate the circumference	u =	10/3rπ	12/3rπ	14/3rπ
Calculate the circumference close Radius(r)? mm How many circles? Circumference(u): mm
Calculate the Radius(R)	Radius(R) =	3*r	4*r	5*r
Calculate the Radius(R) close Given Radius(r)? mm How many circles? Radius(R): mm

If, let's say, we want to design an oval with a fixed width or a fixed length, we simply choose the specific formula.

Example:

We want to construct a table-top in the shape of an oval having a length of 120 cm. We have a look at the oval which has been constructed using 3 circles.

How to calculate it:

r = oval width / (6-0.866*4)

r = 120 cm / (6-0.866*4)

r = 47.32 cm

r = 473 mm

Now you can start constructing. Please see our sketches to see how the construction works.

Geometric Construction – Step-by-step explanation

Defining The Dimensions
At first, we need 3 circles with the radius calculated in the previous step. The centre of the outer circles is on the intersection of the central axis and the circle which has been drawn first. As a tool you can use a self-made compass which is made of a wooden or plastic strip, in which you have drilled a hole for the pencil. For precise constructions, we recommend using compass heads, for example our Veritas Beam compass heads or our Kunz compass heads. Our wide product range also offers rulers and squares.
Determining Intersections
The next step is to draw lines at a 60 degree angle to the top and bottom, starting from the central line of the circle in the middle. These lines make equilateral triangles together with the central line.
Drawing In The Sides Of The Oval
Use the points of intersection of these triangles as the centre for the next circles. You can calculate the radius or use the compass to take the measure.
The Oval Is Done