The loss in the processing of stone products is inevitable, and it must be calculated and understood during production and processing. It cannot be confused, as it is related to the profit and economic benefits of stone processing enterprises and must be taken seriously. Circular arc board products are of high value in stone products, and the materials used are very particular. In addition, the area of one circular arc board is larger than the lines, so the calculation of circular arc board loss is more important than the lines. It should be accurately calculated before material selection, which can reduce stone waste and loss, improve the utilization rate of stone, and thereby increase the profits of stone processing enterprises.

Circular arc plates include wall circular arc plates, hollow column circular arc plates, door arch circular arc plates, window arch circular arc plates, etc. The products of these circular arc plates are the same, and the calculation of losses is also the same. The calculation method in this article can be universal. Hollow columns are an important application product of stone in building columns. They are columns enclosed by circular arc plates with an empty center, mainly used for decorating various supporting columns in buildings.

The key to calculating the yield of a cylinder lies in calculating the translation distance. The calculation methods for medium thickness include the mathematical calculation method, Autocad layout diagram method, Excel formula table calculation method, and table lookup method. Each method has its own characteristics, strengths, and shortcomings. Mathematical calculation methods are cumbersome, requiring the calculator to have a good knowledge of plane geometry and algebra; The Autocad method requires calculators to be proficient in using Autocad drawings; I think the Excel formula table calculation method is the most practical and simple, without any special skills, as long as you know the simple Excel operation; The table lookup method can only approximate the medium thickness, with relatively large deviations, but it can basically meet the requirements when used for calculating the yield rate. In actual calculations, it can be determined based on personal preferences.

Circular arc plates have a common characteristic – circular arc. When processing, using the characteristic of the common circular arc can reduce stone waste, improve stone utilization rate, and reduce stone loss.

**1. Texture knowledge of arc plate processing**

The circular arc plate has two directions, one is the height direction and the other is the arc length direction. Therefore, the texture of the circular arc plate can be along the height of the circular arc plate or along the chord length direction. For stones with a texture of approximately 45 °, there are directions for texture left rotation and texture right rotation. It is important to be clear during processing and not make any mistakes in the direction.

**2. Theory of arc co-arc surface machining**

Use the principle of arc surface consistency to process irregular plates. Used for processing concentric arc plates, non-equal thickness arc plates with the same radius. Cut the arcs of two irregular arc plates with one knife, saving processing materials and time.

**3. Circular arc plate translation formula**

The calculation of the loss rate of circular arc plates must use an important formula, namely the translation distance formula. Calculate the volume of the material used based on the translation distance. Of course, the calculation of the yield of circular arc plates can also be done using the method of drawing a layout diagram. For those who are proficient in using Autocad, using the layout drawing method to calculate the material yield is faster, more convenient, accurate, and intuitive. However, many production site employees in stone processing enterprises do not know how to use computers, and those who know how to use computers may not necessarily know Autocad. Therefore, mathematical calculations can be used to calculate the material consumption of circular arc plates and the loss of stone.

Volume of circular arc plate with two or more components V=[L+30mm] × [H+30mm] × [X × N+h]. Among them, L represents the outer chord length of the hollow column circular arc plate, H represents the height of the hollow column circular arc plate, X represents the translation distance, h represents the arch height of the hollow column circular arc plate, and h=the image. The unit of calculation above is mm. According to the processing requirements, X must be greater than the distance between the two centers after the arc trajectory is offset in order to process the arc plate of a certain thickness as required by the customer.

The calculation of material usage for circular arc plates is a common practice in stone processing technology. If the customer needs to process N circular arc plates, we can obtain the cutting formula for the circular arc plates based on the translation distance algorithm already exported above.