JPS6233693Y2 - - Google Patents

Description

[Detailed explanation of the idea]

Technical Field of the Invention The present invention relates to a liquid-filled paper container formed by folding blank paper, and more specifically, to a rectangular square-bottomed paper container with a triangular roof for filling a liquid. To provide a liquid-filled paper container capable of reducing costs by minimizing the total area required for blanks to be formed, and giving the paper container the best aesthetic appearance by making the outer dimension ratio of the paper container approximately the golden section ratio. Prior Art Conventionally, the above-mentioned paper containers are automatically formed from blank paper into a container shape by an automatic forming and filling machine, and then automatically filled with a predetermined amount of a liquid drink such as milk or juice. The top was sealed and the container was completed as a liquid-filled paper container. Therefore, in order to improve efficiency, it is necessary to improve the operating efficiency of the automatic forming and filling machine, and in addition to improving the operating efficiency, it is necessary to reduce the total area required for blank paper for paper containers for a given filling amount to reduce the cost of blank paper. There was no other way. It is naturally possible to obtain the minimum total area of the paper container for the required filling amount by using a square cube-shaped paper container, but in the past, how was the required amount of blank paper for a triangular roof and square bottom paper container? There was no concrete solution to reducing the total area, and even more so, there was no concept of achieving the aesthetic appearance of a paper container while making such a reduction. Purpose of the invention In view of the above points, the present invention makes it possible to reduce costs by minimizing the total area required for blank paper for a given liquid filling amount in a triangular roof square bottom paper container for liquid filling. The object of the present invention is to provide a paper container with a triangular roof for filling liquids, which can be used to fill liquids and provide the best aesthetic appearance. Summary of the invention The triangular roof paper container for liquid filling according to the invention is a rectangular square bottom paper container with a triangular roof for liquid filling formed by folding blank paper. and the adjacent side is approximately 0.7, and the ratio between the height of the four circumferential sides excluding the triangular roof and the adjacent side is approximately 1.3, and furthermore, the ratio between the adjacent side and the total height of the paper container is approximately 1.3. The blank paper is characterized in that the total area of the blank paper is approximately minimized for a predetermined liquid filling amount by making the ratio approximately equal to the golden section ratio. The characteristics of the present invention as described above are as follows: The present applicant set the shape ratio of each side of a paper container with a triangular roof to various dimensions, and conducted various comparative studies on the filling amount of completed paper containers. This was obtained through research into whether or not it was possible to make the appearance more beautiful, and the results of various mathematical calculations to determine whether this could be theoretically proven or not proved to be correct. Embodiment of the invention Figure 1 shows the external appearance of a container with a triangular roof and a rectangular bottom incorporating the invention.
, the triangular roof part is formed by folding the blank paper shown in FIG. ,
The roof top tongues,' are sealed together after filling with liquid. Since the form of such a paper container itself is well known, it will not be described in detail here. As mentioned above, the features of the present invention minimize the total area of blank paper required for a given liquid filling amount, and also reduce the shape and dimensions of the paper container to facilitate calculations when beautifying the appearance of the paper container. As shown in Figure 3, the depth is 2W, the width is 2L, and the total height is H (first
The tongue piece in the figure, ′ is omitted). Also the fourth
As shown in the figure, the dimensions of each side of the blank paper before folding are as follows: height of the side is B, and 1/2 of the width of the bottom is W.
(Tangular circle omitted) The height of the triangular roof is A, and the entire paper container is divided into four equal parts by the bisecting vertical planes of the paper container at right angles to each other.The volume and area of the blank paper are as shown in Figure 7. We will calculate the required value based on the result. In this way, the blank paper is folded to form a paper container as shown in FIG. 5, and both sides of the triangular roof are inclined inward as shown in FIG. However, generally, the entire volume of a paper container is not filled with liquid. That is, in order to ensure that the triangular roof is sealed during manufacturing and to prevent overflow during actual use, a portion of the interior of the paper container is left unfilled with liquid. Usually, part of the volume of the triangular roof is this space. However, in any case, the volume required to fill a predetermined amount of liquid is the total volume of the container including this space, so the explanation here will be based on the surface area relative to the total volume of the paper container. The calculations are shown below for the stated purpose using the signs set as above. First, as a condition, assume that the total volume of the paper container is 200 cm ³ , that is, the volume of the portion divided into four equal parts is 50 cm ³ ,
Also, since the width of the blank paper used to make paper containers of this size is generally 20cm, the dimensional conditions for the depth width 2W and width 2L of the blank paper are (2W + 2L) x 2 = 20cm ∴W + L = 5cm ... (1 ). In order to make the above-mentioned paper container external dimension relationship the golden section ratio, H/2L=H+2L/H...(2) C+B...(3) W ² +C ² =A ² (Figure 6)...(4) Blank Letting the total area of paper be S, S=(A+B+W)(W+L) (Figure 4) From (1), W+L=5 ∴S/5=A+B+W S'=S/5 If S→min, then S' →min. S'=A+B+W...(5) 1. Referring to Figure 7, V ₁ = 1/3C (W・W) = 1/3CW ² V ₂ = 1/2C {w (L-w)} = 1/ 2Cw (L-w) V ₃ =B (W・L) ∴V=V ₁ +V ₂ +V ₃ = 1/6w (3CL-Cw+6BL) = 200/4 ∴W (3CL-Cw+6BL) = 300...(6) From the above, the unknowns in these equations are A, B,
There are seven equations, C, W, L, H, and S, and the number of equations is six, and the area S' can be expressed by W. From (2), H ² −2LH−4L ² = 0 ∴H=L±√ ² +4 ² = (1±√5)L Since H>0, H=(1+√5)L≒3.236L …(7 ) By substituting (7) into (3), we get C+B=3.236L ∴B=3.236L−C …(8) By substituting (8) into (6) Substituting (9) into (8) Substituting (9) into (4) Substituting (1), (10) and (11) into (5) gives us In order to find the minimum value of S, it is sufficient to find the value of W, that is, the value of S, that satisfies the conditions dS'/dw=0, d ² S'/dw ² > 0, but the calculation is troublesome. Search calculations (Try and
Error) as follows. That is, first, the possible numerical range of W is determined. From (1) L=5−W>0 ∴0<W<5 …(13) From (9) Here, since 3L+W>0 and W>0, ∴19.416L ² W−300>0 ∴L ² W>15.45 …(14) Substituting (1) into (14), (5−W) ² W＞15.45 …(15) Also, from (10) Substituting (1) into (16), we get 3.236 (5-w) w ² −9.708 (5-w) ² w>-
300 ∴W(W-5)(W-3.75)<23.18...(17) In equations (15) and (17), f(w)=(5-W) ² W g(w)=W(w -5) (W-3.75), the curves of f(w) and g(w) become as shown in Figure 8. Therefore, the value of W that satisfies f(w)>15.45 and g(w)<23.18 falls between ranges A and B in FIG.

[Table] When the values of L, B, C, A, and S' for (0.93<W<2.53) are determined by search calculation, the above-mentioned values that minimize S' from the values in Table 1 are W≒ 2.1 L≒5-2.1=2.9 H≒3.236L=9.4 A≒W ² +C ² =2.8 Here, H/2L=9.4/8.5≒1.621 H+2L/H=9.4+5.8/9.4≒1.617 Also, S=4×(A+B+w)(w+L )≒248cm ²
(Minimum value) Therefore, the area of the blank paper can be minimized, and the appearance of the paper container can be maintained by satisfying the above-mentioned golden section ratio of the outer shape of the paper container. The paper container of the present invention constructed as described above has a standard value of the ratio of the side parallel to the base 2W of the triangular cross section of the triangular roof to the adjacent side 2L: 2W/2L=4.2/5.8 ≒0.7, and the reference value of the ratio of the height B of the four circumferential sides excluding the triangular roof to the adjacent side 2L is set as B/2L=7.5/5.8≒1.3, and furthermore, By setting the standard value of the ratio of 2L and the total height H of the paper container to the golden section ratio, the total area required for blank paper for a given liquid filling amount is minimized within the practical manufacturing tolerance range of paper containers. This is done in a limited manner.

[Table] Furthermore, the total capacity V is V=V ₁ +V ₂ +V ₃ = 1/6W (3CL-Cw+6BL) ≒1/6×2.1 (3×1.9×2.9−1.9×2.1 +6×7.5×2.9) ≒50.1≒ 200/4 In other words, it can be seen that the quantitative value is approximately as expected. Effects of the invention As described above, according to the invention, the total area of blank paper required for a given liquid filling amount can be minimized to achieve economical production, and the outer dimensions of the paper container can be made to the golden section ratio. By doing so, the aesthetic appearance of paper containers can be achieved. It is clear that when the amount of liquid to be filled is changed, the total volume of the paper container, including the space volume that is not filled with liquid, may be changed proportionally to satisfy the dimensional relationship.

[Brief explanation of the drawing]

FIG. 1 is an external perspective view of a triangular roof rectangular square bottom paper container for filling liquids incorporating the present invention. FIG. 2 is a plan view of a blank paper for making the paper container shown in FIG. 1, and FIG. 3 is a perspective view showing a simplified shape of the paper container to facilitate calculation. FIG. 4 is a plan view showing a portion of blank paper for the paper container of FIG. 3 for calculation. FIG. 5 is an end view showing how the blank paper of FIG. 4 is folded to form a paper container. FIG. 6 is a partial side view showing the inclined state of the end surface of the triangular roof of the paper container. FIG. 7 is a perspective view of a portion of the paper container shown in FIG. 3, which is a calculated end view, divided into four equal parts by vertical planes perpendicular to each other. FIG. 8 is a diagram showing a curve of the end view equation f(w) versus W for determining the minimum value of the area of blank paper. FIG. 9 is a perspective view showing an example of the specifications of a paper container obtained by the present invention. −...area of each side of the paper container of the present invention, W...1/2 of the depth width of the paper container, L...1/2 of the width of the paper container, H...total height of the paper container, B...
... Height of the vertical surface of the paper container, A... Length of the slope of the triangular roof of the paper container, C... Height of the triangular roof, S... Area of blank paper, V... of the paper container. Total volume.

Claims (1)

[Scope of utility model registration request] In a rectangular bottom paper container with a triangular roof for liquid filling formed by folding blank paper, the standard value of the ratio of the side parallel to the base of the triangular cross section of the triangular roof to the adjacent side is 0.7. , the standard value of the ratio of the height of the four circumferential sides excluding the triangular roof to the adjacent side is set to 1.3, and the standard value of the ratio of the ratio of the adjacent side to the total height of the paper container is set as the golden section ratio. A liquid-filled paper container characterized in that the total area of blank paper required for a predetermined liquid filling amount is minimized within the practical manufacturing tolerance range of paper containers.