- Kari kolehmainen Samaa tarkoittava suhdelaskenta

These pages are for

Strength of Materials
Studying products
Visual Geometry

Nämä sivut ovat:

Näkemisen geometriaa
Tuotteiden tarkastelua

Visitors - Kävijät

Käyntejä kotisivuilla:396515 kpl

Products by Calculating

The calculation leads to compare the products by calculating. Since everything is the same, the calculations is shown sometimes to strength calculation, visual geometry, physiology and physics.


  1.      Product Comparison by Calculating.

  2.      Commercialized Athletic Sport.

  3.      Observation I.

  4.      Weight of a Product by Calculating.

  5.      Product Value Space.

  6.      Screw Conveyor as a Product

  7.      Screw Conveyor in the Product Value Space.

  8.      Different Measures

  9.      Golden Ratio

10.      Golden Ratio Today

11.      Golden Ratio in Products

12.      Nature Modular Structure

13.      Trust to Measuring Devices

14.      Defining Values Through Comparing Method

15.      Metric Standard Nuts

16.      Weight Determination

16.1    Lifting Beams 500 kg

16.2    Bridge Elements for Pedestrians

16.3    Lifting Tables 1

16.4    Lifting Tables 2

17.      Product Line Formation of the Screws

18.      Formation of the Steel Rope Product Series (time dilation)

18.1    Incandescent Light Bulb

18.2    Steel

18.3    Steel Rope

19.      Lifting Lugs for Steel Constructions

20.      Lifting lugs from 500 to 40,000 kg

21.      Single Girder Crane 2 t, 14 m

1.   Product Comparison by Calculating

An interesting application of the calculation is the product comparison by calculating. Comparing means comparing between own products or to competitor's products. We compare well-known products and for which the information is verified. In addition, we compare the products that few people know the process of comparing. We can compare the products, which are not made or for one reason or another do. This means, the product does not necessarily need to be produced in order to identify its characteristics.


 Shadows open the product values

We may well start calculation with the Golden Ratio and in connection with Homo Sapiens as a "product'. Physical design as a standardized man, is in connection with the Golden Section Ratio, and allows for mass-produced goods. We have expertise in product design, but what about the performance characteristics between individuals? Is it possible compare the performance of people. That is for the calculation to find it out.

We understand the car's performance, acceleration, maximum speed, engine power, etc. The value represents the extreme limit of the product characteristics, which we normallly rarely need. 1-dimensional competitive sports, based on the progression, tries to find the extreme value of the performance. On the other hand the 3-dimensional products, are not valued to be the products of a 500 kg load, but by the sports term having breaking load of 2000 kg. This would lead to a dangerous situation, without realizing the fatigue of the products.

For example we compare products on the Fibonacci Sequence 1 - 1 - 2 basis. We take two 1 - and 3-dimensional products; human performance and an auxiliary lifting equipment as a lifting beam. Have these any possibility of comparing? Yes, although this is not recognized. Through the mathematics the Golden Section Ratio does not open. Through the proportionality we understand why this has happened.  (871)

2.   The commercialized competitive sports

Competitive sports are commercialized, so the practical calculation does not differ from the technical products. The calculation takes into account energy use during the trip, as well as the energy production of the person in relation to the size and weight. Further, we calculate the energy use in accordance with the condition of the human age groups, wherein the human size does not matter. Cooper test is not asking weight or length, just age. The calculation produces a surprise for the human in terms of size and muscle power returns among athletes. The golden section is with in this. We can calculate the energy in the run, get the answer to each age group, travel length and condition group. The calculation does not include hocus-pocus. The calculator in your hand you determine the sport mode. When one of the previous relation is known, the rest is known. Perhaps you do not want to get it out?

Condition is energy production, in practice oxygen uptake. For example, we calculate the running position impact on the performance. This is compared to the main girder of the bridge crane. How much energy is bound to deflection, because the question is of a poor running position which consumes energy.

When hoisting something, the main girder of the bridge crane is not bending of the load power. It can say for example the hydroelectric power potential energy converted into electricity, lifts the the load. In the hoisting machine, placed on the main girder. It is the potential energy, which is transferred to the elastic energy of the main girder. We are talking about compression and tensile stress, as a visible deflection. We have not calculated what the energy is, how much and why. Wire bending in the hands we know, without calculating the amount of the wire produced energy. In the strength calculation much time is used to stresses analyses in the construction, still the shape stransformation is often the most important.

Finally, let us consider the metal punching machine, which bends the piece. One stroke takes a fraction of a second and the bend required energy has mostly transferred to the piece. After punching there remains a physical form of the piece which after cooling has the same energy amount as before the punching. Runner also eventually produces only heat. Things can be viewed simply by taking the case at a time. Worldrecord statistic is a good tustustua in advance, when the resulting flow records cover the consciousness. The calculation is often of the best results, so it is good to be familiar with the World Records.  (909)wikiped.jpg

World Records

3.   Observation 1

The value of a product or phenomenon, representing the value point on the curve. Between the two first smallest points of the whole, be drawn a straight line.


Fibonacci Sequence 1 - 1 - 2

                                                                                 1 + 1 = 2

100 m + 100 m = 200 m

9.58 s + 9.58 s =*19.16 s

The first thing is to determine the minimum value. Everyone knows the hundred meters as the shortest athletic run distance. The next distance is two hundred meters run, in which the time in practice is two times a hundred meters time. The same show the domino blocks in the photo.

The two smallest value points can define on the addition principle. From this point on, not by this way, because the values ​​would be directly determined. Some books have mentioned the exponential structure of the universe, but not explaining it. The principle of this mentioned Fibonacci.  (912)

(*200 m ME - WR 19.19 sec)

4.   Weight of a Product by Calculating

In the products, I interested in to study the weights. Smaller product did not get be heavier than the bigger one was. There was no need for fracture size of the product, if benefit of the weight was small with respect to the next size. The first observations were common like. I observed coming to the same in many meanings. I tried straightforwardly resolve the weight in the product, having no succeed in this. This phase stayed behind without telling of that. Each product and measurement were individual, which were unparalleled, neither come to mess to the other products. Computers developed quickly and these certainly would tell soon all necessary knowledge of the products. When buing a computer, I thought them including information. I did not think them to be empty electrical boxes, and where  the collected knowledge does not always willingly locate.

In those days was important to be familiar with calculation formulas. Machine elements had eaten into the brains. It was natural use those parts and material, which easily were ordered from brains by way of the commands, for the lines onto the paper or plastic.

Design work was carried out at 80's beginning by drafting boards. The computer to the parts lists become in the middle of the decade and programming happened by Basic program. My computer had the ability to calculate five programs together to the tape drive and print. Although there were single programs for the calculation, but receipt like printouts did not open to draw conclusions. Haven't such kind coming to my mind. Each calculation was separate. Was that so or did I too anxious conclusion? (1052)


Proportionality by way of the shadows

5.   Product Value Space

The Value Space concept was developed in the context of the design of products. This, using a systematic design methodology to complete product families. I designed the products using a computer since the early 80s. At first the small computer programs, outputted a coherent whole that will impress even today.


The concept of the Product Space Value was necessary for the calculation. This was based on the law of the universe, and this also joined to the engineering. The idea of ​​a separated universe in the machine building universe, is a dead duck. In physics can change values ​​of different units, without EP-calculation getting outside. In the case of gravity, science is powerless to explain it. EP-calculation is based largely on gravity, still attempting to explain the phenomenon. Much of its nature may, however, find the calculation.

In addition to experience we need something to detect the reflected information from the Product Value Space. I developed the software for this purpose that collects and produces knowledge of product design. The procedure collects the dispersed information and centralizes the collected information to create new knowledge. EP-calculation has born by this procedure. The calculation based on products is a fact that can not be denied. Following from this is a equal procedure for the physiology and physics. (220)

6.   Screw Conveyor as a Product

ruuvikuljetin_1.jpgTechnically screw conveyor is simple and cheap, but harmful aspect is the wear and power demand putted in proportion to the material amount. The capacity of the conveyor is generally 5 - 40 m3/h , whereby the larger conveyors can be over 200 m3/h. On the big material flow, other conveyor solutions come often more reasonable.

The buoyancy force of the screw conveyor in the Product Value Space


Modell of the Calculation

The calculation gives a model, how the data known of the conveyor, is comparable to other similar conveyors data. For example knowing the weight of the screw conveyor, this is changed for the comparable conveyor values. Supporting length can grow or be shorter and so on. We calculate all conveyors in series and in addition to this we study exceptions. The accuracy of the calculation is under 5 percent.

Alternative defining way

Without the EPC calculation,  can calculate power and the capacity for the conveyors. The weight defining is more difficult. How many controls this task? With the help of the EPC calculation, all control this. The calculation is being ensured by comparing the data of the conveyors to data of product deliverers about the products. In addition to this, is in use a calculation program, based on to the standards and to experiences of the conveyors. Flattening the screw is one of the screw conveyor associated task. We study a way to flatten the screw correct. Some literature given pattern make the disk part incorrect sized.  (931)

7.   Screw Conveyor in the Product Value Space

ruuvikuljetin_1.jpgI am listening the marketing man of the productization, when the sentence falls on the ear: When the first product, it has to think whether more models and where in the product space, is located. This is like the introduction to the Equivalent Proportional Calculation, which has as many spaces as products.

For example, screw conveyors to wood chips and conveyors to rock material have their own product spaces. This is because the latter products are constructed against wearing and have a stronger construction.


Let us imagine the screw conveyor is located into the product value space. It seems affected by gravitational force, minus the centrifugal force of the Earth's rotation. There remains the gravity G of 9.82 m/s2. Second square (m/s2) is an interesting note of the surface area. It has a result as a buoyancy force, because the surface area is subjected to pressure. Calculated values ​​of the conveyor rise up, such as a submarine in the photo. The idea Archimedes discovered in his own time, located to the present day.  (867)

8.   Different Measures

1,0 - 1,25 - 1,6 - 2,0 - 2,5 - 31,15 - 4,0 - 5,0 - 6.3 - 8,0 - 10,0

                      1 km     -    1,618 km

                      1 cm      -   1 Inch = 2,5 cm

                      1 Inch    -    Mile  =  63.700 x 1 Inch

Once I talked of calculation method to one Engineer. He said, he is specialized in strength calculation. He was looking my calculations and said, "Calculations do not include mm measuring units. We have been taught that, the calculation must be made in millimeters, and he does not understand the other units." I am speechless of this opposition, with regret on behalf of millions of people who do not know this when using inches and pounds. I can imagine being in ancient Rome to present the Arabic numerals, and particularly the number zero, which they lack. Empty, however, they were able to leave between.

Calculating has the idea, ​​the unit may be the mind of the user. These can be calculated with each other, without changing the outcome. This realization can be difficult, but we unerstand the different measuring units in the world. We consider first the Golden Ratio of 1.618, kilometer length of 1000 m and mile length of 1609 m. In the calcution there is between them a 9-meter error that affects to the third decimal place. The thought as the length 25 mm is the ratio of the calculation. From this by continuing one Inch is the 63.700 part of the mile, in other words in accordance with the ratio 6,3. Different measures, does not mean a problem. We can calculate such as earlier and mix the measures for calculating.


mutterit_ja_avaimet.jpgFrom the point of view of the calculation, dimensions are often together countable, without modifications of the system measurement. For example 20 mm screw having the factor 1,25 is 25 mm (in practise M24 sized), which is one inch.

From this on having the factor 1,25, pipe diameter 33,7 mm is 1" pipe in other words 1,25 x 25 mm = 31,25 mm. Through the Equavalent Proportional Calculation, these two dimensional worlds come closer each others. Because the strength calculation is made  finally, can calculations have been mixed between. If the pipe is not sufficient as the cross-sectional area, pipe's wall thickness will add. For the next we would have to select measurement 33,7 x 1,25 = 40 = 42 mm (pipe or screw). From extraordinary sized components, there is better available inch sized products. I continued on the purpose from 25 mm screw to the pipe, which are available both the metric and inch sized.

In pipes there are any difficulties after the initial inconvenience. Threads has the same and from outside a nut can surprise in American or in Japanese product, by being on the other measurement as we assumed. When I did install the exhaust pipe and I observed the missing nuts to be metric sized, but they were UNF or UNC threads. You gess, did I have them.

42 x 1,25 = 63 mm  - 80 mm - 100 mm - 125 mm - 160 mm - 200 mm - 250 mm

Different kind of cross-sections of materials and components.  (375)

9.   Golden Ratiofinnish_translation.jpg

Kultainen suhde

golden_ratio.jpgTwo quantities are in the Golden Ratio if the ratio of the sum of the quantities to the larger quantity is equal to the ratio of the larger quantity to the smaller one. The Golden Ratio is an irrational constant, approximately 1.61803398874989.


Golden ratio

a) From the heel to the knee  -  From the heel to the nave

b) From knee to the hip joint  -  From the nave on top of the head

In philosophy, rationality is the exercise of reason and irrationality is the opposite. EPC Calculation is coming to show irrationality to be partly wrong. Other names frequently used for the Golden Ratio are the Golden Section (Latin: sectio aurea) and Golden Mean. Other terms encountered include extreme and Mean Ratio, Medial section, Divine Proportion, Divine Section (Latin: sectio divina), Golden Proportion, Golden Cut, Golden Number, and mean of Phidias. In this calculation the Golden Ratio is denoted by the Greek lowercase letter phi φ.

( a + b ) / a = a / b = (fii) = 1,618 033 988

  5 / 3  /1.03 = 1.618     5 >  The proportional limit of the calculation  <  5             8 / 5 = 1.6

All living bodies, and machine components have the relationship. Based on the golden section may make different kinds of comparison, because all relationship is predetermined.

In Other Words

Cut off the rod 100 cm into two parts, so that a longer section is 61.8 cm. The rod is cut to the golden section ratio 100 cm /61.8 cm = 1.618

A shorter length is 38.2 cm. Golden section gives a partly false impression of designation, as a certain ratio of a cutting. Golden ratio is the matter related factor, which determines the forces acting between. Dangerous sharing is a concept which can be used for modeling the drawing below.


The golden ratio as visual geometry

Pascal's triangle factor between rows 1.1, as well the strength calculation coefficient 1.12. "Cutting" can continue five times, after which the proportional limit is exceeded. The same can try folding the paper neatly five times.  (891)

10.   Golden Ratio Today

It is advisable to become acquainted on the Golden Ratio by way of Internet pages. Commonly saying, a large part of Internet pages join to the art by mean of the composition. Some pages look at the Golden Ratio topic by way of the nature examples which can be found numerous. Later the Equivalent Proportional Calculation illuminates the nature associated calculation. We calculate also ageing fatiguing in different forms and so on. The next time we travel to watch the pyramids, we will examine them in others in thought. After all, they are also products of their time.


Become familiar with Internet pages, so the figure 1,618 remain to mind by way of the examples. On some pages there is question of commercialness, and offer to the topic associated products. The architecture gets also attention. This happens by way of thousands of years ago  prepared constructions. This beginning from the Egypt's pyramids and continuing by way of Greek building to today's space concept. From Internet material we would get a book, but the knowledge of the book in any case would remain for the scratch of surface. In our country has been made at least two university final works of the Golden Section Ratio associated mathematics. These works have like the other comparable final works, not solved the mean of the Golden Section Ratio. The intention of the final works is of course not to solve the Golden Ratio's secret. The golden ratio has fascinated mankind for thousands of years. When it is looked at, the subject has dropped the viewer down. This the Equivalent Proportional Calculation (EPC) will no longer do(387)

11.   Golden Ratio in Products

All around of us we are affected by various proportions, as exemplified by the golden ratio 1.618 in products. I will add products to this page and the first is commercial calculator HP 12 C. The products include visual geometry, which does not need to calculate.  (821)


Hewlett Packard 12C Financial calculator, has a ratio of 1.6125.

Mitat  - Dimensions (W x D x H)
8.0 x 1.52 x 12.9 cm

12,9 / 8,0 = 1,6125

12.   Nature Modular Structure

Imagine the blue lines to be steel tubes and structure forming the half of the roof truss. The relative lengths of the tubes are 1, 1.618 and 2.618. The tubes form a module, so the structure can be prepared of three different length of tubes. The angles between the tubes are 36, 72 and 108 degrees, i.e. the angle of 36 degrees multiples. In the end, 5 x 36 degrees = 180 degrees = pi () radians. Full Angle 10 x 36 degrees = 360 degrees = 2 pi () radians = 6.28.



1.618 x 1 = 1.618      => 1.618 x 1.618 = 2.618     => 2.618 - 1 = 1.618


The nature has the symmetry concept. When the left side is known, the right side is at the same known. Do you think the nature does the support constructions by different way as we humans are them doing? Constructions in the nature look different, but have you calculated them? No, you have not, but the roof truss is familiar to you. Yes, they are familiar to many of us, but we have not strength calculated them.

When the calculation proceeds, we load the truss and look the distribution of the forces. Only a limited mind determines the images as the roof trusses. A similar grid structure have values and phenomena, but the calculation is not known. Through the EPC calculation, the patterns and formulas have the same meaning. Everything is formed of the surface area, length, volume and time. We are dealing with the visual geometry. Looking at the images, there is not a simpler functional measure of the relationship than the golden ratio 1.618. Finally, the nature modular thinking, is the industry requested modular structure. A good example of this Lego blocks.  (925)

13.   Trust to Measuring Devices



I will tell an example of weekday realness. In cottage in Southern Finland had the TV a bad picture quality. The host told, how he had asked an antenna specialist to come and visit to his cottage. He would have some special equipments for antenna directing. The specialist arrived to the cottage, whereby I asked from his measuring devices. He said, that he has nothing measuring device with. The antenna and television will be such kind of devices. If the picture on television is good, is direction then in the place. He said that in the known point of compass is a powerful field and antenna must focus in that direction. We did so and the picture quality became such kind, as it was possible in the conditions get.

The Equivalent Proportional Calculation has the same function. We don't necessary need any formulas to define same, as we do with the help of the formulas. The calculation method is right and accurate, if it does describes the same, as by on other way described.

As the television, a calculator will show the clear picture(548)

14.   Defining Values Through Comparing Method


                                        Bearing                                      Calculated

Click on the image to open the spreadsheet

In connection with the matters and events, there are situations in which we know someone's value. We need a comparable value of some same kind of value. This value is not known, but can it define out? In the following Excell-example we calculate bearings which can be checked from some bearing catalogue.

w'll look at the ball bearing series, in which is measured the ball-bearing's width, outer and inner diameter. We have the external dimensions of the bearing, but no information of the bearing lifetime. The measurements of the bearing are in accordance to ball-bearing 6017. However, it is known the bearing C value to 5 mm shaft. How we can define the value C of bearing 6017? The starting point; the bearing life has been determined in the laboratory conditons. It is not possible to determine by calculation. Five rows on the left side of the table is from the bearing book, the sixth is obtained by calculating the value. Is found by calculating the values ​​obtained with high accuracy, for the same values ​​that the manufacturer of the bearings (SKF) has announced.

The comparison procedure makes it possible to determine the unknown value, in this case, the ball-bearing lifetime of 6017, when a well-known is the equivalent bearing a first product information. The Excell example calculates on the second row the C value of ball-bearing 618/6. Then the formula is withdrawn to other rows of the table. I think there would not be an issuer which otherwise may be calculating the value of the bearing outer dimensions. The ball-bearing can not see inside, it has a grease lubrication and protection plates to protect the balls. C is the value of the experimental assay, the conditions agreed to tabulated value. The table can be calculated proceeding one line at a time. This allows you to view when you open the spreadsheet.

In the connection with the calculation, I tell of the possibility of identifying the products and values ​​that do not exist. Who said the bearing 618/6 to be of this world, and it is ever made? It does not need to know. The calculation examples, however, there are the sizes and can be found to ensure what I write.

Perhaps this kind of elegance of the values ​​was Albert Einstein's desire to find a more comprehensive explanation of the universe.
We do not know this, but I think he was finding a similar perception, the calculation presents. I will present a calculation of the bearings and later, how it applies to the rest of the calculation.

(436 - 714)

15.   Metric Standard Nuts

0,8 - 1,0 - 1,1(2) - 125

Nut dimensions can be calculated as the Equivalent Proportional Calculation.


                  S            E                                                    M

    M3        5,5         6,08          1,11 x 5,5 = 6,11            2,4       0,8 x 3,0 = 2,4

    M4        7,0         7,74          1,11 x 7,0 = 7,77            3,2       0,8 x 4,0 = 3,2

    M5        8,0         8,87          1,11 x 8,0 = 8,86            4,0       0,8 x 5,0 = 4,0  

    M6       10         11,05          1,11 x 10 = 11,20           5,0       0,8 x 6,0 = 4,8

    M8       13         14,38          1,11 x 13 = 14,43           6.5       0,8 x 8,0 = 6,4

  M10       17         18,90          1,11 x 17 = 18,87           8,0       0,8 x 10 =  8,0

  M12       19         21,10          1,11 x 19 = 21,09         10,0       0,8 x 12 =  9,6

  M16        24        26,75         1,11 x 24 = 26,64          13,0       0,8 x 16 = 12,8

  M20        30        33,53          1,11 x 30 = 33,30         16,0       0,8 x 20 = 16,0

  M24        36        39,98          1,11 x 36 = 39,96         19,0       0,8 x 24 = 19,2

                           174,56                           174,36

The idea of how almost anything can be calculated through proportionality, when you know the procedure for the calculation. For this reason, should be familiar with physics, strength calculation, and keep your open mind. What about the dimensions of the M39 screw, if you know the dimensions of the screw M3?

                  S            E                                                      M

M3           5,5         6,08          1,11 x 5,5 = 6,11            2,4       0,8 x 3,0 = 2,4

M39         60          69,3                                                  31        0,8 x 39 = 31,2

1,2511x 55 = 64

              1,2511 x 6,08 = 70,8                                            

                                                                          1,2511 x 2,4 = 27,9


 ... M24  -  M30  -  M39

      9.           10.       11.


16.   Weight Determination

16.1   Lifting Beams 500 kg

The Fibonacci Numbers

1  -  1   -  2

Weight 1 m = 13 kg  -  Weight 2 m = 25 kg

The smallest product of 1 meter between the hook, set the weight of the twice longer product. This is the same as the time of the 100 and 200 m athletic races. The minimum set the larger. This time, the designed lifting beams followed the rule. Economical manufacture may require a second construct, wherein a second product weighs more. We look at this, having one manufacturer's catalog of the lifting beams.


1 + 1 = 2     => 13 kg + 13 kg = 26 kg       difference1 kg = 4 %.

As a percentage, the difference seems large, but is smaller than we have been able to calculate. The material weight 1 kg, means one euro cost of the product. More specifically, the formation of the weighst are explained later. The example illustrates the procedure for the products and accuracy that the calculation can be achieved. Product weight was calculated on the basis of the material data. Equally, it can be said that the product was 26 kg than the weight of 25 kg. This applies especially if the tube length and the material thickness has + tolerance, as it actually has. Proportionality should be understood as a comprehensive vision for a product weight and values ​​formation. The example of the lifting beam shows the weight within the limits of accuracy of the calculation, or may be the exact weight of the item.  (930)

16.2   Bridge Elements for Pedestrians

Bridge elements are an easy way for pedestrian traffic guidance over open canals during city utility works. These are real products and are widely in use in Southern-Finland. We calculate the product weights using EPC method, which is easy understand  in the mind. This is not always the case, but still all follow the laws of nature. It is good to start with the easy products and move of these to more difficult.


Type                                3141                 3142                 3147               3148 

Canal width                 1.2 - 1.5 m        2.0 - 2.5 m         3.4 - 3.8 m      4.2 - 4.6 m

Width for walkers         1220 mm          1220 mm          1220 mm         1220 mm

Overall length               2440 mm          3660 mm           4880 mm         6100 mm

Overall height               1043 mm          1063 mm           1063 mm         1063 mm

Weight                            170 kg               275 kg                380 kg             490 kg


1.5 x 170 kg x 1.1(2) = 286 kg            1,5 x 2440 mm = 3660 mm         4.00 % 


2 x 170 x 1.1(2) kg = 381 kg               2.0 x 2440 mm = 4880 mm         0.26 %


2.5 x 170 x 1.1(2) kg = 476 kg            2.5 x 2440 mm = 6100 mm         2.85 %

                                                                                         Average         2.37 %

The table has the weight of the shortest bridge element. We are interested in to know weights of other products. Values ​​are not visible, which are defined to the first product. For this reason, the weights are measured. After this is discovered, the first product determined the weight of others. Pascal's Triangle row factor 1,1(2) does not sureprise. (974)


                1         1

           1         2         1

     1 ....etc

16.3   Lifting Tables 1


A company manufactures lifting tables, but the company has nothing to do with the product in the photo.

The product has the same table size through the serie starting from lifting capacity of 500 kg to 3 000 kg. We calculate sizes from 1 000 kg to 3 000 kg. Later we will calculate the product of 500 kg and see some things belonging to it. We will see how the serie of products will form the weight.

Pascal's Triangle and calculation

The manufacturer has specificated values of weight. Lifting table capacity of 1 000 kg and 185 kg. Lifting table capacity of 3 000 kg and 265 kg. There is no need to inform the table weights between 1 000 - 3 000 kg, because they come from calculation.


Lifting capacity kg    Weight kg              Calculated weight kg

 1 000                              185                      The known weight

 1 250                                 -                        1,08 x 185 = 200

 1 600                                 -                        1,08 x 192 = 216

 2 000                                 -                        1,08 x 205 = 233

 2 500                                 -                        1,08 x 219 = 252

 3000                                265                               -

 3 150                                 -                        1,08 x 252 = 272


We can expect the quality and safety have remained at the same level

Lifting equipment like hoists and auxiliary lifting equipment have often capacity of 3200 kg. Now we have to guess is the marking 3 000 kg the rounded figure.  Also this can be determined by strength calculation, but we do not know that. In practise the difference  in weight 7 kgs and 3 %  means nothing. We have studied to Pascal's Triangle and there to five steps idea. In this calculation we have six steps, and still having the accuracy of calculation. But how the value of 1,08 has formed itself. Later we will see the value in many calculation.  (461)


                              1    1

                           1    2     1

        The factor between the lines 1.1

The value 1.1 means as progressive increase 1.25   => 1 000 kg - 1 250 kg - etc.

1.1 x 1.1 x 1,03(4) = 1.25.

The Universal Friction (1.03) reduces the exponential weight increase

1.03 => 1.12 / 1.03(4) = 1.08

16.4   Lifting Tables 2

A lifting table has the weight of 185 kg to the table size 80 x 135 cm. Litfting height onto the table is 82 cm. It has to determine the weight to a table size 100 x 200 cm. Lifting capacity 2 000 kg and lifting height 110 cm. The manufacturer has announced the weight of 350 kgs.



This time I will mention the factor 1,1 between rows in Pascal 's Triangle. Especially on Finnish pages the factor has shown enough.

We will itemize the calculation, but later we can do the calculation without this itemization. Later ofn this calculation there are examples of that.

1,1 = 1,25

1 - 1,25 - 1,6 - 2,0

1. The calculated weight to table size 80 x 135 cm, lifting capacity 2000 kg.

Lifting Capacity           Weight                 Calculated weight

   kg                                 kg                        kg             

 1 000                              185                      Known weight

 1 250                                 -                        1,08 x 185 = 200

 1 600                                 -                        1,08 x 192 = 216

 2 000                                 -                        1,08 x 205 = 233   Lifting height 82 cm   


16.4.1   The factor to table length of 200 cm.

Pöydän pituus kasvaa arvosta 1,25 (135 cm) arvoon 2 (200 cm)  = 1,12 = 1,21.

The table length increases from 135 cm to 200 cm  -  value 1,25 (135 cm) to value 2 (200 cm) = 1,12 = 1,21.

125 - 160 - 200

  1  x 1,1 x 1,1


16.4.2   The factor to table width of 100 cm

The width of the table increases from value 0,8 (82 cm) to value 1 (102 cm) = 1,1

1,25 x 82 cm = 102 cm

1 x 1,1


16.4.3   The factor to table rise 110 cm

The table rises 1,34 times higher  =>  factor 1,1 * 1,03 = 1,166

110 cm / 82 cm = 1,34

82 cm => 102,5 cm = 1,25 = 1,1

102,5 cm => 110 cm = 1,07 = 1,03

Final Conclusion

Four dimensions increase having factor 1,1 and from lifting height once a factor 1,03.


185 kg x 1,083 x 1,14 x 1,03  = 351 kg


We can expect the quality and safety have remained at the same level in both table sizes.


17.   Product Line Formation of the Screws

Metric Screws

It is known as the screws M4 and M5 and of this may indicate. The size of screw will grow by 5 / 4 = 1.25, ie a factor of 1.25. In practice, the M20 screw is the maximum which is normally used. Larger screws have slightly different dimensions, but this is not significant.


1,25 x 1,25 x 1,03 = 1,618 = The Golden Section ratio

4 - 5 - 6(,3) - 8 - 10 - 12(,5) - 16 - 20 - 25


1,25 x 4 = 5 mm

1,25 x 5 = 6 mm

1,25 x 6,3 = 8 mm

1,25 x 8 = 10 mm

1,25 x 10 = 12 mm

1,25 x 12,5 = 16 mm

1,25 x 16 = 20 mm

Golden Section Ratio 1,618

4 mm screw: 4 x 4 = 16

5 mm screw: 5 x 5 = 25         =>  25 / 16 = 1,6(18)


8 mm screw: 8 x 8 = 64

10 mm screw: 10 x 10 = 100   => 100/64 = 1,57 x 1,03 = 1,6(18)


16 mm ruuvi/screw: 16 x 16 = 256

20 mm ruuvi/screw: 20 x 20 = 400   =>  400 / 256 = 1,57 x 1,03 = 1,6(18)


The following calculated screw sizes are M25, M32 and M40. In practice, the corresponding screws are M24, M33 and M42. Of these, M33 screw sizes are not favored, although the size of the screws are still available. Similarly, M40 mm screw size has been selected size of 42 mm. This has its own reasons, which can not be guessed or determined in this context.

The quality features of the product are usability and safety. We find the screw sizes to comply with the Golden Section Ratio, which ensures safety. When calculating the stresses, they are found to be at the same level for all screw sizes.

0,785 x1,25 x 1,03 = 1

0,785 neliön ja ympyrän poikkileikkauksen pinta-alojen suhde

0.785 is the square and circular cross-sectional area ratio

 0.785 is the specific gravity of steel

We calculated the size formation of the screws & the strength formation of the product. As all phenomena are derived from the simple formula E = m c c, the products are determined by a simple product, such as a screw. Prior to this, however, is the need to understand many things. I am writing of this on my pages.  (707)

18.   Formation of the Steel Rope Product Series (time dilation)

We look at the steel rope 6x26 Warrington-seale and we find that the behavior as a phenomenon does not differ from a incandescent bulb.


Steel rope         -   Light from lamp
By hand touchable    -       Not by hand touchable



Length  -  Area  -  Volume  -  Time

Speed of light is area c2



Why did I chose this time steel rope, due to the fact that I finished the previous writing  to visual geometry patterns. The square and the circle area ratio are defined by time dilation and the the area of the unit circle is the specific gravity of steel. Calculation throug figures would not be possible without this connection.

1 / (1.25 x 1.03) = 0.78

18.1   Incandescent Light Bulb


We get the energy from the Sun. We cannot look at the Sun, so we need to create a small-scale space. To this we take the light bulb in the image. An electric light inside the lamp is produced with a filament wire heated to a high temperature by an electric current through it, until it glows.

Most incandescent bulbs convert 3 - 5% of the energy they use into visible light, then the light is friction of the heating process.

100  / 1.0328 = 96.82 %

                                    Universal friction 1.033

18.2   Steelwire.jpg


Steel is an alloy of iron and carbon that is widely used in construction and other applications because of its hardness and tensile strength. Carbon, other elements, and inclusions within iron act as hardening agents that prevent the movement of dislocations that naturally exist in the iron atom crystal lattices. The carbon in typical steel alloys may contribute up to 2.1% of its weight.

Varying the amount of alloying elements, their formation in the steel either as solute elements, or as precipitated phases, retards the movement of those dislocations that make iron so ductile and weak, and thus controls qualities such as the hardness, ductility, and tensile strength of the resulting steel. Steel's strength compared to pure iron is only possible at the expense of ductility, of which iron has an excess.

18.3   Steel Rope

The steel rope is intended for supporting. The analysis shows a range of the steel rope formed the same way as in the previous example. Steel Rope values ​​are in the revised tables.

Diameter          Weight

 D mm             kg/100 m 

  10                      38.0          

  12                      54.7           54,7/38,0  = 1.779             

  16                      97.3           97,3/54,7  = 1.772

  20                    152.0           152/97,3   = 1.562

  24                    219.0           219/152    = 1.441

  32                    389.0           389/219    = 1.777

  40                    608.0           608/389   =  1.562

                                                Average = 1,649

 1.618 x 1.0165 = 1.645

1 + (0.033/2) = 1.0165

10  -  12.5  -  16  - 20  - 25  - 32  - 40

The rule in the two-dimensionality of the universe; twice as far to be four times larger. Status value = 10 => 16 is two times higher.

  4 x 38 kg/100 m = 152 kg/100 m

16 x 38 kg/100 m = 608 kg/100 m

6x26 Warrington -Seale (the breaking strength of the yarn 15.7 kN/cm2)

Tabled Data

 D mm             kN/cm2

  10                   55.9

  12                   80.6              8,06/5.59  = 1.442

  16                  143.0              143/80.6  = 1.774

  20                  224.0              224/143  = 1.567

  24                  322.0              322/224  = 1.438

  32                  573.0              573/322  = 1.780

  40                  895.0              895/573  = 1.562

                                             Yhteensä  = 1.593

                                      1.618 / 1.0165 = 1.591

                                        1 + (0.033/2)  =1.0165

Minimum breaking load is to be attained or surpassed during the tensile-test.

 4 x 55.9 = 223.6 kN/cm2

16 x 55.9 kN/cm2 = 894.4 kN/cm2

(1,649 + 1.593) /2 = 1.62   =  Golden Ratio 1.618

1.033 x 1.593 = 1.645


Determining the bulb radius to the relative value of 1.

The spherical body surface area A = 4 Pi r2

r1 => A = 4 pii 12 = 12,56 Unit area

r2 => A = 4 pii 22 = 50,24 Unit area

r4 => A = 4 pii 42 = 200,96 Unit area

In the formula, the radius increases twice bigger, the surface area will increase by a factor of four. Thinking about the heat evenly distributed onto the surface area. When the radius (r) increases twice bigger, decreases the amount of heat on the surface area to 1/4 per unit area. In the end the rope and lamp values ​​formation does not differ from each other. The same goes well, as long as everything is derived from the formula E = mcc

Note! Solar constant magnitude near the outer surface of the Earth's atmosphere is 1,37 kW/m2

19.   Lifting Lugs for Steel Constructions

These lifting lugs are not to an angle lifting. Sharp edges removed.

Use to equipment and structures assembly. These are not lifting equipment.


 Material  S235JRG2

The variables are the material thickness and stress in relation to the load.

Capacity     Plate       Width       Height       D         Weight

   kg             mm          mm         mm         mm          kg             Calculation

 1 500            8            100           90           58           0,30         Known weight

 3 000          12            100           90           58           0,52         1,253 x 0,30 = 0,58 kg

 5 000          20            100           90           58           0,87         1,255 x 0,30 =  0,91 kg

D = 40 mm from the bottom

1,6 - 2,0 - 2,5 - 3,15 - 4,0 - 5,0

                                                           1.     2.      3.       4.     5  (steps as powers)


How About the Lifting Lug 6 300 kg?

1.6 - 2.0 - 2.5 - 3.15 - 4.0 - 5.0 - 6.3

                                                      1.     2.      3.       4.      5.     6.

1.256 x 0.30 =  1.14 kg


0.3 -  0.4 -  0.5 -  0.63 -  0,8 -  1,0 -  1,12    kg

                                      1.5     2.0    2.5    3.15    4.0     5.0     6.3    x 1000 kg

                                                 1.     2.        3.       4.       5.       6.

The sixth step exceeds the proportionality and must often therefore be crossed out. In this case the sixth step is quite accurate value of the lifting lug. Still take material S355 for this product, because the material cost difference is small. (1000)

20.   Lifting Lugs from 500 to 40,000 kg



The leftmost lifting lug is the smallest in size. On the basis of one ligfting lug, the other lifting lugs can be detemined. For example, the weight of the 40,000 kg lifting lug differs 5 kg of the manufactured lifting lug. The difference in weight between the smallest and the largest is about 200 times the smallest. The calculation takes a moment to calculate on the paper and on spreadsheets, only for a few seconds.

125 kg x 1.25 x 1.12 = 175 kg is the last line of the calculation of the 40,000 kg lifting lug.

Of the product weight formation, there is a need to understand the proportionality in different dimensions. Calculation shows later the weight determination of the lifting lugs. The parabola of the curve joins to visual geometry. (593)

21.   Single Girder Crane 2 t, 14 m

Crane in the drawing was designed for 30 year ago and represents the smallest size of the product. The smallest determine the biggest, but also other way round. By comparing this product, it can determine the other cranes through the calculation.


The calculation shows how an unusual structure can be calculated. We compare products of large crane manufacturers. A small one single girder crane is calculated to double girder crane and back to the crane in the picture. We calculate them to same meaning, which means the products have the same operation functions. To lift and move, such as bridge cranes are perceived to work.  It makes easy for the calculation that the crane design is based on standards. Standards define the allowable stress level, etc. Like this set of standards, makes the propotionality to products.  (230)

21.6 2018*08:00