As a rule, the simplest turnouts should be used to connect tracks. However, different operating conditions caused the network to railways turnouts appeared, differing in design and having different outlines in plan.

Available three main type of turnouts:

• single;
• double;
• cross.

1) Single turnouts connect two paths into one. They in turn are divided into:

• ordinary, in which one path is straight, and the second branches off to the right or left (right- or left-hand translation);
• symmetrical and asymmetrical - curvilinear.

2) are manufactured according to individual projects for connecting three paths into one in especially cramped places.

3) Cross turnouts are a combination of one right-hand and one left-hand translation.

Now let's take a closer look at each type of turnout.

(Fig. 1) are used when the side path deviates from the straight main path. Such switches, as a rule, are laid on the main and receiving-departure tracks and they are most widespread on the railway network (accounting for 95% of the total number of switches on station tracks of all categories);

Rice. 1 - Ordinary single turnout type P65, grade 1/11

Asymmetrical - curved turnout(Fig. 2) are used in cramped design conditions, when the deviation of two connected paths from the main rectilinear direction in one direction cannot be accomplished by ordinary translation, and can be one-sided or multi-sided;

Rice. 2 - Single asymmetrical turnouts: A- one-sided; b- versatile

(Fig. 3) are used when branching the main straight line into two, for example, on the territory of locomotive and carriage facilities, freight yards, as well as when designing marshalling yards. It is also possible to lay symmetrical turnouts during the reconstruction of stations in cramped areas, when it is necessary to reduce the neck of the receiving and departure yards as much as possible. The use of symmetrical transfers makes it possible to reduce the length of connections due to the fact that these transfers, due to the smaller angle of rotation on the conversion curve, can have, with the radius of the transfer curve of the same value as in a conventional transfer, a shorter length of this curve, a steeper cross mark and, as a result, less length. The length of the symmetrical translation is approximately 8-11 m shorter than the ordinary one;

Rice. 3 - Symmetrical turnout type P50 grade 1/6

Double symmetrical and asymmetrical turnout branches the main track into three directions and is used in particularly cramped areas of the station, when sequential laying of two ordinary transfers is impossible (Fig. 4);

Rice. 4 - Double turnouts: A- asymmetrical one-sided; b- asymmetrical versatile; V- symmetrical

Double cross translation(Fig. 5) makes it possible, when crossing paths, to move from one path to another in both directions of movement. It has eight points (1-8) and four crosses, of which two are sharp (9) and two are blunt (10). For each crossover, the rolling stock can follow six routes in two directions, since it replaces two ordinary turnouts (Fig. 6), laid opposite each other, but its length is significantly less than their total length. Cross switches shorten the length of the necks and reduce the number of curves with changing directions of curvature on the routes for receiving and departing trains. However, due to the complexity of the structures, they require more careful maintenance and limited speed. Such transfers are laid in cramped conditions on receiving-departure and other tracks, as well as when constructing straight passages crossing several tracks at large stations to shorten shunting movements. On lines where the non-stop passage of trains is envisaged, re-laying cross switches on the main tracks of stations is allowed only if this does not limit the established speeds.

Rice. 5 - Double cross switch

Rice. 6 - Possible intersection of two paths using two ordinary transfers

The individual ones discussed above types of turnouts may differ in the types of rails on the tracks connecting and adjacent to the transfer, P75, P65, P50 and P43 and brands of crosses 1/22, 1/18, 1/11, 1/9 and 1/6. The brands of crosses and types of switches on the main tracks are taken depending on the intended speeds of trains on the line.

Turnouts of grade 1/11 are laid: on passenger receiving and departure tracks; on main tracks where passenger trains can pass onto side tracks; on the main tracks when constructing dispatch ramps, as well as when constructing interchanges for the routes of freight and passenger trains at approaches to junctions.

Turnouts of grade 1/9 are laid: on the main tracks, if the movement of passenger trains on such switches passes only in a straight direction; on receiving and departure tracks for freight traffic.

1/8 grade turnouts are used on other station tracks.

Symmetrical 1/6 grade turnouts can be installed on other station tracks. They are most widely used in the design of marshalling yards and should be more widely used on the territory of locomotive, carriage and other facilities. These turnouts can also be used on receiving and departing tracks for freight traffic.

Symmetrical turnouts of grade 1/4.5 are used on other station tracks in especially cramped conditions, for example, when entering tracks into industrial buildings and warehouses.

For non-stop movement of trains along side tracks, flat switches are designed on the lines. In the Russian Federation, grade 1/18 is adopted, at which the speed of movement on the side track is allowed up to 80 km/h, and grade 1/22 with a permissible speed of no more than 120 km/h. When driving on a straight track at speeds above 120 km/h, switches of grade 1/11 of a special design are used. (for more details, see the PTE)

Turnouts on the main tracks of stations, sidings and passing points must match the type of rails on adjacent tracks and allow trains to travel in a straight direction at the same speed as on adjacent sections. On other tracks, the switch, crosspiece, connecting tracks between them and one rail link on both sides of the transfer must be of the same type. The rails adjacent to the new turnouts must also be new and of the same type, and the rails adjacent to the old turnouts being laid must be old ones of the same type and with the same wear.

When using electric traction, automatic blocking or electrical centralization, the metal elements of turnouts must be isolated from the under-rail and under-rail base. Wooden transfer beams, for example, are impregnated with non-conductive oil antiseptics, and electrically insulating gaskets are placed between reinforced concrete slabs or beams and rails. The ballast layer under the switches must be crushed stone or asbestos with the necessary drainage.

| Computer Science and Information and Communication Technologies | Lesson planning and lesson materials | 10th grade | Planning lessons for the academic year (FSES) | Converting numbers from one positional number system to another

Lesson 13
§11.1-11.4. Converting numbers from one positional number system to another

11.1. Converting an integer decimal number to a number system with base q

To convert an integer decimal number to a number system with base q:

1) successively divide the given number and the resulting integer quotients by the base of the new number system until a quotient equal to zero is obtained;
2) the resulting balances, which are the digits of the number in new system numbers, bring them into line with the alphabet of the new number system;
3) compose a number in the new number system, writing it down starting from the last remainder.

Let's look at examples of converting integer decimal numbers into 2-ary, octal and hexadecimal number systems.

Example 1.

Example 2.

Example 3.

Example 4. Separated by commas, in ascending order, indicate all bases of number systems in which the decimal number 22 ends in 4.

Since writing a number in a number system with a base q ends in 4, the remainder when dividing 22 by q is 4: 22 mod q = 4 1) . Therefore, 18 mod q = 0. This is true for q ∈ (18, 9, 6, 3, 2, 1).

1) The mod operation is the calculation of the remainder of an integer division.

Since in the new number system the number ends in 4, then q > 4. Consequently, the conditions of the problem are satisfied by the bases: 18, 9 and 6.

With this online calculator You can convert whole and fractional numbers from one number system to another. A detailed solution with explanations is given. To translate, enter the original number, set the base of the number system of the source number, set the base of the number system into which you want to convert the number and click on the "Translate" button. See the theoretical part and numerical examples below.

The result has already been received!

Converting integers and fractions from one number system to any other - theory, examples and solutions

There are positional and non-positional number systems. The Arabic number system, which we use in everyday life, is positional, but the Roman number system is not. In positional number systems, the position of a number uniquely determines the magnitude of the number. Let's consider this using the example of the number 6372 in the decimal number system. Let's number this number from right to left starting from zero:

Then the number 6372 can be represented as follows:

6372=6000+300+70+2 =6·10 3 +3·10 2 +7·10 1 +2·10 0 .

The number 10 determines the number system (in this case it is 10). The values ​​of the position of a given number are taken as powers.

Consider the real decimal number 1287.923. Let's number it starting from zero position of the number from the decimal point to the left and right:

Then the number 1287.923 can be represented as:

1287.923 =1000+200+80 +7+0.9+0.02+0.003 = 1·10 3 +2·10 2 +8·10 1 +7·10 0 +9·10 -1 +2·10 -2 +3· 10 -3.

IN general case the formula can be represented as follows:

C n s n +C n-1 · s n-1 +...+C 1 · s 1 +C 0 ·s 0 +D -1 ·s -1 +D -2 ·s -2 +...+D -k ·s -k

where C n is an integer in position n, D -k - fractional number in position (-k), s- number system.

A few words about number systems. A number in the decimal number system consists of many digits (0,1,2,3,4,5,6,7,8,9), in the octal number system it consists of many digits (0,1, 2,3,4,5,6,7), in the binary number system - from a set of digits (0,1), in the hexadecimal number system - from a set of digits (0,1,2,3,4,5,6, 7,8,9,A,B,C,D,E,F), where A,B,C,D,E,F correspond to the numbers 10,11,12,13,14,15. In the table Tab.1 numbers are presented in different systems Reckoning

Table 1
Notation
10	2	8	16
0	0	0	0
1	1	1	1
2	10	2	2
3	11	3	3
4	100	4	4
5	101	5	5
6	110	6	6
7	111	7	7
8	1000	10	8
9	1001	11	9
10	1010	12	A
11	1011	13	B
12	1100	14	C
13	1101	15	D
14	1110	16	E
15	1111	17	F

Converting numbers from one number system to another

To convert numbers from one number system to another, the easiest way is to first convert the number to the decimal number system, and then convert from the decimal number system to the required number system.

Converting numbers from any number system to the decimal number system

Using formula (1), you can convert numbers from any number system to the decimal number system.

Example 1. Convert the number 1011101.001 from binary number system (SS) to decimal SS. Solution:

1 ·2 6 +0 ·2 5 + 1 ·2 4 + 1 ·2 3 + 1 ·2 2 + 0 ·2 1 + 1 ·2 0 + 0 ·2 -1 + 0 ·2 -2 + 1 ·2 -3 =64+16+8+4+1+1/8=93.125

Example2. Convert the number 1011101.001 from octal number system (SS) to decimal SS. Solution:

Example 3 . Convert the number AB572.CDF from hexadecimal number system to decimal SS. Solution:

Here A-replaced by 10, B- at 11, C- at 12, F- by 15.

Converting numbers from the decimal number system to another number system

To convert numbers from the decimal number system to another number system, you need to convert the integer part of the number and the fractional part of the number separately.

The integer part of a number is converted from decimal SS to another number system by sequentially dividing the integer part of the number by the base of the number system (for binary SS - by 2, for 8-ary SS - by 8, for 16-ary SS - by 16, etc. ) until a whole residue is obtained, less than the base CC.

Example 4 . Let's convert the number 159 from decimal SS to binary SS:

159	2
158	79	2
1	78	39	2
	1	38	19	2
		1	18	9	2
			1	8	4	2
				1	4	2	2
					0	2	1
						0

As can be seen from Fig. 1, the number 159 when divided by 2 gives the quotient 79 and remainder 1. Further, the number 79 when divided by 2 gives the quotient 39 and remainder 1, etc. As a result, constructing a number from division remainders (from right to left), we obtain a number in binary SS: 10011111 . Therefore we can write:

159 10 =10011111 2 .

Example 5 . Let's convert the number 615 from decimal SS to octal SS.

615	8
608	76	8
7	72	9	8
	4	8	1
		1

When converting a number from a decimal SS to an octal SS, you need to sequentially divide the number by 8 until you get an integer remainder less than 8. As a result, constructing a number from division remainders (from right to left) we get a number in an octal SS: 1147 (See Fig. 2). Therefore we can write:

615 10 =1147 8 .

Example 6 . Let's convert the number 19673 from the decimal number system to hexadecimal SS.

19673	16
19664	1229	16
9	1216	76	16
	13	64	4
		12

As can be seen from Figure 3, by successively dividing the number 19673 by 16, the remainders are 4, 12, 13, 9. In the hexadecimal number system, the number 12 corresponds to C, the number 13 to D. Therefore, our hexadecimal number is 4CD9.

To convert regular decimal fractions (a real number with a zero integer part) into a number system with base s, it is necessary to successively multiply this number by s until the fractional part contains a pure zero, or we obtain the required number of digits. If, during multiplication, a number with an integer part other than zero is obtained, then this integer part is not taken into account (they are sequentially included in the result).

Let's look at the above with examples.

Example 7 . Let's convert the number 0.214 from the decimal number system to binary SS.

		0.214
	x	2
0		0.428
	x	2
0		0.856
	x	2
1		0.712
	x	2
1		0.424
	x	2
0		0.848
	x	2
1		0.696
	x	2
1		0.392

As can be seen from Fig. 4, the number 0.214 is sequentially multiplied by 2. If the result of multiplication is a number with an integer part other than zero, then the integer part is written separately (to the left of the number), and the number is written with a zero integer part. If the multiplication results in a number with a zero integer part, then a zero is written to the left of it. The multiplication process continues until the fractional part reaches a pure zero or we obtain the required number of digits. Writing bold numbers (Fig. 4) from top to bottom we get the required number in the binary number system: 0. 0011011 .

Therefore we can write:

0.214 10 =0.0011011 2 .

Example 8 . Let's convert the number 0.125 from the decimal number system to binary SS.

		0.125
	x	2
0		0.25
	x	2
0		0.5
	x	2
1		0.0

To convert the number 0.125 from decimal SS to binary, this number is sequentially multiplied by 2. In the third stage, the result is 0. Consequently, the following result is obtained:

0.125 10 =0.001 2 .

Example 9 . Let's convert the number 0.214 from the decimal number system to hexadecimal SS.

		0.214
	x	16
3		0.424
	x	16
6		0.784
	x	16
12		0.544
	x	16
8		0.704
	x	16
11		0.264
	x	16
4		0.224

Following examples 4 and 5, we get the numbers 3, 6, 12, 8, 11, 4. But in hexadecimal SS, the numbers 12 and 11 correspond to the numbers C and B. Therefore, we have:

0.214 10 =0.36C8B4 16 .

Example 10 . Let's convert the number 0.512 from the decimal number system to octal SS.

		0.512
	x	8
4		0.096
	x	8
0		0.768
	x	8
6		0.144
	x	8
1		0.152
	x	8
1		0.216
	x	8
1		0.728

Got:

0.512 10 =0.406111 8 .

Example 11 . Let's convert the number 159.125 from the decimal number system to binary SS. To do this, we translate separately the integer part of the number (Example 4) and the fractional part of the number (Example 8). Further combining these results we get:

159.125 10 =10011111.001 2 .

Example 12 . Let's convert the number 19673.214 from the decimal number system to hexadecimal SS. To do this, we translate separately the integer part of the number (Example 6) and the fractional part of the number (Example 9). Further, combining these results we obtain.

On the basis of a welded crosspiece P65 grade 1/11 with welded rail ends, a turnout type P65 grade 1/11 for grade 1-2 tracks, project 2750, on reinforced concrete beams, was created and has been mass-produced since 1997. In these translations, an elastic rail fastening was introduced, which provides a constant force for fastening the sole to the lining, eliminating the hijacking of the rail from the interaction of load and temperature, reducing the cost of current track maintenance by eliminating the work of tightening the terminal bolts during operation.

The switch is made with flexible points that increase the operational durability and reliability of the switch by at least 10% compared to manufactured switches with insert-on-plate fastening, primarily in conditions of high train speeds and heavy traffic areas.

An anti-theft device, consisting of an anti-theft stop and an anti-theft lining, eliminates theft of the wit in the longitudinal direction in relation to the frame rail.

Pads with high flanges maintain a constant rail track width within the entire turnout; dampen longitudinal loads; provide enhanced fastening of rail elements to the base.

Rubber-cord gaskets between the rail sole and the lining eliminate the rigid connection between the rail and the front beam due to the inclusion of an elastic element, which ensures uniform elasticity along the entire length of the switch, weakens the transmission of vibrations that cause destruction from the rails through fastenings and transfer beams to the ballast. Shims with welded pads instead of riveted ones make it possible to eliminate the defect associated with the weakening of the rivets of the arrow pads.

The service life of the turnout is increased due to the use of hardening of rail parts with high frequency currents. Welding of the blades with the adjacent rail is carried out at the factory using the electric contact method.

A crosspiece with welded rail ends makes it possible to improve and strengthen the track structure by 1.5 times, increase service life by 15-20%, eliminate steps when joining high-manganese steel cores with an adjacent rail, and reduce ongoing maintenance costs.

A counter rail that is not connected to the track rail increases service life, as it is made of stronger rolled steel, and also reduces the time for routine maintenance of the counter rail (due to quick adjustment of the grooves using a set of compensating plates supplied by the factory).

The use of insulating joints of the "APATEK" type increases the reliability and service life, has higher insulating properties (compared to conventional iso-joints), and also reduces the cost of ongoing maintenance (excludes the replacement of worn-out insulating gaskets during the operation of a conventional iso-joint).

Characteristics of the main technological equipment

Since the laying and changing of turnouts with a reinforced concrete base is most often carried out by track laying machines UK-25, and on electrified lines it is advisable to lay turnouts with a reinforced concrete base using track laying cranes UK-25, then we accept this crane as the main technological equipment, i.e. UK-25/9-18 SP. Let's look at its design and technical characteristics.

The laying crane UK-25/9-18 of the V. I. Platov system (Fig. 4.1) consists of a self-propelled motor platform with two special portal frames on which the boom is mounted 12 With lifting equipment.

Fig.4.1. Laying crane UK 25/9-18:

1 - three-axle traction trolley; 2 - frame; 3 - power plant; 4 - platform control panel; 5 - control cabin; 6 - electrical equipment of the platform; 7 ,1 3 ,15 - winches; 8 - cargo traverse; 9 - cargo trolley; 10 ,11 - blocks; 12 - arrow; 14 - remote controller; 16 - middle transverse beam; 17 - load limiter; 18 - folding beams; 19 - portal carriage; 20 - boom lift hydraulic cylinders; 21 - portal stand; 22 - fencing; 23 - roller conveyor; 24 - electrical equipment on the boom

The motor platform MTD is designed for hauling packages of track grating links from the supply train to the track-laying crane during track laying, and when dismantling the track - for moving packages of links to the train platforms on rollers and for shunting work during track laying. The crane platform has two 1D6 diesel engines, two generators and four DK-305A traction motors, each of which drives one wheel pair, so in four-axle cranes and motor platforms all axles are driven. The traction motors are mounted on the frame of the undercarriage and drive rotation of the wheelset by means of a cardan shaft, gearbox and gear wheel rigidly fixed to the axis of the wheelset.

The UK 25/9 tracklayer consists of a frame, two three-axle bogies, a power unit, a boom, crane mechanisms, winches for hauling packages, braking equipment and two control cabins.

The crane boom is raised into working position by hydraulic cylinders mounted on four telescopic legs of the crane platform. In the working position, the crane boom extends cantilever forward in one direction or another. The crane mechanisms are controlled from the upper cabin, and the movement of the crane and platform mechanisms are controlled from the lower cabin. Diesel generator sets, traction engines and electric winches are controlled from one of the consoles located in the middle part of the platform on both sides. Each console has an instrument panel and brackets on which a removable mechanic's cabin is suspended.

In UK-25 tracklayers, the portal frame racks are sliding. In the transport position, the truss is lowered and the crane fits into the dimensions of the rolling stock. In the working position, the frame racks move apart and rise to the required working height. In electrified areas, due to the overhead wire, the lifting height of the truss is limited. The racks are moved apart by hydraulic cylinders. In UK-25 the truss can move along its axis. In the transport position it is located symmetrically relative to the portal frames, and in the working position it moves towards the stacking side.

The mechanism for lifting the track structure link is a double-drum cargo winch. The mechanism for moving the link along the crane boom consists of a double-drum traction winch and crane trolleys moving on road rollers. When the drums rotate in any direction, the cable is wound from one drum and wound onto the other. The direction of movement of crane trolleys is changed by changing the direction of rotation of the drums. A limit switch is installed at the end of the truss, which breaks the power supply circuit of the traction winch electric motor when the crane trolley is pressed on it and stops the movement of the latter.