Parameters for simulations

We will on this webpage describe how we classify cars and beams, and how these classifications provide the necessary parameters for computer-based simulations of a beam network. As of this writing, the text has not been completely worked out. This page will only deal with the FLYWAY® system. We have a page titled "Computer Simulation of the Network" for those who want more general information.		What do we want to do? Calculating guideway coordinates Parameters for beams Parameters for vehicles Parameters for berths Parameters for stations Parameters for beam supports Parameters for lifts Parameters for paths General parameters

Artfical nodes are used on this page as a way to split beam sections into smaller sections, for calculation purposes, the reason being that such a section has a varying nature along its way. One stretch might be straight, the next one curved or sloping, etc. Beam parts are the various parts that a beam consists of; sides, top, bottom, runways... Beam segments are the physical segments that are joined together at the construction site. Beam sections are the stretches of beams between two points designated as "nodes". A beam section can consist of several segments. Guideways are the assembled beams, laid out to guide the beamcar along its way. The word is here used to designate the path of the beams in the terrain, usually in a coordinate system, so that geographical position of the beams are known.

Nodes are logical points where beam sections come together. They can consist of many shunts. The term "node" is also used to specify the shunts themselves, as regards function. Thus, you can have a weaving node, where traffic from two beams merge into one beam. And you can have a divergence node, where traffic on one beam split into two. Physically, there is no difference in design. One type of node could thus be turned into the other type at different times, as the need arises. Paths are alternative ways to travel from one node to another. A path could consist of several beams that are mounted in parallel, if they are counted as belonging to the same route. Paths are logical creations, as opposed to beams. If beams with different characteristica are drawn in parallel between 2 nodes, they would therefore be counted as separate paths. Paths are one-way, while a beam could carry traffic in different directions at different times. There is good reason not to use the word "beam" for this. It could be that there is no path from one node to another, although there is a beam in place. Why? Because the beam only carries traffic in the opposite direction.

Path Table is a database for calculating the values that subsequently are entered into the Routing Table. Routes are used to designate alternative ways through a network from start to destination. Routes usually cover several nodes. Routing Table is a database of alternative routes from any pair of start- and destination points. These routes can cover several intermediate nodes. These routes are weighted and thus allows the vehicle to choose the "best" route. Shunts are the physical joining together of 3 beams in a Y-shaped fashion, forcing the beamcars to either choose a way to travel (left or right) or adapt its speed so that it can merge with traffic arriving on the other leg. There can be many shunts to a node. Berths are stop sites for beam cars. A berth can handle one car at a time. Stations are larger entities than berths. Although a station could consist of only one berth, it is usually an assembly of berths within a relatively small area.

We have detailed on another page how to go about making a computer simulation of a beamnetwork. This page concerns itself with the FLYWAY® system; what parameters are used, and what information we can get out of these parameters. Showing a nice reproduction on the computer monitor, with stations and moving cars, is only one way to produce visible results. More important are tables and curves showing how various inputs generate relevant outputs, such as operating costs, power requirements, etc. All these calculations are simulations, since they simulate a scenario that does or does not exist. So what do we want? We want: Above, you´ll find some definitions for the terminology we use on this page. We might not always be consistent in the use of these terms, partly because some definitions are of our own making and because this site has grown and changed during the years. But we have tried to use correct language on all pages.

A matrix, showing the transportation needs between all points in the proposed geographical area to be serviced A mathematical model of the intended beam network, with all stations, nodes, etc, that would indicate transport capacity between all nodes, bottlenecks and alternative routs between different points Total and incremental cost estimates for building and maintenance of whole and various parts of the network Total and incremental power consumptions for whole and part of the network, as traffic varies Anticipated passenger flows at various points at various times as result of different configurations Anticipated passenger flows as result of different pricing systems Anticipated passenger travel patterns as result of different system configurations Optimal beamcar sizes at different times of day and week Optimal beamcar sizes for various parts of the network Optimal capacities at different routes in the network relative to cost and anticipated revenues Anticipated freight as result of different pricing models Anticipated freight as result of different network configurations A visual, computer-generated model of the intended beam network, with all stations, nodes, etc. And other kinds of information....

Using XYZ-coordinates How would one go about simulating a desired network of beams? Well, one way would be to imagine a 3-dimensional cube that covers the area to be served. 3-dimensional, because the terrain usually undulates, and the beams have to adapt to that to some extent. Moreover, there might be sloping beams at stops, and so forth. To calculate coordinates and angular orientation of curved, constant-speed guideways in a series of segments, containing curves, slopes, off-line stations and straight runs, we will start at a given set of coordinates for X, Y, Z. The coordinate Z is of course the height above a "reference" ground. The sea-level could be a suitable reference, beacuse in other calculations, air density comes into play (Because it affects air resistance). Figure 2:1		Figure 2:2 The "artificial nodes" are used as an aid in calculating the charactersistics of different beamsegments, as explained further down.

Guideway Parameters XYZ-coordinates of node "2" distance in kilometers (D1 =xx; if coordinate distances and actual distances are kept as separate entities, the screen display could be made to better provide an overview of the network. I.e.long, empty stretches cold be compacted, crowded areas expanded for better view.) Capacity of the route (C1 = xx; This parameter reflects the capacity of the beam, based on its dimensions, i.e. how heavy vehicles it can carry. Several parallel beams, carrying traffic in the same direction, could here be counted as one.) Maximum allowable speed on this beam section (V=xx kilometers) is the section a straight run? (S = 1, otherwise 0) is the section a lateral curve to a new direction? (H= angle of curvature) is the section a lateral transition to a parallel path? (P=1).

does the section have an off-line station? (S-off = Number of stations) is there a need for stopping vehicles to slow down? (S1 = required speed when going through the shunt). do vehicles that pass by a station have to slow down to let departing cars out on the track? (S2 = required speed when going through the shunt) does the section have an on-line station? (S-on = Number of stations) is the section a continued curve with some parameters? (C = 1, with more parameters needed). is the section only available at certain times? (T = 1 for "available at the time of simulation", otherwise zero. Or one could note the time of day and day of week that the section is available. The reason for this limited availability could be that it is one-way in alternating directions at different times, or that work in the vicinity demands that the beam is taken out of traffic at certain hours).

As can be seen, a beam section that varies a lot might have to be sub-divided into smaller sections, separated by "artificial nodes". Having thus specified the character of the connection between nodes 1 and 2, using either of these two methods, one proceeds in the same manner with the connections from node 1 to node 3, from node 1 to node 4 and so on. When node 1 is all done, one proceeds to use node 2 as a starting point, and specifies the connection from node 2 to node 1. But this connection has already been specified, you say? Yes, but we must specify these connections in the direction of travel. If traffic from node 1 to node 3 is not allowed (as shown in figure 2:6), then that connection should be skipped, until the time comes to specify the connection from node 3 to node 1.

Using the The Azimuth angle Another way would be to use the azimuth angle. The azimuth angle is, in astronomy, the angle on the horizon, between due south and the point towards the western horizon where a straight line from zenith through a certain star hits the horizon, as illustrated here. Thus, the position of a star in heaven, at a certain time, could always be determined by the 2 angles: the azimuth the angular hight from that point on the horizon towards zenith. Figure 2:4 We could use the azimuth to provide the angle from the starting point of the beam section under consideration.

Figure 2:5 Generally speaking, all curved beams could be regarded as part of a circle, with a specific radius of curvature. We then need to determine the center of this imagined circle, the angle at the start of the segment and the angle at the end of the segment, counted from a reference point in the azimuth plane. The advantage of this method is that if we build this simulated network in real life, we will get beam sections with constant radiuses of curvature. This means that we could calculate with a certain speed and a certain acceleration for this section. Care must of course be taken that the beams are not joined in such a way so as to create sudden changes in this radius of curvature. Using this method, we would need som extra parameters in addition to those in the left column: For those interested in mathematics, the next page provides some insight into the calculations behind the assembly of a beam network.

is the section a change in grade? (G = degrees of climb (+) or slope (-)) is the section a vertical transition to a new level? (V = 1; this parameter could be used if there are a few fixed vertical levels) is the section a transition to a new direction? and a new level? (N = distance to the transition) is the section a change first in grade and then in azimuth? (GA = distance to the transition) is the section a change first in azimuth and then in grade? (AG = distance to the transition) is the section a transition from a curve? (D2 = distance to the transition). Figure 2:6 The page titled "Computer Simulation of the Network" gives further details about this work, and shows how we end up with a matrix-shaped database. From this database we can process the information we need, to have the matrix sow us the desired information.

The beams are welded together from standardized side- and top-parts, all with the same thickness. Ribs are added for strength at regular intervals, as are attachments for mounting the beams on supports. From the dimensions of these elements, the carrying strength of the resulting beam can be calculated. We have to calculate with 5 different kinds of beam elements: Straight and level Straight and sloping Curved and level Curved and sloping Shunts. Thus:		For all 5 categories, we have to specify: Width of beam (w; could be 50, 70, 80 or 90 cm.) Heigh of beam (h; could be 60, 90 or 110 cm.) Needed width of beam (W; this takes the ribs into account, and other additions, such as a walkway on top.) Needed heigh of beam (H; as can be seen from the illustration of the parts the outer height of the beam has to account for the assembly method, and for the ribs.) Needed horizontal space of beam (this refers to the width of the widest cars that could travel on this beam, and taking due consideration to the fact that the car might swing about a bit when going through curves.) For sloping beams, we have to specify the angle of inclination. For curved beams, we have to specify the angle of curvature. To some extent, this might also apply to the sloping beams, i.e. we have to specify the vertical angle of curvature, as sloping beam elements are joined to level elements.

The beam vehicles are classified, and these classes have of course individual attributes. Some attributes have default values (shown in parenthesis). For each such class, the following attributes have to be specified: Class of Vehicle Highest permissible speed with load (120 km./hour) Highest permissible speed empty (120 km./hour) Vehicle length, width & height Weight of empty vehicle Speed-independent road resistance coefficient (0.004) Speed-dependent road resistance coefficient (0.0003) Air-drag coefficient (0.33; depends on shape of cabin/flatcar/load) Door opening and closing time (3 seconds) Mean loading time (5 seconds) Variance in loading time (3 seconds) Maximum loading time (15 seconds) Minimum loading time (2 seconds). Dynamic classification of every trip (see the chapter about "Parameters for paths" below) Operational time before being due for checkup. topview and sideview showing a motorcar being secured on a flatcar.

Vehicle classes in FLYWAY Using this illustration as an example, one can see how the various models have a logical class number. These are: 1101 (PRT-car; takes 1 passenger) 1102 (PRT-car; takes 2 passengers) 1103 (PRT-car; takes 3 passengers) 2202 (PRT-car; takes 2 passengers) 2204 (PRT-car; takes 4 passengers) 2206 (PRT-car; takes 6 passengers) 2208 (PRT-car; takes 8 passengers) 2210 (PRT-car; takes 10 passengers) 3309 (PRT- or GRT-car; takes 9 passengers) 3315 (PRT- or GRT-car; takes 15 passengers) 3318 (PRT- or GRT-car; takes 18 passengers) 3321 (PRT- or GRT-car; takes 21 passengers) 3532 (GRT-car; takes 32 passengers) 4112 (for passengers & freight; takes 1 passenger) 5222 (for passengers & freight; takes 2 passengers) 5224 (for passengers & freight; takes 2 passengers) 5244 (for passengers & freight; takes 4 passengers) 5226 (for passengers & freight; takes 2 passengers) 5246 (for passengers & freight; takes 4 passengers) 6339 (for passengers & freight; takes 3 passengers) Flatcars (for freight and transportation of road vehicles; see illustration at left) Grappling hooks (for carrying containers) Roof attachments for adapted road vehicles)

Some common parameters Air density (0.076; used to calculate air resistance for travelling cars) Mean passenger weigh (75 kg) Variance in passenger weight (60) Air density is between 1.20 och 1.29 kg/m3, depending on pressure and temperature. p/Dens = R*T/M; Dens = p*M/(R*T) where p = pressure in N/m2 M = molecular weight = 29 kg/Kmol R = General gas constant = 8.314 J/mol*K If temperature T expressed in Kelvin = 273 (corresponding to 0o Celsius), Dens = 1.277.

The berths used by beamcars to load passengers and freight could be of 5 kinds: For passengers and freight; unprotected For passengers; protected by the FLYWAY cubicles For loading loose freight For loading containers (with grappling hooks) For loading road vehicles with roof attachments

The second kind; those berths that have cubicles for the protection of passengers, are classified according to this illustration: 1102 (for cars 1101 & 1102) 1103 (for car 1103) 2202 (for car 2202) 2204 (for car 2204) 2206 (for car 2206) 2208 (for car 2208) 2210 (for car 2210) 3309 (for car 3309) 3315 (for car 3315) 3318 (for car 3318) 3321 (for car 3321)

These classes of berths then have their attributes: Length of berth (number of vehicles that could dock at the same time.) Door arrangements Outer dimensions (Length, width & heigh) Roofs? (Yes/No/What kind) Extra equipment Actually, the first item is only a design feature. One could build cubicles that can dock seveveral cars behind each other, in order to save on space and wall material. But operationally, each place where one beamcar docks is considered as being one berth. This is because each such place is individually addressable and communicates directly with the beamcar which is using it.

The stations could have as many varied designs as there are stations in a network. It therefore would not make much sense, trying to sort stations into various classes. Instead, Each station would have its own list of attributes: Number of parallel beams Number of berths in a row for each beam Number of berths for different purposes Number of berths of different classes Total passenger handling capacity Total freight handling capacity Other characteristics.

The FLYWAY beam supports consist of standardized parts, as shown in these illustrations. It is anticipated that most supports will be beams, but some of these parts could be used for roof attachments (in tunnels and indoors) or wall attachments (to buildings). They have these characteristica: Vertical parts have a round cross-section Horisontal parts have a rectangular cross-section Most parts are hollow, in order to carry wires and cables They have standardized interfaces, A through D, as seen in the illustration at right. The parts consist of: part 1: The base, with the option of attaching a small passenger interface for ordering cars part 2: Extension elements of standardized lengths part 3: Horizontal elements of standardized lengths, depending on a) number of beams b) width of beams and cars part 4: Interface elements between horizontal and vertical elements. These come in 4 shapes, depending on use part 5: Extension elements of varying, customized lengths Footing for the poles. A standardized part, ususally set in reinforced concrete; this will depend on ground conditions. Some of these footings have to be hollow to allow for cables for communication and power supply. In addition to this, it is quite possible that "swan-necked" and other forms of supporting poles will be used.

The cabin lifts are unique for the FLYWAY system. The lifts would be divided into types, according to their attributes. Important attributes would be: Type designation Dimensions (width and lateral) Length (contracted) Length (when fully extended) Strength of lift engine Time to lower (to fully extended) Time to raise (from fully extended) What type of cabins it could be attached to Maximum lift capacity (i.e. allowable weight) Angle of maximum sideways swing (due to centrifugal force in curves) Angle of maximum rotational swivel (see below) Operational time before being due for checkup.	Figure 8:1	Figure 8:2

These are not defined yet. But a preliminary list (with default values in parenthesis) is: Number of vehicles Minimum headway Fraction of vehicles designed for wheelchairs (0) Fraction of vehicles passengers requiring wheelchairs (0).