It is dangerous to be sincere, unless you are also stupid!(George Bernard Shaw, 1856-1950)

he beams are the arteries of the system, in a manner of speaking. They have a rectangular crossection and are hollow. Their interior floors are used as roadbeds for the propulsion vehicles that are travelling inside the beams. One could use 2 or 3 sizes of beams for carrying the traffic, depending on the size of the largest and heaviest cars that are supposed to travel on them. Or rather, since, in general, most beams are meant to carry varying sizes of beamcars, the beams will have to be sized according to the weight of the heaviest load that each beam segment will be subjected to. We realize, of course, that there are as many solutions to beam design and function as there are imaginative inventors. This webpage reflect the thoughts of us at SwedeTrack, but it certainly is not the "Gospel according to SwedeTrack". We have had many fruitful discussions with other developers.	This is a rather technical page. We will deal with:	General considerations The sensors in the beams Dimensioning the beams The theory behind the dimensioning of beams The extra load of elevating the cars Joining the beams; the inflexion points What are those ribs for? Calculating the bending radius Camber The need for Active Suspension Sloping beams and shunts are dealt with on other webpages. The special considerations pertaining to the FLYWAY® system are also dealt with on a separate page.

he dimensions on the first 2 lines for the so-called b-beam agrees with those of SIPEM's in Dortmund, Germany. The SIPEM-beam is dimensioned for 11-ton-cars, and since the SwedeTrack cars will be much lighter, this would allow for more than 1 car between the poles at any one moment. In a big network, it is reasonable to expect tempory queues of cars at rare intervals. One can always use other criteria to dimension the beams, but it is more convenient, considering the standardized width of propulsion cars, to only vary the height of the beams to accomodate various loads.	Figure 1:1	To be reasonably compatible with FLYWAY®, the beams should contain: Runway for the propulsion cars (R in figure 1:1), or a suitable MagLev arrangement Conductor rails for power supply to the cars (P in the figure). In the vicinity of the shunts, these conductors would be on both sides of the runway 3 kinds of sensors to aid passing cars Power cords to supply regular power to lighting on the poles and the like (Pw) An optional wave guide in the ceiling for communication between node computers and beamcars (W) Digital communications media of some kind (fiber?) for communication between central, regional and node computers (C)

Suitable construction materials he debate about the best material to be used in beams and supports is still going on. This is excerpts from Eunitrans-discussions. The main criterias are, of course: Strength Durability Price Ease of manufacture. With the present labour costs it is not economical to produce welded steel in the western countries. The price of manufactured beams would be about US $ 6 per kilo in the US and Norway and US $ 2.5 in Poland and even less in countries like China. To keep production in the high labor cost countries, the manufacturing process would have to be highly automated. Generally speaking, the difference in raw material cost does not matter at all. Labor is what costs. The raw material cost of steel is perhaps one percent of the total system and can almost be ignored as such. Pressed aluminum might be an alternative in the future due partly to the capital intensity in production. Aluminum beams of the same strength as steel are slightly more expensive than welded steel beams, but this is compensated for the first time one does not have to maintain the guideway. And there is no downtime for maintenance, which is critical in transport hubs. The manufacture of pressed or "extruded" alumuminium saves a lot of labor compared with welded steel. An alu beam will weigh half of a steel beam with the same strength, but alu is 3 times costlier as material. Thus, one ends up with some 10-20 % more costly alu beams. But they are much cheaper regarding maintenance, so the end long term result is that alu would be cheaper. Experts on materials at the Norwegian Technical University in Trondheim recommend that far more attention should be spent into using more expensive materials like composites in the vehicles, since some 85 % of the weight carried by the beams would on average be due to the weight of the vehicles and not the people inside. On the other hand, when reflecting over the arguments that labour counts, not raw materials - then that argument diminishes a bit, though it still remains as important for energy usage.

Since steel is dead cheap, the cost of more steel is not the problem per se. However, weight as such is a problem since foundations must be more solid. Transport also would be more costly. But again you have the maintenance factor and in the very long run, aluminum wins. However, "in the long run we all are dead" meaning you have to sell the product first, and caring how long something will last has a limit for the buyer, when he considers the far more immediate investment cost. It is difficult to say in general what is cheapest when all factors are taken into consideration. "It all depends" as usual. Zinced steel doesn't need any maintenance. Welding of guideway sections must be automated. One can buy ready sections of guideway in countries where labor cost is low. Motorcars are often zinced, and that does not stop them from rusting. It only postpones the problem, like an efficient paint. Steel eventually rusts and have a costly downtime period during maintenance. One has to evaluate the cost of automated welded and zinced steel against extruded aluminum. It seems that the winner in the long run would be aluminum, or possibly magnesium, but a buyer may have a shorter time-horizon and that gives steel an opening. Some observations: There is no bridge (even footbridge) in the world with aluminum longitudinal beams. At the best handrail or flooring are made of aluminum. In Sydney (Australia) many masts of the railway electric contact network are double tee steel zinced beams. They are not painted! The city is situated on a coast of the Pacific ocean, and rains can last weeks here. The railway was constructed right after the Second World War. There were not the slightest signs of rust on these masts till now! Aluminum "Audi" is very expensive. It is meaningful to make the body of plastic on a steel frame, like in some cheap cars. The probability of collisions of PRT vehicles is very small. Besides, lateral collisions are impossible, and hydraulic bumper take up all impact. It is not known how long aluminum can withstand sign-variable bending loadings. There is a weariness of metal, and only static calculations were carried out (if any). The limits of elasticity are important, as long as plastic deformations do not appear. In this respect steel is excellent material.

Thickness of the cars’ steel sheet is many times less than thickness of steel beams of guideway. The steel beams will not rust significantly for a hundred years. Pure magnesium corrodes quickly. It is very fragile. It may burn on air at the high temperatures necessary for extrusion. Guideways can be covered with casing (for example, strong water-proof fabric covered with aluminum powder) which protects steel beams from precipitations. Consumption of aluminum in China increases much faster than manufacture of aluminum in China. China will become a net importer of aluminum soon. Zinc not only isolates steel from precipitations and oxygen, but also stops corrosion of steel due to arising difference of electric potentials. The combination of cable-stayed structure and longitudinal double tee steel zinced beams (which are rails also) is extremely cheap. There is no toilful welding. This structure is very lightweight. To extrude the aluminum beams on site is perhaps a good thing and would save some transport costs for big clumsy beams. However, a downside may be that more of the finished product must be made on site and not as prefabricated modules. This may have negative effect on economics of scale regarding the other elements that go into the guideway. It seems like: On the financial side, efforts must be focused on the downwriting conditions. On the socio-economic side, efforts must be made to gain a high traffic density and a high fare. On the technical side, every effort must be made to lower vehicle costs. Other factors to consider: The stiffness to weight ratio of steel, aluminium, magnesium and concrete is about the same, so to achieve a particular limit of bending with the same external cross section, you will need more of the lighter materials in inverse proportion to their weight. I think concrete will win in terms of stiffness per US $. Aluminium has just over twice the thermal expansion of steel and concrete, meaning that more expansion joints will needed. Steel will be cheap if it is in standard rolled sections such as "I" beams or tube.

s stated in the listing above, a beam network which is to be scalable and complex needs at least 3 kinds of electronic sensors inside the beams. They would communicate with passing propulsion cars and exchange relevant information. This would serve 3 different purposes:	Figure 2:1

One group of sensors would be placed at strategic points and at regular intervals along the beams, to enable the nodes to keep track of the vehicles that move in their respective areas. These sensors will note time, speed, travelling direction and identity of every passing car, and report this to the node in charge (To be more precise, the node computer will put a time stamp on the report when it arrives, and then it will be logged in the node with that time). This would serve 2 important purposes: to quickly localize a faulty vehicle, so that other vehicles may be warned and so that rescue vehicles could be directed to the right place, if needed to serve as booking points in the point-synchronous network, for vehicles approaching a weaving node. Read more at "Emergency breaking". The second group of sensors are for vehicles looking for their berths of destination. There would be one sensor above every berth, to tell the car when it is in exactly the right position to lower the lift, as indicated by the blue dots in the illustration above (figure 2:1). Also, the buffering areas, where the cars are parked in wait for assignments, need sensors (B in the figure) to tell them when they have arrived. These sensors all need addresses, as explained elsewhere. In addition, these sensors need to be complemented by "alert sensors", indirectly telling the car how far it is to the berth of destination, so that the car wonīt overshoot the berth. One such sensor would be sufficient for a station area, as indicated by A in figure 2:1 above. Since the car need to be able to identify these "alert sensors", they need addresses as well. You can read more about this on the webpage "Berthing at a stop". The third kind of sensor is needed at every single shunt to tell the car when itīs time to shunt. The other illustration above (figure 2:2) gives an idea how a beamcarīs positioning above a berth would be facilitated with the aid of a sensor. The sensors transmit carrier waves in the microwave-range. These would both serve to transmit data and function as radar. The range is very short, about 10-15 yards, as these waves are quickly attenuated as a function of the square of the distance from the transmitter. When a car approaches, it will be detected by this radar, and the sensor would identify itself and send a "who-are-you?" request. The car would identify itself. This identification of the car is not necessary if this is a sensor above a berth, but if it is the first kind of sensor among those listed above, this beamcar-identity would be relayed to the local node. However, the car has 2 transponders, one at each end of the propulsion car. As the car nears the sensor, those transponders will register a gradually stronger signal from the sensor. As the car slowly passes the sensor, the fore transponder will register a weaker signal, while the aft transponder will still register increasing signal strength. When both transponders get the same signal strength from the sensor, the car is in the right position.

Figure 2:2 Techniques for deciding the position of moving objects is coming into use more and more. The best-known system is the GPS, which is short for Global Positioning System. It has been created by the US Military and consists of 26 satellites that orbit the Earth in such a way that they are reasonably evenly distributed at any single moment. If the GPS-receiver can receive the signal from at least 3 of these satellites, it can use a mathematical technique known as triangulation to determine its position on Earth. Each satellite transmits its location, i.e. longitude and latitude for the place it happens to be above at the moment. The receiver detects the angles between the three signals, and the rest is mathematics. Aircrafts, detecting the signals from 4 satellites, can also use these signals to determine their altitudes. Vertical measurements can also be incredibly exact; in November 1999, the correct altitude of Mount Everest was put to 8850 meters above sea level, 2 meters higher than previously determined. (This does not necessarily mean that previous measurements were less exact, though. The Himalayas are still rising.) The US Military have introduced disturbances to the signals that makes it hard to determine the position of an object with any better precision than 100 meters. For that reason, EU has decided to introduce its own positioning system, called Galileo. This should be available by the year 2008. In the meantime, the GPS-system is complemented by a groundbased system called DGPS, which enhance the precision by very nearly compensate for the built-in error. In this system, the base stations help the mobile unit to decide which satellites to tune in to, instead of the mobile unit having to check all available satellite signals and decide for itself which signals are the strongest. This saves time and power for the mobile unit. The established GPS-system is not usable for positioning beam-vehicles, mainly because: Itīs not accurate enough Itīs not available in tunnels. But the technology as such could very well be applied to the beam traffic system. In this case the satellites would be replaced by ground-positioned transmitters.

It can rather easily be calculated how the dimensions and the thickness of a hollow, rectangular profile influences its ability to withstand sideways strain. Using Wy as a symbol for the profileīs ability to withstand vertical bending, and the proportional measurements from the figure at right, we get: Wy = (B*H3 - b*h3) / 6*H. The amount of material required for the profile is of course proportional to its dimensions and its thickness. Using M for the amount of material per unit length, we get:	M = BH - bh. One can thus see that increasing H-h at the expense of B-b leads to the most vertical-bending-resistant beam for a given beam-mass. For a solid beam the bending resistance Ws = B*H2/6 which means that Ws = M*H/6 = M2/6*B. In other words, for a given mass per unit length, the H/B ratio of the beam should be as large as practicable. Intuitively, one realizes that this applies to the (H-h)/(B-b) ratio as well.	Figure 3:1

e naturally want the beams to be as light and slim as possible, while still performing their function satisfactorily. We can identify five factors that are relevant for this aim: Make the beam higher, at the expense of its width. Decrease distances between support points. Distribute the traffic load over more, but lighter, vehicles. Join the beams at the inflexion points instead of at the supports. Provide "active suspension" for the vehicles so that they wonīt be bothered by the beamsī downward bending between support points. The primary factor limiting the beamīs dimensions is not that it will break but that it will bend. When a beam is loaded down by its own weight and the weight of passing vehicles it will in fact hang down somewhat, like a clothesline hanging between two trees. In the case of the beam, you should not be able to see this downbending - but it is there. And it will be felt by the travellers, unless some cushioning is built into the beamcars. This bending of the beams causes the vehicle to go up and down during travel, like in a ski lift. At high speeds, this makes the ride uncomfortable for passengers. The faster you go, the worse it will feel, and therefore the straighter the beam must stay, as the beamcars pass by. How much the beam will bend under load depends on how elastic the beam material is, and that elasticity is inversely proportional to the E-module of the material in the beam. When a vertical force Fy is applied to a horizantal beam with cross-sectional area A and lenght l, the downhang in the middle between the supports is Dl = l * Fy / E * A where E is a material-dependent constant called the elasticity module, or E-module for short. Steel has an E-module of 200 GN/m2, whereas unallyoed aluminum is weaker with 70 GN/m2. Thus, steel is more suitable than aluminum from this point of view, as it is almost 3 times as strong. Plastic has an E-module which is about one tenth of steel. Arming the plastic with fibers will however significantly increase the E-module. Figure 4:1. Figure 4:1 shows, in our case quite exaggeratedly, the forces at play. The upper picture shows the downhang when beams are joined at the inflexion points and the lower picture the 5 times increased downhang when joining the beams on top of the supports. l = span in meters between supports (in our example 30 meters) Q = Total distributed load in N (N = Newton; we assume here an even load distrbution along the beam segment) E = Modulus of Elasticity (in our case 206 GPa) I = Moment of Inertia Another important factor is the geometric resistance to bending of the beam. Assuming that: the cross section area of the "roof" of the beam is the same as the "floor" (i.e. the sidewalls are parallel to each other and roof and floor have the same thickness) the sidewalls in the beam are strong enough to keep the roof and floor separated, the beam walls are thin, and that the sides of the beam contribute very little to the beamīs stiffness, a simplified formula for the resistance to bending could be written: Ix = 2 * B * S * (H/2)2 = B * S * H2/2, where Ix is the moment of inertia. It has the dimension m4, and is defined as the square of the distance from the elastic bending line (measured from the centre of the beam) multplied with each area element of the beam that opposes the bending force, illustrated in figure 4:2 below B is the width of the beam, S is the total thickness of the floor and roof (i.e. (H - h)/2) and H is the vertical distance between the floor and roof.

Figure 4:2 Ix = the sum of all dA * y2 if S is much smaller than H, then Ix = 2 * S * B (H/2)2 A rectangular beam which is 1 meter high and 1 meter broad made of 2 cm. thick steel will have a resistance for bending of about 1* 0.02 * 1/2 or 0.01 m4. If you choose to make the beam 0.5 m high and 2 m broad from the same material, it would have a resistance to bending of about 2* 0.02* 0.25/2 = 0.0025 cm4 or one fourth of the beam in the first example. Both beams would weigh the same per meter length. Clearly, it is essential to make the beamsī vertical dimension as big as practícable. When a beam is erected between two vertical supports and uniformly loaded, it will flex down between these supports with a vertical distance of Dl = 5 * Q * L3/(384 * E * I). As an example, let us assume a load of 20 tons or 200 kN (= kiloNewton; Newton is kilos * 9.81 at sea level, or roughly 10) and that the distance between the two beam supports is 30 meters. Assume Ix = 0.02 m4 and that the E-module is 200 GN/m2. At the middle between the two supports the beam would then flex down: Dl = 5 * 200 000 * 30 * 30 * 30 / (384 * 200 000 000 000 * 0.02) = 0.017 of a meter, or 17 mm. Figure 4:3 At a low velocity this will clearly not be felt at all. Even when travelling at 30 m/s or 108 km/h the up-down acceleration will be 0.014 m2/s which is neglible compared to the gravitational constant 9.81 m/s2. We could thus make a weaker beam in this case. This is a very simplified way to look at the problem, though. When taking vibrations, wind induced loads etc into account the picture gets much more complex. However, the basic facts remain, for instance that a high beam is stronger (relative to the amount of material used) than a broad one. Figure 4:4 In order to set a standard, it might be best to adopt the present interior measures of the Sipem beam in Dortmund (about 1.1 m high and 0.8 m wide). Or, in order to standardize production, one could use the dimensions of 0.8 * 0.8 meters for the smallest vehicles. As heavier vehicles and/or longer spans are required, extra heights could be successively added as reinforcements, as shown in figure 4:4 above. In conjunction with adding these reinforcements, the polesī upper parts could be raised correspondingly by adding prefabricated vertical extensions to them, above the beams. Using this method, the bottom of the beam would have to be strong enough from the beginning to handle the heaviest vehicles, as indicated by R in figure 4:4.

5. The Extra Load of Elevating the Cars

Figure 5:1

hose readers that are familiar with mechanics realize that there will be en extra, momentary downward strain upon the beams when the lowered cabins have to be elevated from the ground up to the beams to continue their journey. As shown in figure 5:2, the weight of the car when it leaves the ground (orange arrow) is transferred to the beam (yellow arrow) as a downward pull. In addition to this, there is an extra downward strain on the beam, proportional to the acceleration of this lifting process. One can see in the illustration the advantage of putting a support at precisely this place (as in B) rather than far away from a beam support (as in A). The acceleration component of this strain is, however, not as big as one might think. The downward pull (F) is proportional to the applied upward acceleration of the car, according to the formula F = m*a where m is the mass of the cabin (including its load) and a is the acceleration. As an example, let us assume that:

Figure 5:2 the cabin has to lifted 5 meters It is accelerated for 2.5 m, and then decelerated the acceleration takes 2 seconds To this we will apply the formula: x = 0.5*a*t2 meter,

where x is the lifting height (in meters) and t is the time (in seconds). Using our figures, we get: 2.5 = 0.5*a*2*2 = 2*a, which makes a = 1.25 m/s2. In the first formula, F = m*a, a is normally put to 9.81 m/s2 for an object at rest. This is the Earthīs acceleration at sea level. So, comparing "our" acceleration to that of the Earth, we get 1.25/9.81 = 0.127. This means that lifting the cabin from the ground up to underneath the beam using these figures, will add about 12 - 13 % of the cabins weight to the strain that the beam must carry. This added strain is rather marginal. The beam segments are only joined at the poles, and thus cannot all have standardized lengths. There are 2 ways of joining beams that are most common: On the pole (A in figure 5:1 below) At the inflexion points on each side of the pole (B in figure 5:1).

etīs hang a string of boiled spaghetti on 2 supports, as shown in Figure 6:1. If itīs cooked "al dente" it should have some stiffness left (every cook knows that spaghetti should not be boiled too long!). Using the x-y coordinate system, we can discribe the curvature of the spaghetti as y being a function of x, or y = f(x). At points B1 the spaghetti is level, while at points B2 it has the steepest slopes. These slopes can be mathematically expressed as the rate at which the value of y changes as a function of x, or yīs first derivate of x, or dy/dx = f '(x). As can be readily realized, the tendency for the spaghetti to bend is largest at points B1, where dy/dx = f '(x) = 0. Why is that? Because at those points the rate of change in the sloping is at its biggest. From dy/dx = f '(x) > 0 it reverses to dy/dx = f '(x) <0 and vice versa at those points (which is indicated in the figure with the plus and minus signs). This rate of change of the slope can be expressed as yīs second derivate of x, or d2y/dx2 = f ''(x). Clearly, if we could find a place where this tendency to bend is zero, or d2y/dx2 = f ''(x) = 0, It would be an ideal point to join two beam segments together. This point would not then be subjected to any bending stress, only the force of pull, which would be easier to handle. These points are found at B2 in the figure, and, when it comes to steel beams, these points are about 1/6 of the distance from one support to the next. These points are called inflexion points. When considering the beams, these inflexion points must not be stiff; the beam segments must be able to move. This is motivated by the fact that the beams will expand and contract in response to variations in temperature, at least if they are made of metal, such as steel beams.

Figure 6:1 Figure 6:2 Figure 6:3 Considering that steel has a tendency to absorb direct sunlight and can become much hotter than the surrounding air; the beamīs temperature might vary between +50o and -20o Celsius at the most extreme, and with a beam section of 20 meters, this would result in a lengthwise movement of about 1.5 cm. at each end (about half an inch). Figure 6:4. To allow for this, a casing (figure 6:4), something like in the cut-through figure at right, will have to cover an expansion gap at these inflection points. This gap will be quite insignificant, though, since in reality the beams will move vertically or sideways to accomodate this expansion. The distance between the inflexion points on each side of a support should be about one-third the distance between the poles, as indicated in figure 6:2. Another reason for these inflexion points is that the beams could be prefabricated with an upward bent (grossly exaggerated in figure 6:3 to compensate for the downward stress of passing beamcars. When the cars pass, the beam will bend down and its ends will need space to move outwards, somewhat (indicated by the blue arrows).

o doubt you have noticed ribs on the beams on our drawings. They resemble cooling flanges, but intuitively you have probably felt that they serve the same stabilizing purpose as the ribs in old-time wooden sailing vessels. But why are they needed here? Consider the downbending force that each beam section is subjected to by its own weight and the weight of passing cars. This force tends to press the roof and floor of the beam closer together. This means that the sidewalls will tend to be flayed out, as shown by arrows F1 in the drawing at right (figure 7:1), which shows cross-sectional views of the beam. This is because the sidewalls have nowhere else to go, and the slit at the bottom of the beam permits them to move outwards. That slit is thus, in a way, a structural weakness with suspended beam traffic systems, as compared to supported systems. This bending movement will spread upwards along the sides of the beam as shown by F2, until the roof will either tend to sink or buckle down in the middle (shown by F3), depending on which force wins out. To prevent this, one could of course make the sidewalls thicker. But if you look at the mathematics further up on this page, you will realize that thicker walls do not contribute much to the stiffness of the beam. This extra material is better spent in forming ribs at regular intervals along the beams, to counteract this outflaying force. They will need to cover the roof as well as the sides of the beam, resembling an inverted "U". They will have to cover the bottom of the beam as well, meeting up with the slit. Now, these ribs could either be applied externally or internally on the beam, as indicated by the brown coloring in the drawing. Internal ribs have two advantages: They would not be visible from the outside They would not require extra arrangements regarding the beam vehiclesīstabilizer wheels. The disadvantage with internal ribs is that they would make the beams larger. Another consideration would be to decide upon the distance (D) between the ribs, and the thickness (T) of the ribs. Calculations show that D should be somewhere around 120 cm and T about 5 cm.

Figure 7:1 Figure 7:2

What is "bending radius"? ake a look at figure 8:1 to the right. One of the beams goes around a street corner in the middle of the street. If you draw perpendicular lines (i.e. lines that are at right angles to the beam) from the beam, you will find that they meet at certain points. If the curvature is the same all the way, you will find that all these perpendicular lines meet att the same point. The lines drawn closest to the bent section are (hopefully) found to be of equal length.	Lines drawn from their meeting point (at "x") towards the beam at any point on the bent section will have the same length, no matter at what angle they are drawn. That distance (r in the figure) from "x" to the center of the beam is termed "bending radius". In the case of turning round street corners, berthing at stations and the like, we will have to consider a radius of about 6 meters. In all other cases, this radius will be much larger.	Figure 8:1.

ake a look at figure 6:3 above once again! It illustrates the upwards pre-bending (or "camber") at the time of manufacture, to compensate for gravityīs impact on the beam. This camber could be made a bit more than what is required for the dead load alone (i.e. the weight of passing beamcars and of the beam segment itself). The live-load vertical deflection caused by the moving car, with a maximum at center-span (i.e. equi-distant between the beam supports), can be added to the dead load camber, so that the unloaded beam support would bend slightly upwards. Otherwise, the beamcar, on passing each beam segment, would create a hammock-effect. This means that it would travel slightly downhill to the middle of the beam segment, then be faced with a small hill to climb, which will flatten out as the car reaches the center of the support. The downhang would of course, in such a case, spring back up when the load is gone. These vertical movements of the beam as the beamcar pass will hardly be noticeble by the eye, but they might be felt by the traveler at high speeds, unless the pre-cambering is done right.

Essentially, the travelers might experience a yoyo-effect which is more emphasized the faster the car travels. On the other hand, the downward bend gets smaller, the faster the car travels. This is because of the beamīs inertia; it takes time for the beam to react to the weight of the beamcar. The quicker the car passes the beam segment, the smaller vertical distance the beam will travel in response to the carīs weight, before the car is gone. This can be seen from the table at right, where the required camber for different speeds has been calculated. One realizes intuitively, then, that one should avoid: heavy cars slow traffic many cars close together parking of cars Since these requirements cannot be met everywhere, one has to take due consideration to the beam dimensions and/or placing the vertical beam supports closer together at certain places.

Continuous beam deflects into a sine curve For the smallest of the FLYWAY beams, we can calculate like this: a = vertical acceleration, m/sec^2 d = vertical deflection, in meters L = horizontal span, in meters v = beamcarīs velocity, meter/sec.2 then: a = 2 * p2 * d/L * v2/L a is a function of the beam material and proportional design, and is a measurement as to how quickly the beam segment would respond to an applied weight. For a given a, one gets the vertical deflection d from: d = a * L2 / (2 * p2 * v2) One can thus see that the beamīs vertical deflection is proportional to the square of the length of the beam segment (which is natural) but inversely proportional to the square of the speed of the passing cars. Maximum vertical deflection (in meters) if a = 0.2 Horizontal span (L) in meters Velocity, meters per second 10 20 30 40 30 0.091 0.023 0.010 0.0057 40 0.162 0.041 0.018 0.010 50 0.253 0.063 0.028 0.016 60 0.365 0.091 0.041 0.023 70 0.496 0.124 0.055 0.031

oth supported and suspended beam-traffic systems are subject to the (hopefully) small vertical undulations that are due to the downward bending of the beams between beam supports. These bendings are (of course) caused by earthīs gravity and their sizes are functions of: Distance between beam supports Stiffness of the beams Weight of the beams themselves Degree of pre-bending (camber) that the beams have been subjected to Weight, number and positions of beamcars on the beam segment Speed of passing beamcars. The faster they travel, the less time will there be for the segment to react to their weight.

At slow travel, these undulations do not matter much. But at high travel speed, they get uncomfortable, unless one enjoys riding rollercoasters. It is true that passive springs will dampen this effect to some degree, and the FlyWay system has a built-in dampener in the form of the lifts. The beam traffic systems that aim for high speed will need an active suspension system for comfortable travel.

What is Active Suspension? With active suspension we mean a computer-controlled hydraulic or pneumatic system that actively compensates for unwanted movements of the cabin or load. Such active suspension systems are already in existence, and function quite well. In beam traffic systems, they can also to some degree compensate for vertical movements of slow-moving or stationary cabins, caused by other beam vehicles that are entering or leaving the beam segment, thereby straining the beam at varying degrees.