Issue 4/2004
07/02/04
Research Works on super-high-speed lifts
Gongxin Shen, Albert So and H. L. Bai
The construction of super-high-rise intelligent buildings is not just the trend, but the fashion, of the modern construction industry. The most distinctive building system serving such a building is the lift system. A few years ago, the world’s speed record was 750 mpm and now the most updated one is 1,010 mpm. We can see a gradual increase in the near future. However, there are problems hindering the design and construction of super-high-speed lifts, and they are mainly mechanically based. In this article, the development history of super-high-speed lifts is discussed, followed by the research work conducted by your authors during recent years.
Category: Issue 4/2004
Posted by: Editor
As cities are becoming more and more densely populated, buildings are getting taller and taller. The tallest building in Hong Kong is about 400 meters and 88 stories. The tallest building in Mainland China is 421-meters-high with 88 stories in Shanghai; the next world’s record will also be in Shanghai by 2007. The world’s existing tallest building is 508 meters high with 101 stories in Taipei, which is structurally taller than the world’s second tallest in Kuala Lumpur, 452 meters high with 88 stories. In 1998, a plan to build a 610-meter-high building in Chicago was announced. The concept of a “mile-high building” was suggested by Frank Lloyd Wright in 1956. He proposed constructing a 1,609-meter building, the Illinois. Other proposals included the 900-meter M Tower in Shanghai, the 840-meter Millennium Tower in Tokyo and the 701-meter World Trade Center in Chicago. It becomes obvious that super-high-rise buildings will be inevitable in the 21st century. The most distinctive requirement of a super-high-rise building is, of course, a fast, safe, comfortable and efficient vertical transportation system.
The rated speed of 600 mpm (10 mps) was achieved in 1977 in Tokyo and then 750 mpm (12.5 mps) in 1993 in Yokohama, both by Mitsubishi. A few years ago, lifts up to 840 mpm (14 mps) were developed by Hitachi. The Taipei 101 has express lifts with a rated speed of 1,010 mpm (16.8 mps). If we talk about the 900-meter Shanghai standard as mentioned above, a rated speed of 30 mps (108 kph) is not unreasonable. Although 108 kph is not a huge figure from an automobile point of view, the technology of lifts certainly requires a revolution to accomplish the goal. Mechanical problems associated with the lift car inside the lift shaft, including aerodynamic noise, pressure variation and excessive vibration, are genuine problems that hinder the development of super-high-speed lifts.
These problems come from the increasing drag force exerted by the extremely high speed of air movement around an ascending or descending car. Excessive air-pressure variation causes noise of high amplitude that cannot be tolerated by passengers and generates both horizontal and vertical vibrations that are detrimental to the car structure, suspension ropes and the driving gear assembly, or sometimes beyond the comfort or even safety limits of human beings. Air-pressure variations also have a significant impact on the air resistance to car movement and hence, a direct implication on the energy consumption of the drive. These mechanical constraints must be studied in an integrated manner to arrive at an ultimate solution. Lift manufacturers normally build real models to test their high-speed lifts or carry out small-scale simulation studies, which are either very expensive or not comprehensive nor effective. The worst scenario to technological development is that they all treat such information or research results as a top commercial secret. As super-high-speed lifts become standard building systems in the 21st century, the technological solution must be in the public domain.
In ordinary lift designs (usually at 3~4 mps, highest being approximately 10 mps at present), the aerodynamic load may be neglected when compared with other kinds of loads. The development of super-high-speed lifts (speed reaching 25~30 mps) becomes obvious as more high-rise buildings are constructed in the future. Thus, the speed issue cannot be ignored anymore throughout the whole development. When a high-speed lift is moving along the hoistway, a tunnel-air-operated effect will occur, producing great tunnel pressure variations, air-operated noise and so on. Similar problems happen on a high-speed train when it travels in a tunnel, creating tunnel effects. Massive research has been carried out using experiment and mathematical computation methods to generate the tunnel time lift-drag ratio, as well as some key parameters that influence resistance [1-3]. However, the physical geometrical parameters and the running status of a high-speed lift is very much different from that of a high-speed train, such as higher blocking ratio, lower open ratio, and the reciprocation movement of cars, etc. Therefore, particular research should be launched in this area.
People have been trying to carry out aerodynamic simulation tests for lifts with wind tunnels. However, owing to the limitation of movement in a wind tunnel, these tests are unable to forge the key tunnel effect simulations, only a partial flow of simulation being possible. Inside the wind tunnel, it is difficult to simulate a moving car. Normally, the air is moving around a stationery car, which is not identical in the case of lift operation. Some special testing equipment is essential to simulate the movement of a high-speed lift car. Apart from the moving speed of the car, aerodynamic performance can be affected by many other elements such as the size and shape of the hoistway as well as the car shape.
Therefore, it is necessary to find out all kinds of structural parameters that influence the aerodynamic characteristics of lifts and formulate reasonable arrangements of these parameters. The data obtained can be used to validate the engineering calculations and can serve as a standard design guidance for reference. In addition, the air flow pattern due to tunnel effect is one of complex flow phenomena, with very limited knowledge so far. In this article, the research work done by others and by your authors are highlighted and discussed. We have developed a relatively simple simulation platform for testing high-speed lifts with different hoistway-based parameters and car-shape designs. With the application of digital particle image velocimetry (DPIV) observation techniques, an initial velocity profile around a high-speed moving lift car can be obtained. With pressure measurement, it is possible to judge the best car shape design for super-high-speed applications.
The Problems and Previous Approaches
It is obvious that due to the increasing density of super-high-rise buildings in megacities, the reliance on super-high-speed lifts is also increasing accordingly. However, there are technical problems, mainly mechanical or more specific, aerodynamic by nature, associated with the development of such lifts, thus hindering the advancement of technology in this area. We can see a rough figure of around 2 mps growth in the rated speed per decade, which cannot catch up with the requirement in the coming century. Our target is to design lifts with a rated speed up to 30 mps.
At present, there are two major problems, namely aerodynamic noise and excessive vibration due to the drag force exerted on a super-high-speed ascending or descending car. In accordance with CIBSE Guide D[4], in-car noise levels, machine-room noise levels and lobby-noise levels must be under control. Although the problem can be partially solved by introducing building materials with good sound insulation and absorption properties, the basic solution is to reduce the noise generated by a moving car. For vibration, human response is greatest at low frequencies, and therefore, vibration limits in the range from 1 to 80 Hz must be met. Hence, excessive vibration of a super-high-speed car is not acceptable. Drag force must be reduced to keep a longer life for the suspension ropes and the driving gears. Lift shafts of larger sizes can help, but the price of land becomes a significant problem in a densely populated city. With a view to all the problems, it is an absolute necessity to make a revolution on the external structure of the lift car and/or the lift shaft so as to keep the noise levels, vibration levels and drag force to a minimum subject to a limited size of the lift shaft. This is a totally new design concept where the initial step is to produce a physical model of a super-high-speed lift car inside a conventional lift shaft so that the aerodynamic properties can be studied thoroughly. This model can form a basic foundation for designing the best lifts in the 21st century.
In 1992, some very preliminary experimental works were carried out by Mitsubishi and Toshiba. Mitsubishi was responsible for installing the 12.5 mps lifts in Yokohama. They studied two types of noise associated with a high-speed car [5], namely mechanical noise at the contact between the car and the guide rails and aerodynamic noise due to the air flow around the car inside a narrow lift shaft. They found that aerodynamic noise became greater in proportion to the fifth through the sixth power of the air speed around the car. Owing to this fact, aerodynamic noise is usually much greater than the mechanical noise for high-speed lifts. When a car travels either up or down, air flow splits at either the top or the bottom and then merges again at the other end. The air flow moving over the side faces of the car will vibrate the entire car body, causing excessive noise inside the car. They therefore proposed to use a streamlined cover at both the top and bottom of the car. A wind tunnel experiment was carried out with two streamlined covers mounted on a 1:12.5 scale miniature lift. These streamlined covers were removable, and it was possible to observe the air flow around the lift with and without the covers. An “oil flow pattern method” was applied to visualize the air flow patterns over the surfaces of the car. It was discovered a reduction of 4.1 dB(A) to 4.3 dB(A) could be achieved with the covers.
Over the same period of time, Toshiba [6] carried out another experiment in a water tank to observe the overall flow and to visualize the flow around the model submerged in water using a tracer. The Renumber based on the car width and the speed of the water stream was approximately 800. This value was approximately 10-4 times smaller than that of the actual lift car. What Toshiba wanted to study was the effect on the air flow with and without an apron which was compulsorily installed at the bottom of each lift car due to a legal requirement. Large-scale horse-shoe-shaped vortices were produced due to the existence of the apron. This could explain why a higher level of noise was produced for a downward moving car as compared with an upward moving car. Using the setup, Toshiba was able to design a guide plate for each apron so as to reduce the magnitude of the aerodynamic noise.
Both experiments performed by the two reputable lift manufacturers in Japan faced one common problem. The car and the shaft wall were static while the air was dynamic. This was a total deviation from the real situation where both the car and the air are dynamic. Furthermore, both experiments were used to improve the car design by a small amount, i.e., either the addition of streamlined covers or the installation of guide plates for the aprons. The research work was quite narrowly confined to one or two detailed technical issues. Having said that, their works, though quite primitive, did provide your authors with a very important insight. The aerodynamic performance of super-high-speed lifts needs to be studied in detail so as to arrive at the best design.
Regarding the development of a computer model to study the aerodynamic performance of super-high-speed lifts so as to arrive at an optimal design in the coming years, some preliminary work has been carried out before. The theme was simplified to consider the situation under one dimension [7] and two-dimension [8]. Some encouraging and consistent results were obtained, thus opening the road to look into the general three-dimensional case. However, at the same time, problems were discovered when the computer simulation was carried out, such as the difficulty in convergence when handling the optimization to solve the partial differential equations and the relative motion between the car, the air and the stationery wall of the lift shaft. There are various computational fluid dynamics (CFD) software packages available in the market, such as CFX-4 from AEA, Flow3D from Flow Science and Phoenics from Cham. But we discovered four problems. First, it was difficult to input the velocity profile of the lift car, which was an acceleration/rated speed operation/deceleration profile. Second, we encountered divergence from time to time. Third, we spent much time on studying how to use the package. Such time would effectively be spent to write the codes ourselves. Furthermore, all such packages are very expensive and need annual renewal. Therefore, it was concluded that pure computer simulation could not reveal the whole picture. A real physical model needed to be built so that experimental data could tell us what the characteristics of air flowing around a super-high-speed moving car were.
The Model Design of Computer Simulation
The simplified two-dimensional car/hoistway model is shown in Figure 1. It shows all relevant parameters that reflect the car/hoistway structures and the overall geometry for a moving car. During car movement, the rear-end and front-end air pressure P1, P2, and air density p1/p2 etc. change continuously according to the car speed and position. For the car, as pressure increases in Area II, air in this area will flow to open 2 of the hoistway, whereas some air passes through the gap between the car and the hoistway, and flows back into Area I. As the air pressure of Area I falls, air will enter from outside the hoistway by passing through open 1 into Area I.
All physical geometrical parameters, including the area of the hoistway A1, the diameter of the hoistway D, the open areas A01, A02, the cross-sectional gap size between the car and hoistway A (or A1-A2), total length of hoistway L, the reserved length (overhead runby) of the front-end L0, car moving speed u, external air pressure Pa and temperature Ta (being constants considering the entire hoistway temperature and external temperature), as well as the current position of the car, x, influence the front-end and rear-end air pressure of the car. To determine the impact of aerodynamic characteristics, a list of non-dimensional combination of these parameters has to be generated for practical application. The pressure difference between the front-end and rear-end of the car can be described in Equation 1:
Taking Pa, D, u, R as basic physical geometric forms and using non-dimensional analysis, we are able to generate the non-dimensional Equation 2:
With the hoistway rear-end open ratio (i.e., open area at the terminal of hoistway at the rear-end/hoistway cross-sectional area) A01/D² = k1; front-end open ratio A02/D² = k2; block ratio (cross-sectional area of the car/hoistway cross-sectional area) A2/D²= 1 –A/D² = z; length-diameter ratio (i.e., total length of hoistway/diameter) L/D = ld; overhead runby reserved ratio (reserved length of space at the terminals of the hoistway/diameter) L0/D = g, Equation 2 can be written in Equation 3:
The High-Speed Lift Testing Model
The non-dimensional analysis obviously shows the necessary structural parameters required in designing the lift model, i.e., rear-end open ratio k1, front-end open ratio k2, block ratio z, length ratio ld and overhead runby reserved ratio g.
This testing model allows the car to slide up and down freely in the vertical hoistway. Through PIV observation, the speed profile of moving air around the car can be obtained. To ensure the accuracy of this model, both model air speed (speed of air in this model) and real air speed (speed of air in a real hoistway) should have a single value of geometric similarity. The reduction ratio of the model is 1:30, including the hoistway, adjustable openings at both terminals of the hoistway, the car and the supporting structure at the bottom. The whole setup is shown in Figure 2 and a photograph of the real model is shown in Figure 3.
Pressure sensors are installed close to the two ends of the lift hoistway in order to obtain the actual air pressure at both front-end and rear-end areas. At the top and bottom of the hoistway, four square holes are provided, and these holes are equipped with valves so that the front-end and rear-end open ratios, ranging from 0 to 1, of this model can be adjustable.
The block ratio is achieved through the usage of cars of different cross-sectional areas. There are three parts for each car design, namely the central, upper and lower parts. The central part is made of steel to ensure the weight is sufficient enough to overcome the air resistance along the hoistway to ensure a higher falling speed. Furthermore, guided rollers are installed on the four sides of each car so that the car can slide up and down the hoistway with minimal resistance due to friction. We have constructed two sets of cars, with block ratios equal to 0.8 and 0.72 respectively. The external shape of cars is believed to be an essential element that greatly affects the aerodynamic performance of the cars due to the resultant air resistance. The four different shapes, including rectangular, spherical, conical and parabolic, are shown in Figure 4.
At this initial stage of the project, up/down and radial symmetries have been maintained. According to theoretical estimation, when the car reaches the testing range, i.e., the lower part of the hoistway, the speed should have reached 10 to 12 mps. Although there is a difference between this experimental speed range and the conceived or desirable speed range of super-high-speed lifts to be used in this century, the non-dimensional parameter, TaR/u², can be used to extrapolate the experimental test results to reveal the real situation under a super-high-speed condition. This is the true beauty of the overall design of this experimental platform to use the approach of non-dimensional analysis.
The DPIV velocity estimation system is used to observe the surrounding air movement during the course of car falling. The tracing particles are from propylene glycol which volatizes in high temperature and generates mist. A double-pulsed Nd:YAG laser is the light source for generation of the laser sheet, with a frequency of 10 Hz and pulsed energy equal to 10 mJ. Image acquisition is performed by a CCD video camera (with 1008 x 1018 pixel resolution). The velocity vectors are obtained using a digital auto-correlation technique in which the flow domain is subdivided into a grid of “interrogation regions” and auto-correlation is employed within each interrogation region to determine the most like translation of the particles over the time increment. When the car falls and enters the section of the glass pipe designed for image capturing, the images showing the front-end and rear-end air velocity patterns are taken respectively. Further calculations on the captured particle images generate the two-dimensional cross-sectional flow field velocity distributions.
Testing Results of Velocity Profiles
Under different moving conditions, the practical car speed can reach 10-13 mps. This is even better than the original designed speed. Supposing the open ratio at the rear-end region is kept at 0.3 and open ratio at the front-end region is kept at 0 and 0.2 respectively, with a combination of block ratio at 0.8 and 0.72, the velocity at both car front-end and rear-end can be observed for all four kinds of car shapes. During the imaging procedure, the car hinders itself so that the laser beam cannot reach the back side of it. Only the front side facing the laser source can be imaged. Figure 5 shows an ordinary velocity vector diagram. This front-end velocity testing result is under the testing condition of a spherical lift car shape with open ratio k1=0.3 and k2=0, block ratio z=0.8.
The initial testing observations indicate the existence of a complicated and abnormal flow pattern around the lift car. No matter the block ratio at the condition of z=0.8 or 0.72, with different open ratio k2, we can see the existence of separate vortices within the flow pattern around the car. This happens apparently when air pressure is created as a result of the car sliding down and air current at the car front-end area flows to the rear-end by two routes. Some air currents flow toward the gap, while others group together to produce a force namely second ordered vortices, against vortices that come forward. The formulation of second-order vortices refers to air currents that fail to flow to the rear-end when the car moves. Actually, these second-order vortices normally appear at the center area at the front-end.
Pressure Measurements in Front of and Behind the Car
Taking into account the so-called “tunnel aerodynamic effects” of lifts is very different from that of high-speed trains passing through a tunnel [9], recent research articles discussing such “tunnel aerodynamic effects” have been limited [10, 11]. By using our testing model, the average pressures in front of and behind the moving car as well as the instantaneous speed at five different positions along the hoistway were measured with the four different shapes of car and variable hoistway-based parameters, including open ratio and block ratio.
The five positions to measure instantaneous speed are located at X1 = 345 millimeters, X2 = 1,365 millimeters, X3 = 3,495 millimeters, X4 = 5,125 millimeters and X5 = 7,375 millimeters from the top of the pipe and the measuring method of instantaneous speed, u, at a particular position is as follows: u = L/∆t, where L = 50 millimeters which is the distance between two optoelectronic gates positioned 25 millimeters above and 25 millimeters below the measuring position so that the time interval, ∆t, for the car to pass through the two gates can be measured.
Owing to the existence of tunnel-based aerodynamic effects when the car is moving in the hoistway, the aerodynamic drag on the car includes three components:
- the skin friction which is due to the air viscosity;
- the shape drag on the car because different shapes of car lead to different pressure distribution on its surface when the car is moving in the fluid;
- the tunnel-based pressure difference due to the existence of tunnel wall; air in front of the car is pressed and the volume of air is reduced, while on the other hand, the volume of air behind the car is increased when the car is moving forward along the hoistway, thus resulting in a pressure difference in front of and behind the car.
It is convenient to visualize tunnel-based pressure differences from the pressure curves when the car moves along the hoistway. In order to visualize changes of the total aerodynamic drags on the car, it is necessary to analyze speed curves because changes of acceleration of the car, which is proportional to the total forces on it, can be obtained from the speed curves. Changes of average pressure in front of and behind the car along the hoistway were studied with respect to different open ratios and block ratios. Curves of air pressures (P1-P2) versus dropping time S are depicted from Figures 6–9 as derived from experimental data for different car shapes. S is counted right from the instant the car starts to accelerate from the top of the hoistway. It is obvious that more differences in pressure changes among different car shapes can be obtained as the open ratio is getting smaller.
Results of different shapes of car under the different conditions of hoistway-based parameters are then analyzed. When the block ratio is 0.72, Figure 6 and Figure 7 can be obtained, showing changes of average pressure difference for four shapes of car with bigger open ratios, 0.3 and 0.2 respectively. We can see that changes of average pressure differences are only slightly dependent on different shapes of car because air in the hoistway can freely flow through the orifices and the air gap between the vertical car surface and the pipe wall without much resistance.
Then, curves of average pressure differences for four different shapes of car with the same block ratio of 0.72, but open ratios of 0.1 and 0 respectively are shown in Figures 8 and 9. With the reduction in open ratio, less air can pass through the orifices and more air is forced to flow through the air gap between vertical car surface and the wall of the hoistway. The result is that the shape of car then plays a more significant role on the flow field characteristics inside the hoistway. Different shapes of the car lead to distinct average pressure differences in front of and behind the car along the hoistway. Particularly with an open ratio of 0, the parabolic shape of car, among the four different shapes, can achieve the best performance significantly due to its smallest average pressure difference in front of and behind it.
The main factor which influences the tunnel aerodynamic pressure is not only the shape of the car, but also the open ratio and the block ratio. From Figures 6-8, the open ratio is reduced from 0.3 to 0.1, while the block ratio is kept constant at 0.72, i.e., a bigger air gap between the car wall and hoistway. As a result, the tunnel-effected-aerodynamic pressure difference is not significantly different between four different shapes of car. In Figure 9, with an open ratio of 0, air flow along the hoistway is forced through the car side/hoistway wall gap. Then, the shape of car strongly influences the tunnel-effected-aerodynamic pressure difference.
Conclusion
The high demand for super-high-speed lifts due to the construction of super-high-rise intelligent buildings in this century is obvious. Problems associated with the development of super-high-speed lifts have been discussed, leading to the establishment of the experimental platform to study the aerodynamic performance of these lifts inside the hoistway. Although lots of research has been done on aircraft and racing cars, they are not applicable to lifts because of the existence of “tunnel effected pressure difference.” Work on trains in tunnels are similar, but usually the block ratio is very large for trains, and thus the “tunnel-effected-pressure difference” is not distinct.
Based on our experimental work, there can be a few observations and considerations. First, computational fluid dynamics cannot be conveniently used in lift design due to the existence of non-linear turbulences. Studies on DPIV-based air-velocity profiles are useful in finding out such turbulences. It seems that the skin friction and shape drag related to the car are much smaller than that caused by the “tunnel effected pressure difference.” So, it is very important during the design stage of super-high-speed lifts that reasonable hoistway-based parameters, i.e., open ratios and block ratios, be selected. The average pressure difference in front of and behind the car along the hoistway is distinctly affected by different shapes of car under the condition of small open ratios and big block ratios. Finally, with a small open ratio, and a big block ratio, our experimental results have revealed that the order of favorable car shapes, according to the consideration of average pressure difference, is parabolic, spherical, triangular and cylindrical.
It should be noted that cars with a flat top and a flat bottom, cylindrical in our experiments, are the normal design. That means, they are totally unsuitable for super-high-speed applications. The “tunnel effected shape drag” considered by us, which is mainly caused by the average pressure difference, very much differs from the normal concept of shape drag when vehicles are moving in an open space under a high speed. It is because this “tunnel effected shape drag” is a result of the high-speed movement of a the car with the existence of in-hoistway aerodynamics.
This project has been financially supported by the Strategic Research Grants No. 7001379 and 7001109 of the City University of Hong Kong.
Reprint with friendly permission from Elevator World.
References
[1] Schetz A. “Aerodynamics of High-Speed Trains.” J. Annu. Rev. Fluid Mech, 2001, Vol. 33, pp. 371-414.
[2] Arturo B., M. Michele and S. Stefano. “The Alleviation of the Aerodynamic Drag and Wave Effects of High-Speed Trains in Very Long Tunnels.” Journal of Wind Engineering and Industrial Aerodynamics, 2001, Vol. 89, pp. 365-401.
[3] Zhu W. “Wind Tunnel Test Study of the Aerodynamic Shape of High-Speed Trains.” J. Experiments and Measurements in Fluid Mechanics, 1997, Vol. 11, No. 2, pp. 105-107.
[4] CIBSE Guide D Transportation Systems in Building, 1993 and 2000 Editions.
[5] Matsukura Y., E. Watanabe, Y. Sugiyama and O. Kanamori. “New Mechanical Techniques for Super-High-Speed Elevators.” in G.C. Barney eds., Elevator Technology 4, IAEE, 1992, pp. 174-181.
[6] Teshima N., K. Miyasako and H. Matsuda. “Experimental and Numerical Studies on Ultra-High-Speed Elevators.” in G.C. Barney eds., Elevator Technology 4, IAEE, 1992, pp. 276-285.
[7] So A. T. P., T. T. Chow, G.X. Shen and H. W. Yang. “An Aerodynamic Mathematical Model for Super-High-Speed Elevators.” in G.C. Barney eds., Elevator Technology 7, 1996, pp. 204-213, reprinted in Elevatori, Vol. 27, No. 5, 1998, pp. 23-34.
[8] Yang H. W. and A. T. P. So. “A 2-Dimensional Aerodynamic Model for Super-High-Speed Elevators.” International Journal of Elevator Engineering, Vol. 2, 1998, pp. 19-32.
[9] Schetz A. “Aerodynamics of High-Speed Trains.” Annual Rev. Fluid Mechanics, 2001, Vol. 33, pp. 371-414.
[10] Munakata T., H. Kohara, K. Takai, Y. Sekimoto, R. Ootsubo and S. Nakagaki. “The World’s Fastest Elevator.” ELEVATOR WORLD, September, 2003, pp. 97.
[11] Duan Y., G. X. Shen, Y. G. Zhang and A. T. P. So. “Aerodynamic Testing Simulation Facility for High-Speed Elevator.” Journal of BUAA, 2004 in press.
[5] Matsukura Y., E. Watanabe, Y. Sugiyama and O. Kanamori. “New Mechanical Techniques for Super-High-Speed Elevators.” in G.C. Barney eds., Elevator Technology 4, IAEE, 1992, pp. 174-181.
[6] Teshima N., K. Miyasako and H. Matsuda. “Experimental and Numerical Studies on Ultra-High-Speed Elevators.” in G.C. Barney eds., Elevator Technology 4, IAEE, 1992, pp. 276-285.
[7] So A. T. P., T. T. Chow, G.X. Shen and H. W. Yang. “An Aerodynamic Mathematical Model for Super-High-Speed Elevators.” in G.C. Barney eds., Elevator Technology 7, 1996, pp. 204-213, reprinted in Elevatori, Vol. 27, No. 5, 1998, pp. 23-34.
[8] Yang H. W. and A. T. P. So. “A 2-Dimensional Aerodynamic Model for Super-High-Speed Elevators.” International Journal of Elevator Engineering, Vol. 2, 1998, pp. 19-32.
[9] Schetz A. “Aerodynamics of High-Speed Trains.” Annual Rev. Fluid Mechanics, 2001, Vol. 33, pp. 371-414.
[10] Munakata T., H. Kohara, K. Takai, Y. Sekimoto, R. Ootsubo and S. Nakagaki. “The World’s Fastest Elevator.” ELEVATOR WORLD, September, 2003, pp. 97.
[11] Duan Y., G. X. Shen, Y. G. Zhang and A. T. P. So. “Aerodynamic Testing Simulation Facility for High-Speed Elevator.” Journal of BUAA, 2004 in press.
Gongexin Shen and H. L. Bai work for the School of Aeronautic Science and Engineering, BUAA, in Beijing.
Albert So works for the City University of Hong Kong.
4/2004
