On the generation of lift force in random, soft porous media its application to an airborne jet train

Feng and Weinbaum (2000) developed a theory which demonstrated that highly compressible soft porous materials could transiently support very large loads beneath a planing surface for short duration if the trapped fluid within the fibrous medium could not escape on the time scale of the passage of the planing surface. They also showed that there is a remarkable hydrodynamic similarity between the motion of the red blood cells and a human skier or snowboarder skiing on soft snow powder even though they differ in mass by 1015 . Thus, the lift forces in each case can be four or more orders of magnitude greater than classical lubrication theory. In more recent papers, Wu et al. (2005) utilizes a porous cylinder apparatus to measure for the first time the dynamic pressures that develop on the time scale of skiing or snowboarding. Using this novel apparatus, Wu et al. (2006) predicted that fully 50 percent of the total lift on a snowboard traveling at 10 m/s arose from the excess pore pressure that developed due to the transiently trapped air beneath the snowboard and the increased hydraulic resistance of the compressed snow. In this dissertation, the generalized Reynolds equation derived in Feng and Weinbaum (2000) to random porous media is extended using the Carman-Kozeny equation for a random fiber array. This extended analysis is then applied to planning surfaces moving in a channel in which the loss of pressure at the lateral edges is eliminated by using impermeable sidewalls. We show that dramatically different behavior is obtained depending on whether the porous medium is attached to a stationary horizontal lower boundary or to a moving inclined upper boundary. We then explore the quantitative feasibility, performance and stability of an airborne jet train (AJT) that flies on a soft porous track within centimeters of the earth's surface. We first show that it is possible to support a 70 metric ton jet train carrying 200 passengers on a confined porous material if its Kp is approximately 5x10-9 m2. Using random porous media theory, we predict that one can achieve lift-off at only 5 m/s if the porous material has a fiber radius of 5mum and a solid fraction of 0.005. Furthermore, we predict that by using jet engines of 10,000 lbf thrust, about 1/5 that of a jet aircraft, one can accelerate to a cruising velocity of 700 km/hr in less than 2 minutes. Since energy expenditure is thrust times distance, fuel consumption should be less than 1/5 that of commercial jets. In addition, combustion products are not released high in the atmosphere where global warming effects are greatest.