Transportation Systems and TechnologyTransportation Systems and Technology2413-9203Eco-Vector1075910.17816/transsyst201843s1328-339Research ArticleHigh-speed vacuum air vehicleMishraRajat<p>Bachelor of Technology student</p>Rjrajat678@gmail.comhttps://orcid.org/0000-0002-0332-2561SharmaHimashu<p>Bachelor of Technology And Master of Technology</p>himanshu.sharma@kiet.eduhttps://orcid.org/0000-0002-6973-1069MishraHarshit<p>Bachelor of Technology</p>rajatmshr179@gmail.comhttps://orcid.org/0000-0002-0860-7355ECE Department, KIET Group of InstitutionsECE department KIET group of institutionsDr. K. N MIET1911201843 suppl. 132833921122018Copyright © 2018, Mishra R., Sharma H., Mishra H.2018<p><strong>Background: </strong>There are a number of problems in the prior art, those are topics of research inputs likes ranges of the drag force generated by the vehicle, lift force at high vehicle motion velocities for compensation of the vehicle weight, Aerodynamic aspects of operation of the vehicle,</p>
<p><strong>Aim: </strong>Stream wise stability of vehicle motion and levitation and breaking of the vehicles and supersonic speed is not achieved in any mode of transportation. But this present invention related to high speed magnetic levitating transportation. More particularly, present invention is related to high speed magnetic levitating transportation using compressed air chamber in the transportation vehicle.</p>
<p><strong>Methods: </strong>The present invention is more particularly related to high speed vehicle levitated on a vacuum tunnel by using electromagnetic levitation. As this vehicle will move from one place to another in a vacuum environment and this vehicle will levitate above track with the help of electromagnets.</p>
<p><strong>Results</strong><strong>:</strong> The important thing is its motion, which is possible due to reaction force of high pressure air, coming out from compressed air chamber present in vehicle.</p>
<p><strong>Conclusion: </strong>It can give us the acceleration as per load requirement and it can achieve supersonic speed in few seconds.</p>Magnetic levitationElectromagnetsMagnetic trackHigh Speed vacuum vehicleAir TrainTransportationCompressed air Train.<h2 style="text-align: left;">INTRODUCTION</h2>
<p style="text-align: justify;">Along with the increase of population and expansion in living zones, automobiles and air services cannot afford mass transit anymore. Accordingly, demands for innovative means of public transportation have increased. In order to appropriately serve the public, such a new generation transportation system must meet certain requirements such as speed, reliability, and safety. In addition, it should be convenient, environmentally friendly, low-maintenance, compact, light-weight, unattained, and suited to mass transportation. We waste our precious life time for travelling from one place to another. So we need a high-speed transport system which will save our time. Yes, we have such kinds of transport systems like airways, which can reach up to one thousand km/h and we also have present magnetic levitation technology which cannot reach sonic speed. Here with this invention, transportation method will be safe, quick, efficient and, most significantly, high-speed. And it can change the future scenario of transport method. We also have Hyperloop system, but that idea limits the speed of transportation as it consists of the air compressor in front.</p>
<h2 style="text-align: left;">DETAILED DESCRIPTION</h2>
<p style="text-align: justify;">Here Fig. 1 shows exemplary representation of mechanism for formation of compressed air and vacuum creation mechanism according to one of the embodiment of the invention. Here we have used vacuum tunnel as shown in Fig. 1. Inside this tunnel, vacuum will be created with the help of vacuum pump, This pump will suck the air from tunnel. Next, we will compress air with the help of air compressor.</p>
<p style="text-align: justify;"></p>
<center>
<div class="preview fancybox" style="text-align: center;"><a title="Fig. 1. Setup for vehicle motion on magnetic track" href="/files/journals/18/articles/10759/supp/10759-18868-1-SP.jpg" rel="simplebox"><img style="max-height: 300px; max-width: 300px;" src="/files/journals/18/articles/10759/supp/10759-18868-1-SP.jpg" /></a></div>
</center>
<p style="text-align: center;"><strong>Fig. 1. Setup for vehicle motion on magnetic track</strong></p>
<p style="text-align: center;"></p>
<p style="text-align: justify;">Here outlet ports, as shown in Fig. 1, are the part of the air compressor to transfer compressed air to vehicle. And in Fig. 1 magnetic track is the track on which vehicle will levitate and move.</p>
<p style="text-align: justify;"></p>
<center>
<div class="preview fancybox" style="text-align: center;"><a title="Fig. 2 shows detailed view of vacuum tunnel. Now we come to a vehicle which will levitate above the track and move with a very high speed." href="/files/journals/18/articles/10759/supp/10759-18869-1-SP.jpg" rel="simplebox"><img style="max-height: 300px; max-width: 300px;" src="/files/journals/18/articles/10759/supp/10759-18869-1-SP.jpg" /></a></div>
</center>
<p style="text-align: center;"><strong>Fig. 2 shows detailed view of vacuum tunnel. Now we come to a vehicle which will levitate above the track and move with a very high speed.</strong></p>
<p style="text-align: center;"></p>
<p style="text-align: justify;">Fig. 2 shows detailed view of vacuum tunnel. Now we come to a vehicle which will levitate above the track and move with a very high speed.</p>
<p style="text-align: justify;"></p>
<center>
<div class="preview fancybox" style="text-align: center;"><a title="Fig. 3. Vehicle side look" href="/files/journals/18/articles/10759/supp/10759-18870-1-SP.jpg" rel="simplebox"><img style="max-height: 300px; max-width: 300px;" src="/files/journals/18/articles/10759/supp/10759-18870-1-SP.jpg" /></a></div>
</center>
<p style="text-align: center;"><strong>Fig. 3. Vehicle side look</strong></p>
<p style="text-align: center;"></p>
<p style="text-align: justify;">In Fig. 3, we have explained the basic components of a vehicle such as battery area, crew cabin and passengers room. And here we have also used high reusable silicon insulation (HRSI) tiles as it does not allow heat transfer in passenger sitting area for safe journey. Here C-clamp is the base of the vehicle, which makes vehicle levitate above the magnetic track. Here compressed air chamber is the closed chamber in which compressed air is filled. Here inlet ports are shown which are used to fill compressed air chamber with compressed air.</p>
<p style="text-align: justify;"></p>
<center>
<div class="preview fancybox" style="text-align: center;"><a title="Fig. 4. Look of compressed air chamber" href="/files/journals/18/articles/10759/supp/10759-18871-1-SP.jpg" rel="simplebox"><img style="max-height: 300px; max-width: 300px;" src="/files/journals/18/articles/10759/supp/10759-18871-1-SP.jpg" /></a></div>
</center>
<p style="text-align: center;"><strong>Fig. 4. Look of compressed air chamber</strong></p>
<p style="text-align: center;"></p>
<p style="text-align: justify;">Inside view of compressed air chamber look is shown below in Fig. 4(a) and Fig. 4(b)</p>
<p style="text-align: center;"></p>
<center>
<div class="preview fancybox" style="text-align: center;"><a title="Fig. 4(a)-(b). Forward-Backward motion of piston" href="/files/journals/18/articles/10759/supp/10759-18872-1-SP.jpg" rel="simplebox"><img style="max-height: 300px; max-width: 300px;" src="/files/journals/18/articles/10759/supp/10759-18872-1-SP.jpg" /></a></div>
</center>
<p style="text-align: center;"><strong>Fig. 4.(a) Forward motion of piston - (b)Backward motion of piston</strong></p>
<p style="text-align: justify;"></p>
<p style="text-align: justify;">Now we will discuss the mechanism of motion of vehicle in forward direction. The outlet ports, as shown in Fig. 1, will transfer compressed air to inlet ports, as shown in Fig. 3, of the vehicle. As the pin, as shown in Fig. 3, gets pushed inside, the entry of compressed air into compressed air chamber starts. This charging of compressed air chamber is done when the vehicle is in rest. See Fig. 4 (2D view of chamber), as compressed air gets inside compressed air chamber, it accumulates until the chamber is full, and then we will release compressed air with the help of valve as shown in Fig. 4(a) and Fig. 4(b), and to enhance effect we have used nozzle which will allow releasing compressed air. As we need a constant pressure throughout exit of the compressed air, we have used a piston. Fig. 4(a) and Fig. 4(b) represent forward and backward motion of piston. And when compressed air comes out from compressed air chamber via nozzle in control of valve with constant pressure, it provides a huge reaction force which will accelerate our vehicle in opposite direction of the air coming out. Once it gets a required velocity, the valves will be shut off by the command from crew cabin, as shown in Fig. 3, and hence the vehicle will maintain its velocity as it will be in the environment of negligible friction. Compressed air chamber should be made in such a way that it can tolerate high temperature and high pressure.</p>
<p style="text-align: justify;">Here a clear look of nozzle is shown below in Fig. 4(c), anda proper explanation of all the parameters shown in Fig. 4(c) is given as well.</p>
<p style="text-align: justify;"></p>
<center>
<div class="preview fancybox" style="text-align: center;"><center>
<div class="preview fancybox" style="text-align: center;"><a title="Fig. 4(c). Close view of nozzle" href="/files/journals/18/articles/10759/supp/10759-18873-2-SP.jpg" rel="simplebox"><img style="max-height: 300px; max-width: 300px;" src="/files/journals/18/articles/10759/supp/10759-18873-2-SP.jpg" /></a></div>
</center>
<p><strong>Fig. 4(c). Close view of nozzle</strong></p>
<p></p>
</div>
</center>
<p style="text-align: justify;">Parameters are explained below as follows:</p>
<p style="text-align: justify;"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mtext>T</mtext><mtext>t</mtext></msub></math>- Total temperature of compressed gas inside compressed air chamber;</p>
<p style="text-align: justify;"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mtext>T</mtext><mtext>e</mtext></msub></math>- Temperature of gas on its way out from nozzle;</p>
<p style="text-align: justify;"><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mtext>A</mtext><mtext>*</mtext></msup></math>- Area of cross-section of choked flow region;</p>
<p style="text-align: justify;"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mtext>A</mtext><mtext>e</mtext></msub></math>- Area of cross-section of exit;</p>
<p style="text-align: justify;"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mtext>p</mtext><mtext>t</mtext></msub></math>- Total pressure of compressed gas inside compressed air chamber;</p>
<p style="text-align: justify;"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mtext>p</mtext><mtext>e</mtext></msub></math>- Pressure of gas on its way out of from nozzle;</p>
<p style="text-align: justify;"><em><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mtext>p</mtext><mtext>o</mtext></msub></math>- </em>Free stream pressure;</p>
<p style="text-align: justify;"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mtext>M</mtext><mtext>e</mtext></msub></math>- Exit Mach number;</p>
<p style="text-align: justify;"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mtext>V</mtext><mtext>e</mtext></msub></math>- Exit velocity.</p>
<p style="text-align: justify;"></p>
<center>
<div class="preview fancybox" style="text-align: center;"><a title="Fig. 5. C-Clamp analysis" href="/files/journals/18/articles/10759/supp/10759-18874-1-SP.jpg" rel="simplebox"><img style="max-height: 300px; max-width: 300px;" src="/files/journals/18/articles/10759/supp/10759-18874-1-SP.jpg" /></a></div>
</center>
<p style="text-align: center;"><strong>Fig. 5. C-Clamp analysis</strong></p>
<p style="text-align: justify;"></p>
<p style="text-align: justify;">Fig. 5 shows an exemplary representation of magnetic levitation and braking system according to the present invention. In Fig. 5, the C-clamp has two L-shaped electromagnets named as C-clamp levitation electromagnets, attached to its base side. And the other L-shaped electromagnet, named track levitation electromagnet, attached to the upper side of the magnetic track. The four track brake electromagnets are placed at the lower side of the magnetic track. The C-clamp has a metal sheet. The metal sheet is attached to the C-clamp in such a manner that it is placed between at least two track brake electromagnets at the lower side of the magnetic track. This metal sheet is covered with a diamagnetic cover. This cover can be covered and uncovered by control of the vehicle by its control system in crew cabin, as shown in Fig. 3, during braking and levitation of vehicle.</p>
<p style="text-align: justify;">These C-clamp levitation electromagnets of C-clamp and track brake electromagnets of the magnetic track both generate similar poles and develop repulsive force during the normal position of the vehicle. The repulsive force is developed in such a manner that the vehicle loses its contact with the magnetic track and it starts levitating above the magnetic track. If the weight of the vehicle changes then intensity of these electromagnets also changes accordingly automatically.</p>
<p style="text-align: justify;">As Fig. 5 shows, during braking of the vehicle, the four track brake electromagnets of the magnetic track and metal sheets attached to C-clamp come in action. The metal sheets are kept in a diamagnetic envelope until braking is not required. When the vehicle transportation control system, present in crew cabin, as shown in Fig. 3, provides signal to retard motion of the vehicle, then the vehicle transportation control system creates north-south poles in each pair of electromagnets. It is done in such a way that metal sheet lies in between north and south poles of two track brake electromagnets of the magnetic track. As metal sheets are attached to the vehicle body, hence it cuts the magnetic field created by track brake electromagnets of the magnetic track. During this activity the flux is changed in metal sheets which create eddy currents as described by Faradays law of induction. By Lenzs law, the circulating currents in the metal sheet create their own magnetic field in the sheet. Thus metal sheet will experience a drag force from the track brake electromagnets of the magnetic track. So it opposes its motion. The kinetic energy of the moving vehicle is dissipated as heat is generated by the current flowing through the electrical resistance of the metal sheet. By the reason of this activity, the metal sheet should bear a high temperature.</p>
<p style="text-align: justify;">The whole magnetic track is divided into segments, and when the vehicle comes near segment electromagnets get active accordingly. Now as our vehicle will face negligible air friction and negligible friction from track, so it is highly efficient. Here in this vehicle we will coat its body with diamagnetic substance so that magnetic field does not affect inside the vehicle.</p>
<p style="text-align: justify;"></p>
<center>
<div class="preview fancybox" style="text-align: center;"><a title="Fig. 6. Changing direction of vehicle" href="/files/journals/18/articles/10759/supp/10759-18875-1-SP.jpg" rel="simplebox"><img style="max-height: 300px; max-width: 300px;" src="/files/journals/18/articles/10759/supp/10759-18875-1-SP.jpg" /></a></div>
</center>
<p style="text-align: center;"><strong>Fig. 6. Changing direction of vehicle</strong></p>
<p style="text-align: center;"></p>
<p style="text-align: justify;">Fig. 6 is responsible for reversing the direction of vehicle clockwise or counterclockwise with rotating disk.</p>
<h2 style="text-align: left;">ANALYSIS</h2>
<p style="text-align: justify;">Analysis of detailed description</p>
<p style="text-align: justify;"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mtext>T</mtext><mtext>t</mtext></msub></math>- Total temperature of compressed gas inside compressed air chamber;</p>
<p style="text-align: justify;"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mtext>T</mtext><mtext>e</mtext></msub></math>- Temperature of gas on its way out from nozzle;</p>
<p style="text-align: justify;"><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mtext>A</mtext><mtext>*</mtext></msup></math>- Area of cross-section of choked flow region;</p>
<p style="text-align: justify;"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mtext>A</mtext><mtext>e</mtext></msub></math>- Area of cross-section of exit;</p>
<p style="text-align: justify;"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mtext>p</mtext><mtext>t</mtext></msub></math>- Total pressure of compressed gas inside compressed air chamber;</p>
<p style="text-align: justify;"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mtext>p</mtext><mtext>e</mtext></msub></math>- Pressure of gas on its way out of from nozzle;</p>
<p style="text-align: justify;"><em><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mtext>p</mtext><mtext>o</mtext></msub></math>-</em>Free stream pressure;</p>
<p style="text-align: justify;"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mtext>M</mtext><mtext>e</mtext></msub></math>- Exit Mach number;</p>
<p style="text-align: justify;"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mtext>V</mtext><mtext>e</mtext></msub></math>- Exit velocity.</p>
<p style="text-align: justify;"><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mtext>m</mtext><mtext>*</mtext></msup></math>- Mass flow rate;</p>
<p style="text-align: justify;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>R</mtext></math>- Gas constant;</p>
<p style="text-align: justify;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext></mtext></math>- Specific heat ratio.</p>
<p style="text-align: justify;"></p>
<p style="text-align: justify;">Mass flow rate:</p>
<p style="text-align: center;"><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mtext>m</mtext><mtext>*</mtext></msup><mtext>=</mtext><mfrac><mrow><msup><mtext>A</mtext><mtext>*</mtext></msup><msub><mtext>p</mtext><mtext>t</mtext></msub></mrow><msqrt><msub><mtext>T</mtext><mtext>t</mtext></msub></msqrt></mfrac><msqrt><mfrac><mtext></mtext><mtext>R</mtext></mfrac></msqrt><msup><mfenced><mfrac><mtext>+1</mtext><mtext>2</mtext></mfrac></mfenced><mrow><mtext>-</mtext><mfrac><mtext>+1</mtext><mrow><mtext>2</mtext><mfenced><mtext>-1</mtext></mfenced></mrow></mfrac></mrow></msup></math>(1)</p>
<p style="text-align: justify;"><em></em></p>
<p style="text-align: justify;">Area ratio:</p>
<p style="text-align: center;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><msub><mtext>A</mtext><mtext>e</mtext></msub><msup><mtext>A</mtext><mtext>*</mtext></msup></mfrac><mtext>=</mtext><msup><mfenced><mfrac><mtext>+1</mtext><mtext>2</mtext></mfrac></mfenced><mrow><mtext>-</mtext><mfrac><mtext>+1</mtext><mrow><mtext>2</mtext><mfenced><mtext>-1</mtext></mfenced></mrow></mfrac></mrow></msup><msup><mfrac><mfenced><mrow><mtext>1+</mtext><mfrac><mtext>-1</mtext><mtext>2</mtext></mfrac><msup><msub><mtext>M</mtext><mtext>e</mtext></msub><mtext>2</mtext></msup></mrow></mfenced><msub><mtext>M</mtext><mtext>e</mtext></msub></mfrac><mfrac><mtext>+1</mtext><mrow><mtext>2</mtext><mfenced><mtext>-1</mtext></mfenced></mrow></mfrac></msup></math>(2)</p>
<p style="text-align: justify;">Temperature ratio:</p>
<p style="text-align: center;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><msub><mtext>T</mtext><mtext>e</mtext></msub><msub><mtext>T</mtext><mtext>t</mtext></msub></mfrac><mtext>=</mtext><msup><mfenced><mrow><mtext>1+</mtext><mfrac><mtext>-1</mtext><mtext>2</mtext></mfrac><msup><msub><mtext>M</mtext><mtext>e</mtext></msub><mtext>2</mtext></msup></mrow></mfenced><mtext>-1</mtext></msup></math>(3)</p>
<p style="text-align: justify;"></p>
<p style="text-align: justify;">Pressure ratio:</p>
<p style="text-align: center;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><msub><mtext>p</mtext><mtext>e</mtext></msub><msub><mtext>p</mtext><mtext>t</mtext></msub></mfrac><mtext>=</mtext><msup><mfenced><mrow><mtext>1+</mtext><mfrac><mtext>-1</mtext><mtext>2</mtext></mfrac><msup><msub><mtext>M</mtext><mtext>e</mtext></msub><mtext>2</mtext></msup></mrow></mfenced><mrow><mtext>-</mtext><mfrac><mtext></mtext><mtext>-1</mtext></mfrac></mrow></msup></math>(4)</p>
<p style="text-align: justify;"></p>
<p style="text-align: justify;">Exit velocity:</p>
<p style="text-align: center;"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mtext>V</mtext><mtext>e</mtext></msub><msub><mtext>=M</mtext><mtext>e</mtext></msub><msqrt><msub><mtext>RT</mtext><mtext>e</mtext></msub></msqrt><mi></mi></math>(5)</p>
<p style="text-align: justify;"></p>
<p style="text-align: justify;">Force applied on the vehicle:</p>
<p style="text-align: center;"><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mtext>F=m</mtext><mtext>*</mtext></msup><msub><mtext>V</mtext><mtext>e</mtext></msub><mtext>+</mtext><mfenced><mrow><msub><mtext>p</mtext><mtext>e</mtext></msub><msub><mtext>-p</mtext><mtext>o</mtext></msub></mrow></mfenced><msub><mtext>A</mtext><mtext>e</mtext></msub><mi></mi></math>(6)</p>
<p style="text-align: justify;"></p>
<p style="text-align: justify;">Now taking values of following parameter.</p>
<ul style="text-align: justify;">
<li><em>R</em> = 287 JKg<sup>-1</sup>K<sup>-1 </sup>(For air)</li>
<li><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mtext>M</mtext><mtext>e</mtext></msub></math>= 2.5</li>
<li><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext></mtext></math>= 1.4 (For air)</li>
<li>1 atm = 101325 N/m<sup>2 </sup></li>
<li>Now from ideal gas law <em>p<sub>t</sub>V=mRT<sub>t</sub></em></li>
</ul>
<p style="text-align: justify;">Pressure of the air inside compressed air chamber</p>
<ul style="text-align: justify;">
<li>Taking <em>p<sub>t </sub></em>= 2.5 atm =2.5x101325 N/m<sup>2</sup>=253312.5 N/m<sup>2 </sup></li>
<li>Taking <em>V= L</em>x<em>B</em>x<em>H</em></li>
</ul>
<p style="text-align: justify;"><em>L</em> = Length of compressed air chamber (17 m)</p>
<p style="text-align: justify;"><em>B</em> = Width of compressed air chamber (2m)</p>
<p style="text-align: justify;"><em>H</em> = Height of compressed air chamber (4m)</p>
<p style="text-align: justify;">So, <em>V</em>=136 m<sup>2 </sup></p>
<ul style="text-align: justify;">
<li>Now <em>m</em> = mass of air; [1 mol = 0.02897 Kg (For air)]</li>
<li>Mole of air in chamber =<math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mtext>136</mtext><msup><mtext>22.410</mtext><mtext>-3</mtext></msup></mfrac></math></li>
<li>Mass of air (<em>m</em>) = no. of moles x 0.02897 Kg= 02897 = 175.8892857 Kg</li>
</ul>
<p style="text-align: justify;">Now <em>T<sub>t</sub></em> =<math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><msub><mtext>p</mtext><mtext>t</mtext></msub><mtext>V</mtext></mrow><mtext>mR</mtext></mfrac></math></p>
<p style="text-align: justify;">Temperature of air inside compressed air chamber</p>
<p style="text-align: justify;">=<math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mtext>253312.5136</mtext><mtext>175.8892857287</mtext></mfrac><mo>=</mo><mn>682</mn><mo>.45535</mo><mtext></mtext><mi>K</mi><mo>.</mo><mi></mi></math></p>
<p style="text-align: justify;"></p>
<ul style="text-align: justify;">
<li>Now taking equation 3, the temperature of air at exit from vehicle:</li>
<li><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mtext>T</mtext><mtext>e</mtext></msub><mo>=</mo><msub><mtext>T</mtext><mtext>t</mtext></msub><msup><mfenced><mrow><mtext>1+</mtext><mfrac><mtext>-1</mtext><mtext>2</mtext></mfrac><msup><msub><mtext>M</mtext><mtext>e</mtext></msub><mtext>2</mtext></msup></mrow></mfenced><mtext>-1</mtext></msup><mtext>=682.45535=303.313488K.</mtext></math> </li>
</ul>
<p></p>
<ul style="text-align: justify;">
<li>Now taking equation 5, the exit velocity:</li>
<li><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mtext>V</mtext><mtext>e</mtext></msub><mo>=</mo><msub><mtext>M</mtext><mtext>e</mtext></msub><msqrt><msub><mtext>RT</mtext><mtext>e</mtext></msub></msqrt><mo>=</mo><mtext>2.5</mtext><msqrt><mtext>1.4287303.313488</mtext></msqrt><mo>=</mo><mn>872</mn><mo>.7519674</mo><mtext></mtext><mi>m</mi><mo>/</mo><mi>s</mi><mi>e</mi><mi>c</mi></math></li>
</ul>
<p></p>
<ul style="text-align: justify;">
<li>Now taking equation 2, the radius = 2 <em>m </em>of choked flow region</li>
</ul>
<p style="text-align: center;"><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mtext>A</mtext><mtext>*</mtext></msup><mo>=</mo><msup><mtext>r</mtext><mtext>2</mtext></msup><mo>=</mo><mtext>4</mtext><mo>=</mo><mtext>12.56637</mtext><msup><mi>m</mi><mn>2</mn></msup></math></p>
<p></p>
<ul style="text-align: justify;">
<li>Exit area of cross-section of nozzle:</li>
</ul>
<p style="text-align: center;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mo></mo><msub><mtext>A</mtext><mtext>e</mtext></msub><mo>=</mo><msup><mtext>A</mtext><mtext>*</mtext></msup><msup><mfenced><mfrac><mtext>+1</mtext><mtext>2</mtext></mfrac></mfenced><mrow><mtext>-</mtext><mfrac><mtext>+1</mtext><mrow><mtext>2</mtext><mfenced><mtext>-1</mtext></mfenced></mrow></mfrac></mrow></msup><msup><mfrac><mfenced><mrow><mtext>1+</mtext><mfrac><mtext>-1</mtext><mtext>2</mtext></mfrac><msup><msub><mtext>M</mtext><mtext>e</mtext></msub><mtext>2</mtext></msup></mrow></mfenced><msub><mtext>M</mtext><mtext>e</mtext></msub></mfrac><mfrac><mtext>+1</mtext><mrow><mtext>2</mtext><mfenced><mtext>-1</mtext></mfenced></mrow></mfrac></msup><mo>=</mo><mtext>12.56637</mtext><msup><mfenced><mfrac><mtext>1.4+1</mtext><mtext>2</mtext></mfrac></mfenced><mrow><mtext>-</mtext><mfrac><mtext>1.4+1</mtext><mrow><mtext>2</mtext><mfenced><mtext>1.4-1</mtext></mfenced></mrow></mfrac></mrow></msup><msup><mfrac><mfenced><mrow><mtext>1+</mtext><mfrac><mtext>1.4-1</mtext><mtext>2</mtext></mfrac><msup><mtext>(2.5)</mtext><mtext>2</mtext></msup></mrow></mfenced><mtext>2.5</mtext></mfrac><mfrac><mtext>1.4+1</mtext><mrow><mtext>2</mtext><mfenced><mtext>1.4-1</mtext></mfenced></mrow></mfrac></msup><mo>=</mo><mn>12</mn><mo>.566372.6367187</mo><mo>=</mo><mn>33</mn><mo>.133985</mo><mtext></mtext><msup><mi>m</mi><mn>2</mn></msup></math> </p>
<p style="text-align: justify;"></p>
<ul style="text-align: justify;">
<li>Now taking equation 1, here it is mass flow rate:</li>
</ul>
<p style="text-align: center;"><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mtext>m</mtext><mrow><mtext>*</mtext><mo></mo><mo></mo></mrow></msup><mtext>=</mtext><mfrac><mrow><msup><mtext>A</mtext><mtext>*</mtext></msup><msub><mtext>p</mtext><mtext>t</mtext></msub></mrow><msqrt><msub><mtext>T</mtext><mtext>t</mtext></msub></msqrt></mfrac><msqrt><mfrac><mtext></mtext><mtext>R</mtext></mfrac></msqrt><msup><mfenced><mfrac><mtext>+1</mtext><mtext>2</mtext></mfrac></mfenced><mrow><mtext>-</mtext><mfrac><mtext>+1</mtext><mrow><mtext>2</mtext><mfenced><mtext>-1</mtext></mfenced></mrow></mfrac></mrow></msup></math></p>
<p style="text-align: center;"><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mtext>m</mtext><mtext>*</mtext></msup><mtext>=</mtext><mfrac><mtext>12.566372.5101325</mtext><msqrt><mtext>682.45535</mtext></msqrt></mfrac><msqrt><mfrac><mtext>1.4</mtext><mtext>287</mtext></mfrac></msqrt><msup><mfenced><mfrac><mtext>1.4+1</mtext><mtext>2</mtext></mfrac></mfenced><mrow><mtext>-</mtext><mfrac><mtext>1.4+1</mtext><mrow><mtext>2</mtext><mfenced><mtext>1.4-1</mtext></mfenced></mrow></mfrac></mrow></msup><mo>=</mo><mn>4925</mn><mo>.02765914</mo><mtext></mtext><mi>K</mi><mi>g</mi><mo>/</mo><mi>s</mi><mi>e</mi><mi>c</mi></math></p>
<p style="text-align: justify;"></p>
<p style="text-align: justify;">Now taking equation 4, the pressure of the air on its way out from the vehicle</p>
<p style="text-align: center;"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mtext>p</mtext><mtext>e</mtext></msub><msub><mtext>=p</mtext><mtext>t</mtext></msub><msup><mfenced><mrow><mtext>1+</mtext><mfrac><mtext>-1</mtext><mtext>2</mtext></mfrac><msup><msub><mtext>M</mtext><mtext>e</mtext></msub><mtext>2</mtext></msup></mrow></mfenced><mrow><mtext>-</mtext><mfrac><mtext></mtext><mtext>-1</mtext></mfrac></mrow></msup></math></p>
<p style="text-align: center;"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mtext>p</mtext><mtext>e</mtext></msub><mtext>=2,5</mtext><msup><mfenced><mrow><mtext>1+</mtext><mfrac><mtext>1.4-1</mtext><mtext>2</mtext></mfrac><msup><mtext>(2.5)</mtext><mtext>2</mtext></msup></mrow></mfenced><mrow><mtext>-</mtext><mfrac><mtext>1.4</mtext><mtext>1.4-1</mtext></mfrac></mrow></msup><mo>=</mo><mn>2</mn><mo>.5</mo><mo></mo><mn>0</mn><mo>.058527663466</mo><mo>=</mo><mn>0</mn><mo>.146319158665</mo><mtext></mtext><mi>a</mi><mi>t</mi><mi>m</mi></math></p>
<p></p>
<ul style="text-align: justify;">
<li>Now taking equation 6.</li>
</ul>
<p style="text-align: center;"><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mtext>F=m</mtext><mrow><mtext>*</mtext><mo></mo><mo></mo></mrow></msup><msub><mtext>V</mtext><mrow><mtext>e</mtext><mo></mo></mrow></msub><mtext>+</mtext><mfenced><mrow><msub><mtext>p</mtext><mtext>e</mtext></msub><msub><mtext>-p</mtext><mtext>o</mtext></msub></mrow></mfenced><msub><mtext>A</mtext><mtext>e</mtext></msub></math>[Here<math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mtext>p</mtext><mtext>o</mtext></msub><mo>=</mo><mn>0</mn><mo>=</mo><mo>(</mo><mn>4925</mn><mo>.02765914</mo><mo></mo><mn>872</mn><mo>.7519614</mo><mo>)</mo><mtext></mtext><mo>+</mo><mtext></mtext><mo>(</mo><mn>0</mn><mo>.14631915</mo><mo></mo><mn>101325</mn><mo>)</mo><mo></mo><mn>33</mn><mo>.133985</mo><mo>=</mo><mn>4298327</mn><mo>.549464</mo><mtext></mtext><mo>+</mo><mtext></mtext><mn>491237</mn><mo>.433022</mo><mo>=</mo><mn>4789564</mn><mo>.982486</mo><mtext></mtext><mi>N</mi><mo>=</mo><mn>4789</mn><mo>.564982486</mo><mtext></mtext><mi>k</mi><mi>N</mi></math></p>
<p style="text-align: justify;">This significant amount of force will act on the vehicle if we provide parameter as stated above. As per our requirement related to high or low force on vehicle we can adjust parameter accordingly.</p>
<ul style="text-align: justify;">
<li>For levitation of the vehicle.</li>
</ul>
<p style="text-align: center;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>F=</mtext><mfrac><msup><mtext>AB</mtext><mtext>2</mtext></msup><msub><mtext>2</mtext><mtext>0</mtext></msub></mfrac></math></p>
<p style="text-align: justify;"><em><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A</mtext></math></em>- Total area of magnet under bogie.</p>
<p style="text-align: justify;"><em><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>B</mtext></math></em>- Magnetic flux density.</p>
<p style="text-align: justify;"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mtext></mtext><mtext>0</mtext></msub></math> - Permeability of the vacuum.</p>
<p style="text-align: justify;"></p>
<center>
<div class="preview fancybox" style="text-align: center;"><a title="Fig. 7. Levitation" href="/files/journals/18/articles/10759/supp/10759-18876-1-SP.jpg" rel="simplebox"><img style="max-height: 300px; max-width: 300px;" src="/files/journals/18/articles/10759/supp/10759-18876-1-SP.jpg" /></a></div>
</center>
<p style="text-align: center;"><strong>Fig. 7. Levitation</strong></p>
<p style="text-align: center;"></p>
<p style="text-align: justify;">As shown in Fig.7, when Fmg then levitation of vehicle occurs.</p>
<h2 style="text-align: left;">CONCLUSION</h2>
<p style="text-align: justify;">We were able to successfully demonstrate the feasibility of high-speed vacuum air vehicle. As with this technology vehicle will face negligible friction due to which force will only act to accelerate the vehicle. Dimension of the track and vehicle should be accurate in order to get better results. As per our requirement, that is high or low force on the vehicle, we can adjust parameters accordingly. With this technology we can achieve very high speed with safety ensured, and this technology can be utilized for not only train application but also for aircraft launching systems and spacecraft launching systems.</p>[Sinha P. Design of a magnetically levitated vehicle. IEEE Trans.Magn. 1984;MAG-20(5):1672-1647. doi: 10.1109/TMAG.2006.879572][Takahashi T, Kurita K. Computation of eddy currents induced in a conducting sheet under moving magnets. IEEE Trans. Magn. 1988;24(1):197-200. doi: 10.1109/TMAG.2006.879572][Tsuchimoto M, Miya K, Yamashita A, Hashimoto M. An analysis of eddy current and Lorentz force of thin plates under moving magnets. IEEE Trans. Magn. 28(2):1434-1437. doi: 10.1109/TMAG.2006.879572][Nakao H, Yamashita T, Sanada Y, et al. Development of a modified superconducting magnet for Maglev vehicles. IEEE Trans. 1999;9(2):1000-1003. doi: 10.1109/TVT.2017.2657201][Fujimoto H, Kamijo H, Higuchi T, et al. Preliminary study of a superconducting bulk magnet for the Maglev train. IEEE Trans. 1999;9(2):301-304. doi: 10.1109/TVT.2017.2657201][Sasakawa T, Tagawa N. Reduction of magnetic field in vehicle of superconducting maglev train. IEEE Trans. Magn. 2000;36(5):3676-3679. doi: 10.1109/TMAG.2006.879572][Weh H, Shalaby M. Magnetic levitation with controlled permanentic excitation. IEEE Trans. Magn. 1977;13(5):1409-1411.doi: 10.1109/TMAG.2006.879572][Atherton D. Maglev using permanent magnets. IEEE Trans. Magn. 1980;16(1):146-148. doi: 10.1109/TMAG.2006.879572][Yoshida K, Umino T. Dynamics of the propulsion and levitation systems in the controlled-PM LSM maglev vehicle. IEEE Trans. 1987;23(5):2353-2355.doi: 10.1109/TMAG.2006.879572][Morishita M, Azukizawa T, Kanda S, et al. A new MAGLEV system for magnetically levitated carrier system. IEEE Trans. 1989;38(4):230-236. doi: 10.1109/TVT.2017.2657201][Onuki T, Toda Y. Optimal design of hybrid magnet in maglev system with both permanent and electromagnets. IEEE Trans. Magn. 1993;29(2):1783-1786. doi: 10.1109/TMAG.2006.879572][Tzeng YK, Wang TC. Optimal design of the electromagnetic levitation with permanent and electro magnets. IEEE Trans. Magn.. 1994;30(6):4731-4733. doi: 10.1109/TMAG.2006.879572][Wang TC, Tzeng YK. Anewelectromagnetic levitation systemfor rapid transit and high speed transportation. IEEE Trans. Magn. 1994;30(6):4734-4736. doi: 10.1109/TMAG.2006.879572][Sen PC. On linear synchronous motor (LSM) for high speed propulsion. IEEE Trans. Magn. 1975;MAG-11(5):1484-1486.doi: 10.1109/TMAG.2006.879572][Albicini F, Andriollo M, Martinelli G, Morini A. General expressions of propulsion force in EDS-MAGLEY transport systems with superconducting coils. IEEE Trans. Appl. Supercond. 1993;3(1):425-429. doi: 10.1109/TASC.2016.2534760][Sakamoto T, Shiromizu T. Propulsion control of superconducting linear synchronous motor vehicle. IEEE Trans. Appl. Supercond. 1997;33(5):3460-3462. doi: 10.1109/TASC.2016.2534760][Burke P, Kunts S, Slemon G. A dual linear synchronous motor for Maglev vehicles. IEEE Trans. Magn. 1977;MAG-13(5):1415-1417.doi: 10.1109/TMAG.2006.879572][Koseki T, Hayafune K, Masada E. Lateral motion of a shortstator type magnetic wheel. IEEE Trans. Magn. 1987;23(5):2350-2352.doi: 10.1109/TMAG.2006.879572][Ohashi S, Ohsaki H, Masada E. Running characteristics of the magnetically levitated train in a curved track section. IEEE Trans. Magn. 1997;33(5):4212-4214.doi: 10.1109/TMAG.2006.879572][Wang J, Wang S, Ren Z, et al. Guidance forces on high temperature superconducting Maglev test vehicle. IEEE Trans. Appl. Supercond. 2003;13(2):2154-2156.doi: 10.1109/TMAG.2006.879572][Shibata M, Maki N, Saitoh T, Kobayashi T, Sawano E, Ohshima H. On-board power supply system of a magnetically levitated vehicle. IEEE Trans. 1992;28(1):474-477. doi: 10.1109/TVT.2017.2657201][Andriollo M, Martinelli C, Morini A, Tortella A. Optimization of the on-board linear generator in EMS-MAGLEV trains. IEEE Trans. Magn. 1997;33(5):4224-4226. doi: 10.1109/TMAG.2006.879572][Cassat JM. MAGLEV Projects Technology Aspects and Choices. IEEE Transactions on Applied Superconductivity. 2002;12(1):915-925. doi: 10.1109/TASC.2016.2534760]