# Physics of Airtrack Operation, specifically, how an airtrack causes the glider float

Tags: airtrack, float, glider, operation, physics, specifically
HW Helper
P: 6,902
 Quote by adamxrt second pressure loss as it passes out of the hole just above the surface of the track, again which i was aware of. But you are saying theres a sub loss after this?
The pressure of the air a short distance away from the edges of a slider is ambient. Assuming the slider is "floating", you have a pressure gradient than decreases from higher than ambient towards ambient as you get closer to the edge of a slider. The issue with the radial flow outwards and perpendicular to a hole is that the cross sectional area of the flow increases by the radius from the center of that hole (cross sectional area = 2 π x radius x height), so mass flow per unit area decreases with radius from a hole. This means you need sufficient mass flow as well as pressure to keep a slider "floating". I assume hole size and density of the holes are also factors.
P: 28

 To be more precise about the requirement, you would need to decide what clearance you would need for the glider over the track (both for the right friction and to clear any bumps). Then you would have to calculate the pressure needed (weight / area) and the rate of flow of air out, under the glider (that's where one of your formulae would come in. Then you'd have to work out how much excess pressure you would need inside the track, to keep this pressure under the glider from the hole size and number of holes. Then you would need to know the capacity of the blower if it is to maintain this internal pressure with ALL the track holes leaking all the time. Several steps in there but I think that's the logical way to tackle it. The clearance would depend on how precisely you can engineer it but you could google airtrack design perhaps for some details like that. The friction is something else to work out, of course, for the dynamics bit of the experiment. There are formulae for working out friction for air bearings.
Can anyone postulate or think of a relationship or equation for an air gap which will output a friction value? Obviously i want friction low as possible.
P: 28
This is really getting to me! I get a really a lower pressure inside the track than i have under the glider when i use the method my instructor gave me!!!!!!

Can i just use the density of air as 1.2 the whole time? or will it be different at different pressures. See im assuming incompressible flow!

heres what im doing roughly.

 Say i have a slider base area 0.016m^2, 200mm long, and 300g(minimum) in weight; A track 2m long (square tube), hole spacing 50mm with 2 horizontal rows on either side to make a total of 76 holes either side. How im approaching this is, im assuming the glider ride height will be 0.1mm. this is my starting point. I then resolve the forces for the minimum pressure, P=F/A , or P=(mg)/(Base area under glider) that is needed to suspend the glider. This is the minimum pressure between the glider and the airtrack. il then need to figure out the flow from under the glider to atmosphere(incompressible assumed) Q=VA, (is the area cross sectional area of the gap beteeen the airtrack and the glider using my value of 0.1mm for the gap????? or the base area under the glider?), i then use v=sqrt(2*(Patm-Punderglider)/Density) to find airspeed under the glider. this is where im stuck. Do i use 1.2 as my air density? Im unsure as to how i can get the pressure ill need in the track from here on in, because ill have to factor in the holes etc. I tried Q=VA, because Qoutside=Qinside? so Qouside=Vinside*Areainside? So i work out the area of the faces inside the track.....to give me a value for Vinside...then..... I tried using Pressure inside track = (Pressure underglider)-((density*Vt)/2) All rearranged from Bernoullis Equ
Using this i got a ridiculously small pressure around 250pa which isnt right. Im going to redo eveything AGAIN for the upteenth time and try and upload a picture of my working out. Am I on the right track? Or can anyone point out any flaws?

Can anyone help with equations? And if i have done anything stupid please point out vigourously, im not the most intelligent of people but im trying! Im not going to coast this year!!!
 Sci Advisor PF Gold P: 11,105 When you say that you get less pressure inside the track than under the slider, what do you actually mean? It seems to me that you must have calculated some things in the 'wrong order'. There is bound to be a formula which gives an indication of the volume of air needed to produce a given pressure under the slider, based on squirting air through a slot (all the way round the edges). Using this value of pressure and the required volume of air, with another formula, you can then work out the pressure on the inside of the (covered) track holes which will achieve this flow. This pressure has to be greater than the pressure under the slider for air to flow in the direction you want. This internal pressure must be sustained whilst losing air from the covered holes plus all the uncovered ones- which tells you the total capacity of blower needed. Whatever the formulae are, there is a logic that tells me that, if you apply them in the right order, you could never have less pressure inside than under the slider. Stick at it. You'll get there in the end.
HW Helper
P: 6,902
 Quote by adamxrt Can i just use the density of air as 1.2 the whole time?
Yes, the required pressure won't be so much more than ambient that density will change enough to affect your calculations.

Getting back to the main problem, it would seem you need to determine the air flow rate between track and slider to achieve the required pressure to get the sliders to hover, then work your way back determining how much pressure (and minimal flow rate) is required to acheive that flow rate through the holes in the track.

Another potential issue is that between track and slider, the pressure will be greater and flow rate somewhat slower than the rest of the track.
PF Gold
P: 11,105
 Quote by rcgldr Another potential issue is that between track and slider, the pressure will be greater and flow rate somewhat slower than the rest of the track.
They will appear as two 'parallel loads', as an electrical analogy - but at least they will appear as constant as the slider moves (if the slider is an integral number of hole spaces long). But the 'direct' path is only relevant when working out the blower capacity that's needed. (One thing at a time.)

I just wonder how much the tutor who set this problem actually knows just how open ended (no pun intended) this assignment is. Did he ever give anyone else the same assignment in the past, I wonder?
P: 28
 Quote by sophiecentaur They will appear as two 'parallel loads', as an electrical analogy - but at least they will appear as constant as the slider moves (if the slider is an integral number of hole spaces long). But the 'direct' path is only relevant when working out the blower capacity that's needed. (One thing at a time.) I just wonder how much the tutor who set this problem actually knows just how open ended (no pun intended) this assignment is. Did he ever give anyone else the same assignment in the past, I wonder?
Im not sure he does, although its is to be expected, as final year projects are supposed to be very challenging.

rdgldr, I will attempt that, thought the problem is i cannot arrange bernousllis equation to fit/cant find the appropriate equation that describes the air motion inside the airtrack. During my education on thermodynamics, we only ever looked at pipe flow issues and head loss etc, nothing as abstract as this.

I also have another method to try. It as been suggested that i try using the "impulse of a jet " as im told the situation is very similar to that of air leaving a nozzle.
So, tonight, I belong to the girlfriend (necessary evil) and am off to a rugby match, but tomorrow night i have/ infact i will have time and wont be doing anything tomorow night so I will be back to continue this.

Also if anyone is interested, once the project gets fully under way i will continue this thread as a progress update on the build with pictures etc, so keep tuned if you are interested in momentum physics and collisions! I just need to solve my flow problems first!
 Sci Advisor PF Gold P: 11,105 I don't think the air flow along the pipe and inside the track is too significant. It's a massive chamber compared with the small exit holes and the pressure is not likely to vary much along its length. The main, and very relevant, unknown is the flow of air under the slider and the friction there. All the other bits are much more straightforward. This all seems a bit unfair unless you are allowed to do some practical measurements along the way. No serious engineering project would get away with a purely theoretical treatment before getting down to building something. It just wouldn't make commercial sense.
P: 28
well guys, im very happy to say i have a solution for this problem. Please see below, im going to get it checked tomorrow.

=D

let me know if it looks dodgy...because it probably is! this is all my own work, apart from being given a structure to follow. All equations looked up and checked by myself.

Assuming incompressible flow. density of 1.2
Attached Files
 Initial Airtrack calculation unchecked.doc (95.5 KB, 5 views)
 P: 28 Tutor liked the problem solution, though he says there are some minor mistakes, and my initial static velocity its far too big! Over all good news though, will redo and repost!
 P: 28 Yeah i appreciate what you are saying! I compiled that solution at 4am last night. I have no idea how I didnt pick up on the 407 being too big myself, put things into perspective, im unwell feel like crap, and had a nosebleed during one of my lectures earlier!! tutor was all over me about it aswell. Though i am still embarassed about that value. No engineers should miss something as glaring as that ever! he says my method seems to be right though? the v squared equation is rearranged from bernoullis equation. He himself suggested this 2 weeks ago, and i went away , rearranged it, came back and he said it was the right starting point. what i got wrong was i thought the 260 had to be taken away from atmosphere, when it is ALREADY the pressure difference (P-P(absolute)). SO that V^2 is now, Sqrt(2*260/1.2), which gives me a V value of =20.817m/s! And like you say, i then use Q=VA to find the airflow under the glider, this value will pretty much define everything...although thats what i was doing anyway in that solution? May I politley ask if you read the entire document, sophiecentaur? I do include this and also number of hole and ride height into the problem. Maybe it snot laid out that well. But yes, i am using air flow through orifice equations too, that is where i got the impact of a jet and the mass flow rate equation later on in the document. Im currently reworking the whole problem now, have class though very soon so ill not have it up until tonight maybe tomorrow.
 Sci Advisor PF Gold P: 11,105 Hi No I didn't read it thoroughly after I came to your 'little gaff' haha. You're not the first to fail to make a reality check. Me too, frequently. Can you take me through this jet equation? Even there, you end up with a velocity of 300m/s. Is that realistic? Wouldn't a real system with those speeds involved make a huge amount of noise? 150holes! But, if the volume of air in equals the volume of air out, it should end up moving somewhat faster through the holes. I think that vsquared equation must be too simplified for finding the air flow. It assumes laminar flow and also that pressure is the same all over the bearing surface. This won't be true. There will be more pressure away from the edge (hence, less pressure where you are applying that volume flow calculation). The air in the centre will stay there because its pressure is only a bit higher than the air next to it. (That earlier practical comment of someones, about needing no holes up there confirms what I say. There will be a steep gradient of pressure, I think, between holes and edge. As a reality check, we wouldn't dream of putting the holes right near the edge, would we? So the pressure must be different all over the underside. I have no idea what the right solution is but I can't even believe an exit speed of 20m/s is right, now I think of it. That's 72km/hr! It would blow your hat off - and, as for the air coming out of the holes at 300m/s, that would drill holes in your skin I think. This is turning out to be quite hard ain't it? btw, If you are shifting 0.012m3 at 3.42kPa, doesn't that represent over 4kW? Sorry but I think that's right.
P: 960
 Quote by sophiecentaur Hi No I didn't read it thoroughly after I came to your 'little gaff' haha. You're not the first to fail to make a reality check. Me too, frequently. Can you take me through this jet equation? Even there, you end up with a velocity of 300m/s. Is that realistic? Wouldn't a real system with those speeds involved make a huge amount of noise? 150holes! But, if the volume of air in equals the volume of air out, it should end up moving somewhat faster through the holes. I think that vsquared equation must be too simplified for finding the air flow. It assumes laminar flow and also that pressure is the same all over the bearing surface. This won't be true. There will be more pressure away from the edge (hence, less pressure where you are applying that volume flow calculation). The air in the centre will stay there because its pressure is only a bit higher than the air next to it. (That earlier practical comment of someones, about needing no holes up there confirms what I say. There will be a steep gradient of pressure, I think, between holes and edge. As a reality check, we wouldn't dream of putting the holes right near the edge, would we? So the pressure must be different all over the underside. I have no idea what the right solution is but I can't even believe an exit speed of 20m/s is right, now I think of it. That's 72km/hr! It would blow your hat off - and, as for the air coming out of the holes at 300m/s, that would drill holes in your skin I think. This is turning out to be quite hard ain't it? btw, If you are shifting 0.012m3 at 3.42kPa, doesn't that represent over 4kW? Sorry but I think that's right.
20 m/s sounds believable to me. That's not that fast, and it will dissipate fairly quickly coming out of the holes (especially due to the small jet diameter). As for the power required? The change in volume during compression is only going to be about 3% (assuming standard sea level conditions), so as a really quick estimate, the change in volume will be 3% of 0.012m3/s, and the average gauge pressure will be about 1.8 kPa. This gives a power required of less than 1 watt. Admittedly, this is a very quick and dirty estimate, but it should at least give a decent order-of-magnitude guess.

(300 m/s definitely sounds too high though - I definitely agree about that)
 Sci Advisor PF Gold P: 11,105 It isn't the change in volume that counts, surely. You are pushing all the air out with that pressure difference. Your argument would imply that an incompressible fluid would take no power to pump across a pressure difference.
 P: 960 True enough. I was in a hurry, and accounted for the compression work but not the flow work. Compression work, as I said before, is less than a watt, so that can safely be neglected. Flow work is still only 41 watts though (0.012 m3/s * 3.42 kPa).
P: 28
I have taken everybodys concerns and considerations into mind and have kept them there for now.

this is a nasty old problem, and im feeling my way though it as best as possible.
Sophiecentaur, youre so right about the crappy v squared equation, but its the best i can muster right now! lol Im literally just trying to get a raw feel for whats going on.

I have rejigged the whole lot and delved a bit deeper. Im still assuming laminar flow like you said, we'll tackle the matter of it probably actually not being that simple in due course. For now, Im looking at 13Kpa blower and 0.019m^3/s flow rate. I need to add in losses through an orifice to this somehow (not a clue how to, but will have to look) so i anticipate this pressure value possibly rising????? not sure.

V=20 at glider edge @ Q=
V=15 at hole exit
v=6inside track
V=26 inside blower air inlet.

I also did a conversion for hydraulic diameter in ther somehwere, for the square airtrack tube. Does anyone know if this was the correct thing to do?
Anyhow, for anyone that has MATHCAD 15 i will upload the mathcad file, and for anyone that hasent, you will have to settle for a very very long RTF! lol

All feedback welcome, as usual point out silly mistakes and other crap! Its 5am here and im exhausted, have an exam in 2 days and generally worn thin of this! But i think im making progress.
thanks
Attached Files
 fyp calcs revised 3.zip (74.0 KB, 0 views)
 P: 28 Hey guys. i want to put a pendulum impact rig on one end of my track. I.E, have assembly attached to one of the endstops which can be deployed for use or retracted if its not needed. the idea of this is to use the pendulum as a start mechanism for the gliders, so that we can control the speed we send them down the track at if it was to be in a horizontal position, i.e no acceleration down the track due to gravity. I need to design one pretty much for the end of my track (a small one) , and the impact needs to measurable. i have seen "impact pendulum" testers in the lab and online, and on these you are able to measure the impact though the use of a circular read out at the centre of the pendulums swing. You think i should make a new thread for this bit? Im not sure how to start.

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