Designing an Airtrack for Mechanical Experiments: How to Get Started

[adamxrt]

Hello,

Could anyone help me understand what I am doing here. This is NOT a homework question. I am a mechanical engineer in my final year at uni, and my project is to design and build an airtrack for a range of undergraduate mechanical experiments.

Im sure many of you have seen videos of airtracks operating on youtube and the like,... well my project is to take those airtracks and expand and make them better so that they may be used for a range of experiments through different topics, and eventually actually design and build it.

My understanding of mechanics and dynamics is decent enough, but definitely not my strongest point. I am more of a concept/cad/design minded engineer, but i took this project in order to challenge myself.Now, I am trying to go through the basics of how airtracks operate, and give near frictionless movement. Obviously i have to create this environment with my airtrack, so i have to know how it works. I know the airtrack creates a layer of air underneath the slider to counteract the downward force of the slider. But i don't know where to start with the actual maths etc behind it.

The airtrack is going to be a 2m long triangular(isosceles with the 90 degree apex pointing up) aluminium tube, and i need to set the air pressure, need to define how many holes to drill through the surface, their spacing, how heavy to make the sliders... etc etc.So there are a lot of things to work out, but in order to do all these i need to do th emaths first.

Can anyone help me start? where do i start? The area in particular i am focusing on at the moment is how the air coming out of the airholes creates a pressure and forces to hold the slider in equilibrium..
heres an airtrack in operation.

Many Thanks!

 

[technician]

The apparatus you describe is a fairly standard piece of equipment and usually uses aluminium 90 angle 'sliders'. In my school we made one along the lines you suggest, the air exit holes were very small, about 1mm diameter and spaced evenly on each side of the tube about 50mm apart. It worked well.
We also bought a commercial one which was very similar.
the air source was an old vacuum cleaner set on blow.
I think the main thing to realize that the air arrangement is to supply a thin film of air between the slider and the track rather than to provide a pressure to lift the sliders any great distance. With such small diameter holes the air flow problem is negligible. think it is a practical exercise to get it working rather than a mathematical exercise to design something that will work.
Hope this helps...it is not a difficult thing to make, just take care drilling and de-burring the holes.
PS
You need to go to some trouble to see that the tube is well supported with some means to adjust the level.
Tomorrow I will photograph our set up and if you are interested I will post the photographs.

 

[sophiecentaur]

I guess what you're after is an idea of the actual pressure that's needed. Not an easy question to answer fully but, for your glider to be supported, the pressure underneath it needs to be at least its weight divided by the area of the base. Air will come out of the small holes in the track and, mostly, spray out into the atmosphere. The air from the holes underneath the glider will be 'trapped' or 'delayed' on their path to the atmosphere via the base of the car.
The leakage from under the glider will depend on the clearance and 'flatness' of the contact and the balance. If the car is lopsided then air will escape from one side and lower the pressure enough for the car to 'ground'. Assume that everything is just right, for a start.

From memory, a standard glider will have a mass of about 0.5kg, so a weight of about 5N. The area is around 0.02m². The minimum pressure to keep it up would be
5/0.02=250Pa.

Atmospheric pressure is about 10⁵Pa so the minimum pressure needed would be only 1/400 Atmospheres. That's not very helpful but is IS a minimum value. Allow a factor of 10 (why not?) and you're up to 1/40 Bar or 2.5kPa. I should think that. if your blower can maintain that pressure when supplying all the holes you have then your glider should 'glide'.

I guess the point is that you need a LOT of air at low pressure, rather than a high pressure source with not much volume.

PS. I feel very smug because I just found a link for an air track system that is requires > 5.8kPa - only twice what I estimated. YES MY SON!. Note the tight tolerances there are for clearance.

 

[adamxrt]

Sophiecentaur, that's the type of info I am after. Surely there's more to it though? I mean what youve described to me is very basic.


Look at it this way.. how do i go about finding an arrangement and a pattern for drilled holes to provide me with adequate pressure of 250Pa??



Hi technician, i see what you are saying. Unfortunatley i cannot just get one to work in a practical sense...this is my final year project and everything will have to be pre thought out and calculated before anything gets made. so Unfortunatley i will have to mathematically design it!



And surely there would be some flow rate equations to be applied due to air flowing though the holes?

After all this is my final year project and detail is required where it can be found!

 

[adamxrt]

I have attached a cad picture to this post of what i have for a preliminary design. (very Early) the airtrack will have modifiyable angle of incline via a leadscrew. I am also looking at the use of reed swith magnet circuids and bicycle pedometers for the measurement of the slider postion times. We're also looking into a laser. but what you see along the edge of the track are small magnets.

 

[technician]

I don't know what your brief is but I would suggest that air flow and pressure problems were the last thing you needed to worry about.
The only other practical advice that I can offer is that the holes along the sides of the track should be towards the edges of the riders, I would say about 2/3 of the way from the apex. Thefirst one I made had the holes near the apex and the riders tilted and touched the track. I blocked these holes with plasticene and drilled a new set furthe down the track and that worked.
If I had to guess I would say it had something in common with hovercraft. The first hovercraft was a large fan blowing air down from the centre of the craft. A great improvement was to deflect the air into a skirt, this meant that the air from the fan 'trapped' air underneath the hovercraft and less power was wasted because less air escaped.
I like to think that the holes lower on the rider 'trap' air above them and ensure a more stable hover.
I would also add... as a guide... that you need at least 3 holes along the length of a rider.
If your brief requires a tilt mechanism do you realize that you will need a bearing of some sort to cope with the changing angle of the screw as the track is raised?

 

[adamxrt]

I don't know what your brief is but I would suggest that air flow and pressure problems were the last thing you needed to worry about.
The only other practical advice that I can offer is that the holes along the sides of the track should be towards the edges of the riders, I would say about 2/3 of the way from the apex. Thefirst one I made had the holes near the apex and the riders tilted and touched the track. I blocked these holes with plasticene and drilled a new set furthe down the track and that worked.
If I had to guess I would say it had something in common with hovercraft. The first hovercraft was a large fan blowing air down from the centre of the craft. A great improvement was to deflect the air into a skirt, this meant that the air from the fan 'trapped' air underneath the hovercraft and less power was wasted because less air escaped.
I like to think that the holes lower on the rider 'trap' air above them and ensure a more stable hover.
I would also add... as a guide... that you need at least 3 holes along the length of a rider.
If your brief requires a tilt mechanism do you realize that you will need a bearing of some sort to cope with the changing angle of the screw as the track is raised?

Yeah. I am well behind on all this stuff. Bearings etc, will all come into play in the final design. What you see there is my early final concept. My Tutor wants me to concentrate on defining the variables included in the mechanics of the airtrack, and also the dynamics behind the possible experiments 1st. My brief is very open.

For example, we're looking at having a dc motor on a lang slider and investigating the vibrations on a frictionless surface,

Possibly attaching a CPU fan to a slider to investigate thrust, have clay end stops to investigate collisions. there's a whole range of things to go through. All in due course though.


This is the thing man, there's so much going on that i literally haven't a clue where to start!


In my notes for my next meeting, i have to determine load capacity, airflow, hole diameters spacing and air pressure, begin looking into a starter mechanism, and begin looking at sleigh design.

 

[technician]

3 holes per slider near the bottom edge. Start with that

 

[adamxrt]

3 holes per slider near the bottom edge. Start with that

Sure, sounds like a decent idea, do you mean that the rider will always be "over" 3 holes at anyone given time in the length of the slider direction?

MY tutor will probably ask me how i came to such an number but ill just have to tell him i made assumptions for this par.

Did you play around with hole spacings in the breadth of the slider direction? or did you have them square 50*50 mm

 

[technician]

I came to the conclusion 3 holes per rider because I do a lot of sawing (metal and wood) and it soon becomes obvious, from a practical point of view, that you need at least 3 teeth in contact with the material.
Thin metal needs fine teeth

 

[sophiecentaur]

Possibly attaching a CPU fan to a slider to investigate thrust, have clay end stops to investigate collisions. there's a whole range of things to go through. All in due course though.

I have used several blowers for a single run of demo airtrack, used in School. We tried various makes of cylinder vacuum cleaner (on blow) and none of them was anything like as good as a purpose built blower. I think a CPU blower would probably be inadequate - because that isn't what it was designed for - and you may be wasting your invested time if you spend too much time on trying it.

If you are doing a design study then I don't think there can be any objection to seeing what existing designs are like ('the shoulders of giants' ,as Sir Isaak said and "genius steals" which I believe Picasso said).
I like the idea of having the holes near the edges of the sliders and the other practical points made by technician.

The sort of calculation that I showed in my other post are pretty certainly what your tutor would like to see - as long as you can justify your assumptions about masses, areas etc. You could also look at data on the flow rates of air through various sizes of small hole for various pressures. Using a value for required pressure and multiplying by the number of holes should give an indication of the volume of air needed per second and help you to come up with a realistic spec for a suitable blower.
Any more calculations about the rate of air escaping from under the slider for a given ride height would be a bit difficult - you'd need to do actual measurements.
Do you have access to a seriously beefy blower or is your suggested CPU blower all you have? You will need to be pretty ingenious with a short length of track design as leaks are a real issue with home made gear of this sort. Consider a vacuum cleaner instead.

 

[Integral]

From looking at your picture my thought is that you do not need that much angle adjustment. If these are very slightly out of level you get a very good acceleration. As steep as you pic shows it is not clear to me that the glider would ride correctly.

 

[adamxrt]

I have used several blowers for a single run of demo airtrack, used in School. We tried various makes of cylinder vacuum cleaner (on blow) and none of them was anything like as good as a purpose built blower. I think a CPU blower would probably be inadequate - because that isn't what it was designed for - and you may be wasting your invested time if you spend too much time on trying it.

If you are doing a design study then I don't think there can be any objection to seeing what existing designs are like ('the shoulders of giants' ,as Sir Isaak said and "genius steals" which I believe Picasso said).
I like the idea of having the holes near the edges of the sliders and the other practical points made by technician.

The sort of calculation that I showed in my other post are pretty certainly what your tutor would like to see - as long as you can justify your assumptions about masses, areas etc. You could also look at data on the flow rates of air through various sizes of small hole for various pressures. Using a value for required pressure and multiplying by the number of holes should give an indication of the volume of air needed per second and help you to come up with a realistic spec for a suitable blower.
Any more calculations about the rate of air escaping from under the slider for a given ride height would be a bit difficult - you'd need to do actual measurements.
Do you have access to a seriously beefy blower or is your suggested CPU blower all you have? You will need to be pretty ingenious with a short length of track design as leaks are a real issue with home made gear of this sort. Consider a vacuum cleaner instead.

I think you maybe misunderstand what i mean about computer fans. We haven't specced a blower yet. I meant that a fan can be attached to a battery, and placed on a SLIDER, to investigate thrust of a fan under frictionless conditions! Thanks for the suggestions on looking up flow rates! ill do that now.Can you clarify some things about your last calculation please??You mention including a factor of 10...that brought you up to up to 2.5kPa...why? i don't fully understand.Also when you were speaking about area of the slider..did you mean just like a flat area? Look at the attached picture to see what i mean.
I made an assumption of, for the sakes of getting some calculations down,
Slider length=200mm
2 rows of holes
Base of slider pitch =100mm
mass=150g so weight=1.47N

i tried to a bit more indepth than your calculation, worked out a load at 45 degrees to the face of the track for either side, to find the normal force it would take come straight out perpendicular to each face, to hold the glider in equilibrium. Maybe I've tried to be too clever and done it stupidly...
anyway i came out with a force of
0.625N to come out of each face...and then the pressure supplied would be the area of that face divided into that force...My area for the face turned out to be 1/150m^2 so pressure is 94Pa, if i included a factor of 10, 940PaObviously I've probably calculated for too light a weight. But its a start anyway.What do you make of it? But if you could clarify the point above?

 

[adamxrt]

From looking at your picture my thought is that you do not need that much angle adjustment. If these are very slightly out of level you get a very good acceleration. As steep as you pic shows it is not clear to me that the glider would ride correctly.

Yeah that became apparent once i thought about it afterwards. I maybe got over zealous with the CADing up of it. there's no way it would need to be that high i should think. Plus i need to leave room for adding in a starting mechanism.

Thinking a compression spring..., maybe a blast of compressed air (very hard to measure how much force this would give though), or a pendulum impulse hammer, which u see a very very very vague one half modeled in the picture.

 

[adamxrt]

Ok back onto this tonight! i had a meeting with my project overseer on thursday. He was expecting a lot more indepth work for the pressure and airspeed bwtween the glider and the track! he gave me a lot of stuff on bernoullis theorem and told me to assume incompressible flow (Q=VA) for this area and go work on it further. i wish i had gone straight back onto it after he spoke to me because I've forgotten the most of the things he said and i can't find where i wrote it down! Just have the equations.
anyone have any idea how to apply this?

 

[sophiecentaur]

2adamxrt

You asked me why I chose a factor of 10 up on my estimate. That's a pragmatic / practical approach so as to err on the safe side. Fluid engineering is not my field - in Electronics, you'd be working to within +/- a few % and with antenna design you would be happy within a factor of 2, perhaps.

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.

 

[rcgldr]

The math for this is somewhat complicated. You need a required rate of flow at some amount of pressure going into the track. There's a pressure loss as air flows through the holes, and a second pressure loss as air flows from the holes outwards towards the edges of the slider. Compounding the matter is that the air flow expands radially outwards from the holes in the track to the edges of the slider which contributes to the pressure loss from the holes to the edges of the sliders.

The sliders themselves are somewhat self-stabilized, since if one side "pinches" the air flow, the pressure increases and corrects the slider. The hole spacing will need to be fairly uniform with the holes lined up at any cross section of the track to maintain stability.

 

[adamxrt]

thanks for the replies. that seems like the best logical structure to approach from, SC.

rcgldr. If i understand you correctly, pressure loss occurs when the air particle is still in the cutout of the hole. I was aware of that. There is then another 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 there's a sub loss after this? I don't fully understand how that comes to be? is it something to do with roughness of the glider surface?

 

[rcgldr]

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 there's 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.

 

[adamxrt]

to anyone reading

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.

 

[adamxrt]

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 I am assuming incompressible flow!

heres what I am 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 I am approaching this is, I am 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 I am 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 isn't right. I am 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, I am not the most intelligent of people but I am trying! I am not going to coast this year!

 

[sophiecentaur]

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.

 

[rcgldr]

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 achieve 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.

 

[sophiecentaur]

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?

 

[adamxrt]

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 I am 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 won't 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!

 

[sophiecentaur]

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.

 

[adamxrt]

well guys, I am very happy to say i have a solution for this problem. Please see below, I am 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

 

[adamxrt]

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!

 

[sophiecentaur]

adam
I spotted a dodgy bit as soon as I saw your calculated air velocity (407m/s). The speed of sound in air is only 330m/s and that would imply some pretty extreme conditions in your track! Sorry, but is supersonic flow likely?The required (excess) pressure under the glider seems right @ 260Pa but I don't see how you get your next step at all (which gives you that unreal answer). That 'v²' equation springs up out of nowhere and what does it relate to? You seem to be assuming that air is flowing from a region of Atmospheric Pressure, in an uncontrolled way, into a region of 260Pa pressure. That, surely, is not what's happening. The pressure under the slider is Atmospheric Pressure PLUS 260Pa. In which case the air flow would, at least, be outwards.

You still seem to be tackling this the wrong way round. What is important is that there should be sufficient pressure under the glider as air leaks out. So, surely, you first need to be working out the airflow through the gap underneath the glider in order to maintain your 260Pa excess pressure. I suppose your equation could give you an airspeed under the edges of the slider which could be the right sort of value. The actual volume of air being moved per second would be the 'exit slot' CSA times this new velocity (area times velocity is volume flow rate). Here, you need to choose a ground clearance value.

Then you have to think about how many holes you have under the slider and the air flow required for each, with AP+260PA at their exit. Google Airflow through Orifice for some info. This is easier to find out about because it's 'gas stove engineering', which is a much more common field of study. Once you have done this, you can find just how much air needs to be pumped into the track, to maintain this pressure with a hundred or so little holes in it - same 'orifice' calculations.

Do you appreciate why I say it should be done this way round?

[Edit: I'm not sure your tutor has his eye on the ball if he doesn't spot that pressure error! Don't tell him I said so, though]

 

[adamxrt]

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, I am 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 that's 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.

 

[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.

 

[cjl]

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)

 

[sophiecentaur]

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.

 

[cjl]

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).

 

[adamxrt]

I have taken everybodys concerns and considerations into mind and have kept them there for now.

this is a nasty old problem, and I am 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 I am literally just trying to get a raw feel for what's going on.


I have rejigged the whole lot and delved a bit deeper. I am 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, I am 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 I am exhausted, have an exam in 2 days and generally worn thin of this! But i think I am making progress.
thanks