Subject:
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Re: "real" LEGO Hovercraft ? (with/without batteries/RCX "onboard")
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Newsgroups:
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lugnet.robotics
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Date:
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Fri, 29 Nov 2002 21:40:51 GMT
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Original-From:
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Steve Baker <sjbaker1@&StopSpam&airmail.net>
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Viewed:
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857 times
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Jim Choate wrote:
> On Fri, 29 Nov 2002, Steve Baker wrote:
>
> > You know that the pressure of the air inside the skirt multiplied
> > by the area of the ground enclosed by the skirt has to equal
> > the weight of the hovercraft.
>
> There's an echo in here ;)...you'll get to the answer faster if you'll
> think of mass and force instead of weight.
So long as we are down here on the surface of the earth talking about
the air pressure under the skirt of a hovercraft and whether it'll
lift or not, weight and mass are equivelent concepts.
> > If the skirt made a perfect leak-proof seal against the ground,
> > and there were no leaks anywhere else, you wouldn't need a fan
> > at all...you could just fill the skirt with air one-time and
> > it would hold the weight of the hovercraft forever.
> >
> > The only thing the fan has to do is to replace the air that
> > leaks out from underneath the skirt.
>
>
> Which is where the ratio of the input plenum to the skirt (the output
> plenum) comes into play.
Yes - I understand that.
> > That's a function of the perimeter of the skirt and the
> > quality and nature of the skirt.
>
> No, that's a function of the area of the exposed 'ring' or torus around
> the bottom of the skirt which lets the air out.
Yes...although I'd think of it as a cylindrical gap rather than as a
torus.
> Think of it as a box with
> two holes in it. The input hole is fixed and the output hole changes
> area; the input hole moves a fixed volume of air per time and the bottom
> hole has variable volume of air per time (mediated by STP) [1]. You design
> the skirt to keep this output area as small as possible.
Yes - so minimising the surface area of the cylindrical gap between
the ground and the bottom edge of the skirt seems like a good idea.
There are two ways to minimise that area: Control the height of the
bottom edge of the skirt above the ground - and minimise the
circumference of the skirt.
The former seems to be a complex thing to manage - the latter is just
to do with the basic geometry of the craft.
> If that gap gets very big for very long you're going to dump your pressure
> and the hover settles.
Yes...but if (and it may be a BIG 'if') your craft is stable - then
the hover height should be self-controlling. If the pressure becomes
more than needed to support the craft, it'll rise - the gap between
the ground and the skirt will increase, more air will leak out and
we'll lose pressure - causing the craft to sink again. If the the
thing is stable and there is enough air going into the skirt to keep
it pressurized enough to lift the craft - then the gap at the bottom
of the skirt should look after itself.
Of course the ground isn't always perfectly level - and there are
all these complicated issues about the construction of the skirt
keeping it the right shape, etc...but boiled down to it's simplest,
this is a feedback system with inherent hover height stability.
> [1] This is a simple problem, think of a bucket with a fixed input flow
> and a variable hole in it, and you're asking to find the volume of
> contained water at time tau given the function describing the variance
> of the output hole...for a hover sitting still this function is a
> constant (at least for our purposes).
Yep.
> > It's going to be near impossible to figure out the rate of
> > air loss under the skirt - that requires aerodynamics which
> > are beyond the abilities of most (if not all) of us!
>
>
> Actually it doesn't (but if it does, so what?). It does require you to
> think in terms of volume/time however (hint: a given propeller will move a
> certain volume of air in each rotation with various boundary conditions).
> And how do you make the very bottem of the skirt flexible enough it
> follows the ground, -but- not so flexible that the internal air pressure
> blows out the seal...
Dunno - for now, I'll settle for an idealised skirt and a perfectly
flat ground plane - because if a Lego mechanism can't keep *that*
hovering, we can't solve the problem - period.
Once someone can build something that can hover under perfect
conditions, I'm sure we can concern ourselves with the deeper issues.
Right now, we are trying to answer the most basic question of all.
> If folks will stop thinking in terms of open plenum skirts (ie they are a
> simple sheet or curtain hanging from the running board to the ground) and
> more into 'constant volume' skirts (eg tubular skirts) you'll make a lot
> more progress a lot faster.
I don't understand what that means. I kinda assumed the tubular
skirts were simply helping to keep the skirt in the idealised shape.
The hovercraft that people built during the TWO episodes of
Junkyard-Wars (aka Scrapheap Challenge) were little more than
a vertical curtain draped around a large flat plate - and they
all hovered successfully. There was a certain amount of crimping
of the skirt at the corners - and the most recent of the two
episodes had one craft with a more sophisticated skirt - but it lost
out to the 'simple curtain' design.
> A compound design you might try is a tubular skirt with a very short
> sheet skirt attached at the bottem of the tubular skirt. This way the
> tubular skirt gets your height managed and the sheet skirt will take care
> of ground coverage (which tubular skirts are bad at).
OK - I can understand that.
> One of the primary maintenance tasks of real world hovercract is the
> replacement of the ground side skirt edge, they wear a -lot-.
I can believe it.
> > * Minimising the perimeter length of the skirt is a good thing
> > because it reduces the amount of air loss. The size of the
> > gap between the bottom of the skirt and the ground must play
> > an important factor here - and that area is the 'flying height'
> > of the bottom edge of the skirt times the perimeter length
>
> Not sure what you mean by 'perimeter length' but I suspect you're talking
> about the length of the line of ground contact with the skirt.
Yes - exactly.
> If you
> reduce this you also -increase- the necessary forces and air volume needed
> to get this thing off the ground to start with.
Why?
Seems to me that the rate at which air can escape from a container
under pressure must increase if the size hole it's escaping through
increases...that's just common sense.
So if you had a 'skirt perimeter' (definition above) of 1 meter and
a gap of 1cm between the bottom of the skirt and the ground...then
the hole that the air is escaping through is 0.01 meters-squared. If
I reduce the 'skirt perimeter' - to just a half meter - and maintain
that 1cm gap - then the hole that the air is escaping from is half
as much.
This leads me to assume that minimising the skirt perimeter would
reduce the amount of air flowing out from under it...all other things
being equal.
So can you explain the flaw in my reasoning? I'd like to learn.
> Probably -not- a good
> design constraint to play with. If we assume we're going to stay with a
> open plenum or curtain skirt (we can use this same assumption for tubular
> skirts) then we need to look at the -area- of the ground enclosed by this
> perimeter, rather than the perimeter itself. That should be taken as the
> area of the running board in most designs.
Right - the area seems to be vitally important. However, the ratio
between the area and the perimeter seems to be the important thing.
Increasing the area lowers the pressure you need...but
Increasing the perimeter increases the air lossage under the skirt.
...but: Doubling the diameter of the craft quadruples the area and
only doubles the perimeter - so "Big is Beautiful".
> An additional factor is that with smaller ground surface covered you need
> increased pressure inside the skirt, which means when you do get a gap
> the air moves out at a very high speed (rho=mv). You want just enough
> pressure to get the skirt inflated and a reasonably steady bleed of air
> around that ground contact line. This means that you want the skirt to be
> only just enough above ambient pressure to do the job. That is why you
> don't need a lot of power with a good design.
Right...we agree.
To keep the pressure only *just* above ambient, you need a LARGE area
to distribute the weight of the hovercraft over.
> > The flying height will minimise itself - if the air loss is
> > too great, we'll lose air pressure, the hovercraft will start
> > to sink - which will reduce the amount of air loss - which will
> > allow the air pressure to build up again.
>
> No it won't, what it will do is blow the bottem of the skirt out and dump
> all your pressure and settle the hover.
That depends on the design of the skirt. If it's very stiff, that
won't happen.
> The input plenum is fixed
> volumetrically. Additionaly, you'e got momentum effects, so that when one
> corner starts to dump it will lower, and this -raises- the opposite
> corner thus dumping there. It's somewhat similar to a see-saw (but don't
> take that too literally). And around and around we go...
Yes - I can imagine that stability is an issue.
> You're hover will bob like a bouncing ball, that is considered a -very-
> bad design. This effect is one of the primary reasons most hovers work
> over water and area of smooth surfaces only. It makes the job of keeping
> ground contact easy because it's smooth.
Yes.
> > If you let the air out of a pressurized container, it flows out
> > fast to start with when the relative pressure is high - and then
> > slows down to zero as the pressure drops.
>
> Assuming that on inflow replaces that escaping. Not true in a hover. Your
> basic idea is right, you need to refine the variables you're thinking a
> bit.
I didn't mean this example literally. I was merely pointing out that
if the pressure inside the skirt is low, the rate of loss of air under
the skirt will be lower.
What I don't know is *how* it's related.
Is the loss rate proportional to the difference in pressure - to the
square of the difference? The square root of the pressure? The
phase of the moon times the obliquity of the ecliptic times the
pressure? What?
> > So, a large footprint seems like a good idea. However, it
> > all depends on how the speed of the air leaking out from under
> > the skirt varies as a function of the air pressure inside.
>
> Volume of air leaking out from the skirt.
...which depends on the speed of the airflow times the cross-sectional
area it flows through. Since the cross sectional area is the
height of the bottom of the skirt above the ground times the
skirt perimeter, what I actually would like to know is the SPEED
so I could get some idea of how the size of the craft affects the
amount of air we have to pump in to get it into hover.
> > If halving the air pressure (P) halves the speed of the air that
> > leaks out (S):
> >
> > S = P x constant
>
>
> It's not linear, it's exponential.
OK - that's nice to know.
So we'd expect that halving the relative pressure would more than
halve the rate of air lossage?
That would definitely indicate that we want the hovercraft to be
as large as possible.
> > In terms of engine RPM and propellor design, we know that the
> > propellor has to push enough air under the skirt to exactly
> > equal the lossage from the edge of the skirt.
>
>
> The propellar most move enough volume. One way to think about this volume
> is to ask the question:
>
> How far will the propellar move as it turns if it is left unconstrained?
>
> If the propellar is constrained then the air will do the moving...
Yes - and a good first approximation is to figure out the pitch of
the prop and from that you can figure out the distance it would
travel in each revolution - multiply that by the area of the disk it
sweeps out and you can easily estimate the air volume it'll shift at
a given RPM.
However, that all presumes that the pressure on each side of the
propellor are the same...in the case of a hovercraft, the pressure
on the 'skirt side' of the prop is higher.
Once again, a large skirt area is desirable because that decreases
the pressure you need inside the skirt - and that increases the
efficiency of the propellor.
---------------------------- Steve Baker -------------------------
HomeEmail: <sjbaker1@airmail.net> WorkEmail: <sjbaker@link.com>
HomePage : http://web2.airmail.net/sjbaker1
Projects : http://plib.sf.net http://tuxaqfh.sf.net
http://tuxkart.sf.net http://prettypoly.sf.net
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