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 15:21:44 GMT
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Original-From:
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Steve Baker <sjbaker1@airmail./IHateSpam/net>
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Viewed:
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834 times
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Jim Choate wrote:
> On Sat, 30 Nov 2002, SuperFly wrote:
>
> > i want to do it but i think we would have to figure out the power to weight
> > ratio does anyone no the formula
>
>
> It's not one formula.
>
> The first hurdle is to balance the force of gravity.
>
> F=ma
>
> m is the weight of the hovercract assembly.
>
> a is the -negative- acceleration due to gravity.
>
> F is the total force the fan must provide.
>
> Then you've got to figure for a given fan/rpm design what
> the air flow is.
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.
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.
That's a function of the perimeter of the skirt and the
quality and nature of the skirt.
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!
So - we won't know the QUANTITATIVE answer without testing
some designs.
However, some QUALITATIVE things are evident:
* 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.
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.
* Maximising the area of the ground enclosed by the skirt
reduces the pressure you need. (a one pound hovercraft with
a 100 square inch 'footprint' needs 1/100th psi of air pressure
to lift it...but a one pound hovercraft with a 200 square inch
footprint only needs half of that!)
* Decreasing the air pressure inside the skirt also reduces the
amount of leakage around the edges. The speed that the air
flows out from under the skirt must be related to the pressure.
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. If low pressure means
the air leaking out is moving slower - then the amount of air
we have to pump back in to keep the skirt inflated will be less.
* Keep the hovercraft light - the pressure needed under the skirt
is directly proportional to the weight of the hovercraft.
The trouble is that these design aims are contradictory. Increasing
the area of the footprint also increases the perimeter length and
the weight.
Having a nearly circular hovercraft minimises the perimeter to
area ratio - because a circle is the shape that encloses the
largest area for the smallest perimeter (that's why soap bubbles
are spherical).
For a circular hovercraft, doubling the radius of the skirt
quadruples the area of it's footprint and only doubles the
perimeter size. That's good - quadrupling it's area reduces
the pressure we need by a factor of four - but doubling the
length of the perimeter only doubles the rate of air lossage.
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.
If halving the air pressure (P) halves the speed of the air that
leaks out (S):
S = P x constant
- then very large footprints are a good idea. However,
if the relationship between the air pressure and speed of loss
is (say):
S = sqrt(P) x constant
- then doubling the size of the skirt reduces the pressure by
a factor of four - but that only reduces the speed of loss by
a factor of two - which is exactly compensated for by the
doubling of the skirt's perimeter.
Of course it could be that we have:
S = square(P) x constant
...in which case, the efficiency of the system goes up dramatically
with larger skirt sizes.
Unfortunately, that also quadruples the weight of the 'decking'
but only doubles the weight of the skirt.
This suggests that LARGE hovercraft will do better than small
ones - providing you can keep the deck light. If the deck were
made of a circle of thin foam polystyrene - you could have a very
large footprint with a relatively short perimeter.
While we are looking at non-lego solutions, you could note that
balsa wood construction is lighter than foam polystyrene in many
cases because it can be much thinner and still be strong enough.
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. However, the
amount of that lossage as a function of the air pressure
is not well known because it depends on nasty aerodynamics
calculations that I at least can't do.
---------------------------- 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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