Water Power

[Pete (Nebula)]

Last weekend, I tried to induce a little more interest in science into
the kids by taking them to a local park armed with a water bottle
rocket, an electric car tyre inflator, some batteries and water.

Aside from getting very wet (and having to agree to build a bigger one
out of 40mm plastic pipe), I wondered if it were possible to go much
higher with water. A quick search revealed:

http://tinyurl.com/6hyd4t

Did anyone else have a similar idea to this fellow?

Pete

[MisterQED]

I ran into this link a while back and what impressed me most was the
parachute deployment and multiple staging.
I wonder what pressurizing devices are allowed for the record as
peroxide would have more punch than air, N2 or CO2.
I will do some testing this weekend and see how my attempts at this
style of rocketry compare to yours. :-)

MisterQED
Team Daedalus

[Pete (Nebula)]

QED

Done! I'm coding the engine management system right now which just
involves a lot of sitting around, drinking wine and tapping at a
keyboard so I could do with a bit more field work. I'll do a video and
we can compare results!

Best

Pete

[Sage (LMR)]

QED,

Regarding H2O2, you can actually get much higher Isp (than these types
of water rockets) not only because of the increased pressure but
because of the thermal conditions (assuming catalytic decomposition) –
quite different. Steam rockets (flash boiling) also provide thermal
advantages as you gain kinetic energy due to the change in enthalpy
through the nozzle – you can generally get a significantly higher Isp
than the equivalent pressure might provide in a ambient temperature
compressed gas water rocket.

But, I don't think that H202 or steam would qualify for this type of
rocket! On the other hand, if you're just looking for a gas
pressurant itself in a traditional water rocket, there are many
interesting possibilities, but N2 and CO2 are both quick and easy.

~Sage
www.littlemonsterrocket.com

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[Sage (LMR)]

Pete,

Good stuff! I love water rockets... It's just one of those
things... I even considered making a little side business doing it.

Several years back an acquaintance of mine told me about a student
outreach program that his employer (Rocketdyne) was conducting. So,
we made a pitch to them to present rockets to students. They turned
us down due to liability concerns. So, we re-pitched the idea with
water rockets – and, they still turned us down due to liability
concerns! Their comment was to the effect: “Well, what if it hits
someone in the head?! Then what will we do?!” As ridiculous as that
is, it's 'actually' what they said. When people are that afraid to do
anything, there's something terribly wrong.

Anyway, this guy in the video is certainly kidding around (at least I
think he is)... For a really rough calc, assume no losses,
incompressible flow and adiabatic conditions... velocity of the fluid
by Bernoulli (ignoring losses, thermal, etc.) is about pressure1 +
density*velocity1^2/2 = pressure2 + density*velocity2^2/2... treat
the velocity in bottle as ~0 for a rough estimate, then exit
velocity=sqrt(2*deltaPressure/density). Assuming 2L bottle, ~0.5 full
of water (thus ~1L of compressed air), the air pressure will drop to
about Pstart*1.0/2^1.4 during expansion (assuming ideal gas and air
approximated as diatomic) before all water is released. He states
1150 psi starting on the video. Thus, starting deltaP= 1150-14.7 = ~
1135.3 psi, or ~7.828e6 N/m^2.... density of the water is about 1000
kg/m^3, thus Ves=~sqrt(2*7.828e6/1000.0) = ~125 m/s... starting exit
velocity. Ending deltaP= ~435.8-14.7 =~421.1 psi, or ~2.903N/m^2...
Vee=~sqrt(2*2.903e6/1000.0) = ~76.2m/s... ending exit velocity.

So, a very rough estimate (averaged over the “burn”) of perhaps
100-105 m/s water exit velocity given adiabatic conditions (of course,
it's not actually linear but for this rough estimate I'll let it go);
the remaining air expansion gives some thrust as well, but we'll
ignore it for this quick check... That means the average Isp is
perhaps a “massive” 10 to 11s! Starting at around 12.8s and dropping
to about 7.8s. Hey, that's not bad for a water rocket, actually (it
is after all, at 1150 psi -- just a little more than your average
water rocket(!))...

So, I guess it's the definition of orbit that counts! I mean, the
Earth is in orbit , so technically the rocket is in orbit too(!)...
thrust =~ velocity * mdot and from the video it looked looked like
about a 2.5 sec “burn” time... about 1kg of water (assuming 0.5
full)... average thrust= ~101 x (1.0/2.5) = ~40.4N or about 9 lbs.
Not too shabby for a water rocket...

BTW, very roughly via the approximate average exit velocity:
deltaV(ideal) = ~ 101*ln(MR), assuming 100g for the bottle rocket,
MR=1.1/0.1=11...
deltaV(ideal) = ~ 242 m/s – of course much of this is lost (obviously)
to atmospheric drag and gravity...


...and certainly don't put too much into these immensely rough
calcs... they're meant only as quick “water rocket level” ballpark
estimates (at best!)...


~Sage
www.littlemonsterrocket.com

[Sage (LMR)]

BTW, note that the thrust mentioned would be delivered average over
the “burn” time estimated from the video... some water rockets are
made really high thrust (relative to a water rocket, of course!), but
quite short duration...

~Sage
www.littlemonsterrocket.com

[Pete (Nebula)]

Hi Sage

I get the feeling from what you say that Rocketdyne just weren't
interested in a student outreach programme. You can get around just
about all public concerns with a suitable (and usually very small)
insurance premium - at least here in the UK.

That's a very nice analysis of the water rocket, especially since the
guy's use of an incompressible liquid means the system is more akin to
plumbing than to rocketry, however I think the performance is
considerably lower than even this since I don't believe the losses to
be inconsequential.

To get an average flow rate of 100m/s over the observed 2.5 second
burn time, the outlet pipe would have to be around 1.6mm in diameter,
and looking at the picture it seems considerably more than this. If we
go a step further and estimate an outlet pipe length of around 5cm at
this diameter, then the pressure drop between the ends of the pipe
(assuming an initial 1150psi in the bottle) is of the order of 370psi,
with a Reynolds Number of 1.6x10^5 .

Incidentally, don't you just hate the fact that MathML /LaTeX is still
largely unsupported by these fora. Your last post is excellent in that
it brings together in an easy-to-follow fashion, a number of equations
that comprise a good first-order explanation of the complete system.
This is something that I'm sure a lot of people will find useful and
would greatly benefit from display in mathematical notation.

I've had a go at using MathML on my site, but found that a couple of
popular browsers don't support it (Firefox does natively, and IE does
with a plugin). However, I'm going to have a go at putting the
derivations for my solution on the site for public use/examination.
Have you bent a braincell in this direction - the one thing that seems
to be missing from the competition so far is a good individual
explanation of what direction each team is taking towards the n-prize,
and I'm going to try to address that at least from the Nebula point of
view.

Best


Pete

[MisterQED]

Hey Peter, how did you do the launcher?
A quick search seems to lead me to an idea based loosely on this plan:
http://www.opentutorial.com/Make_a_water_bottle_rocket
I like the fact that it can hold it and then I release when I get the
correct pressure.
I am intrigued to try a water bottle wrapped with fiber packing tape.

MisterQED
Team Daedalus

On Jun 5, 2:00 am, "Pete (Nebula)" <pe...@nebula-prize.com> wrote:
> Hi Sage
>

> I get the feeling that Rocketdyne just weren't interested in a student

> outreach programme. You can get around just about all public concerns

> with a suitable (and usually very small) insurance premium.
>
> That's a very nice quick analysis of the water rocket, especially

> since the guy's use of an incompressible liquid means the system is
> more akin to plumbing than to rocketry, however I think the
> performance is considerably lower than even this since I don't believe
> the losses to be inconsequential.
>
> To get an average flow rate of 100m/s over the observed 2.5 second
> burn time, the outlet pipe would have to be around 1.6mm in diameter,
> and looking at the picture it seems considerably more than this. If we
> go a step further and estimate an outlet pipe length of around 5cm at
> this diameter, then the pressure drop between the ends of the pipe
> (assuming an initial 1150psi in the bottle) is of the order of 370psi,
> with a Reynolds Number of 1.6x10^5 .
>
> Incidentally, don't you just hate the fact that MathML /LaTeX is still

> largely unsupported by these fora. It would make life a lot easier.
>
> Best
>
> Pete

[Pete (Nebula)]

Hi QED

The first variant used a simple rubber bung stuffed into the opening -
sorry, rocket nozzle - that had a v. small diameter tube passed
through the middle to allow the compressed air in. Once the pressure
had built up to the point the bung lost stiction, the bottle went up
and the bung/compressor stayed on the ground.

Since then however, I've built another based around 40mm waste pipe
that resembles more than anything an AIM 9L sidewinder. This one uses
a reusable stopper from a wine-bottle (the kind with an expanding
centrepiece) so that I can release at the correct pressure with the
flick of a lever. Unfortunately, this means I have to be near it to
set it off which means that I still get wet. The good side is that I
now have an excuse not to save a partly-drunk bottle of wine for
later.

If the weather improves this weekend, we're all stomping off to a
nearby field to give it a go. I'm not hopeful however, because the new
one weighs a ton (not literally).

Good luck with your bottle wrapped with Gaffer/Duck tape. I'm still
not sure how the Canadian chap managed to get the bottle-rocket
altitude record when he had to wrap the bottle in kevlar!

Best

Pete

[Sage (LMR)]

Hi Pete,


1)
Well, believe it or not, Rocketdyne was actively looking for such
student outreach programs at the time! They were all for us doing
other “types” of programs (such as presentations, simulations, etc.),
just no live demonstrations. The problem, as it was explained to me,
was that Boeing (who then owned Rocketdyne) simply did not want to
expose themselves to that type of a liability (live demonstrations).
Basically, the larger the company, the more likely the lawsuit, and
they didn't think it was worth it for the outreach.


2)
Yes, I endeavored (in my earlier post) to emphasize that the actual
performance would be lower (due to various losses). The flight losses
themselves constitute a major hit (in other words, the drag and
gravity losses), so even with exceptional “engine” performance itself
the delta-V obviously won't get there in the atmosphere – much of it
will be lost to drag and gravity (as I had mentioned earlier), but
that was just a quick check on the ideal.

The other thing is that I was really 'generous' with the mass ratio; I
selected a weight around 100g (a bottle is about 50g, so I simply
doubled it), but with all that bottle reinforcement it could easily be
several times heavier (possibly even 500g or more). Obviously, if
such were the case the ideal delta-V would be far lower. The overall
concept here was simply a rough estimate of potential capability in an
ideal sense.


3)
As I noted in the earlier post, certainly the engine itself is going
to have flow losses and such; they may be significant depending on the
design (but you might be surprised). I didn't include such flow/
discharge coefficients because I wanted to get an idea for the maximum
performance and this was intended just as a quick check on the ideal.

The flow rate was among the most rough estimates since it was a guess
gathered from simply watching the video and observing the water until
it seemed as though the main thrust stopped, which had appeared to be
about 2.5 seconds or so (could have been somewhat more or less). It's
also a guess that the amount of water is ~1L (about 0.5 full); could
be more or less. These are unknowns, and they would obviously affect
the actual figures. Again, just a rough ballpark...

Anyway, 0.4L/s and 100m/s is roughly about A=qdot/v, or ~4mm^2 area,
or ~2.26mm (0.9”) diameter throat, this would be under fairly ideal
conditions and assuming those rough flow rate estimates. The venturi
nozzle (assuming it has a proper entrance cone) might provide a fairly
high discharge coefficient. But in any case, I watched the video
again and the “burn” is perhaps closer to 2s, which increases the flow
rate somewhat and also the nozzle diameter. So, let's say somewhere
between 1.5s and 2.5s (again, could be a bit more or less) and do them
both... Again neglecting a flow coefficient (assuming k=~1) and just
treating qdot=~kAv, 0.0004/100=4e-6 m^2, or about 4mm^2 area... That's
about 2.26mm (0.089”) throat diameter given the first 2.5s estimate.
With the second 1.5s estimate, 0.00067/100=6.7e-6, about 6.7mm^2 area,
or about 2.92mm (0.115”) diameter.

As a secondary check, thrust is about 2*dP*At, linear average delta
pressure is around 793 psi, and via midway expansion around 652 psi.
Selecting the original 2.5s burn, throat is ~0.089” diameter or
0.0062in^2. Thus, original average thrust estimate should somewhere
around 2*(652-14.7)*0.0062=~7.9lbs and 2*(793-14.7)*0.0062=~9.65lbs.
The average estimate at 2.5s burn and 1L was ~9lbs, so this checks.

So, if the flow rate guesses are reasonable, I would surmise that the
throat diameter might be around 0.09” to 0.125” (roughly 2-3mm) given
an ideal case, and the actual perhaps a bit more depending on the
nozzle, it's design, and design exit pressure, but probably not much
more than about 0.15” (~3.8mm) with k=~1. So it's probably somewhere
within that general ballpark, say about 0.12” +/- 0.03” (3mm +/-
0.762mm).

Re hovers around 2.2e5 through the throat section at 100m/s, but by
the time the fluid enters the section, it would have dropped to
roughly atmospheric pressure (via the venturi) based on the nozzle
design assumption used in the rough estimate. I simply used
atmospheric at the exit to roughly approximate the highest reasonable
exit velocity attainable. I didn't notice any extra long throat
sections in the clip, but if there was a desire for an extended throat
pipe, the venturi contraction ratio could be adjusted to account for
added loss (thus slightly larger throat) and/or some pressure recovery
attempted with a relatively shallow expanding exit cone, but most
likely the throat section and exit can probably be made quite short
and give better performance.

Anyway, this is all very rough and depends on the accuracy of all
those quick estimates (like the flow rate, etc.)... if those are
different then the figures will also change. Again, just a quick
check, first pass on the ideal...


4)
Appreciate your positive feedback on my post!

I agree with your assessment on MathML and LaTeX. I've considered
writing (and may write) a tool/plug-in that converts the “typical” way
we tend to convey equations (in common text) into a reasonable
graphical format. Basically, those existing options (at least right
now) rely heavily on the user for formating nearly each aspect, but it
would be nice (and perhaps better) if we could use typical software-
style language conventions (C, for instance) and have the tool
recognize reserved key symbols (like rho, *, etc.). Matrix
representation, etc., could be handled by separate commands if
needed. I'd like to see something such as: for (i=0;i<100;i++) {q
+=someFunc(i);} automatically convert into sigma notation, for
example.


5)
As far as putting up the derivations for N-Prize solutions, you're
correct in that not many teams are providing significant details as to
their chosen direction. But, I think this may have some positive
effects (and some negative effects also). I would like to discuss
this with you more, perhaps in private or on a separate thread; I have
a lot to say on this issue but I'll have to do it a bit later...


~Sage
www.littlemonsterrocket.com

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