Test casting.

My ultra sensitive and ultra cheap scales have arrived at last!

I celebrated by immediately making a test casting of inert rocket proppellant i.e. propellant that can not be ignited and will not burn (well, it'll burn worse than sugar. Sugar is safe, isn't it? isn't it?! :O).

It is important to note here that the way I treat the inert propellant must not be applied to the handling of the real deal. The inert fuel I'm using is dextrose and table salt. So it is almost like KNDX but instead of potassium nitrate, we use table salt instead. So: NaCl + C6H12O6.

I was previously misinformed about the local regulations regarding rocket candy, so now I know that this country has some really crappy laws that prohibits nice guys like me to do things like this that I am most passionate about.

No, seriously. It is good with these laws since they prohibits evil people (terrorists) to demolish our beautiful country. It's like walking on a tightrope. On one hand safety is important but are we really enjoying ourself being safe all the time? Do we all benifit from being locked up in our houses, or even better, in isolation cells. That would be very safe. No one gets hurt. But how fun would that be?? Hmm.. perhaps I should make a huge raft and sail it out to the middle of the atlantic and proclaim it to be a new nation. The amateur rocketry nation!

Anyways... I've updated my disclaimer. So until I have gotten a waiver or license I'll not make any real propellant. After all I'm a nice guy, remember?

Ok. Here goes. First I started out by purchasing dextrose. As I've mentioned in an earlier post, it can be bought in supermarkets. It is often waterbound so do as Nakka says and bake it for 2h in the oven on 80 centigrades:

Ok, so here's what you do: After baking it for about an hour, the dextrose will cake itself into a hard sugary plate. Break it up into pieces (probably not necessary, but this was how I did it). I did this once in a while and eventually, after two ours I weighed it out to see if the water was gone. However, back then (2-3 weeks ago) I didn't have a digital scale at home, but a crappy analogous scale that showed different results everytime I put something on it :P.

Anyhow, see that 9% mass is gone (hopefully) and when that is done, put it in a mortar and grind it to a fine powder (warning, tedious). Nakka suggests an electric coffee grinder. Perhaps easier.

Then put the stuff in a sealed container. The more sealed off from the air outside the better. Best wood be a vacuum packer device thingy. This stuff is said to be hygroscopic, so keep it away from air if possible.

So, fast forwarding to friday this weekend. I wanted to mix this stuff with table salt and cast it into a mold (another 16mm VP-pipe). Ok, found an extremely old electromagnetic toy I constructed when I was in elementary school and thought physics was easy and I didn't know how to calculate on magnetic fields :D.



I remember it was supposed to produce a powerful magnetic field that would fire out this little metal rod to the side (also coil-wire on it) with a high velocity. Never succeeded though. Naturally.

Stripped it down to this:



Made a plastic plug to be plugged in from the bottom, stopping the rcandy to sip through the bottom.





The funnel idea wasn't very good or didn't work well for me:










My first cast was horrendous:



The candy was too hard when pouring it into the mold so I had to heat it up again. I heated it far too much (150 centigrades) which should be fine with the water driven off, but somehow this was too much. Maybe I didn't get rid of the crystal water after all?
So poured the rest into the mold and it got this ugly turd. :P



Since I'm fore a conical shape at the bottom I started making a plug with a positively conical shape to get a negative conical impression in my propellant. The plug melted however, but I got some nice result now:







I succeeded to fill the complete mold this time!






Here's the plug afterwards. It melted of course. (I'm such a idiot).
Anyways, it did it job, sort of.






Beautiful, isn't it? Ok, it wasn't perfect, but much better than my previous attempt.






Anoter view.
As you can see it has air bubbles in it.
Air bubbles are bad since they produce a sudden increase in burning area.


All in all, I'm satisfied with my experimentation, however noting that this grian design along with the motor design will not be feasible. I noted that the VP-pipe quickly started getting sloppy at degrees higher than 100 centigrades (or maybe lower?). How on earth will it hold for 1703 K in 0.17 s or 1 second evenso??? Ok, maybe 0.17 s might work. But that is too quick for me. I need at least 1 second burn time (don't want to wreck my model rocket). An endburner will be too slow I think, and the pressure buildup will probably take too long. Hence, VP-pipe "myth" is "busted"!

I think I will focus on metal-based motor designs henceforth. Much more reliable IMHO.
I will see if I can make a motor chamber out of aluminum and a nozzle out of graphite (or possibly aluminum, but it will probably erode to fast due to the aluminum being prone to erosion/oxidation). Stay tuned!

Burn rate simulation.

I felt the need for creating a program that can take any grain shape and analyze what the maximum burn depth would be. Noting that we are assuming ideal condition we therefore know that the burn time must be longer in reality since the burn rate increases with pressure and we use the burn rate under steady state conditions, i.e. maximum pressure.

The upper limit of the burn time is good to know since it has an impact on the chamber. Longer burn time will lower the tensile yield stress of the material and in this case it will melt the plastic casing if the grain doesn't burn quickly enough. How to obtain the upper limit of the burn time is probably more difficult and involves analysing the pressure buildup at the start up phase. I have not looked into this matter but my intuition tells me it's a matter of solving a linear (or linearized) ordinary differential equation and analysing the transient behaviour. It should depend on such things as throat diameter, burn surface as a function of time, initial available chamber volume and propellant density.

The tail off phase seems to me to be less interesting. But I'm sure the same ODE can be used for that as well.

Here are some screenshots from my program prototype with inhibited grain geometry, long grain and short grain:

Inhibited short grain:
Uninhibited short grain:
Long grain (uninhibited):
The distance field can then be used for finding the longest burn depth which can be done by analysing the smallest values in the distance field up to a given threshold value.

We can use these smallest field values to draw normals from the edges of the polygon (for those edges that it is possible) to these field points.

Then the largest surface normal pointing to the remaining depth field values is our burn depth. This depth is then used to calculate the ideal burn time tb.

Edit: Here's a recent update:


Just another thought on burn time.. The longest theoretical radial burn time is < 6.5/11.7162 = 0.55 s. This is still too short IMO. To get higher values an end burner must be used! Maybe a catalyst must be used.

As can be seen in the figures above, it doesn't matter which shape is used at the bottom end of the grain. The shape of the burn surface seem to always converge to a flat surface. :(.
At least I might utilize the initially increased burn area to get the pressure up quickly in the beginning.

If anyone has any hint on how to solve this problem, I'm all ears. Otherwise I'll have to make a regressive grain by shaping it as a solid cylinder but being unhibited, so it won't be an end burner. The burn surface will decrease with time.

A possibility would be to make a solid version of bates grain, but that would surely overpressurize.

Hmm.. maybe it will have to be an end burner after all. Seems I can't get around this in a smart way. I will just think about this a little more and then decide what to do.

Burn rate.

I just hope my propellant will be close enough to the one Nakka's using. I'll probably have to do the burn rate tests myself later on, but right now I just need a figure to work with.

The burn rate for KNDX follows mainly the Saint Robert's law but deviates from it slightly. The law goes as follows:
where r0 is usually set to zero or neglected.

Nakka provides us with a table of pressure ranges in which certain pressure exponents and factors are valid:
Since we are using SI units, the table to the right is of interest. The maximum allowed chamber pressure is P0 = Pmax = 5.0600 MPa. Therefore the third row gives us the correct parameters:
So the burn rate for this propellant is:
Note that the pressure value is scaled to MPa in the expression and that it is dimensionless. This is really weird, but it works this way. It's like having a factor in front of the pressure variable r = a(cP)^n that scales it down with a value of c = 10^-6 Pa^-1. Models can be really strange sometimes.

Now when we know the burn rate, we can actually estimate the burn time and the average thrust!

We know that the thickness of the grain is 4mm, therefore the burn depth d = 2 mm before all of the propellant is consumed. The burn time is then:
This is clearly too fast! It is possible that we could even increase the pressure in order to gain more thrust since the plastic is not that exposed to the heat as it would if it would burn for as long as 1 second. Burn rate exponent is smaller than 1, the burn rate doesn't stagnate asymptotically, but it increases more slowly with higher pressure, so if the exponent isn't to high or to low, we might do that. A higher chamber pressure results in higher mass flow and a higher exhaust velocity ve.

However, in this phase of the design I'm not willing to compromise safety. The chamber might explode and it's better to address that issue later when I got a working design. Instead, I believe it is better to at least try to change the grain geometry. A burn inhibiting doping might work, but I rather have a higher burn rate if possible in order to ensure a quick pressure buildup in the beginning.

Next, I will analyse the possibility to use an inhibited cylindrical grain with an inverted conical shape at the bottom. It has a nonuniform profile axially, but the idea I have is that the burn surface should be as even as an end burner, but the inverted conical shape would increase the burn surface area. It might be prone to erosive burning due to turbulence, but I have no idea yet. That's a thing to find out during test firing.

This was a setback, but a well expected one. I should've found out earlier, but this is a learning process. At least I seem to have a working design methodology going and that's a good thing. See ya'll.

(Please read the safety guidelines before attempting anything like this on your own.)

The ball is rolling.

I'm doing pretty well now. I've ordered some KNO3 from cavemanrocketry, won two auctions at eBay and got two scales 2000/0.1g and 100/0.01g and they almost didn't cost me anything. Soon I hope to be able to make some inert propellant (using NaCl as "oxidizer"), do some test casting to see how well the grain holds before breaking and see how drilling works etc.

These are indeed exiting times! At least for me :).

I've done some calculations on burn rate and it looks really promising! Stay tuned!

Thermodynamic calculations.

Now to the fun part!

By now we have enough information to estimate the characteristic velocity c*, the theoretical Isp, the exhaust velocity ve and the theoretical upper limit of the total impulse Itot.

The characteristic velocity is important in the design of the nozzle. It allows us to solve for the throat area At from the equation:
We will come back to this equation later.

In the next section we will estimate the burn rate r for the KNDX 65/35 propellant for the given maximum chamber pressure.

By putting the established quantities mf, mo and Pmax from the previous sections we can now calculate what species will result from the combustion, steady state combustion temperature, number of moles of gas and condensed matter and other quantities related to combustion performance. By using PROPEP we retrieve the following output:

KNDX 65/35 Run using June 1988 Version of PEP,
Case 1 of 1 12 Apr 2009 at 1:47:49.89 am

CODE WEIGHT D-H DENS COMPOSITION
1102 DEXTROSE (GLUCOSE) 6.650 -1689 0.05670 6C 12H 6O
821 POTASSIUM NITRATE 12.350 -1167 0.07670 1N 3O 1K

THE PROPELLANT DENSITY IS 0.06827 LB/CU-IN OR 1.8897 GM/CC
THE TOTAL PROPELLANT WEIGHT IS 19.0000 GRAMS

NUMBER OF GRAM ATOMS OF EACH ELEMENT PRESENT IN INGREDIENTS

0.442935 H 0.221467 C 0.122147 N 0.587907 O
0.122147 K

****************************CHAMBER RESULTS FOLLOW ***************************

T(K) T(F) P(ATM) P(PSI) ENTHALPY ENTROPY CP/CV GAS RT/V
1703. 2606. 49.93 734.00 -25.64 31.70 1.1317 0.450 111.021

SPECIFIC HEAT (MOLAR) OF GAS AND TOTAL= 10.683 15.132
NUMBER MOLS GAS AND CONDENSED= 0.4497 0.0577

0.16588 H2O 0.08500 CO 0.07873 CO2 0.06106 N2
0.05772 K2CO3* 0.05237 H2 0.00631 KHO 0.00032 K
3.47E-05 K2H2O2 1.21E-05 NH3 3.30E-06 H 2.20E-06 KH
1.06E-06 KCN 5.56E-07 HO 4.37E-07 CH4 3.64E-07 CH2O
2.96E-07 CNH

THE MOLECULAR WEIGHT OF THE MIXTURE IS 37.441

By following Nakka's instructions and calculation example we begin by calculating the effective molar mass of the exhaust matter:
Furthermore, we need to know the mass fraction of condensed matter versus total mass of propellant in the chamber. We note that the only product that is condensed in the liquid state (*) of the combustion species is K2CO3.

The molar mass of this molecule in the chamber is M(K2CO3) = 138.2055 g/mol. Thus the mass fraction is:
Now we need to calculate the specific heats for each of the products that is of significance!
Richard Nakka has compiled this nifty chart (hope you wont mind me borrowing it):

In order to find the proper values we perform linear interpolation over the temperature range marked with yellow. The interpolation parameter t is estimated to:
Here follows the resulting specific heats for the chamber temperature T0 from the interpolation:
Remaining species from the PROPEP output are negligible.

In order to calculate the ratios of specific heat for gas, mixed and two phase particles we use the following set of equations derived by Nakka:

and lastly the ratio of the specific heat for the 2 phase flow follows:

Now we can finally calculate some interesting combustion properties such as the characteristic velocity which tells us how efficient the combustion is:
If we assume that the exit pressure is matched with the ambient pressure such that Pe = Pa = 1 atm, and further note that the maximum chamber pressure is P0 = Pmax = 5.0600 MPa = 49.938 atm we can calculate the theoretical exhaust velocity which is due to the divergent portion of the nozzle:
Here we use the 2nd phase flow version of the ratio of specific heat since this is a dynamic condition.

The theoretical (ideal) specific impulse is then very easy to calculate:
We have a relationship between the actual specific impulse and the total impulse. If we assume that we have a perfect rocket motor then the total delivered impulse would be:
Which of course is the exact same thing as mg ve. I might use mp as a symbol for propellant mass further on which of course is the same thing as grain mass mg.

The total impulse indicates we got an E-class motor. The actual total impulse will be lower due to thermal losses, pressure buildups and nozzle friction etc.

In my next post I will try to find an estimate for the burn rate for the design pressure (i.e. maximum pressure). This will be the last piece of the puzzle for the rough design of the rocket motor.


Please read the safety guidelines before attempting anything like this on your own.

Grain size.

The grain is designed to be a free standing grain, i.e. no case bonded (inhibited) grain. Further it is a hollow cylindrical grain. This is the same design as the one Nakka has on one of his earlier KNSU-motors.

In order to establish the burn area we use the following equation:
and for the grain volume we have:

We start off with a grain with the following dimensions:
Where Dc is the chamber inner diameter, xg is the spacing between the chamber and the grain, wg is the "width" of the grain, hg is the height of the grain, Ab is the effective burn area, Vg is the grain volume, Do is the outer grain diameter and Di is the grain inner diameter (the hollow part).

This is the starting condition, but what about the final burn surface area? Is it larger or smaller than the initial surface area? If we assume that the burning is performed uniformly over the whole grain surface then the final effective burn surface would be:
By analysing the burn surface as a function of burn depth, we notice that the largest burn area occurs at the start up phase.

Now, Ab is known and it's value is 5227.6102 mm^2. However, we might need to change this later. That is, the height of the grain. This is after all an iterative process in order to achieve the desired performance.

We also know that the total grain volume is 10053.0965 mm^3. By PROPEP we get that KNDX 65/35 has a density of 1.8897 g/cm^3 = 1.8897E-3 g/mm^3. Thus the grain mass is mg = 18.9973 g. Furthermore, this gives us the fuel and oxidizer masses mf = 6.6491 g and mo = 12.3483 g. This is put into PROPEP together with the earlier obtained maximum chamber pressure in order to estimate the combustion efficiency (i.e. specific velocity c*), specific impulse and a theoretical value of the total impulse! The c* will then be used to calculate the minimum nozzle throat area that we can have in order to build up the pressure level we want.

Next up is the thermodynamic calculations for this design. Stay tuned for more gory details!


Please read the safety guidelines before attempting anything like this on your own.

Pressure calculations.

Since I've got a number of PVC-pipes in different dimensions at home already I thought it would be wise to start with the smallest first (same thickness as the medium sized one). It should be the strongest of the three kinds of pipes I have. It is a 16mm VP-pipe for electrical installations.
















I use the following equation derived by the DARK society of amateur rocketry:
Using the following physical data for PVC plastics, a 16mm european VP-pipe has the following allowed maximum chamber pressure:

Just for comparison, using the same formula for Richard Nakka's PVC chamber pressure test with a 1" pipe:

Which can be compared with 1330 psi by Nakka. As you can see, the ultimate strength predicted by the equation is too high. If it is as I suspect, the yield strength I'm using (7500 psi) is too high.

It is actually quite simple. The yield strength is not a constant but vaires with temperature. Since it's a plastic, it will become even more plastic when exposed to heat. Hence the tensile yield strength must decrease with temperature.

By using the pressure at the instant of failure provided by Nakka, we can deduce an empirical value for the tensile strength of the material that works better for these higher temperatures:
Note that this is highly dependent upon both temperature and burn time. The burn time for his experiment lasted between 0.5 and 1.0 seconds (probably more like 0.65 to 0.7 s by visual interpolation). However, the temperature is unknown (it might be deduced somehow though). But this is as close as we can get to the "real" yield stress.

So readjusting the first calculation (2) we get the following maximum chamber pressure for the 16mm PV-pipe:
This will be used in the calculations for estimating minimum throat area. Stay tuned!

Please read the safety guidelines before attempting anything like this on your own.