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.

Project KNDX.

My friend suggested we better build a rocket motor. He really missed working with the lathe so I thought why not. This isn't exactly the first time I've been dreaming about makin me own rocket motor(s).

I read through Nakka's site. Was a long time since I was there and it felt great reading it again. It kind of fired up my enthusiasm again.

I thouhgt a lot about what casing to use and since I know that Nakka has done single use pvc motors and pops got vp-pipes in his job I thought that'd be a great idea.

Then comes the decision on what propellant to use. KNDX seemed to be the perfect choice both because dextrose monohydrate is readily available as dextropur and the point of decomposition is high.

Next issue is to find the oxididizer KNO3. That is not very easy to get. It is sold as fertilizer. If you can't get it then you can produce it by mixing NaNO3 and KCl. If I can't get hold of the fertilizer then this is how I will obtain the potassium nitrate. More about that later.

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

Focus on safety.

What will follow on this blog is my attempt to build rocket motors in a safe and reliable way.
For the sake of safety I will start small and simple. I will attempt to build a single use C-motor in PVC with KNDX fuel. I will mainly use the descriptions and advice from Richard Nacka's comprehensive website for amateur rocketry enthusiasts: KNDX , PVC-motor.

Mind you that everything I do on this blog is strictly for adults. You should at least be of age 18 before attempting to become an amateur rocket scientist. I would advice that people of age 18 are supervised by parents until they get at least 25 years of age. I can tell from own experience that I my sense for security and carefulness didn't come until I was about that age.

I have been thinking a lot about whether I should write about my endeavours here or not. However I arrived at the conclusion that it is better to write about how to conduct rocketry in a safe way than not write about it at all. After all, you can't really stop kids from experimenting. That is a law of nature. I plead to all youngsters out there. Don't do this until you're at least 25 years of age and/or are a very cautious person. See further Nakka's safety rules and thoughts on which people better not do amateur rocketry:

• Safety rules (important!)
• More safety rules
  
• Nakka's main page (read the introduction)

I will refer to the safety page in every blog post related to my rocket project where safety concerns are of importance.

I haven't barely started myself, but I have read a lot of rocket theory. Besides studying spacecraft engineering at Chalmers University of Technology, I have read books such as Sutton's Rocket Propulsion Elements (2nd edition), and various articles in the subject. I don't know if I will succeed, but I hope my knowledge and common sense will guide me to my goal.

Note that I cannot take any consequences of any unfortunate outcome due to reading and following my steps. My blog must be read with criticism and taken with grave seriousness! If you attempt to conduct rocketry based on anything I have written here you are on your own!
However, I might guide you in your endeavours, but you must take the consequenses of your own actions! I can not be held responsible for your actions. Jada jada jada... I must say this anyway. :P

Edit:
A closer look at local laws and regulations about pyrotechnical substances are very prohibitive and hence impedes my work. I was misinformed and in in my belief that there was a loophole in the law I was really fired up to carry out this project. I will still continue to perform the calculations that are necessary and eventually construct the motor itself, but until I've recieved a wavier and/or a license that permit me to produce rocket propellants I will have to wait with that part.