Working on a mass model | Rocket body discussion | Forum

rpulkrabek said:

I've completed the rest of the mass calculations. You can find all of the data from this OpenOffice spreadsheet. I tried to clean it up a bit and make it easier to read, also.

The next steps are to determine the correct values to use in OHKLA. How is the needed mass of the propellant determined? Once this is known, I understand how we then determine chamber and tank dimensions. I just don't see how propellant mass is determined. Does it come from USOFS? 

The Tsiolkovsky rocket equation relates dry rocket mass, wet rocket mass, specific impulse and delta-v (under ideal conditions).  If you give it any three of these, it will give you the fourth.  We know the Isp (see above).  We know the required delta-v – USOFS suggested an impulsive delta-v of 1500 m/s will result in an apogee of 100 km, and a Wikipedia article (though I now forget which one) gave precisely the same figure for suborbital flight.  Thanks to your work, we now know how to figure out dry mass as a function of propellant mass.

So, suppose we use x kg of propellant.  Using your mass models (plus some estimates for various things like the length of the recovery section, etc), we can figure out the dry mass of a rocket large enough to contain that x kg of propellant.  The wet mass is just the dry mass plus x kg, and the Isp is known.  So we can plug all of this into the Tsiolkovsky rocket equation and get out the resulting delta-v.  If it's higher than what we need, we make x a little bit smaller, and if it's lower than what we need, we make x a little bit bigger.  Rinse and repeat until we've zeroed in on a propellant mass which gives us the delta-v we want to whatever level of accuracy we desire.  This is exactly the process I used to get my mass estimate from last night.

My thought is that we should probably aim for a delta-v of 1600 m/s rather than 1500 m/s, just to be on the safe side, since USOFS is not exactly perfect.

Once we have decided on a quantity of propellant, we will know the rocket dimensions and so we can begin to model the thing in OpenRocket to get an independent confirmation that we're on the right track.  Of course, we don't have a thrust curve for our rocket, but we can "make up" some realistic ones since we know the Isp and the total propellant mass.  E.g. if we specify that the thrust is linearly decreasing over time and specify the total burn duration, then the thrust curve is uniquely specified.  I figure we can just do this for various thrust times in increments of 5s and see just how long a burn (or low a thrust) we can handle before we stop breaking the Karman line.  Unless the results of this tell us we need a really short burn time, we should be okay.

rpulkrabek said:

 

Ok, maybe this is a good number to use a starting point for our calculations. Is there any way we can calculate it, or is this something that is better to measure experimentally.

Will we measure Isp from the scaled rockets we test and then use these values for the full scale OHKLA rocket?

If Isp=v_e/g, where v_e is the exhaust velocity, I think we can obtain this via a CFD analysis. Perhaps it's good to trust the number provided, but I would prefer to also validate it.

Could we really get it out of a CFD analysis?  The exit velocity isn't simply determined by the engine geometry and the tank pressure, otherwise all propellants would have the same Isp.  It depends on how much energy is released by the combustion reaction, and on the masses of the molecules which are the products of that reaction.  In the case of a complex polymer like PE, I think there are in fact many different combustion reactions going on because the solid PE pyrolises into all kinds of gaseous and liquid compounds.  We would need to know the chemistry of all these reactions and also the relative proportions of those reactions going on in the combustion chamber.  I'm not saying it cannot be done, but I don't think it will be easy.

Post edited 7:32 am – July 21, 2010 by Luke Maurits

Okay, I have now done a complete and proper version of the propellant investigation.

I did length and mass regressions for the 10, 20 and 30 cm chambers and tanks, and interpolate between these models to get estimates for arbitrary diameters – e.g., a 27.5 cm diameter chamber is modelled as having a dry mass which is 0.25 times the mass of a 20 cm diameter chamber plus 0.75 times the mass of a 30 cm chamber.  This is not perfectly accurate, of course, but it should be good enough for rough estimation purposes.  In addition to this, I also did a regression of the combustion chamber flange diameter against the combustion chamber diameter.  Then, when considering rockets, I would set the combustion chamber diameter, estimate the flange diameter using the regression, and then set the tank diameter to equal the flange diameter, so everything fits together just like it would in the actual rocket (modulo some wall thicknesses, but that's quite a small error).  I set the nosecone to be 5 times as long as it is in diameter.  The results are as follows:

+-----------------------+--------------------+-------------------+----------------+---------------+-----------------+
| Chamber diameter (cm) | Tank diameter (cm) | Rocket length (m) | Fineness ratio | Dry mass (kg) | Propellant (kg) |
+-----------------------+--------------------+-------------------+----------------+---------------+-----------------+
|           10          |      13.90333      |     13.156959     | 94.6317105327  | 103.019438461 |       96.5      |
|           11          |      14.94033      |    12.460042385   | 83.3987092989  | 103.182064337 |       96.7      |
|           12          |      15.97733      |    11.71429244    | 73.3182104895  | 102.862703985 |       96.4      |
|           13          |      17.01433      |    10.940101105   | 64.2993353544  | 102.118250364 |       95.7      |
|           14          |      18.05133      |    10.14712772    | 56.2126320886  | 100.970946884 |       94.6      |
|           15          |      19.08833      |     9.3517395     | 48.9919207181  | 99.4850038118 |       93.2      |
|           16          |      20.12533      |     8.58479267    | 42.6566554188  | 98.0448186538 |       91.9      |
|           17          |      21.16233      |    7.935636125    | 37.4988771321  |  98.721486819 |       92.5      |
|           18          |      22.19933      |     7.2725272     | 32.7601202379  | 99.2811430166 |       93.0      |
|           19          |      23.23633      |    6.601368825    | 28.4096878681  | 99.7554289662 |       93.5      |
|           20          |      24.27333      |     5.9167947     | 24.3757024685  | 100.084416952 |       93.8      |
|           21          |      25.31033      |    5.877518044    | 23.2218151403  | 101.825969364 |       95.4      |
|           22          |      26.34733      |     5.83347134    | 22.1406546318  | 103.496161153 |       97.0      |
|           23          |      27.38433      |    5.780182672    | 21.1076286037  |  105.03827619 |       98.4      |
|           24          |      28.42133      |    5.722720212    | 20.1353005366  | 106.507282134 |       99.8      |
|           25          |      29.45833      |     5.65914613    | 19.2106821059  | 107.875624438 |      101.1      |
+-----------------------+--------------------+-------------------+----------------+---------------+-----------------+

As you can see, required propellant mass is minimised at 91.9 kg with a chamber diameter of 16 cm and a tank diameter of 20 cm. However, this results in a very long rocket, 8.5 m long, with a fineness ratio of 42.  This is really rather impractical.  The difference in propellant between the best and worst cases is only about 10 kg, so we probably shouldn't worry about it too much.  Contrary to my expectations, it looks like the fineness ratio is going to be the main driver in sizing the rocket.  I think we should not consider any chamber diameters less than 20 cm, which corresponds to keeping the total rocket length under 6 m, which seems reasonable.  With a 20 cm chamber, we get a fineness ratio of 24, which matches the Atea 2 hybrid suborbital  rocket at Rocket Labs in NZ.  This is also roughly the same ratio as the Lambda LS-A, a Japanese solid suborbital rocket which has a fineness ratio of 21.  If we go all the way out to a 25 cm chamber (any larger and the flange diameter exceeds 30 cm, which means we can't accurately model the tank), we have a fineness ratio of 19.  I haven't seen that exact ratio before, but I've found several rockets with fineness ratios of 17, which is close.  So basically, anywhere within this range, the overall shape of the rocket is going to be quite close to other successful suborbital rockets, so we don't have to worry about much in that regard.

All of the above, of course, is based on rough estimates for the masses of everything (I'll fill out the table in an early post shortly to show the values I used for these calculations), so it's not exact – but it should be a pretty good ballpark.

So we now can say with some good confidence: we're looking at a rocket that's about 25-30 cm in outer diameter, 5-6 m long, with a dry mass of 100-110 kg and a propellant requirement of 90-100 kg.  Obviously we should do work to refine these ranges, but these are definitely the kind of ranges we're going to end up working in, unless some of our assumptions turn out to be very wrong.  It feels good to have this clear an idea of how things are going to look.  I'm really amazed at how close the dimensions are to the very first OHKLA design which was basically pulled out of our collective asses without any real engineering work!  We lucked out there.

One thing we should consider as we choose final dimensions is that we have to be able to actually find metal in the appropriate sizes.  Just because 26 cm turns out to be a great chamber diameter for us (to pick a number at random) doesn't mean that there are lots of people manufacturing and selling 26 cm diameter aluminium tubing with the wall thickness we want  – but it might be that 25 cm or 27 cm is the diameter of a very commonly used standard kind of tubing and so we have to settle for that because it will making finding materials easy.  In particular, if we're going to buy and build this rocket in the US, we might want to choose dimensions which are round numbers of inches to make this easier.  It's worth noting that 8 inches is 20.32 cm, so that metric and imperial almost overlap at that point, in terms of "nicenes".  Ideally, we want the design to be such that it's very easy for people all over the world to find materials in the appropriate dimensions.

EDIT: forgot to mention, the above data is also based on the assumption that the aerostructure is 2mm thick 6061 Al 6T.  I don't really know if that's appropriate – if we can make the walls thinner or need to make them thicker, propellant masses will go down or up, respectively.

Bad news. :(  While I still think something fishy is going on with the drag coefficients in OR, that doesn't actually explain the low altitude I was seeing.  It turns out that by the time that coefficient gets crazily high, the air density is low enough that there is minimal drag.  OR lets you plot the actual drag force in Newtons and I can see very clearly that there's no significant drag for most of the free-fall part of the flight.

The problem is the delta-v.

I found this really good article on suborbital delta-v requirements and all the different considerations which need to be taken into account.  Anyway, long story short, the 1.4 km/s figure on Wikipedia is actually ignoring all drag.  The fact that USOFS gave us almost the same figure when it was trying to take drag into account is obviously just due to USOFS being really, really poor.  Once you take drag and other losses into account, that article I linked to suggests a delta-v of 2,100 to 2,400 m/s to reach 100 km.

I reran the propellant mass calculations for a delta-v of 2400 m/s and that requires about 175 kg of propellant – an awful lot more than before!  The rocket is now 7.8 m long, for a fineness ratio of about 22.  I put an engine with this much propellant into OR (using a 30 second burn time with a constant thrust of 7000 N (really fairly small)) and now I'm getting an apogee of 113 km.  So it seems that we really do need a lot more propellant. :(  Perhaps not 175 kg, since that's getting us 13 km higher than required (although maybe we should shoot for 110 km, giving OR a 10% margin of error), but definitely a lot more than 90-100 kg.

The one positive of all this is that the longer rocket has much better stability margins, with 3.2 calibres of separation between the CG and CP.

As an alternative to adding propellant, we could drastically lower the dry mass somehow.  Replacing the aerostructure with fibreglass or carbon fibure could be one way to do this, although it would make construction a lot more problematic and perhaps more expensive to the point of cancelling out the cost of more propellant.  Another alternative would be to take advantage of the fact that hybrid engines can be throttled – rather than just opening the N2O valve up at launch and leaving it like that, we could throttle back somewhat during the thickest part of the atmosphere and then open it up again once we were higher up.  This would reduce drag losses somewhat.  It does complicate our valve-control and avionics requirements, though.

rpulkrabek said:

 

Is there a reason that some sort of plastic can't be used for the aerostructure?

No reason, as long as the plastic was strong enough not to bend due to wind-shear etc.  This is certainly something to consider, since it might be possible to find plastic tubing in the appropriate diameters of the shelf.  We may still need to use Al for the propulsion section, since that also has to deal with the weight of the engine plus the thrust (which is transferred to the aerostructure via the engine-mounting bolts).  There is also the possibility of some moderately high heat during the faster parts of the flight through the atmosphere.

Did you have any particular plastics in mind?

rpulkrabek said:

Our delta-v was wrong, but luckily we discovered why, and didn't have to spend any money it. We just have to understand the drag forces involved a bit better.

It's true that we didn't have to spend any money to find this out, but the amount of money we'll need to spend per launch will now be almost twice what it was if we have to go from 100 kg to 175 kg, so it's still kind of a bummer.

Since the problem turned out to be entirely delta-v related, I don't think there's that much more understanding of drag to be done.  I checked Sampo's thesis and it turns out that OR does tend to overestimate drag at supersonic speeds – so, if OR says drag is not enough to keep us below 100 km, then that's probably correct.

rpulkrabek said:

 

While this is a setback, it's not necessary bad news. It just means we have to reconfigure our rocket model. Going to space is a difficult task, it's up to us to find the most efficient way we can.

Our delta-v was wrong, but luckily we discovered why, and didn't have to spend any money it. We just have to understand the drag forces involved a bit better.

Actually, there's some silver lining to this cloud.

One thing I always wanted us to be able to do was to cluster a few OHKLA engines together to make a minimal TLI stage for very basic lunar and interplanetary probes.  To get from LEO to the moon takes a delta-v of about 3200 m/s.  Back when I thought OHKLA would need 1600 m/s, I thought we'd need to double the delta-v to send something to the moon, but if OHKLA needs 2100-2400 m/s then it's considerably less of an increase.