Working on a mass model | Rocket body discussion | Forum

I was thinking today about the question of choosing materials for the oxidiser tank and combustion chamber for OHKLA today, and have decided that the approach we have just started trying, of choosing based on paramters like density and tensile strength, probably doesn't make a lot of sense.  We can't approach the problem so abstractly, I think we need to look at the actual penalty in extra propellant mass that the heavier materials will incur.

Basically, my reasoning is this: aside from its higher mass, steel is by far the better choice for both components: it is easier to acquire, cheaper, easier to weld, and has a higher melting point.  The only reason to consider something else is to save on mass.  Saving on tank and chamber mass means we save on propellant mass.

But the thing is, our propellants are actually quite cheap.  If using aluminium over steel ends up saving us, say, 10 kg of propellant, then I think the appropriate response is: "who cares?".  10 kg of PE and N2O will not cost that much relative to the overall cost of the project, and it's not going to increase the mass or size of the rocket by enough that it's actually harder to handle or something.  It's really a very small price to pay for the convenience of using steel.  On the other hand, if going with steel would increase our propellant needs by 100 kg, then that perhaps makes switching to aluminium worthwhile.  The 10 kg and 100 kg numbers are completely made up, of course, but hopefully the point is clear: we can't really make the choice just by comparing densities and tensile strengths, we need to actually go all the way through to calculating the quantity that actually matters at the end of the day: required propellant mass.

Unfortunately, this is not exactly straightforward to calculate.  To know the required propellant mass, you need to know the dry mass of the rocket.  To know the dry mass of the rocket, you need to know the dimensions of the tank and chamber – and to get those you need the propellant mass, so there's a dependency.  In order to actually solve this situation you need to be able to express the empty rocket mass as a function of propellant mass.  So I think we should work on doing this.

The approach would be basically this: for a wide range of propellant masses (say 10, 20, 30, …, 100 kg), we compute the empty rocket mass, like rpulkrabek has done for us before using Pro Engineer.  Then we can plot this data and fit a straight line to it, or a power law, or whatever fits the best.  If we do this for an all-steel construction rocket and then again for an all-aluminium construction rocket, we can use the rocket equation to find our required propellant masses and compare them.

Rpulkrabek, are you able to do these mass calculations?   Basically there would be a big list of lengths and diameters for tanks and chambers, and you would have to model them in ProE, using aluminium and steel, setting the wall-thicknesses in each case to whatever it needs to be for that material to contain the relevant pressures with an appropriate safety margin (I assume ProE can do this automatically?), and record the masses.

We'd also need to make an effort to estimate the mass of things like the nose cone, fins and avionics stack, but I don't think that should be too hard, certainly not as hard as the tank and chamber masses.

We'd also need to decide on some details of the grain geometry to model it, but this wouldn't have to be a final decision, just something sane to get the chamber dimensions in the correct ballpark.

If rpulkrabek (or, for that matter, anybody else with access to ProE or something else suitable) is either to do the heavy lifting on this we should all work together on the easier stuff and try to get a little report written on this in the nearish future.  This will hopefully make the materials choice fairly clear, and once it's made we'll really be in a position to move forward, including starting work on simple small-scale engines, which will be exciting!

It's true that aluminium is not really hard to come by in a modern industrialised country, which is really our main concern, but I imagine as you gradually move into less developed countries there comes a point where aluminium becomes harder to source while steel remains cheap.  This is not really a big practical concern but I feel like it would be nice if, wherever practical, we made our stuff as universally buildable as possible.  More or less the same holds for welding concerns, etc.  Even if they are fairly small benefits, they are benefits nevertheless, and they are worth purchasing if the price in kg of propellant is low enough.

Certainly the mass calculations are not complicated, and I did indeed imagine we'd approximate the tank and chamber as perfect cylinders.  I just thought ProE or the like would be easy because (i) it would save us manually looking up densities etc. to put into a spreadsheet and (ii) it might be able to quickly and easily calculate for us the required wall thickness given maximum pressure and safety factor.  But whichever way you think most efficient is fine.  If the wall-thickness calculations can be easily done in a spreadsheet then by all means use a spreadsheet, it will make the results more accessible to people anyway.

Coming up with a table of values should not be too difficult, it will mainly just be based off the densities of the propellants.  One subtlety we should probably include is to add some pre-combustion and post-combustion space on either side of the fuel grain, but that isn't hard at all.

I'll put together a spreadsheet in the very near future with some diameter and length values, and also try to get some maximum pressures for you.  750 psi will do for the oxidiser tank, I'll have to look up some values for the combustion chamber.  Then you can get to work on that part of the model.  The combined mass of the nose, fins, etc, will be a constant – anybody who wants to estimate parts of this mass by whatever means they like, please proceed!

Post edited 10:58 pm – June 30, 2010 by Luke Maurits

Oh, right, you need the pressures!

The oxidiser tank pressure should be around 750 psi (about 5.2 MPa) at room temperature, based on what I've read at multiple sources and on Nick's actual experience.

This small N2O/PE hybrid claims a 15-20 bar (1.5-2 MPa) drop in pressure across the injector, so in the worst case that would put the combustion chamber pressure at about 5.2 – 1.5 = 3.7 MPa.  I'd like to find a better source on those pressure drops before we actually plan anything too serious, but the purposes of a simple mass model which we'll tack a 10% error margin onto anyway, these pressures should do.

EDIT: Just found the data for Project Daedalus: "The chamber contains the solid fuel for the hybrid, and is designed to

burn the plastic fuel grain (made of HDPE) at 600 psi so that the oxidizer tank, which is pressurized by N2O at 750 psi, has a pressure difference of 150 psi with which to move the oxidizer (N2O) into the combustion chamber".  600 psi is about 4.1 MPa, a slightly higher figure than the 3.7 MPa from the smaller rocket, so maybe go with 5.2 and 4.1?

So, the oxidiser tank walls must be strong enough to hold 5.2 MPa, with a safety factor, and the combustion chamber walls must be strong enough to hold 4.1 MPa, with a safety factor.  With these numbers and the dimensions I emailed you, is this everything you need to make a start on this?

No problem, whenever you have the time to do it.  Thanks a lot for this work, I think it will really help us move ahead with the OHKLA design.

Enjoy the wedding!

It seems like using plastics for the fins is probably a bad idea, due to the great forces that act on the fins during transonic flight.  Replacing the density of polycarbonate above with that of aluminium (2.7 g/cm^3), which I assume is more suitable, yields a per-fin mass of around 1kg, so the entire set comes to around 4 kg, upping our estimate of avionics, parachutes and fins to about 10 kg.

Glad to see you concur on the avionics mass.

I've realised that estimating the non-propellant-size-dependent parts of the rocket is actually not at all required to evaluate the mass penalty of steel over aluminium, although obviously we should still work on it.

My biggest concern with the mass model right now is the question of overall rocket architecture.  The very early plan shown in this diagram does not seem well thought out to me.  In particular, the fins being mounted directly to the combustion chamber strikes me as a bad idea, as it involves putting holes in the combustion chamber, which is a pressure vessel, and also potentially exposes the fins to relatively high temperatures.  With all the welding and connectors between components, too, we'll end up with a fairly rough exterior surface which is bad for drag.  It seems more common in my reading to slide the various components into a more-or-less monolithic aerostructure tube and bolt them in place, and bolt the fins to that tube.  This is slightly more massive than our current approach, admittedly, but the aerostructure tube could probably be made from relatively thin aluminium – we shouldn't need to weld anything to it and it won't be a pressure vessel.  We could possibly even use fibreglass.  This would also allow us to set the diameter of the combustion chamber and oxidiser tank to be slightly different, which could be handy in the case of getting the L:D of the fuel grain closer to optimum.  Finally, the outside of the tube could be polished and painted for reduced drag, which is apparently a more important factor than one would intuitively think.

Thoughts?

Looking forward to seeing the results of your simulations very much!

With regards to the decision between using connectors to link the combustion chamber and tank, so that the outer surfaces of those components are also the wetted area of the rocket in flight, or using an aerostructure that things are inserted into: I've actually been mentally banging my head against this issue for the last few days, after I discovered that Copenhagen Suborbitals are in fact doing the connector thing like our original rough plan (which I understand was not suppose to be final and correct).  If you look at the diagram at the bottom of this page you can see how they're doing it.  This approach is far less heavy than the aerostructure approach, but for one thing I worry about how sound it is structurally (especially since CS have never actually flown anything as far as I can see) and for another I think it makes it much harder to construct the combustion chamber in a way that makes it reusable without impacting on the aerodynamics.

The alternative approach, using an aerostructure, is shown below:

basically everything is contained inside the structure and fastened to it with bolts or the like.  The outer surface of the aerostructure is very smooth, and any rough weld joints or flanges etc. on the tank and chamber are on the inside and so not exposed to the airflow, and hence don't contribute to drag at all.  I think (but I'm no structural engineer) that this is stronger, too – snapping the aerostructure based rocket in half would, I think, be a lot tougher than snapping something built like CS's HEAT, where the connectors are a point of weakness.

The biggest benefit of the aerostructure approach, I think, is that it allows the combustion chamber to have an outer surface which is not flat, i.e. it can have flanges etc. on it.  I think this is important from the point of view of reusability.  In order to be able to insert a new fuel grain to reuse a combustion chamber, either the injector manifold at the the fore-end or the nozzle attachment at the aft-end need to be removable, i.e they need to be joined to the main body of the chamber using an o-ring and bolts, or something like that.  Every detailed image of a combustion chamber I have found on the web (for instance there is one on the 7th page of this document) achieves this by having one end (usually the injector manifold) bolt to a flange on the fore-end of the chamber – but this makes the outer surface of the chamber non-flat.  You can't have the flange on the inside of the chamber (I hope that makes sense – I really dont' have the required vocabulary for discussing this kind of thing) because then there's no opening large enough to slide the new fuel grain into.

I have been looking at diagrams and photos of CS's HEAT to try to see how they have solved this problem, and I am starting to think that their combustion chambers are non-reusable (i.e. you slide in your fuel grain, place the injector manifold over the top of it and then weld the manifold on).  They may also be welding the components together after bolting on the connectors (or however they attach them), which would eliminate the structural strength problems I alluded to above.

This is really bugging me, but I probably shouldn't be thinking about it too hard because this really isn't my area and I'm just likely to come up with a solution that is sub-par.  If anybody feels like they can contribute some insight to this problem, please feel free (probably in a dedicated thread).

That approach could work well as long as the way in which the nozzle butts up against the grain and the way the bolts hold it to the combustion chamber are all such that there is no leakage of combustion gases.  I think this should be possible, though.

On the topic of nozzles, one alternative I have come across to machining a nozzle out of metal that looks like the one in your diagram is to lathe out the inside of a solid cylinder of something like graphite and then slide that block into place (there's a great photo of this here).  I haven't thought too much about the relative pros and cons of these different approaches.

I need to ask you something about the connectors in your latest set of images – I notice in the top one, where everything is assembled, there are a series of "portholes" in the connector – are these to allow access to the bolts?  I ask because I've noticed this exact same system in CS photos and have had to guess at their purpose.  Does this kind of connecting ring have a standardised name in engineering so I can read more about them?  At first I assumed CS were using bolts to join their stages (you can see what look like bolts protruding from the ends of some of their steel tubing), but then I saw a close up and observed the bolt-looking things appeared to actually be smooth.  I then figured they were just pegs used to hold  two sections of tubing together while you welded them, but then what are the portholes for?  To allow access to pipes and valves between the tank and chamber?  I really wish I knew more about actually building thins.

On the topic of the aerostructure approach – I am actually leaning toward this much more heavily now.  I had originally thought that the mass penalty of the outer tube would be too great to justify it, but realised I was misreading the data on some aluminium tubing I had looked up.  What I thought was the mass per metre of the tubing was in fact the mass per 6 metre length, so it's far less heavy than I thought.  That established, I really like the approach because I feel like, in general, we should try to avoid placing bolts through any part of the combustion chamber as much as possible, simply because penetrations of a pressure vessel are obvious points of failure.  One way to attach fins directly to the chamber without bolts would be to weld them on – this is what CS do, it's quite clear in some photos.  I don't quite like this because if the chamber lands roughly at an angle, with one fin taking a lot of the weight, it could bend badly or break and then you need to either scrap the whole chamber, which is wasteful, or cut the rest of the fin off, grind the outside of the chamber smooth again and then do another weld over the top of it.  Bolt-on fins are much more easily swapped out if one gets damaged, and with an aerostructure you can bolt on fins without penetrating the combustion chamber.  I also wonder about painting the outside surface of the combustion chamber (something else CS do) to make it smooth – I fear the heat generated during rocket firing would eventually burn that paint off and so you'd need to sand it back and re-paint each time, whereas with the aerostructure approach the engine needn't be painted at all.