Working on a mass model | Rocket body discussion | Forum

Post edited 3:17 am – July 10, 2010 by Luke Maurits

rpulkrabek said:

For the Nickel Chromium Alloy, I initially chose INCONEL 751, which is said to be similar to INCONEL X-750. Under the notes for X-750, one example of its use is rocket engines :) along with nuclear reactors, pressure vessels and aircraft structures. I think this material is the best choice mechanically, I am just not sure how expensive it is.

I had a hard time finding price data for Inconel 751, but Inconel 600 seems a little more common.  According to this page 1 metre of tube with a 25 mm outer diameter costs 434 pounds – about US$655.  Unless Inconel 751 is a lot cheaper – and I doubt it since it's similar to an alloy used in "fancy" things like rocket engines and nuclear reactors – then we can absolutely rule this out based on cost alone.

Also, this page has a lot of detailed info about working with Inconel 751 – it doesn't seem too hard to weld (TIG welding will do), but with regard to machining it says "This alloy does work-harden during machining and has higher strength and "gumminess" not typical of steels. Heavy duty machining equipment and tooling should be used to minimize chatter or work-hardening of the alloy ahead of the cutting".  I don't know how big of a deal this is, but really we want to use stuff which is as little of a headache to machine as possible – "plain old" steel would be ideal for this, but of course is the worst choice for mass.

I agree thats of this first batch of models comes out strongly in favour of Aluminium.  The NiCr alloy is a "better" material, but the performance increase over Al is utterly swamped by the price increase.  We simply can't afford that much of a materials budget for such a tiny mass saving.  The steel option turned out to be a lot heavier compared to Al than I expected – I thought the increased strength would cancel out the increased density more than it did.  I will need to do a little more reading before I have a strong opion on 6000 vs 7000 series Al, but one of those two basically has to be it.  The tank and chamber will be aluminium, and we should endeavour to choose an alloy and make this official within the space of a week, say.

These are my plans going forward, which it may take me a few days to implement, because I'm a bit busy atm:

• Use the data from this batch of models to come up with a simple equation for estimating oxidiser tank mass as a function of diameter and length, by running statistical regressions on this data.  This will let us estimate the mass of an arbitrary tank with some degree of conidence.
• Do the same as above on the combustion chamber data once it's ready.
• Finish trying to get ballpark estimates for all the other mass components (should not be too hard).
• Use all of the above to estimate our propellant mass requirements.
• Make some rough estimates about thrust and burn profile (which can be extrapolated from our total propellant mass and the Isp).
• Throw all of the above into OpenRocket and see how our estimate flight trajectories look.

The biggest uncertainties I see in all of the above are:

• Estimating the length of the recovery section – I haven't been able to find any good sources on estimating how much space a parachute of a given size and material consumes when it's rolled up.
• Estimating the mass of the nozzle – because we still haven't given much time to choosing between the two options here.

As an aside, since I know avionics work has stalled a little – doing OpenRocket simulations on this basic model should give us a rough idea of the maximum acceleration involved in a flight which is currently, I think, the main unknown stopping us from being able to seriously discuss choice of accelerometers.

Post edited 7:30 am – July 21, 2010 by Luke Maurits

To formalise the above:  Let:

• x be the total quantity of propellant in the rocket, in kg
• Me(x) be the total empty mass of a hybrid motor which can hold x kg of propellant, in kg
• Mc be the total mass of everything in the rocket that isn't the motor or the aerostructure. in kg
• Let Da be the linear density of the aerostructure, in kg/m
• Le(x) be the total length of a hybrid motor which can hold x kg of propellant, in m
• Lf be the total length of the front part of the aerostructure, i.e. the recovery section and the payload compartment

then the total mass of a rocket with x kg of propellant is:

M(x) = Mc + Me(x) + Da*(Le(x) + Lf)

The total delta-v of this rocket after firing, given by the rocket equation is:

Delta-v(x) = Isp*9.8*log( (M(x) + x ) / M(x) )

Our ultimate goal here is to find x such that Delta-v(x) as given above is around what we need.  USOFS simulations found this to be around 1500 m/s, and that very same figure is given as the minimum suborbital flight delta-v somewhere in Wikipedia, I forget where, so it's clearly about right.  We may wish to use 1600 m/s to be safe – the OpenRocket simulations should give us some idea of whether or not we're in the right ballpark.

So, we know exactly what figures we need to do all of this:, where do they come from?

• x is a free parameter that we're trying to find a value for
• Me(x) is what rpulkrabek's current modelling is supposed to help us estimate – this is half-way done and the second half is currently underway.
• Mc is a matter of tabulating everything that contributes to the rocket mass and getting estimates – this is what the rest of us should be focusing on at the moment.
• Da can be figured out pretty easily if we know the aerostructure material (for now, as a starting point, we may as well use 6061 T6 Al again), the aerostructure diameter and the wall thickness.  It's just a matter of looking up a density and doing some area calculations.
• Le(x) follows directly from the optimal O:F ratio for PE and N2O and the densities of those propellants, and is already known – it's part of the data rpulkrabek is using to estimate Me(x).
• Lf requires estimation.  We should probably try to find the corresponding value for as many other, similar rockets as we can and take the average – this is something else the rest of us should be focusing on at the moment.

With regards to Mc, here's a slightly more thorough table of everything I can think of, with estimated values in place where some work was done earlier:

Can anybody think of anything missing from the above?  As discussion proceeds I'll keep editing this post to keep this table up to date with our work.  If anybody wants to provide estimates for anything in the table, just post.  Gut-feeling estimates are probably okay for now for those things which are marked wtih ??? – anything is better than nothing – but ideally we should try to have some basis for most of our estimates.

Obviously, the "maximum payload" is something we get to choose, based on what we want to actually do with the rocket, going forward.  Since OHKLA is supposed to be a kind of getting-our-toes-wet project with regard to hybrid rockets, it probably makes sense to keep payload capacity small and simple, with the understanding that if we succeed in getting OHKLA past 100 km we'll probably have what it takes to build a scaled up version which can carry a serious payload to higher suborbital altitudes.  Do people think 5 kg is reasonable?  That should certainly be enough for us to put some cameras on our early flights, if nothing else.

Great to see this coming along!  I have a really full day today, unfortunately, but tomorrow I might get around to at least doing all the regressions for the 6061 data.  With that done I'll try to make conservative estimates of all the remaining uncertainties about constant masses and get a first ballpark on propellant mass requirement.