Simulations and Load Cases

Haven't updated in a while, busy as ever, but I finally found the time.

So we've outlined approximate basic details of our rocket module:

• Around 40cm in diameter
• ~2.5m long
• GLOW = 305.9Kg
• Empty mass + 20Kg payload of 48.8Kg
• 80% H2O2 and Kerosene propellants

For the single rocket motor at the core of each module I arrived at a thrust level of 5kN. The process of arriving at this thrust level is as follows:

1. The rocket must have at least more thrust than weight at liftoff, so therefore more than 3kN thrust.
2. Most liquid fueled rocket motors can't be throttled by a large amount before combustion instability sets in and deep throttle capability is complexity we can do without. However the maximum period of acceleration of the rocket is just before burnout when weight is at its lowest point (due to fuel consumption), assuming constant thrust from liftoff to space the higher the initial thrust level the higher the final acceleration and the heavier the structure and payload will have to be to deal with it.
3. So we need at least 3kN but with just 3kN the initial acceleration will technically be 0m/s^2 which is equally useless to us, so I set the initial acceleration requirement at 1.5g's and rounded up to the nearest whole number. That's how I get 5kN initial thrust resulting in 1.7g's off the pad.

Given the above details I put together a crude simulation program in Matlab. The simulation assumes constant motor thrust and ISP, a specified pitch rate from vertical to horizontal and works on a flat-earth model but I figure it's good enough to work out if the modules are sized correctly and for working out rough load cases for structural design. A simulation of the 3 module orbital configuration from this rough simulator is shown below:



As can be seen the 3 module system should be ok for making orbit, at least with this simple model. A much more accurate flight simulation system which will be able to handle control system interaction and other nice things is in the works but a ways off yet. Interesting to note the final burnout acceleration spikes up to around 10 g's which is quite violent, too much for a person but ok for pretty much all electronics. Remember how we chose the initial thrust level? If we'd chosen a value set to give higher initial acceleration this value would probably be significantly higher and perhaps too high to work. In reality the rocket motor will probably be slightly throttlable to help reduce this peak acceleration but we now don't absolutely have to which is a good thing.

From this simulation we can start to outline the structural design of the rocket, which will be influenced by the load cases we choose to test the design against. I've broken the various load cases into a few which I think will represent the primary and most demanding situations that will be encountered:

1. Based on the simulation of the 3-1 orbital stack with a peak acceleration of 10g's, a compression limit load of 10g's for a full module and an additional load on the interstage for a possible 3rd stage. Using a margin of safety of 1.5 this gives an ultimate load case of 15gs + 1016.7Kg for a total compression load of 55002N (about 5.6 tons, quite high).
2. The second load case is for a torque load, traditionally longitudinal loads are primarily taken by stringers/spars running the length of the rocket, however these large structures effectively take no torques. The torque load case was abritrarily set as the force required to accelerate/decellerate a fully loaded spinning rocket from/to 300 rpm in 1 second (for example the roll control system eliminating a high roll rate).
3. Case 3 are for arbitraty ground-handling loads. Case 3a) is where the fully loaded module is simply supported at both ends and subjected to 2 lateral g's. Case 3b) is where the rocket is fixed at one end and subjected to 2 lateral g's.

Whether these cases are too conservative or too extreme is yet to be seen, however I tend to think they are towards the extreme side. For example with the ground handling cases, the rocket should never be fully fuelled when on its side and during handling and so these cases should hopefully never occur. However the cases do not account for other loads, such as bending during flight when passing through extreme wind layers. The capabilities of the airframe will be better understood as the design is refined however some things will only be known during ground structural tests and actual flights.

Sorry the posts have been lacking in images to this point, unfortunately all this initial design and envelope-building is kinda boring but it's all part of the design process and will bear fruit in the long run. Next update will be on sizing the structure to deal with these load cases.

Intro to the project

Ok, so the project is to design a small commercial launch vehicle, again I want to stress I'm not a businessman and I don't know if such a market does or will exist, however for arguments sake lets assume there is a viable market for 'cubesat' size and style satellites (small satellites of around 1Kg each).

The rocket design I will be focusing on should therefore be capable of launching around 20Kg (a batch of one large or several small student/academia/scientific payloads) into a number of trajectories including sub-orbital, LEO and escape/TLI. This mission flexibility allows the greatest number of potential uses/customers for the smallest outlay in design, materials and tooling. It is this requirement of mission flexibility which drove me to select a modular design for the rocket. For a quick read on modular rockets take a look at the OTRAG project:

http://en.wikipedia.org/wiki/OTRAG

Interesting read.

To make orbit the modules will have to be staged (as it is not yet practical to develop a single stage to orbit design), assuming each stage operates using the same propellants at a similar ISP the mission delta V will be split evenly over each stage. The minimum practical number of stages to reach LEO is 2, we want the minimum because it means less things to get complicated/go wrong. Therefore for an LEO mission we're looking at a 2 stage rocket of modules. For a LEO mission a good rule is to allow a total of 9200 m/sec delta V, you only need around 7.8 km/sec orbital velocity in LEO but the rest will be burnt up in atmospheric and gravity drag, this means a stage delta V requirement of 4600 m/sec.

Next we need to choose our propellants, I have tentatively selected hydrogen peroxide and kerosene. Why?

- I like storable propellants. LOX may be cheaper, slightly higher performing and easier to work with in some ways but it also makes ground handling more difficult, the design of tanks and plumbing more difficult and the fluid control parts such as valves much more critical and expensive. Additionally you'll end up spending more weight on insulation for tanks and plumbing.
- Hydrogen peroxide is dense, which means a small rocket with low frontal area and lower drag. Smaller tanks are lighter too. It's also relatively safe to work with assuming proper safety gear and precautions are used, toxicity is low compared to other higher performance storables such as hydrazine and nitrogen tetroxide.
- Kerosene is cheap and readily available, it's well known in rocket engine use and is again a room temperature and pressure storable propellant.
- Peroxide has a decent specific heat and its mass flow is a large percentage of total making it a good choice for regenerative cooling.

There are more reasons but those are the primary ones, the primary problem when using peroxide is getting it in the concentration needed (80% +) in any quantity for a good price. As this is currently a paper design that's not such an issue.

80% H2O2 and kerosene at a chamber pressure of 1000psi at the correct mixture ratio and expanded to sea level pressure yields an ISP of around 255 seconds. We may use the rocket equation and an iterative solver (I used the equation solver in excel) to calculate the initial (wet) mass assuming a 20Kg payload and a dry mass of 9.4% the wet mass for a delta V of 4600m/sec. 9.4% was chosen as the inverse mass fraction of the rocket based on existing designs (around the mass fraction of the Saturn 1B rocket stage). From these numbers a fully loaded mass of 305.9Kg and an empty mass (plus 20Kg payload) of 48.8Kg was calculated. Without the 20Kg payload this leaves 28.8Kg for the entire module structure, propulsion system, guidance system etc. Finally based on the density of kerosene (around 700-800Kg/m^3) and 80% H2O2 (1200Kg/m^3) the module envelope was roughly sized to 40cm diameter and 2.5m long.

An Intro to the project and myself

My name is Andrew Burns, for some time I've been interested in rockets and rocketry. To that extent I've been involved in model, high power and amateur rocketry for a number of years and am very close to the end of an Aeronautical Engineering degree.

I think myself somewhere between realist and idealist, I'd love to get involved with real commercial rocketry however living in Australia this is a dream I admit will be very likely unfulfilled. However as pessimistic as I am about the state of aerospace in my country that doesn't prevent me from dreaming up various rocket technologies and even building a lot of prototypes, and that's what I intend the purpose of this blog to be, some realist dreaming.

I recall it being said that a wise man understands how much he doesn't know ( or something to that effect ). I don't even pretend to be wise but I do know that no space rocket is built by one man and I know that man certainly wouldn't be me. Things I'm not:

• Politician/lawyer/businessman. It takes a lot more than making a working rocket to get it off the ground, there's a whole world of bureaucracy ready to kick you while you're down. I've never been one for negotiating this minefield.

• Programmer. I can deal with electronics to some degree, I can program microcontrollers in BASIC and program in matlab to some degree but I'm not a programmer and I doubt I ever will be. You're not getting anything to space without sophisticated telemetry and control systems, my basic programming skills have gotten me pretty far but not that far.

• Space engineer. As a soon-to-be aeronautical engineer I feel I have a good grasp on structures, aerodynamics, thermo and fluid dynamics but I'm no space engineer. Once I actually get into matters of space I'm lacking in my orbital dynamics and vacuum thermodynamics, that's why the blog is about launch vehicles and not cubesats ;)

And the list goes on but those are what I feel most important when considering space launch vehicles. On the other hand I feel that I am/will be a good, practical and hands on engineer with a strong grasp of a lot of the disciplines that go into designing a large functional rocket so that’s what I'll focus on.

Some people may have heard of the n-prize, some might not. If you haven't it's basically a prize to launch a laughably tiny satellite into orbit on a budget smaller than it costs to buy a good home entertainment set and if you manage it you get enough money to actually buy that home entertainment set with some change. Personally I don't think the prize is achievable but that's neither here nor there, I think the main aspect of the prize is to promote thought and discussion on the subject. I do think that with the right people, the money and a favourable regulatory environment, small launch vehicles are possible. As I said before don't ask me if it would be profitable but I think it could be done and I can definitely see some practical uses for it. Like the n prize I'm making this blog to share my ideas and hopefully spark some thought on the subject, pipe-dream or not I can't see the harm in the free exchange of ideas.

So that's it for me and this blog, hopefully I can get to posting something interesting soon, I'll try to get pictures and real information into everything because I know nobody cares about what I had for breakfast.