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.