Assumptions:
- All stages contribute the same DV (Bad assumption)
- 9500 M/Sec Delta V may not be enough for a really small vehicle.
- MR is achieved MR per stage including payload.
- We assume the MR is the same for each stage (again a bad assumption)
MR is down the left side, number of stages is across the top.
| Minimum ISP | ||||
| Stages | 4 | 3 | 2 | 1 |
| MR | ||||
| 2 | 349.3 | 465.7 | 698.6 | 1397.1 |
| 3 | 220.4 | 293.8 | 440.7 | 881.5 |
| 4 | 174.6 | 232.9 | 349.3 | 698.6 |
| 5 | 150.4 | 200.6 | 300.9 | 601.7 |
| 6 | 135.1 | 180.2 | 270.2 | 540.5 |
| 7 | 124.4 | 165.9 | 248.8 | 497.7 |
| 8 | 116.4 | 155.2 | 232.9 | 465.7 |
| 9 | 110.2 | 146.9 | 220.4 | 440.7 |
| 10 | 105.1 | 140.2 | 210.3 | 420.6 |
| 11 | 101.0 | 134.6 | 201.9 | 403.9 |
| 12 | 97.4 | 129.9 | 194.9 | 389.7 |
| 13 | 94.4 | 125.9 | 188.8 | 377.6 |
| 14 | 91.7 | 122.3 | 183.5 | 366.9 |
| 15 | 89.4 | 119.2 | 178.8 | 357.6 |
| 16 | 87.3 | 116.4 | 174.6 | 349.3 |
| 17 | 85.5 | 113.9 | 170.9 | 341.8 |
| 18 | 83.8 | 111.7 | 167.5 | 335.0 |
| 19 | 82.2 | 109.6 | 164.4 | 328.9 |
| 20 | 80.8 | 107.8 | 161.6 | 323.3 |
| 40 | 65.6 | 87.5 | 131.3 | 262.5 |
The second chart shows the vehicle gross lift off weight given a 1Kg payload and assuming that the empty stages weigh the same as the payload they are lifting.
| GLOW multiplier | ||||
| 4 | 3 | 2 | 1 | |
| 2 | 256 | 64 | 16 | 4 |
| 3 | 1,296 | 216 | 36 | 6 |
| 4 | 4,096 | 512 | 64 | 8 |
| 5 | 10,000 | 1,000 | 100 | 10 |
| 6 | 20,736 | 1,728 | 144 | 12 |
| 7 | 38,416 | 2,744 | 196 | 14 |
| 8 | 65,536 | 4,096 | 256 | 16 |
| 9 | 104,976 | 5,832 | 324 | 18 |
| 10 | 160,000 | 8,000 | 400 | 20 |
| 11 | 234,256 | 10,648 | 484 | 22 |
| 12 | 331,776 | 13,824 | 576 | 24 |
| 13 | 456,976 | 17,576 | 676 | 26 |
| 14 | 614,656 | 21,952 | 784 | 28 |
| 15 | 810,000 | 27,000 | 900 | 30 |
| 16 | 1,048,576 | 32,768 | 1,024 | 32 |
| 17 | 1,336,336 | 39,304 | 1,156 | 34 |
| 18 | 1,679,616 | 46,656 | 1,296 | 36 |
| 19 | 2,085,136 | 54,872 | 1,444 | 38 |
| 20 | 2,560,000 | 64,000 | 1,600 | 40 |
| 40 | 40,960,000 | 512,000 | 6,400 | 80 |
The two bold numbers are about where I think my notional vehicle will land on this chart. This was a 1Kg nanosat with 1Kg of support structure would have a gross liftoff mass of ~2200 lbs, and the engine performance is a relatively easy ISP of 232 (Easy in vacuume, a bit harder on the first stage) Total Vehicle empty wt would be between 500 and 600 lbs.
you can do some really gross things... like a monoprop 4 stage launcher... MR 6 Glow for 1Kg payload is 40000 lbs.
20 comments:
No idea why you switch between kg and lbs. Pick one :)
Because my intuitive sense of how big something is /scale etc is permanently poisoned by being born in the U.S.
My scientific calculating is usually done in metric.... but to get a sense of scale I need to convert back....
I agree its pretty lame...
Mentally color coding the upper chart with
- some well known engine ISP boundaries
- real flown stage MRs
gives you nice region of "realm of possiblities"
9500 metres a second seems very generous as a requirement. Are you assuming a launch from a high latitude?
9500 is Margin. I'm also thinking that I might need to launch from Kodiak.
If you look at the paper I presented earlier...http://www.redyns.com/Reference/MinLaunchVehicle.pdf
Figure 2, for a small vehicle I'm on the optimistic side of the chart.
I'm also thinking that my frontal area will be lower....
Try these guys. They have a supersonic fighter and are based somewhere a bit warmer. Could they help? The pylons look tempting:
http://www.lightning422supporters.co.uk/
Another way to reduce your frontal area is to cut down upon beer...
Pardon the ignorant question -- what's "MR"?
Scott, MR = mass ratio.. the part of the rocket equation inside the brackets:
dv = ve * ln(m0/m1)
where ve = isp * 9.8.
MR = m0/m1, or "initial mass on final mass".
How about a 1000 stage rocket with microchip stages.
I would work on the liquid staging process with low altitude experiments. The rocket science I's the easy part.
Steve
For very small launchers I think it is best to calculate/design first stage separately, and with a stagien altitude of over 60 km, have the upper stages operate in vacuum, and, due to lofting from stage 1, mostly horizontal acceleration.
The 100-150 kg GLOW Microlaunchers design appears capavle of one Cubesat, assuming LOX/butane for upper stages.
Hey, Paul, don't let 'em give you a hard time about the kg/lbs thing - metric has its uses, but one does -not- actually have to make a religion of it.
Often physics-based calculations give results in MKS units, but sometimes I build stuff in inches and pounds - I deal with it.
dave, no, it's more the consistency I was referring to. Also, it's no so hard to put lbs in brackets if you're doing it in metric. I tend not to, but that's my own problem.
Interesting. I was just doing some of the same sort of calculations, but assuming an optimal delta-v split between 2 stages figured out using calculus. Doing it analytically is hairy, especially if you allow Isp, ratio of burn-out mass to fueled mass for each stage, and total delta-v to be different values. I can't imagine doing this with more than 2 stages. I already have to resort to a CAS program (Maxima, in this case) to do some of the work of simplifying the expressions for me. Your chart will be nice to be able to sanity-check my own equations.
Finding the optimal delta-v split between the two stages that minimizes lift-off-mass-to-payload ratio is one of those few times it makes sense to actually use real calculus when doing trade studies. Kind of fun, actually.
I'm lazy I just let a C program calculate staging possibilities all night and give me the best split in the morning.
I know I can do that correctly, Multivariate Calculus less likely to be correct....
want to get your input on this:
I am approaching rocket design from the commercial off-the-shelf approach.
let's say we have 10 different off-the-shelf engines, with complete data sheets (Isp, mass, etc).
For a 3-stage launcher, I mix and match the engines I *think* will perform the best, put them into a spreadsheet and get the delta-v produced. I estimate drag losses to be around 2000 m/s (reasonable loss according to some papers )
Delta-v produced minus Drag losses gives me the Actual delta-v. If this is more than 7800 m/s (LEO), then it flies to orbit.
In essence, I'm not doing any multivariate calculus, finding optimum solutions and all. Sure, I lose performance from my non-optimized stages, but at the design is available to buy/build. Might cost a fortune though.
What do you guys think?
.... Microlaunchers. I always liked Charle's moxie to ask how small can you go. On a first order I have these thoughts going through my mind. Out of 250 to 300 kg of mass can you really keep to your allowance to within 1 kg? That's not much margin, some engine underperformance, fuel boil off, or ullage and the mission is lost. That said your Isp is very conservative, so I'm going to suppose you're shooting for H2O2 and Jet-A or some other carbon fuel? By your numbers LOX hydrocarbon looks somewhat doable. I still don't like the lack of margin.
1000 kg fueled. It's denser than a car so it's smaller than a small car. 200 kg empty. Easier to transport than a boat.
I think you could solve some problems by going bigger. :)
Let's say 400 kg empty and 2000 kg fueled.
Still fits really easy weight wise on a compact car towable trailer. 2 cubic meters of tanks, that's 4 meters with 80 cm diameter. Add some interstages etc and you're maybe up to six meters.
You can customize a boat trailer for that.
I don't know at what weight you run into infrastructural issues?
You published good information
Nice information
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