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Stage sizes demo


Blaarkies
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TL;DR
Multi stage rockets are generally more efficient, but what size should the stages be?

I found this cool demo that calculates the final delta-v of a 2-stage rocket, depending on the size of the stages relative to each other. I just wanted to share this with KSP players, and if a good discussion comes out of this, even better :D

https://www.desmos.com/calculator/9dhepscogp
(original link found in stackexchange https://space.stackexchange.com/a/56105)
It is an interactive equation that lets you drag around the mass ratio (b) of 1st stage to 2nd stage, and see the results on the final dv.

My optimal ratio between stages are usually 2/3. To get this. look at the mass of the entire 1st upper stage. Then build a 2nd lower stage that masses 2x the 1st upper stage's mass. Continue doing this for even more stages... I think the included price of engines have an effect here.

But it looks like perfect stage size could get more complicated than that, depending on the specific mission that you have in mind.

Edited by Blaarkies
fixed confusion between KSP counting stage 1 as the upper stage, but NASA counter the bottom boosters as 1st stage
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Uh, what? Second stage double the weight of the first stage below it?

That simply doesn’t add up- putting something heavy on top of something light will result in dreadful delta-V for the lower stage due to the high dry mass of the stuff on top. The lightest stuff has to go at the top; that’s how the rocket equation works.

There’s also the requirement for a surface level TWR greater than 1 for the first stage to actually get to space in the first place, requiring big, powerful engines (and often boosters) to get moving and consequently lots of fuel to feed those engines, whereas the upper stages don’t need that as they’re not fighting directly against gravity and so can get away with smaller, lighter engines and tanks (hence why upper stages often use hydrogen as fuel).

Look at real rockets- Saturn V, N1, Falcon 9, SLS, Ariane 5 etc. etc.- and notice how every single one has the heaviest stage on the bottom, in many cases with solid (SLS, Ariane 5, Atlas V) or liquid (Falcon Heavy, Ariane 4, R-7 and derivatives) boosters for extra thrust.

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2 hours ago, jimmymcgoochie said:

Uh, what? Second stage double the weight of the first stage below it?

My bad

I was counting stages the way that KSP counts them, with stage 1 being at the top, stage 2 below it, and stage 3 at the very bottom as the first thing that fires when you press spacebar on the launch pad

I definitely don't build bobble head rockets :D

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but there are so many more factors contributing to this. a major one is the dry mass/wet mass of your stages. you'll notice that in ksp we tend to make short stages, each providing some 2 km/s, because going much above that the gain decreases exponentially with increased fuel tank mass and increased engine tank mass. real life rockets have longer stages because the dry tanks weight less than in ksp, and the engines are also lighter.

Also, I can't figure out what "Mdry" and "Mpayload" are exactly: is the dry mass referring to the second stage? both stages? how the hell does the equation know? is the "payload" just the dry mass of the upper stage? or perhaps the whole mass of the upper stage= and moving the gauge of the staging separation will skew the wet/dry ratios for all stages involved, with no easy way to account a bigger second stage by increasing its dry mass.

frankly, I'd call that datasheet useless if it was well made, because there are a lot other more important considerations for staging. the way it's organized, with the masses expressed like this? i call it rubbish. I'm sorry for the guy who spent time doing it, but it fails at the basic premise of giving useful information. separating "payload" and "dry mass of the upper stage", with the second being dependant on the additional fuel used - by measure of an additional gauge setting the wet/dry ratio - and doing a similar thing for the second stage would make it at least marginally useful.

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2 hours ago, king of nowhere said:

Also, I can't figure out what "Mdry" and "Mpayload" are exactly:

I didn't make this so I can't confirm if this is 100% correct, but the whole equation is built around the question of:
    Given a certain payload, how big should the launch vehicle be to get that payload up to the specified speed (or delta-v).

So I believe all variables relate to the total mass of the rocket. The main purpose is to show how much less rocket mass is required when staging once, and also the effect that differing the stage sizes have. The green line shows what total rocket mass is needed for the same delta-v, just because it staged instead of going SSTO. To get to the bottom of this, you simply need to read into the equations, they are all on screen showing their interactions in pure math.

Admittedly it is hard to use this as a tool in KSP, because of the limitations that you described. It would still be quite interesting hearing everyone's process for approximating good stage size ratios, or even to see an implemented tool that does that.

Keep in mind that this equation link was part of an answer to a stackexchange question, where someone wanted to know why do all rockets have stages. We take this knowledge for granted, of course staged rocket have so much more delta-v:rolleyes: ...but if you had to explain that to someone without KSP, this equation seems pretty useful in that regard

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4 hours ago, Blaarkies said:

I didn't make this so I can't confirm if this is 100% correct, but the whole equation is built around the question of:
    Given a certain payload, how big should the launch vehicle be to get that payload up to the specified speed (or delta-v).

yes, but the problem is, as built the equation does not make practical sense. it assumes that fuel tanks and engines are weightless, because the rocket size does not influence the dry mass.

a better approach would link the answer to the fuel mass. instead of asking you the dry mass, it would ask you the mass ratio. for ksp, fuel tanks are 12.5% dry mass, plus you need about 5% mass for the engine. so you write mass ratio 0.175, and the program should calculate the dry mass accordingly. this would work.

Quote

Keep in mind that this equation link was part of an answer to a stackexchange question, where someone wanted to know why do all rockets have stages. We take this knowledge for granted, of course staged rocket have so much more delta-v:rolleyes: ...but if you had to explain that to someone without KSP, this equation seems pretty useful in that regard

"you need a huge mass of fuel to lift a small mass to earth orbit. this huge mass of fuel goes into a huge fuel tank, which needs to be pretty thick to not be crushed under its own weight. and then to lift all that huge mass you need a big, heavy rocket engine.

After you burned most of your fuel, you have this huge, heavy empty tank, and this huge, heavy, oversized rocket engine, and they are just dead weight. it's a lot more convenient to dump them, so the rest of the rocket is much lighter and can get a lot more propulsion from the fuel it has left - with a smaller, lighter engine.

on the downside, adding a stage only requires that you add a decoupling mechanism - which is very lightweight compared to the overall rocket - and an additional engine, much smaller than the one for the lower stage, again its weight is a pittance compared to the mass you're discarding. by adding a very small mass to the initial rocket, you get to discard a lot of dead weight. and since you're there, the second stage engine will only need to work in vacuum, so you can optimize it much better for vacuum, getting more propulsion out of it".

 

that's how i would explain it. equations? That equation is hard for me, and I like equations. I wouldn't try it even on my brighter students. you can't use equations on a layman.

 

I could also try with a similitude:

"imagine you have a fuel tanker truck. the truck is full of fuel, which it can use to travel. but it's very heavy, and it consumes a lot.

Now, imagine that you remove 300 kg of fuel from this truck, weighting several tons. it doesn't matter much to your authonomy, right? many tons of fuel, add or remove 300 kg is not a big deal.

but in place of those 300 kg of fuel you put a motorbike and a couple fuel canisters. with those, you can abandon the truck once it runs out of fuel and make over 1000 km on the motorbike.

you get a lot more mileage than if you had carried the truck all the way through"

Edited by king of nowhere
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