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I guess, almost all the rockets have multiple stages. But, I was wondering, why do they have multiple stages? Couldn't they have just 1 stage? With more stages, they would require more engines (meaning more weight, which leads to slower acceleration). Instead, if there was only 1 stage, only 1 engine would be required, meaning less weight, leading to faster acceleration. Then why not use only 1 stage?

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    $\begingroup$ Are you familiar with the Tsiolkovsky rocket equation? space.stackexchange.com/questions/tagged/rocket-equation $\endgroup$
    – PM 2Ring
    Dec 7 '21 at 7:53
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    $\begingroup$ Also relevant en.wikipedia.org/wiki/Single-stage-to-orbit and en.wikipedia.org/wiki/Multistage_rocket $\endgroup$ Dec 7 '21 at 8:32
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    $\begingroup$ It is not quite clear to me why you think keeping everything attached has less weight and throwing stuff away has more weight? $\endgroup$ Dec 7 '21 at 12:49
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    $\begingroup$ @JörgWMittag I think OP is thinking primarily in terms of engines - when you throw an engine away, you need another engine. I think they're neglecting the greater mass of empty propellant tanks that gets thrown away. $\endgroup$
    – Cadence
    Dec 7 '21 at 18:22
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    $\begingroup$ @Cadence even that is faulty. Falcon 9 needs 9 sea-level Merlins to lift off with both stages full of propellant, but its upper stage only needs 1 to continue on after separation. Staging adds an engine but drops 9 of them. The first stage always needs far more thrust, so it needs either more engines or bigger ones. $\endgroup$ Dec 7 '21 at 18:49
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The basic reason: tossing an extra stage can be far, far, more of a mass-savings than trying to make one stage that can do everything.

There's a handful of reasons for this:

  1. Engines weigh much less than the tanks that fuel them. It's better to have an extra engine at the start of a launch than unneeded fuel tanks at the end.

  2. "Enough engines" to get off the ground quickly becomes "far too many engines" once you're in the air. Why? You've lost a lot of mass (by burning propellant) but are still producing the same thrust. Thus, you'll have tremendous acceleration. Tremendous acceleration has two bad effects:

    • Going extremely fast in the low part of the atmosphere makes tremendous drag. Drag is wasteful (you're losing a lot of energy) and in the worst case can make things very hot.
    • Tremendous acceleration means everything (including your massive fuel tank) has to be very strong not to collapse under its own "weight" (and the much-increased "weight" of any stages/payload above it!). Making things this strong is very heavy.
  1. The engines that are good for taking off the ground are quite different than those which are good for traveling in the vacuum of space. Thus, it's more efficient to have two different types of engines. (This can mean different engine size, shape, and propellent type.)
  2. Disclaimer: this is less of an issue today with modern electronics, but it used to be relevant: The power requirements (for computers, control systems, radio antennas, etc) are very different for the part of a rocket that just need to spend 9 minutes getting into Earth orbit & the part that might need to spend days, weeks, or even months sailing through space.

In short, it's more efficient to essentially build two different vehicles: an upper stage, which is optimized to fly in space as it accelerates the payload to the speed needed to stay in orbit, and a lower stage, which is optimized to throw the upper stage into a high suborbital orbit. With this philosophy, the weight savings from discarding the lower stage are always worth it.

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    $\begingroup$ #3, specific impulse or ISP +1. Nothing hammers this home as well as the game KSP. It lists the ISP of all engines twice: once for if it's in an atmosphere and one for when it's in a vacuum. An off-the-cuff average is about 2/3rds less thrust when using an engine where it wasn't designed to operate at peak efficiency. - If there is going to be stages, might as well design it right. $\endgroup$
    – Mazura
    Dec 8 '21 at 18:18
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    $\begingroup$ @Mazura although I should note that KSP tremendously exaggerates this effect: the difference between 1 and 0 atmospheres of ambient pressure isn't really all that much when your chamber's at 6+ kPa. Of course, KSP has wildy over-heavy engines & weirdly light tankage. Strongly recommend trying KSP with RSSRO installed :) $\endgroup$ Dec 9 '21 at 14:57
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    $\begingroup$ @Peter-ReinstateMonica The astronauts themselves aren't that big a deal, mass-wise. The problem is that when you send astronauts, you also need to send a whole bunch of stuff to make those astronauts not die. Air scrubbers, water reclamation systems, climate controls, radiation shielding, seats, space-suits, food, etc. Also the cabin has to be big enough to move around at least a little bit, you need an airlock for spacewalks, etc. All of that adds weight... $\endgroup$ Dec 9 '21 at 15:53
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    $\begingroup$ @DarrelHoffman I was referring to Tremendous acceleration means everything (including your massive fuel tank) has to be very strong not to collapse under its own "weight" ... I mean I almost collapse under my own "weight" at 1g! Need to get stronger! $\endgroup$ Dec 9 '21 at 15:58
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    $\begingroup$ @Mazura designing the day-of-launch ascent trajectory for a real vehicle hammers it home fairly well. $\endgroup$ Dec 10 '21 at 0:01
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Then why not use only 1 stage?

Because we don't know how to do that.

That we don't know how to do make a single stage to orbit is a consequence Tsiolkovsky rocket equation and of the fact that some amount of structure is needed to contain the propellant. The rocket equation dictates that $$\frac{\Delta v}{v_e} = \ln\left(\frac{m_0}{m_1}\right) \tag{1}$$ or $$\frac{m_0}{m_1} = \exp\left(\frac{\Delta v}{v_e}\right) \tag{2}$$

where

  • $\Delta v$ is the change in velocity of the vehicle,
  • $v_e$ is the effective exhaust velocity from the rocket,
  • $m_1$ is the dry mass of the vehicle, and
  • $m_0$ is the initial wet mass of the vehicle (the dry mass plus the mass of the propellant).

The exponential in equation (2) is bad enough. It gets worse because of structural concerns. We don't know how to make a spacecraft whose initial mass is 99% propellant. Most launch vehicles are around 90% propellant at launch; a few get up to 94% propellant at launch.

At some point, adding more propellant means larger propellant tanks and more structure to support the additional mass of the additional propellant and larger tanks. This means that if there is an upper limit on the propellant mass ratio there is a corresponding upper limit to the ratio $\Delta v / v_e$: $$\frac{\Delta v_\text{max}}{v_e} = \ln\left(\frac 1 {1-\alpha}\right) \tag{3}$$ where

  • $\Delta v_\text{max}$ is the maximum possible change in velocity and
  • $\alpha$ is the maximum possible propellant mass to total mass ratio.

For a typical launch vehicle that initially is around 90% propellant by mass, this results in a maximum $\Delta v$ of about 2.3 times the exhaust velocity. Given that $\Delta v$ to low Earth orbit is about 11 km/sec (about 9.4 km/sec ignore drag and gravity losses, plus another 1.6 km/sec after accounting for this effects), a single stage to orbit rocket would need to have an exhaust velocity of about 4790 meters per second. There are no chemical rocket engines that have this high of an exhaust velocity.

There are some tricks to get around this limit. One is to do what jet airplanes do: Get the oxidizer from the atmosphere. This has been a pipe dream for many decades. Nobody knows how to do it. Another is to use side boosters that are discarded upon depletion. Some called the Space Shuttle a "one and a half" stages to orbit vehicle. This wasn't strictly true as the main engine cutoff occurred just below orbital velocity.

Yet another trick is to use a multistage vehicle. The first stage gets the vehicle most of the way toward the desired $\Delta v$ and altitude, the second stage either finishes the job or at least does a bit more. A side benefit of using a multistage approach is that the upper stages can use engines optimized for vacuum operations. A vacuum engine used at sea level most likely would tear itself apart. Given two nearly identical engines except that one is safe at sea level while the other is optimized for vacuum operations, the vacuum-optimized engine will inevitably have a higher exhaust velocity.

An extreme example a multistage vehicle was the Saturn V launch stack, which essentially was a six stage vehicle. Throwing away pieces of the vehicle after they're no longer needed is a way to partially escape the tyranny of the rocket equation.

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    $\begingroup$ As noted by Christopher James Huff in the comments above, staging would still be useful (and possibly necessary) even if you had magic massless fuel tanks, simply because as you burn your fuel and the rocket gets lighter, the optimal size of your engines goes down. (Also, AIUI, the launch profile also contributes to this: at launch, you need a thrust-to-weight ratio well above 1 to counteract gravity and gain some speed on top of that; once you're already going at a decent fraction of orbital speed, however, even TWR < 1 may suffice.) $\endgroup$ Dec 8 '21 at 20:19
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    $\begingroup$ @GlenYates You have the 3 rocket stages themselves (S-IC, S-II, S-IVB), then the Service Module, then the LM landing stage, then the LM return stage. $\endgroup$
    – Nimloth
    Dec 8 '21 at 20:59
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    $\begingroup$ Excellent, excellent answer. Yours is the definitive "here's why" I'd give to a reasonably-informed person asking the same question. Thanks for writing this up! $\endgroup$ Dec 9 '21 at 4:10
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    $\begingroup$ @Nimloth how many if you count the interstage-mounted ullage motors? They were discarded after depletion, making them technically extremely-low-dV stages :) $\endgroup$ Dec 9 '21 at 4:18
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    $\begingroup$ @Michael If you could build extremely lightweight tanks and engines, you could get better payload fractions from staged vehicles as well. Staged vehicles would still be more efficient, would be able to use cheaper and not-so-lightweight construction, would be able to devote more mass to reducing maintenance and improving reliability, etc. $\endgroup$ Dec 10 '21 at 23:53
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Other answers address the core construct of the rocket equation with words and equations, but here it is visually:

benefits of staging

Where the Y-axis is the $\Delta V$ and the X-axis is the propellant mass. $b$ is a slider variable for when to stage. The dry mass change at staging is scaled linearly with the amount of $\Delta V$ remaining until orbit (~$9500$ $m/s$), though it should be noted that real launch vehicles do better than this ratio.

The red curve shows a single stage to orbit (SSTO) vehicle while the green curve shows a two stage launch vehicle. The two stage launch vehicle uses less propellant to bring the same payload to orbit compared with the SSTO.

You can play around with the interactive Desmos graph here.

Both 'stages' in this example have the same $I_{sp}$ but the ability of the two stage launcher to throw away some no longer needed dry mass is how the propellant (and thus mass) savings is realized.

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  • $\begingroup$ So if I understand this right, to summarize: the savings are only about 20%... but based upon the other posts, that 20% if the vital difference between generally not being able to get there, versus having some room for supplies/satellites/etc that you want to take up there? And you're basically starting with similar mass whether 1 stage or multistage (as engines are relatively light), but tossing out the used components halfway through, (particularly the fuel tank?) makes the latter part of the trip require less fuel (and then that feeds back to meaning you need even less launch fuel) $\endgroup$ Dec 10 '21 at 8:34
  • $\begingroup$ Just for good measure, the units of the graph? You mention m/s. I guess it's whatever you use in the ratio, but 20 for $m_{dry}$ and $m_{payload}$... but I'm guessing the most typical units for the set values/graph in current space flight is roughly in Megagrams (thousands of grams)?? Just was wanting to put the shuttle's external fuel tank 26.5 Mg empty into some rough perspective and help broader users have an idea of scale. $\endgroup$ Dec 10 '21 at 8:52
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    $\begingroup$ @JeopardyTempest All mass units cancel so it doesn't really matter what the (mass) units are, in my mind they were tonnes. Speed units are m/s, but not really important; the shapes of the curves are more important than their absolute values. $\endgroup$ Dec 10 '21 at 12:27
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    $\begingroup$ @JeopardyTempest That 20% is a very pessimistic estimate. As mentioned in the answer, real vehicles do better than this. (Second stage engine and nozzle can be optimized for vacuum while an SSTO is either stuck with a compromise between sea level and vacuum or has to carry two sets of engines along, making it SSTO in name only.) $\endgroup$
    – TooTea
    Dec 10 '21 at 12:32
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Without getting deep into the weeds, it's because engines don't weigh much. A Falcon 9 rocket has 10 Merlin engines weighing a total of about 4.7 metric tons, with the full weight of the rocket being about 550 tons. So altogether less than 1% of the total rocket weight. The reason you might want to try and avoid more than 1 stage is because it adds on engineering complexity, additional failure points, and production cost considerations. From a weight perspective alone, however, the choice is pretty clear.

As @ChristopherJamesHuff points out in the comments, the second stage only adds on 1 additional engine. So for a very rough estimate we can just compare the weight of the engine to the weight we lose by ditching the empty first stage. The single engine weighs ~0.5 tons, and the empty 1st stage is ~25.5 tons, therefor it's a clearly beneficial tradeoff from that perspective alone.

The case for staging gets even better for >1 stage because engines can be optimized for where it is being used, which in practice means optimizing for the thick atmosphere found at sea level, or the near vacuum of space. A single stage rocket will always have at least some of its engines operating in non-optimal conditions.

Now, it is true that there are additional considerations and complexity that a multi-stage rocket brings, but they don't change the picture -- a single stage orbital rocket will always be made better by adding at least 1 stage absent a complete revolution in rocket design. The exact numbers will vary, but the weight added (additional engines, connecting parts, etc) will always be significantly less than the weight you dropped by letting the first stage go once the fuel is used up.

Finally, you might wonder why SpaceX stopped at 2 instead of a >3 stage rocket. That is because there are diminishing marginal returns from staging. Going from 1 stage to 2 gives you giant gains in efficiency and payload capacity that clearly outweigh the added engineering and production challenges, but the situation gets more murky as you add more stages.

Weight numbers came from: https://www.spaceflightinsider.com/hangar/falcon-9/ (specifications tab) https://en.wikipedia.org/wiki/SpaceX_Merlin

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    $\begingroup$ "the second stage only adds on 1 additional engine. " for that particular rocket $\endgroup$ Dec 7 '21 at 21:56
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    $\begingroup$ @Uwe, if you can manage a propellant fraction of 95%, you can get to orbit on a single stage with a specific impulse of 375 or better (hydrolox or a few of the exotic fuels). If you can manage 97.5%, that gets you to orbit on kerolox or methalox. 98% gets you some of the hypergolics. 99.9% gets you to orbit with a single hydrogen peroxide stage. $\endgroup$
    – Mark
    Dec 9 '21 at 3:02
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    $\begingroup$ @Mark a propellant fraction of 95%, the atmospheric drag, the structural mass results in negative payload mass for single stage to orbit. $\endgroup$
    – Uwe
    Dec 10 '21 at 0:47
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    $\begingroup$ @Uwe, that 95%/375 assumes gravity and atmospheric drag. Ignore those, and you only need a specific impulse of 253 to get into orbit on a single stage of 95% fuel, or a propellant fraction of 85.5% to get into orbit on hydrolox. No need for negative payload masses. $\endgroup$
    – Mark
    Dec 10 '21 at 0:57
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    $\begingroup$ @Mark Good luck keeping a ton of HTP in check using just a kilogram of tankage. :) $\endgroup$
    – TooTea
    Dec 10 '21 at 12:38
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The important point to consider here is the orbital height you want to reach and the payload mass. For LEO you can do with 1 stage (although not efficient) but for interplanetary missions (or even moon) you cannot have just 1 stage since you require a lot of fuel to go from ground all the way to the moon. This would greatly reduce the payload capacity, which is the main focus of any launch. You don't want to send just a rocket anywhere but also include some useful science experiments. And everything is built around this in rockets. The more payload it can carry, the better !

If you still want to have only a single stage, the structure must be strong enough to hold the fuel and the forces imparted during the launch but then the structure must be made thick enough, which would increase the weight, which would increase the lift-off mass, which would then increase the fuel needed. Hence, staging is decided based on the payload mass, the chemical composition of fuel (translates to specific impulse of your engine) and the structural index of the materials used to build the rocket body.

Also, single stage would not necessarily mean a single engine but would depend on the specific impulse of the engine and the structural index. The engines are also optimised for only one altitude and are not efficient when operating outside of this range, since the atmosphere is always changing during the ascent phase of the launch. When you have these two parameters, you can then go through iterations to find the best possible combination of specific impulse and structural index of each stage.

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    $\begingroup$ "For LEO you can do with 1 stage" is there any example? $\endgroup$
    – Uwe
    Dec 7 '21 at 11:18
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    $\begingroup$ You do not have anything wrong, but you have a bunch of statements that could be more precise. For example comparing the mass fraction of some of the hypothetical single stage to orbit proposals (often sub 1%) against actually built (4-5%) multi stage. Talking about drag losses and why peak acceleration off the pad is not actually useful would be worthwhile as well.. $\endgroup$ Dec 7 '21 at 11:23
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    $\begingroup$ @Uwe There is no actual 1 stage launcher that I know of, except for sounding rockets but theoretically it is possible to have a single stage. This is what I know from my lectures. $\endgroup$
    – lqope54
    Dec 7 '21 at 12:59
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    $\begingroup$ @Iqope54 the original question is written on assumption that a rocket needs high acceleration to work well, while your lectures should have included the concept of drag increasing with the square of velocity, and all fuel spent fighting drag is 'wasted' so there is a complex balancing act tuning rocket performance. Second point that might be worth including is what happens when engines capable of lifting a fully fueled vehicle at say 2G are pushing the same vehicle with almost empty tanks at say 20G and what that means for needed structural strength. $\endgroup$ Dec 7 '21 at 13:22
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    $\begingroup$ I have up voted since your answer brought in some interesting aspects. Unfortunately, it is unconvincing because the reader has to believe what you said is true/relevant. This is perhaps why you have been voted down. Consider adding one or two concrete examples: a representative single-stage rocket and its performance could be a good start. $\endgroup$
    – Ng Ph
    Dec 10 '21 at 10:09
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Consider the following extremely simplified model of a rocket: we have a three stage rocket with each stage having dry mass $m_d$ and containing fuel $m_f$ for a total mass of $3m_d+3m_f$. The rocket equation is given $$\frac{\Delta v}{v_e}=\ln\left(\frac{m_0}{m_1}\right)$$ where $\Delta v$ is the change in velocity, $v_e$ is the exhaust velocity, $m_0$ is the initial wet mass (dry mass + fuel) and $m_1$ is the final mass (dry mass).

First let's launch our rocket without staging. It starts with mass $3m_d+3m_f$ and ends with mass $3m_d$. The rocket equation gives $$\frac{\Delta v}{v_e}=\ln\left(\frac{3m_d+3m_f}{3m_d}\right)=\ln\left(1 + \alpha\right)$$

with $\alpha=m_f/m_d$

Now let's launch the rocket with staging. Each burn it loses mass $m_f$ and during each separation stage it loses mass $m_d$ without gaining $\Delta v$ (it can be seen as a burn with $v_e=0$). For the total $\Delta v$ this becomes

\begin{align} \frac{\Delta v}{v_e}&=\ln\left(\frac{3m_d+3m_f}{3m_d+2m_d}\right)+ \ln\left(\frac{2m_d+2m_f}{2m_d+m_f}\right)+ \ln\left(\frac{m_d+m_f}{m_d}\right)\\ &=\ln\left(\frac{3!\left(1+\alpha\right)^3}{(3+2\alpha)(2+\alpha)}\right) \end{align}

A quick plot shows that the staging always wins over the non staging

enter image description here

The big takeaway: a staged rocket can shed more dry mass and because $\Delta v$ greatly depends on final mass a staged rocket will have a fundamental advantage over a single stage rocket. It is important that as much time is spend thrusting with low mass because if you first burn $3m_f$ of fuel and then ditch $2m_d$ of staging you will not get a boost in fuel efficiency. There are also other factors that benefit staged rockets as mentioned in the other answers but this is still an important aspect

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