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Given how it is significantly easier to achieve suborbital spaceflight, I was wondering about how a rocket spends its energy budget. If you magically could launch a rocket from 0 km/s but from an altitude of 100km, how much energy would you "save" for not having to climb that vertical distance.

I'm wondering this because someone suggested space planes could provide significant savings over rockets due to not having to expend as much energy climbing through the atmosphere, but my understanding is that most of the energy is expended in generating horizontal thrust, so getting to skip 25/50km of altitude but still having to accelerate laterally wouldn't produce savings. I tried finding the answer but I couldn't find much beyond variations on "getting to space: easy, staying there: hard".

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    $\begingroup$ Most of it is spent for horizontal velocity. The second biggest loss is spent for gravity loss (i.e. the "fall" of the rocket until it has not reached the 7.8km/s). Surprisingly, altitude and drag are lesser than these. I hope you will get this in a more detailed answer. $\endgroup$
    – peterh
    Apr 30, 2019 at 21:45
  • $\begingroup$ Do you consider gravity drag and atmospheric drag as energy spent gaining altitude? if so, the answer is straight-forward. if not, then it becomes quite difficult to properly account for all effects... $\endgroup$
    – Polygnome
    Apr 30, 2019 at 21:59
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    $\begingroup$ IMHO, the primary benefit to be gained by "launching" at altitude is the considerable reduction in "max q" that the launch stack has to endure. $\endgroup$
    – Digger
    May 2, 2019 at 16:46

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Potential energy difference at 100 km altitude is about 1000 kilojoules/kilogram and the kinetic energy of a mass moving orbital velocity at 100 km is about 30,000 kilojoules/kilogram.

So it’s frequently pointed out energy the energy of orbital speed is around 30 times as much as potential energy of 100 km altitude. For example this XKCD piece concluding achieving altitude is a piece of cake compared to reaching orbital velocity.

What Randall Munroe fails to consider is gravity loss. Each 102 seconds of vertical ascent inflicts 1 km/s of gravity loss.

So there is a big incentive to minimize the time it takes to reach the Karman line. A booster stage will have more rocket engines and often lower ISP but higher thrust propellent.

Even though a booster only provides a fraction of the delta V budget it can easily be 2/3 or a rocket’s cost. SpaceX’s reusable boosters is very important accomplishment.

I’m attaching graphics of two pages from the coloring book I’m working on. (Note to other Space Stack Exchange particpants -- I’d be grateful to anyone who reviews and critiques this material -- I do make mistakes and hopefully most of them will be caught before publication).

I constructed an Excel spreadsheet attempting to model a trajectory with Saturn V ‘s acceleration profile. My (questionable) model seems to show starting from 100 km would save about 1 km/s delta V. Even starting from that height your thrust must have a vertical component or you would fall back into the atmosphere.

enter image description here

enter image description here

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  • $\begingroup$ Hey these coloring strips are really good. You need to stay with them. $\endgroup$
    – user39728
    Mar 31, 2021 at 4:45
  • $\begingroup$ One thing I'm wondering though---and this is not to take away from the fabulous work you're doing---is that at least some rockets pitchover and do gravity turns beginning immediately after launch (which seems different from the suggestion in your strips that the pitching would mostly happen after the 100 km line?) Just pointing out in case it's an error. But please keep making these things, your graphics are impeccable and the commentary is right up there too. This is pro-level work, really. $\endgroup$
    – user39728
    Mar 31, 2021 at 4:49
  • $\begingroup$ The cartoonized starry sky is the best. My thought when I first saw it is "this guy must have hired a really good illustrator to do the graphics, or he must have had some really good feedback from very creative people." $\endgroup$
    – user39728
    Mar 31, 2021 at 4:52
  • $\begingroup$ I love the coloring book. One spelling error I saw throughout: "Propellent" sb/ "Propellant" $\endgroup$
    – Organic Marble
    Jan 20 at 20:40
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One of the things to think about is rockets don't have energy budgets. They have delta-v budgets. Try and think of it that way but: The majority of the energy in a 100km orbit above earth is in 'going sideways'. However besides the lack of numbers this doesn't answer your question. For example how much dV is needed to gain attitude is at least the amount you would need to coast to your target altitude in a vacuum. But doing this as part of a way to get to orbit is only one (inefficient) way of getting there. The dV saving is at most this. There is no good bound in either direction.

A few things are worth considering to get a feel for the problem:

  • How long you have to spend fighting gravity also depends on how long you need to keep the rocket in the air before centripetal force and gravity balance each other and there's no universal answer to that question. Aero-properties and TWR affect what's optimal.

  • Rockets don't "fish-hop"; they don't go up until they reach orbital height, then sideways until they reach orbital velocity, instead they try and combine the two maneuvers which takes advantage of Pythagoras, but costs some aero-dynamic drag.

  • A little bit of extra or saved dV costs a lot. Anything you gain or loose is necessary the 'first' bit; you have to move the whole fully fueled rocket by this amount.

Let's do the simplified theory first. If dV was the only concern and there was no atmosphere. With infinite TWR, you could reach a "sea-level" orbit without any energy or dV being expended upwards. Further the theoretically most efficient way to use dV to gain altitude is a Hohmann Transfer, the Hohmann transfer from sea level to 100km around earth is small. Concretely around 60m/s, which compared to 7800m/s for the orbital velocity in the first place is tiny.

So yes, there are many meaningful ways in which your intuition and the saying about staying there are correct. If you simplify things down too much, then especially when you consider that going there then going fast enough to stay there is not a very efficient way of doing things: then 100% lifting rockets up before you launch them is silly, it gains very little for a lot of effort.

However, these are way to big assumptions to ignore. When you add these factors back in things start to make more sense. Drag and gravity losses are a significant factor in current rockets and they are designed to compromise these things. If you didn't need to worry about TWR and being aerodynamic rockets could be made much lighter, which is the holy grail as this means less fuel is need, which makes them lighter. Etc, etc.

I know this is anti-climactic but its really hard to put a number on how much mass/money this would save as it changes a lot of factors, but its hard to imagine this not being at least a 20-30% mass saving.

Another thing is wings etc don't just get you altitude, they might also get you speed. By not needing to use valuable dV just to keep you up, you can fly through the air for long enough to make use of atmospheric engines. Jet engines are a lot more fuel efficient than rocket engines at low speeds, so if you can it would make sense in theory to want to use them when you can.

If you usefully use this extra speed and knock mach 1 off your dV requirements the savings could be huge.

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To achieve a low-earth orbit, you must spend about 9.4 km/s worth of fuel. Low earth orbit velocity is around 7.8 km/s. Most of the energy expended goes into moving sideways, and only about 1.6 km/s or 17% is spent fighting gravity/aerodynamic forces/gaining height.

My answer is corroborated by this XKCD what-if. Getting to an altitude that counts as 'space' is relatively easy. Getting the rocket to stay there is much, much harder.

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    $\begingroup$ to balance against that, the early stage of the flight is slow, so a significantly larger fraction than 17% of the propellant is expended gaining altitude $\endgroup$
    – user20636
    Apr 30, 2019 at 21:58
  • $\begingroup$ @JCRM do you have a ballpark/resource on how to calculate how much less propellant you would need from launching at a given altitude X? like if you could magically launch from 25km and 0m/s what kind of effect would that have on fuel requirements? $\endgroup$
    – BWStearns
    Apr 30, 2019 at 22:10
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    $\begingroup$ It's fairly straightforward to calculate the delta-V, although it depends in detail on things like your acceleration at launch and exactly where and in what direction you launch. Converting that into a proportion of your fuel depends heavily on what fuel you are using. $\endgroup$
    – Steve Linton
    Apr 30, 2019 at 22:25
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    $\begingroup$ And also the ambient pressure. You need to expend more fuel for the same delta-V at sea level than you do in vaccuum. $\endgroup$
    – Ingolifs
    Apr 30, 2019 at 22:31
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    $\begingroup$ that case isn't particularly relevant to this question @BWStearns, but Hobbes' answer to another question suggests the "first" 13% of the delta-v requirement uses about 25% of the propellant $\endgroup$
    – user20636
    May 1, 2019 at 7:03

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