One other advantage of larger diameter rockets (posting this at 3:50) is a greater internal volume for less material. The circumference of the rocket will increase linearly with diameter, but the available volume will square. This allows for more fuel with less dry mass. Also, a larger diameter naturally allows for larger fairings. There are also reentry heating considerations, with wider vehicles pushing the shockwave and hence the heating further away. This isn't meant to downplay falcon 9, but rather that's why Starship/superheavy is so different.
Interesting predicament: the height of Starship and Super Heavy are in such a way that Super Heavy’s height is Starship’s height times the square root of 2. It’s not the golden ratio or e, but it’s interesting.
- Drag is mainly important for the first stage as higher up in the atmosphere the drag effect is much reduced. Therefore a narrower first stage than optimal for volume/surface, can still be advantageous. - The rocket with stages that progressively become narrower needs diameter adapters which are a weak point for dynamic pressure, stability and they break the laminar flow. Having a rocket of mostly a single diameter prevents this. You could instead make a rocket conical but this makes manufacturing much more expensive and complex. - Falcon heavy (3 boosters) seems not ideal for volume/surface but the manufacturing benefits together with the lower number of launches, probably outweigh that. Just some thoughts. BTW Kerbal Space Program 1 with realism overhaul does teach this too.
If you have a constant volume and solve for the area, and then find where the derivative of that area reaches 0 (local minimum), you find that v = 10.47r³. Putting that back into the height equation, you find that the optimal height is h = 2r = d. If you include the height of the domes, the best fineness ratio for a tank is 2.
I like your presentation style-great video overall. One issue though - your assumption that material thickness would be held constant as diameters vary is not true. The tank is a thin walled pressure vessel. For a given tank pressure and material, wall thickness changes proportionally to diameter. If you double the diameter you need to double the thickness of the walls to keep the same stresses in the tank material. That effect will pull the optimum point toward lower diameters.
It turns out that effect cancels out the cube square law precisely, such that all pressure vessels of the same pressure and same material maintain the same mass ratio, regardless of scale
This video answered two questions that had crossed my mind recently. Really interesting to see how they optimized Starship and then decided it was better to just make SH the same diameter (likely from a manufacturing/cost perspective). I am curious why they went with 9m over 10m for Starship. I vaguely remember something about 9m being the max for some of the infrastructure at 39A (as opposed to 12m) but can't seem to find any sources on that.
I'm sure there are a lot of different factors. They knew they wanted to put vacuum raptors on Starship, and the size of the nozzle there has a large impact on the Isp you get out of the engine - and therefore the delta-v - so they needed space to fit the engines. I can't think of any big constraints at 39A that would push towards 9m rather than 10m.
I loved the trivia question at the end! And I even knew the answer too! Because this is actually something I found myself wondering about a couple weeks ago. I knew that variants of the S-I were in Saturn I, IB, and V. And that S-II was in Saturn V. And that S-IV was the upper stage of Saturn I, while S-IVB was the much-improved J-2 version used by Saturn IB and V. But I knew there was never an S-III on the I, IB, or V, so I went and looked it up. And sure enough, it showed up in some of the proposed Saturn-C configurations (the earlier ones, it seems): specifically for the C-2 and C-3. And because NASA ultimately decided to go forward with lunar orbit rendezvous, using C-1 (-> Saturn I, Saturn IB) as an earth-orbit testbed and C-5 (-> Saturn V) as the proper lunar launch vehicle, the various other proposals (C-2, C-3, C-4, C-8, etc) weren’t developed. One other cool thing I also discovered back when looking this up, that I’d previously not realized, is that the S-V stage was actually flown (albeit inert) as the third stage of Saturn I for its initial 4 flights! That really took me by surprise. Both that the S-V *was* a thing that existed, and that it really did fly (in a sense) multiple times on Saturn I’s. Also it’s neat that the S-V is effectively just a Centaur-C (a dual RL-10 upper stage); and apparently it’s sufficiently within the Centaur family to the point that the versions of Centaur still used today on Atlas V / Vulcan arguably have a pretty straightforward ancestry directly back to the Saturn I’s S-V stage, of all things!
@@EagerSpace It’s really quite impressive how far in advance they were able to plan things out-before they even had a solid idea of what the overarching mission architecture would look like (whether rendezvous and docking was even necessarily feasible!) and so forth. You can tell that Von Braun et al really knew what they were doing.
@@jgottula I think Von Braun had a rocket like the Saturn V in his head - and his team's heads - when they were working on the V2. But it was really the lunar rendezvous architecture that made it possible. I talk about that in depth in the "solar system road trip" video; even with leaving most of the LEM on the surface and the rest in lunar orbit and ditching the service module on the way back, they barely could get the command module back to earth. Doing lunar with a single vehicle is really hard - you need about 5000 m/s of delta v even if somebody else sends to you the transfer orbit; if you have to make it from LEO on your own it's over 8000 m/s. And that's assuming you do a really hard landing with no hovering.
@@EagerSpace Yeah, looking back on Apollo’s single-launch architecture, it’s actually pretty incredible that they were able to figure out, design, build, and successfully execute on a plan that could do the entire mission with just a single C-5 launch vehicle. And I mean, a lot of that penciled into place long before all the unknowns had even been figured out! (“Is orbital rendezvous and docking feasible?” “Sir, we don’t actually know that yet. Maybe we should launch a thing into orbit first and we’ll get back to you on that.”) I think the direct-ascent approach would have absolutely necessitated the C-8 (or the Nova-as blurry as that designator kinda is), wouldn’t it? The foresight of Von Braun and co in looking ahead to a 1mlbf (much as I detest lbf as a force unit) engine for their eventual launcher, and getting onboard with the E-1/F-1 projects in the mid-to-late 1950s (literally before orbit had even been achieved), is pretty amazing. They of course had a lot of alternative options and backup plans of course; but at the same time they really seemed to have a very good overall sense of what they were doing and where they were headed surprisingly early in the process. Like, even several years prior to the Kennedy speech and the actual commencement of Project Apollo, they already seemed to have quite a bit figured out in terms of engines, the general Juno V launch vehicle concept, and probably plenty more. (Side note: the Wikipedia article on the Saturn C-2 proposal-which I understand was effectively premised on Earth-orbit rendezvous-says that “it was calculated that 15 launches and rendezvous of the C-2 would have been required to assemble a lunar spacecraft in Low Earth orbit.” Which totally blows my mind for something planned for launch in ~1967. On a funnier note, it also sounds like something that Blue Origin, had it existed at the time, would have filed numerous lawsuits and/or infographics against, on the grounds that such a mission architecture was clearly “IMMENSELY COMPLEX AND HIGH-RISK!!!” 😂 Which would actually have been a much more accurate characterization back then, than it is today.)
Great video. I am surprised you didn’t do the classical sensitivity analysis (looking at the total derivative, the sum of partials) which usually comes up in storage tank design. Anyway, a lot to think about. :D
The fact that you basically ignored the pressure and its effect on the tank walls might indicate that the pressure, to some degree just follows form. Indicates! Not sure there yet because I have no clue what the right pressure inside the tank is. It has something to do with buckling but I'm really not sure.
Thanks for this. Is it common for rockets to share a diameter between stages for aerodynamic reasons, and if so does it change the minimum point on your graph if you sum the curves for first and second stages?
It's common for stages to share diameters, though it's generally more for manufacturing reasons than for aerodynamic ones. But historically there have been a lot of rockets with different diameters because of what was convenient. Here's an old poster that shows them: venngage-wordpress-gallery.s3.amazonaws.com/uploads/2016/08/Rockets-of-the-World.jpg I'm not sure there's much of an effect on the minimum point, but I haven't thought about it deeply.
@@EagerSpace Thanks for getting back to me, glad I stumbled across your videos :-) I wondered if the combined weight gave more insight into the tradeoffs. SpaceX is a good example as they are a manufacturing company first and a rocket company second. It would not surprise me if the numbers for the combined weight end up closer to optimum than expected. I think the other consideration for SpaceX was the desire to re-use existing pads and technologies for Falcon. Another manufacturing vs engineering decision.
@@darren8453 My sense is that *in general*, the approach is to build the second stage that works well and then make the booster that can lift it. Sometimes, it's an existing stage - Atlas V and Vulcan both used the existing Centaur stage and the capabilities of centaur drove the booster design. The big stage design constraint for Falcon 9 was the diameter, since they needed to be able to ship it by road. That made it a long thin rocket and it got even longer when they stretched it.
New Shepard is a big and heavy little rocket, so it's not a good choice for trying to get orbital launch. For a comparison, only about 5% of the energy to get to orbit is used to get to an orbital altitude and the remainder is used to get up to orbital velocity. So it's much, much harder to get to orbit.
Interesting idea. I generally ignore drag because on more orbital launches it's not a major factor in terms of delta-v; it's a few hundred m/s while the overall delta-v from the first stage is 3500 (ish) m/s for a rocket that stages low like the Falcon 9. But it probably does matter a little here for the first stage.
@@EagerSpace yeah it's also probably gonna be a giant pain to integrate the air drag with respect to the change in air density and airspeed as the rocket ascends. Would just be curious if this would be sufficient to close the gap between your models predicted diameter and the actual diameter of the rocket. I guess the other big factor that's missing is the mass of the engines, plumbing, and thrust assembly, though my guess is it's not huge compared to the mass of the tanks. Might be more significant than the air drag nonetheless I suppose
@@evil0sheep It's on my list to add to a model at some point, but I think that will put me into a true simulation and that's quite a bit of work. Flightclub.io might be able to do it... hmm...
10:28 maybe a bit of a classic math error here. Instead of phrasing the expression 3(2*Pi*r^2), as the area each dome would be separate from each other, you phrased it 3*2*Pi*r^2, which may make a difference in the calculations as such to affect the outcome of the video.
One other advantage of larger diameter rockets (posting this at 3:50) is a greater internal volume for less material. The circumference of the rocket will increase linearly with diameter, but the available volume will square. This allows for more fuel with less dry mass.
Also, a larger diameter naturally allows for larger fairings.
There are also reentry heating considerations, with wider vehicles pushing the shockwave and hence the heating further away.
This isn't meant to downplay falcon 9, but rather that's why Starship/superheavy is so different.
Agreed.
Interesting predicament: the height of Starship and Super Heavy are in such a way that Super Heavy’s height is Starship’s height times the square root of 2. It’s not the golden ratio or e, but it’s interesting.
That's probably just a coincidence, given how much of Starship's height is not taken up by propellant tanks
- Drag is mainly important for the first stage as higher up in the atmosphere the drag effect is much reduced. Therefore a narrower first stage than optimal for volume/surface, can still be advantageous.
- The rocket with stages that progressively become narrower needs diameter adapters which are a weak point for dynamic pressure, stability and they break the laminar flow. Having a rocket of mostly a single diameter prevents this. You could instead make a rocket conical but this makes manufacturing much more expensive and complex.
- Falcon heavy (3 boosters) seems not ideal for volume/surface but the manufacturing benefits together with the lower number of launches, probably outweigh that.
Just some thoughts. BTW Kerbal Space Program 1 with realism overhaul does teach this too.
Thanks.
Still missing the energia
If you have a constant volume and solve for the area, and then find where the derivative of that area reaches 0 (local minimum), you find that v = 10.47r³. Putting that back into the height equation, you find that the optimal height is h = 2r = d. If you include the height of the domes, the best fineness ratio for a tank is 2.
Alternative title: Why starship is so tall?? ;)
I don't think that SpaceX is designing their second stages first, you're just ignoring atmospheric drag. It's pretty significant for the first stage.
Yep was thinking this same thing and found this video.
I like your presentation style-great video overall. One issue though - your assumption that material thickness would be held constant as diameters vary is not true. The tank is a thin walled pressure vessel. For a given tank pressure and material, wall thickness changes proportionally to diameter. If you double the diameter you need to double the thickness of the walls to keep the same stresses in the tank material. That effect will pull the optimum point toward lower diameters.
It turns out that effect cancels out the cube square law precisely, such that all pressure vessels of the same pressure and same material maintain the same mass ratio, regardless of scale
This video answered two questions that had crossed my mind recently. Really interesting to see how they optimized Starship and then decided it was better to just make SH the same diameter (likely from a manufacturing/cost perspective). I am curious why they went with 9m over 10m for Starship. I vaguely remember something about 9m being the max for some of the infrastructure at 39A (as opposed to 12m) but can't seem to find any sources on that.
I'm sure there are a lot of different factors. They knew they wanted to put vacuum raptors on Starship, and the size of the nozzle there has a large impact on the Isp you get out of the engine - and therefore the delta-v - so they needed space to fit the engines.
I can't think of any big constraints at 39A that would push towards 9m rather than 10m.
They scaled down from 12 to 9 meters back when they were still planning on using carbon fiber.
I loved the trivia question at the end! And I even knew the answer too! Because this is actually something I found myself wondering about a couple weeks ago.
I knew that variants of the S-I were in Saturn I, IB, and V. And that S-II was in Saturn V. And that S-IV was the upper stage of Saturn I, while S-IVB was the much-improved J-2 version used by Saturn IB and V. But I knew there was never an S-III on the I, IB, or V, so I went and looked it up.
And sure enough, it showed up in some of the proposed Saturn-C configurations (the earlier ones, it seems): specifically for the C-2 and C-3. And because NASA ultimately decided to go forward with lunar orbit rendezvous, using C-1 (-> Saturn I, Saturn IB) as an earth-orbit testbed and C-5 (-> Saturn V) as the proper lunar launch vehicle, the various other proposals (C-2, C-3, C-4, C-8, etc) weren’t developed.
One other cool thing I also discovered back when looking this up, that I’d previously not realized, is that the S-V stage was actually flown (albeit inert) as the third stage of Saturn I for its initial 4 flights! That really took me by surprise. Both that the S-V *was* a thing that existed, and that it really did fly (in a sense) multiple times on Saturn I’s.
Also it’s neat that the S-V is effectively just a Centaur-C (a dual RL-10 upper stage); and apparently it’s sufficiently within the Centaur family to the point that the versions of Centaur still used today on Atlas V / Vulcan arguably have a pretty straightforward ancestry directly back to the Saturn I’s S-V stage, of all things!
I found the early Saturn plans fascinating - how they created the S-IB and how they had a bunch of contingency plans.
@@EagerSpace It’s really quite impressive how far in advance they were able to plan things out-before they even had a solid idea of what the overarching mission architecture would look like (whether rendezvous and docking was even necessarily feasible!) and so forth. You can tell that Von Braun et al really knew what they were doing.
@@jgottula I think Von Braun had a rocket like the Saturn V in his head - and his team's heads - when they were working on the V2.
But it was really the lunar rendezvous architecture that made it possible. I talk about that in depth in the "solar system road trip" video; even with leaving most of the LEM on the surface and the rest in lunar orbit and ditching the service module on the way back, they barely could get the command module back to earth.
Doing lunar with a single vehicle is really hard - you need about 5000 m/s of delta v even if somebody else sends to you the transfer orbit; if you have to make it from LEO on your own it's over 8000 m/s. And that's assuming you do a really hard landing with no hovering.
@@EagerSpace Yeah, looking back on Apollo’s single-launch architecture, it’s actually pretty incredible that they were able to figure out, design, build, and successfully execute on a plan that could do the entire mission with just a single C-5 launch vehicle. And I mean, a lot of that penciled into place long before all the unknowns had even been figured out! (“Is orbital rendezvous and docking feasible?” “Sir, we don’t actually know that yet. Maybe we should launch a thing into orbit first and we’ll get back to you on that.”)
I think the direct-ascent approach would have absolutely necessitated the C-8 (or the Nova-as blurry as that designator kinda is), wouldn’t it?
The foresight of Von Braun and co in looking ahead to a 1mlbf (much as I detest lbf as a force unit) engine for their eventual launcher, and getting onboard with the E-1/F-1 projects in the mid-to-late 1950s (literally before orbit had even been achieved), is pretty amazing. They of course had a lot of alternative options and backup plans of course; but at the same time they really seemed to have a very good overall sense of what they were doing and where they were headed surprisingly early in the process. Like, even several years prior to the Kennedy speech and the actual commencement of Project Apollo, they already seemed to have quite a bit figured out in terms of engines, the general Juno V launch vehicle concept, and probably plenty more.
(Side note: the Wikipedia article on the Saturn C-2 proposal-which I understand was effectively premised on Earth-orbit rendezvous-says that “it was calculated that 15 launches and rendezvous of the C-2 would have been required to assemble a lunar spacecraft in Low Earth orbit.” Which totally blows my mind for something planned for launch in ~1967. On a funnier note, it also sounds like something that Blue Origin, had it existed at the time, would have filed numerous lawsuits and/or infographics against, on the grounds that such a mission architecture was clearly “IMMENSELY COMPLEX AND HIGH-RISK!!!” 😂 Which would actually have been a much more accurate characterization back then, than it is today.)
"@@jgottula clearly “IMMENSELY COMPLEX AND HIGH-RISK!!!”"
LOL
Great video. I am surprised you didn’t do the classical sensitivity analysis (looking at the total derivative, the sum of partials) which usually comes up in storage tank design. Anyway, a lot to think about. :D
Would be really interesting if this was in KSP, however in KSP all the tanks of equal volume have equal mass.
The fact that you basically ignored the pressure and its effect on the tank walls might indicate that the pressure, to some degree just follows form. Indicates! Not sure there yet because I have no clue what the right pressure inside the tank is. It has something to do with buckling but I'm really not sure.
Thanks for this. Is it common for rockets to share a diameter between stages for aerodynamic reasons, and if so does it change the minimum point on your graph if you sum the curves for first and second stages?
It's common for stages to share diameters, though it's generally more for manufacturing reasons than for aerodynamic ones. But historically there have been a lot of rockets with different diameters because of what was convenient. Here's an old poster that shows them: venngage-wordpress-gallery.s3.amazonaws.com/uploads/2016/08/Rockets-of-the-World.jpg
I'm not sure there's much of an effect on the minimum point, but I haven't thought about it deeply.
@@EagerSpace Thanks for getting back to me, glad I stumbled across your videos :-)
I wondered if the combined weight gave more insight into the tradeoffs. SpaceX is a good example as they are a manufacturing company first and a rocket company second. It would not surprise me if the numbers for the combined weight end up closer to optimum than expected.
I think the other consideration for SpaceX was the desire to re-use existing pads and technologies for Falcon. Another manufacturing vs engineering decision.
@@darren8453 My sense is that *in general*, the approach is to build the second stage that works well and then make the booster that can lift it. Sometimes, it's an existing stage - Atlas V and Vulcan both used the existing Centaur stage and the capabilities of centaur drove the booster design.
The big stage design constraint for Falcon 9 was the diameter, since they needed to be able to ship it by road. That made it a long thin rocket and it got even longer when they stretched it.
I wonder if the short fat New Shepard could be easily extended and given more engines to become orbital.
New Shepard is a big and heavy little rocket, so it's not a good choice for trying to get orbital launch.
For a comparison, only about 5% of the energy to get to orbit is used to get to an orbital altitude and the remainder is used to get up to orbital velocity. So it's much, much harder to get to orbit.
Surface drag ?
That matters but drag in general is not a significant percentage of the energy cost of getting to orbit.
I'd be interested to see this with a simple model of air drag taken into account
Interesting idea.
I generally ignore drag because on more orbital launches it's not a major factor in terms of delta-v; it's a few hundred m/s while the overall delta-v from the first stage is 3500 (ish) m/s for a rocket that stages low like the Falcon 9.
But it probably does matter a little here for the first stage.
@@EagerSpace yeah it's also probably gonna be a giant pain to integrate the air drag with respect to the change in air density and airspeed as the rocket ascends. Would just be curious if this would be sufficient to close the gap between your models predicted diameter and the actual diameter of the rocket.
I guess the other big factor that's missing is the mass of the engines, plumbing, and thrust assembly, though my guess is it's not huge compared to the mass of the tanks. Might be more significant than the air drag nonetheless I suppose
@@evil0sheep It's on my list to add to a model at some point, but I think that will put me into a true simulation and that's quite a bit of work. Flightclub.io might be able to do it... hmm...
10:28 maybe a bit of a classic math error here. Instead of phrasing the expression 3(2*Pi*r^2), as the area each dome would be separate from each other, you phrased it 3*2*Pi*r^2, which may make a difference in the calculations as such to affect the outcome of the video.
In other words: your final Area should be 3*Area of one dome ( 3(2*Pi*r^2), or 6*3Pi*3r^2, not (6*Pi*r^2)!
@@topsecret1837 that’s not how math works. The 3 does not distribute to each of the terms like that.