# Optimal size for heavy-lift launch vehicle

The primary motivation for the development of large capacity launch vehicles seems to be that of efficiency - a bigger vehicle will be more efficient at delivering a given payload to LEO than multiple smaller vehicles.

However, there seems to be a number of difficulties in scaling up. Factors like chamber pressure and fuel chemistry seem to place a hard limit on the amount of thrust and ISP possible for a given size of engine. Engines only seem to get so big; one factor is combustion instability. Bigger launchers then seem to require larger numbers of engines to achieve a given total thrust. For example, the proposed SpaceX ITS booster would have 42 Raptor engines. That raises questions of reliability; more things that can go wrong increases the prospect that something may go wrong.

My question is: do issues associated with scaling up ultimately place a practical limit on the maximum payload to LEO for a single vehicle launch? Is it a hard limit or one which could increase over time with the further evolution of space technology? What is the current practical limit? What could be the limit in 10 years, 20 years, or 50 years?

• This could only work as an overview or survey question, i think, due to the great number of interdependent factors involved. Even if we limit this only to chemical staged rockets, it would have to be assumed that current designs won't change much. For instance, in the ITS case, a major innovation is being attempted - constructing the rocket of carbon fiber. The limit right now maybe is something that can be answered in general terms, but i'm not sure. – kim holder Oct 3 '16 at 1:35
• @kimholder Perhaps this is several questions rolled into one. The 42-engine ITS booster raises the question of how many is too many to be practical to operate on a single booster stage? Engines like the Saturn V F-1 and M-1 raise the question of how big can one engine get? But, taken together, it puts a practical limit on how big a single rocket can get. – Anthony X Oct 3 '16 at 2:54
• The limit in 10 years ? That would be the BFR – Antzi Oct 3 '16 at 12:51

Note; larger rockets can definitely be cheaper per unit mass to LEO than smaller rockets, through production methods. The Sea Dragon design was intended to be produced in a dry dock, using 8mm steel, and with simple, large engine designs. The intention was to reduce the component count in the engine by two orders of magnitude, compared to the Saturn V. https://en.m.wikipedia.org/wiki/Sea_Dragon_(rocket)

For the SpaceX ITS, 42 Raptors allows a moderate degree of redundancy in the event of several failing, and further, Elon has stated that the optimisation favoured smaller engines, rather than larger ones. Since there are so many engines, the forces can be balanced by throttling or deactivating engines opposite to the defect. In the event of several engines failing; This wouldn't be as much of an issue, as the payloads then go into a parking orbit. So if several engines failed such that the ascent was severely slowed, the second stage would likely still be able to reach orbit, although at a lower level. As it either has to be refueled, or to deliver fuel, this likely wouldn't be a major issue, as burning more fuel would allow the satellite to orbit as previously planned. This could result in further refuelings to compensate.

I'm not sure if the ITS first stage will be able to land when mostly fueled. I'd hope so, although perhaps it is more difficult landing a taller rocket, with fuel mass too. Although the crew compartment would be able to eject from the first stage and land on Earth, as SpaceX implemented in their Dragon design. (Dragon2?).

• +1 for Sea Dragon. As for large rockets being less Efficient, that's not quite the case. The Tsiolkovsky rocket equation only cares about the mass ratio of empty mass to fuel mass, not the actual masses themselves. A rocket that with 9kg of fuel and 1kg of structure mass will have the exact same dV as a rocket with 9kt of fuel and 1kt of structure mass. Large rockets also require fewer weight-saving measures. Adding a half-kilogram flight computer is going to severely hamper your 1 Kilogram rocket, but the 1 Kiloton rocket isn't even going to notice. – UIDAlexD Oct 3 '16 at 13:43

Let me present a very simple mechanism that would limit the size of rockets. Consider, at some height the added weight from structural materials will outweigh any benefit gained from further reduction of dynamic pressure in the climb.

Computing this exactly would be quite difficult, since dynamic pressure varies greatly over the trajectory. However, I'm not interested in complex calculations here. I'll do the simplified version. I'll consider a rocket moving straight up, at its max Q.

Fraction of mass contained in structural materials, approx:

$$\alpha = \frac{ 3 x 3 \rho_{rocket} g h }{ \sigma_{yield} } \frac{\rho_{rocket} }{ \rho_{steel} }$$

The retarding pressure from the weight of the steel would be:

$$P_{steel} = \alpha \rho_{steel} 3 g$$

The tradeoff between more steel vs. higher aerodynamic efficiency will start to become acute when P_steel is roughly in the same ballpark as the dynamic pressure. This is totally a cop-out to obtain a general ballpark figure. Using the above expressions, I can do:

9*(1 g/cm^3)^2*(9.8 m/s^2)^2*(80 m)^2/((500 MPa))*3


(you can plug this into Google)

What I've done here, is that I manipulated the value of h until the pressure came out to around 33 kPa, which I found from this sound was about the Max Q of the shuttle. The values from steel and other stuff are all just educated guesses. Anyway, my answer is 80 meters. A rocket becomes less efficient if it is taller than that.

The Saturn V was actually 110 meters tall, but I think that was counting a relatively slender cone on the top. So historically large rockets might already be close to the "limit". However, this isn't truly a mass limit, just height. Saturn V was very slender. You could imagine its width growing until it was basically a blocky shape... which probably isn't far from what Orion was proposed for. Beyond that, you'd be building some kind of pancake shape rocket, and intuitively something just sounds wrong with that.

• "Some kind of pancake shape rocket" sounds a lot like some designs for spacecraft popular in certain circles (no pun intended). – a CVn Oct 3 '16 at 14:57
• Chrysler's entry in the Space Shuttle design competition is the squattiest booster I know of: history.nasa.gov/SP-4221/p266.jpg – Organic Marble Oct 4 '16 at 3:08

Project Orion claimed to be able to put 6100 tons in LEO in a single launch.

Depending on what you are willing to allow for "the future evolution of space technology", the limit could be pretty large.