# Why are rocket mass on the launch pad and payload mass to LEO not strongly correlated?

What explains the relation between how much a launcher weights on the launch pad, and how much mass it can lift to orbit?

I had expected that more payload requires more fuel to be launched and that a launcher is built around that fuel mass. I'm surprised to see that these two measures are just weakly correlated. The data I use here is indeed sloppy but it can't be that much off, or can it? (I'm getting suspicious). I can understand that Falcon 9 v1.1 is much heavier than v1.0 because it is supposed to be more robust and have fuel enough to be reusable. I note that the (older style) Russian and Chinese launchers are the least efficient according to this simple ratio, but with Ariane 5 a bit worse than Proton. I'm surprised to realize that Atlas V 551 and Ariane 5 both lift about the same mass to orbit, but that Ariane 5 is well more than twice as heavy on the launch pad! Is it because of the large solid fuel boosters? What other factors explain this lack of general relation?

Below are figures I took from Wikipedia about eleven different launchers. I've picked values for the maximum LEO capacity configuration. The four columns are:

• Mass of the launcher on the launch pad (tons).
• Mass payload the launcher can put in low Earth orbit (tons).
• The ratio between the two above (tons on pad / tons in LEO).
• The difference between that ratio and the average ratio in this sample, which is 33 tons on the launch pad per ton payload to LEO, ranging hugely from 21 (Saturn V) to 55 (Long March 2F).

Pad, LEO, Ratio, Deviation from average ratio [tons]

240   6.0  40    7  Antares (not in the chart)

308   6.5  47   15  Soyuz

333  13.0  26   −7  Falcon 9 v1.0

334  19.0  18  −15  Atlas V

464   8.5  55   22  Long March 2F

506  13.0  39    6  Falcon 9 v1.1

531  19.0  28   −5  H-IIB, Japan

694  21.0  33    0  Proton

733  29.0  25   −8  Delta IV Heavy

777  21.0  37    4  Ariane 5

3000 140.0  21  −11  Saturn V (not in the chart)

Chart: Tons payload to LEO versus tons of rocket on the launch pad.

• "If there's a way to make a nicely formatted table,.." The powers that be have always resisted allowing tables in SE sites. :( I've never seen good reason why it cannot be supported. :-/ – Andrew Thompson Aug 16 '15 at 10:11
• What, internet facts wrong? Inconceivable! Your best bet is probably manufacturer sites when they exist. ulalaunch.com/products_atlasv.aspx – Organic Marble Aug 16 '15 at 12:15
• @OrganicMarble I suppose it is with or without the booster rockets. Both are right, given different configurations. French Wiki uses both numbers as a range for Atlas V. I suppose that a launcher's mass "depends" and cannot be as easily captured in one single figure as one gets the impression of at Wikipedia. I learned a lesson, that's good. – LocalFluff Aug 16 '15 at 12:19
• I guess given that the payload mass is only 2-6% of the total mass, a rocket that functions even 1% better or worse than average will make this table only weakly correlated. To me, it is almost surprising that there is any correlation – neelsg Aug 16 '15 at 15:00
• Atlas V 401: 334 tons, 9.8 tons to LEO. Atlas V 551: 587 tons, 19 tons to LEO. Mass fractions are 29 and 30. That removes a big outlier at one side. – Hobbes Aug 16 '15 at 17:15

It typically takes a total expenditure of 9400-10000 meters per second of delta-v to reach LEO.

Per the rocket equation, delta-v is proportional to the log of the propellant mass ratio, but also proportional to the exhaust velocity of the rocket engines or their specific impulse.

Solid rocket boosters have relatively low specific impulse: 275 sec for Atlas V's SRBs. Liquid hydrogen engines have high specific impulse: 449 sec for the Atlas Centaur upper stage. Kerosene engines fall in between. So depending on how heavily a launcher relies on (cheap but inefficient) solids, you can see that the mass efficiency of the launcher as a whole is going to be very different.

There's also a lot of variation in how rocket structures are built, leading to a lot of variation in weight. The tankage can be separate vessels inside the stage fuselage, or the tank walls can serve as the stage; the structure can be cheap, durable, and heavy, or expensive, light, and fragile.

In the end, mass at launch -- particularly first stage mass -- is less important than launch cost, so a heavier but simpler to construct structure may be preferred.

• Also the extent of reusable components may make a significant difference – user2813274 Aug 16 '15 at 21:12
• Missions can be different too : one rocket may have to carry multiple payloads when the other may have only one payload. Multiple payload = different orbits = more fuel for orbit transfer = less payload. – Olivier Aug 16 '15 at 21:46

• Larger tanks have a better volume-to-surface ratio, so there's less structural weight per kg of content.
• Some parts on a rocket don't scale up when the rocket gets larger. For instance the guidance system on a Saturn V isn't 14 times larger than that of a Falcon 9.

And speaking of the Falcon 9: the v1.1 in your chart has its payload listed for the 'reuse the first stage' flight mode. In expendable mode, you can expect the payload ration to be slightly better than the Falcon 9 v1.0.

• It turns out that for pressurized tankage -- which is basically all rocket tankage -- the scaling runs more toward volume-proportional than surface-proportional (yarchive.net/space/launchers/fuel_tank_scaling_laws.html). Some of the parts also scale as a low power of the rocket mass - cable runs, for example, scale with length, so roughly with the cube root of mass. Large rockets are more mass efficient as you say, but not drastically so. – Russell Borogove Aug 18 '15 at 15:26

I believe Russell Borogove's answer is correct but maybe could be stated a little more directly:

The reason your 2 factors of payload mass and liftoff mass don't correlate is that you are ignoring the other factor in the equation. The 3 main factors in the rocket equation are mass ratio, delta-v, and specific impulse.

Since your delta-v is basically fixed (to LEO) you are trying to correlate mass ratio without using specific impulse. If you can calculate a back of the envelope value of system specific impulse for the launchers in your list, I think your data will make a lot more sense.

Here's a simple thought experiment- take 2 boosters that deliver the exact same payload weight to LEO. One has a system specific impulse of 300 and the other has a system specific impulse of 450. The one with bad engines is going to be enormously bigger at liftoff and yet it delivers the exact same payload, so on your chart these data points would look uncorrelated.

I'd expect to see a sheaf of lines on your chart - for launchers with similar system specific impulse, the payload mass and liftoff mass would be somewhat correlated. Launchers with a different system specific impulse would follow a different curve.

I don't know if that adds anything useful, but lets see:

$$\Delta v = c_e* ln(m_0/m_b) = c_e* ln(\sigma/\mu_L)$$ with

$\Delta v$ : characteristic velocity (constant for fixed orbits)
$c_e$ : velocity of the rocket exhaust
$m_0$ : initial total mass
$m_b$ : burnout mass
$\sigma$ : structural mass ratio [σ=(mM+mS)/m0]
$m_M$ : mass of rocket motor
$m_S$ : mass of rocket structure
$\mu_L$ : payload ratio [μL=mp/m0]
$m_P$ : payload mass

The second part of the equation is the only practical correlation between total mass and payload mass that I am aware of.

It's my first answer here at Space Exploration and I'm still a student, so please go easy on me :)

• For a rocket, exhaust velocity is directly related to the specific impulse term mentioned in the other answers. Isp in seconds * 9.81m/s^2 = exhaust velocity in m/s. The use of seconds as the unit for specific impulse is a historical thing. en.wikipedia.org/wiki/… – Russell Borogove Sep 20 '15 at 0:11
• How is your comment related to mine? – cl10k Sep 20 '15 at 0:34