Payload to LEO is commonly used as the bottom line of what a launcher can accomplish. But it must depend on factors which are not launcher specific, such as launch location and orbital characteristics.

  • How is payload to LEO calculated?
  • What error bars should one put on such estimates?
  • Would heaviest or average payload actually launched be better measures, and is such statistics easily available to the public?

Example: Saturn V's payload to LEO is confused online. Encyclopedia Astronautica says 127 tons. Wikipedia says 140 tons. 118 tons is another common figure. The difference of 22 tons is about equal to today's heaviest launcher's capacity. Does this variation depend on unspoken choices of assumptions?

Wikipedia's source is US Congressional Budget Office which mentions 140 mt to LEO at least six times, so this metric might have policy implications. That source says in a footnote:

The payload of 140 metric tons is derived from weight data provided in Richard W. Orloff, Apollo by the Numbers: A Statistical Reference, NASA SP-2000-4029 (National Aeronautics and Space Administration, updated September 27, 2005), available at http://history.nasa.gov/SP-4029/SP-4029.htm. In that reference, 140 mt is the weight of the Apollo 17 command-and-service modules, the lunar module, the spacecraft/lunar module adapter, the instrument unit, and the S-IVB stage (the third stage of the Saturn V), including the fuel remaining in that stage needed to propel the Apollo command-and-service modules and lunar module from low earth orbit to the moon.

Here is Apollo by the Numbers available.

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    It's all in the manual, also depends on the fairing. Always calculated for each batch of launchers. Inclination, location, and seasonal air density variation should also be taken into account. – Deer Hunter Aug 15 '15 at 11:10
  • @DeerHunter I'm sure those who actually make it happen know all about it. But as a popularly published measure, even in the legislator's expert reports, what can we make of the very popular "payload to LEO" tonnage figures? Most launchers, I think, launch from the same place anyway, with the most frequently launched (1957 Sputnik I derived) Soyuz as a notable exception with Baikonur, Plesetsk and Guyana as launch sites. – LocalFluff Aug 15 '15 at 12:19
  • The launch site is definitely taken into consideration when calculating/publishing the payload figures. The published figures for Soyuz from Guyana are rather higher than the same launcher from Baikonur. This is one of the easier variables to take into account. – Hobbes Dec 24 '15 at 8:16
up vote 5 down vote accepted
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  • How is payload to LEO calculated?

These days, they run simulations on everything. The payload to LEO is either an analytical assessment of the payload using worst case assumptions, or else some threshold of simulation. Basically, the rocket is designed to meet a minimum LEO threshold, using a nominal orbit. These values are broken down into what every piece on the rocket needs to accomplish in order to meet said requirements. Then once everything is designed, they again test using the actual limits as found.

Some of the things that might be varied, for instance, is the temperature of the rocket fuel, the exact flow of fuel of each type into the rocket (Resulting in differing thrust and ISP), wind, weather, other kinds of part efficiency, etc. All of this put together will give a worse case to LEO, which is what they advertise.

  • What error bars should one put on such estimates?

The error bars are already assumed in the publicly disclosed mass to LEO. If one wanted to launch an item slightly above the maximum, the company could theoretically do a study to see how likely there would be an issue. If there was likely to be an issue, they could inform the customer, and act accordingly.

It should be noted that the uncertainty in part performance will go down with time, which will usually demonstrate the rocket is better performing than first thought (Unless the rocket truly was off-nominal)

  • Would heaviest or average payload actually launched be better measures, and is such statistics easily available to the public?

Not really. The heaviest payload will under almost all conditions be less than the LEO max mass. The statistics usually aren't available.

Just to give you an idea, every rocket I've seen launch does something like this plot after the launch. In this case, the two lines represent the two SRBs in a Space Shuttle launch. The ones I've seen compare the expected performance, max/min, with the actual performance, to see if there are any serious deviations from the expected performance, and get an idea as to what direction from ideal the performance leans.

enter image description here

Sorry, but this comment is rather long.

Regarding the Saturn V LEO payload questions...

Check out this source: http://forum.nasaspaceflight.com/index.php?topic=12519.20

The Saturn V launch vehicle was upgraded throughout its lifetime. Its engines were uprated and numerous measured were taken to reduce the weight of the rocket. Thus, by the time Apollo 17 came around, the Saturn was quite an improved machine. The link above details its LEO throw weight as having been 140,893kg. Some sources indicate lower or higher than this value, but this one was at hand when I wrote this.

So yes, the Saturn V was capable of delivering over 140t to LEO, but we must remember that this was after a bit of improvement. The final Saturn Vs were pumping out very close to 7.9 million pounds of thrust, which is also a lot more than is usually quoted (7.5 million). I believe the initial lunar landing missions involved LEO masses of somewhere around 133t, with less powerful Saturns.

Also, we must outline what makes up the LEO payload. The 140,893kg figure includes the partially-fuelled S-IVB third stage of the Saturn V. However, upper stages are usually excluded from earth orbital mission payload masses. So why is it included in the LEO payload…

Because Apollo 17’s mission was to go to the moon!

This is where the Saturn V’s quoted LEO payload definition differs from other launch vehicles. In the case of lunar landing missions, LEO is not the end of the line; something is needed to push the Apollo hardware to TLI. This is the S-IVB’s purpose. Upon reaching its low-earth parking orbit, the third stage is still fuelled and is not just inert mass. It still constitutes usable payload, as it is used to go to the moon.

Another important matter to consider is the height and inclination of the earth parking orbit. Early Apollo lunar missions entered LEO at around 185km at around 28.5 degrees. But on later ‘Apollo J’ missions, higher masses were delivered to LEO partly because they orbited at a lower altitude. Apollo 15, 16 and 17 parked at around 167km with similar inclination, meaning there would be more fuel left in the S-IVB upper stage for the TLI burn.

Now for the other values (127t and 118t respectively)

127t is the LEO payload mass given for the Saturn C-5… Take note!

The Saturn C-5 is not the Saturn V!

The Saturn C-5 was Von Braun’s initial design, developed while Apollo mission planners were still deciding on a basic method with which to reach the moon. When ‘Lunar Orbit Rendezvous’ was selected as the way to go, the Apollo CSM and LM combo was developed in greater detail. The payload weights grew, however, and eventually the original Saturn C-5 was found to be too weak to deliver them to TLI. Thus, the C-5 was improved and became the Saturn V. The first stage was kept very nearly identical, but the second stage was lengthened by around 3.5m for increased propellant. Also, the third stage was increased in diameter, again to hold more fuel.

The Saturn C-5 was able to deliver up to 127t (including the third stage) to a 185km LEO, and around 41t to TLI. The later Saturn Vs were able to deliver over 140t to a 167km LEO, and almost 50t to TLI.

118t (and 120t) is up for debate, as far as I know. Some say that it is the theoretical usable LEO payload of the Saturn V three-stage vehicle if the third stage is not included and is depleted upon reaching earth orbit (Apollo weighed up to 48.6t in total, leaving fuel left over for TLI, whereas 118t of payload would not). This is explored in the link at the top of this comment.

However, I have been led to wonder if this could be the maximum 185km LEO payload of a Saturn V two-stage vehicle to LEO, similar to the approach that would have occurred with non-TLI Saturn MLV-V-1 and Saturn MLV-V-3 launches (look these variants up, they’re brilliant). Such a rocket was designated the Saturn INT-21 and was never launched, although the Skylab Saturn V was essentially just that. Yes, the Skylab launcher didn’t deliver that much usable payload to its orbit, but it launched to 434km and over 50 degrees inclination, which requires more performance than 185km at 28.5 degrees. For this orbit, the INT-21 was quoted for 255,000lbs, or 115.7t… Pretty close, and that was studied before even the early Saturn Vs and as such did not include late model uprated engines and weight savings.

In summary, things to remember:

  • Think about what the mission requires. Missions going beyond LEO can still include the mass of the upper stage and its fuel for their quoted LEO masses. Missions only going to LEO cannot if the upper stage is depleted, because there is no more use for the empty fuel tank and engines.

  • Consider the altitude and inclination of the payload’s orbit. Higher orbits require more energy to achieve, and as such less mass will be delivered for a given rocket. Also, higher inclinations take more energy for a given altitude.

  • Think about developments and improvements made to the model of rocket. A rocket that has been in service for a long time will generally be more capable later in its operating life than its initial variants.

For error margins, I can’t say a whole lot on that subject. However, I would believe that it is recommended not to load a rocket to its designated limit. Safety margins are included, and as such a rocket should launch with a little bit more fuel than is absolutely needed, just in case something doesn’t turn out as planned. This would allow the vehicle to reach orbit even in the case of, let’s say, a single engine failure on a multi-engine upper stage (maybe, kind of like Apollo 6).

For historians, I would say that average payload for a launch vehicle variant over its lifetime would be useful knowledge. However, I would say that whatever the current LEO payload rating is for a rocket is the more important value. Assuming the vehicle has been improved over its lifetime (likely), it will generally be more capable than its earlier iterations. But that’s just my opinion.

If you have read all of this, thank you for taking the time to do so. Any feedback is welcome. If you notice anything incorrect about the information listed, please let me know.

Sorry for the ‘essay,’

Alastair.

  • Oh no, thank you for the essay! My take away is that launchers develop even under the same brand name. Falcon 9 exemplifies this today, with one version being 60% heavier on the launch pad than the other. Orbital launchers aren't standardized off the shelf goods. Every launch has some unique conditions. I suppose the military has reduced that, suborbitally, as much as they can with their ICBMs, and worse, with their SLBMs. – LocalFluff Dec 19 '15 at 12:02
  • Yes, LocalFluff. Launch vehicles are gradually improved, but changes might not be so great as to warrant an entirely new model designation. I'm interested in your mentioning of the Falcon 9; I hadn't thought about that. 60% is quite an increase! – Alastair Haslam Dec 24 '15 at 2:31

The payload fraction of a launcher, $\lambda$ is usually given by, $\lambda = \frac{m_{d}}{m_{p} + m_{s}}$

where $m_{d}$ is the payload mass, $m_{p}$ is the propellant mass and $m_{s}$ is the launcher structural mass.

In general, the payload fractions of the launchers are very small, less than 1$\%$ or so.

As far as space launches are considered, each one is unique for all purposes and it is difficult to compare them. For this reason, it is better to compare the $\mathit{actual}$ $\mathit{average}$ payload over the missions rather than any theoretical values.

This is because the launchers are being improved in every flight and other conditions are also different.

The document in the question on Saturn V indicates that the rated thrust of all the three stages increased over the launches. Also, the payload of 140 tonnes is the $\mathit{maximum}$ achieved over the launches.

So, it is better to take only the actual values from th mission for any comparison.

  • That was the same document my question linked to! Other sources claim different "payload to LEO"-numbers. Did Saturn V really ever launch 140 tons to LEO? And by what by what standards, fueled or dry and to what orbit and what else? – LocalFluff Aug 15 '15 at 12:12
  • I meant the document attached to the question. I'll make the appropriate edits. The maximum payload is given here as 130 metric tonnes ~ 140 US tonnes(US). However, even here, there is a discrepancy as Boeing gives the payload as 120 tonnes. Both these values are for LEOs – aeroalias Aug 15 '15 at 12:48
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    That payload fraction formula doesn't help you calculate capability. What you'd need is a delta-v estimate for parameters that Deer Hunter mentions in the question, then use Tsiolkovsky rocket equation's derivation for mass fraction $M_f = 1-e^{-\Delta V\ / v_\text{e}}$ to get first order approximation, or integrate actual flight profiles to get an overall average. I'm afraid there isn't any simple answer to this for launch vehicles that weren't really designed to deliver payload to LEO. But many of these might have used a LEO parking orbit, so that should help. – TildalWave Aug 15 '15 at 13:16
  • I agree. This formula is not going to be used in a real mission. But still, it can be used as rough estimate and a means of comparison between two launchers. As the question asked for an estimate, I gave this. – aeroalias Aug 15 '15 at 13:36

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