# How does the mass of launchers change over time between ground and orbit?

I would like to see some comparison between different launchers wrt how quickly their mass is reduced over time (or altitude or velocity). There are differences in overall size class, propellant type, number and size of solid fuel boosters, common cores, burn time of the first stage and certainly more. It would be interesting to learn something about how current and historic launchers differ in getting rid of mass over time.

• Do you mean just a trawl through Wikipedia dividing stage fuel loads by their burn times? (eg Saturn 5, stage 1 is around 2000 tonnes in 160 seconds or so) ?
– Andy
Commented Feb 16, 2016 at 13:44
• What do you mean by "the mass of the launcher"? Do you mean how quickly fuel is expended? How early stages are separated? When the fairing is dumped? The sum of all? Commented Feb 16, 2016 at 14:47
• @Andy What really interests me is how different launcher designs philosophies compare in this respect. How soon mass (fuel and ejected stages) produce results in terms altitude and velocity. What launch profiles different design choices lead to. I don't want you to waste your time by plowing through specific Wiki numbers per se. Commented Feb 16, 2016 at 14:47
• @Andy, the reason is that the rocket equation only starts to really bare its teeth if you want larger amounts of Delta-v. For the first stage, hydrogen or kerosene doesn't make such a huge difference. Commented Feb 16, 2016 at 15:21
• The answer would simply be the total propellant mass flow...which is why I think potential answer-ers are kind of scratching their heads over this one. For example STS used, in round numbers 3000 lb/sec in 2nd stage. Commented Feb 16, 2016 at 16:20

In almost all cases, the overall mass versus time curve for a multistage launcher will approximate an exponential decay curve; this is the nature of the rocket equation.

Within each stage, if all the stage's engines fire at a continuous throttle setting, the mass decline over that portion of the flight will be linear. Many launchers throttle down over the course of a stage's burn in order to control g-loading, which makes the mass decline more closely approach the exponential decay curve.

Here's one simulation result, for the Saturn V with Apollo payload:

Each stage is generally linear, though there's a slight kink near the end of the first-stage run when the center engine cuts off to limit G-load, and two kinks near the end of the second stage run for center engine cutoff and propellant mix ratio shift. The vertical jumps in the plot are the stage drop events.

Here are some more modern examples: Falcon 9, Delta IV Medium (4,2), Vega, and Proton M. For the F9 and D4, I've simulated abrupt throttle step-downs, so the stage mass curves are kinked. This is accurate for the Delta, but possibly not for the Falcon; if the engine throttles down gradually the stage mass curve would be smooth, but the overall shape would be essentially the same. Vega's first three stages are solids, with poor specific impulse, so its mass curve is quite a bit deeper than the others.

Individual launcher design choices appear to account for more variation in the exact shape of the curve than historical trends.

That said, there is a tendency in modern launchers to use very low-thrust upper stages (Falcon 9 being a bit of an outlier), so their graphs tend a little steeper at the start and shallower at the end. Ariane 5 ES is an exemplar of the trend:

The Atlas LV-3B used for the Mercury orbital flights is the opposite of that trend, with high acceleration throughout and a very short time to orbit; its mass curve is somewhat shallower, but not dramatically so:

• Great answer! Again. You say that the kinks on the curves are caused by throttling down. But what about the mass reduction from ejecting the empty boosters or stages? And even if data is not available, how do those mass/time profiles qualitatively compare with Proton, which (I think) separates its first stage earlier? And with solid only first stages, like ICBMs or India's PSLV. Commented Feb 17, 2016 at 22:44
• Or the Ares I test launch, with a solid fuel first stage. Commented Feb 17, 2016 at 22:56
• The vertical jumps are stage drops; the slighter bends are the throttle-downs. I'll annotate the Saturn V graph since it's got the most going on, and I'll try Proton and a solid-based launcher and see if the graphs are interesting. Commented Feb 17, 2016 at 22:57
• Proton's early first stage separation is due to its 3STO design. It's actually the closest of my examples to an "ideal" exponential decay. Commented Feb 17, 2016 at 23:30
• Vega's an interesting one. Commented Feb 18, 2016 at 0:14