Falcon 9 first stage is enourmous, powerful, sleek, but...

[YNM]

Does anyone know how much dV the second stage of Falcon 9 has ? The CRS-5 mission first stage last night (well, my local time) says that separation happens at 95 km height (well, below Karman line) and 1 km/s speed (not velocity I guess). I mean, heck, is it seriously that much ? Does any other rockets have higher dV on one of it's stages ?

[B787_300]

The first Stage burns out while moving at almost 2 km/s which is quite fast, the main thing is that the first stage pushed the 2nd high enough that its main job was to circularize

[Moar Boosters]

I remember hearing somewhere that the first stage of the Saturn V was capable of SSTO if they'd launched it without the other stages on top.

I expect there's somebody here who could do the math to confirm whether that's true or not.

[GigaG]

^Rocket equation calculator-

http://www.quantumg.net/rocketeq.html

From Wikipedia-

The S-IC stage had a dry weight of about 131 tonnes (289,000 lb) and fully fueled at launch had a total weight of 2,300 tonnes (5,100,000 lb).

Another article cites the sea-level ISP of the F-1 to be 263s.

Plugging those values in (being sure to convert tonnes to kg), the answer is...

7385.454848682849m/s

It takes 9400m/s (or according to the Rocket Equation website, 9000m/s.) So the answer is NO, the S1-C could not SSTO. Now while that is the sea-level ISP, I'm guessing that the fairly large gap between the given value and the value to LEO would not be bridged as the rocket ascended.

A specific impulse of 350s could do it, which is the SSME sea level ISP. That's a completely different engine, of course, but I'm just giving you a reference.

I don't know how to compensate for ISP gains with altitude. I'm guessing there is a formula out there that approximates it, but I'm too lazy to look.

[B787_300]

Oh on a side note... the Falcon is actually on the smaller end of rockets...

and SSTOs dont work because their payload fraction would be TINY

[Nibb31]

Does anyone know how much dV the second stage of Falcon 9 has ? The CRS-5 mission first stage last night (well, my local time) says that separation happens at 95 km height (well, below Karman line) and 1 km/s speed (not velocity I guess). I mean, heck, is it seriously that much ? Does any other rockets have higher dV on one of it's stages ?

I don't see why that sounds unrealistic. You need 9km/s of dV to reach orbit. The job of the first stage is to get the rocket out of the atmosphere while adding as much dV as possible. 1 or 2km/s sounds realistic. The upper stage does the brunt of the acceleration work.

[Jouni]

Quick approximation: The launch mass of a Falcon 9 with a payload to GTO is around 510 tonnes. First stage engines burn for 180 seconds, and they generate 5885 kN of thrust at sea level with a specific impulse of 282 s. Therefore there is around 383 tonnes of reaction mass in the first stage. With an average Isp of 300 s, the first stage would provide around 4.09 km/s of delta-v. This is obviously less with the reusable first stage, as it has to fly back and carry landing legs.

If we assume 9.5 km/s to LEO and further 2.5 km/s to GTO, the upper stage has to provide around 7.9 km/s of delta-v.

[K^2]

The first Stage burns out while moving at almost 2 km/s which is quite fast, the main thing is that the first stage pushed the 2nd high enough that its main job was to circularize

Right. Atmo + gravity eats through about 1.5km/s. So it needs to be closer to 3.5km/s total.

We can also do the math based on the stats. v1.1 is 505T off the pad. It has 5,885kN of thrust at 311s for 180s. That's 347T of fuel leaving 158T ascending at stage separation. Taking average I_SP at 300s, I'm getting 3.4km/s of delta V from the first stage. So 2km/s at separation sounds reasonable to me, given aerodynamic losses.

That leaves second stage with about 5.4km/s to orbit. (Earth's rotation FTW.) Similar math to above (801kN @ 342s for 375s) gives me 90T of fuel in second stage. With the 5.4km/s assumption above, this works out to a 22T rocket reaching orbit, of which 13T is the payload. That means empty, dry 2nd stage is 9T. Fueled with payload, 112T. And that leaves 46T for empty first stage. All entirely within reason.

Disclaimer: I've ignored some finer aspects of the ascent, inclination of the orbit, and done quite a bit of rounding above. Still, it should be pretty close to actual values.

[YNM]

Well, then it's my thinking which is flawed... Forgot that it's Earth. Also, that'd explain why my rockets in game are a bit large...

[architeuthis]

I don't know how to compensate for ISP gains with altitude. I'm guessing there is a formula out there that approximates it, but I'm too lazy to look.

If you can find a function for thrust as a function of altitude for the rocket engine in question (it's easy enough to figure out from the parameters of the engine if you use a simple model for atmospheric pressure as a function of altitude), and altitude as a function of time you integrate thrust with respect to time to get impulse, then divide by propellant mass to get specific impulse. The F-1 engine's expansion ratio was optimized for low-altitude operation so the isp curve may not be especially favorable with them.

[B787_300]

Giga ISP is a exponential curve, but for the MOST part just use sealevel if it ignites while in air and vacuum if it ignites in space.. your numbers will be off but not by too much

[Bill Phil]

The correct term is orbital speed, actually, since velocity is also a direction.