Calculating Launch Capacity to LEO of a rocket.

[fredinno]

How do you calculate launch capacity to LEO of a rocket if it's lift capacity is unknown? I really need help for this for my rocket designs for KSP, but I can't seem to figure it out...

[UmbralRaptor]

It depends on design details, but essentially you invert the rocket equation, using a known ÃŽâ€V and the mass of non-payload portions of the craft to solve for the payload. Simpler designs can do it analytically, but you may need to mess around in Excel or the like for more complicated ones.

I've toyed around with some analytical models. I don't suppose they can help inspire?

Edited June 27, 2015 by UmbralRaptor

[Shpaget]

In KSP?

As it should be done - by trial and error.

[Pipcard]

Kerbal Engineer won't tell you the lifting capacity of your rocket, but it can tell you how much delta-v you have. Delta-v is a measure of change in velocity, but as the KSP streamer DasValdez puts it, it's a measure of the ability to "change your situation in space" (like from going from ground to low Kerbin orbit, or from low Kerbin orbit to an orbit around the Mun, etc)

Here is a "delta-v map."

Edited June 27, 2015 by Pipcard

[Frida Space]

In KSP, I just build the rocket and then attach to it as much mass as I can until Kerbal Engineer says that the DeltaV is <4500 m/s.

[Pipcard]

In KSP, I just build the rocket and then attach to it as much mass as I can until Kerbal Engineer says that the DeltaV is <4500 m/s.

The delta-v requirement is somewhat lower now due to the new atmospheric model in 1.0.x.

[shynung]

Quick-n-dirty math. If anyone found a mistake, please kindly correct me.

Also, this assumes a single-stage rocket. Not sure how to adapt this to multistage, so some help is appreciated.

Starting from the regular rocket equation:

deltaV = ( Isp * g0 ) logN ( mWet / mDry )

Rearranging this gave me:

mDry = mWet / ( N ^ ( deltaV / ( Isp * g0 ) )

where:

deltaV = target delta-V (approx. 3300 m/s, in KSP v1.0.2)

Isp = engine specific impulse

g0 = standard gravity (9.08865, though 9.81 works too)

mWet = craft wet mass (fully-fueled)

mDry = craft dry mass (out of fuel)

Further:

mDry = mStruct + mPay

mWet = mDry + mProp

where:

mStruct = structural mass (tanks, engines, struts, anything that isn't the payload)

mPay = payload capacity, what you're looking for.

[fredinno]

I did that- in KSP, but in the game, I can get the rocket into orbit, but the Delta V is less than 4500m/s.

[shynung]

I did that- in KSP, but in the game, I can get the rocket into orbit, but the Delta V is less than 4500m/s.

As of KSP v1.0.2, deltaV to 80km orbit is approx. 3300m/s. 4500 was from pre-v1.0 days, when KSP hasn't gotten aerodynamics right.

[fredinno]

ok, thanks.

[goldenpeach]

Unfortunately, it's not this simple.

It may work for some design, but not all.

The payload mass decrease the TWR of the rocket, which in turn make you burn more fuel than you would with a smaller payload(there is also the mass of the fairing to take in account if you want a really precise calculation.

In exemple, I once made a rocket, in 0.90, where the limit wasn't because I didn't had enough fuel to circularize, but because the thrust wasn't high enough to allow to circularize before falling back in the atmosphere, even if I had enough fuel to do so.

[fredinno]

That's what launch tests are for. At least I only need to do 1, rather than 10, saving me a lot of time.

[shynung]

Yes, that equation didn't take TWR into account; Tsiolkovsky's original equation didn't either, and that's all I have (understood) to start with.

However, generally gravity drag (from TWR) and aerodynamic drag is taken into account by increasing the target deltaV. In my case, 3900m/s is enough to get to 90km circular orbit, so about 600m/s (from 3300) are for aerodynamic drag and gravity 'tax'. Optimizing TWR is usually by choosing the right engines, whose Isp is then taken into account.

[magnemoe]

Unfortunately, it's not this simple.

It may work for some design, but not all.

The payload mass decrease the TWR of the rocket, which in turn make you burn more fuel than you would with a smaller payload(there is also the mass of the fairing to take in account if you want a really precise calculation.

In exemple, I once made a rocket, in 0.90, where the limit wasn't because I didn't had enough fuel to circularize, but because the thrust wasn't high enough to allow to circularize before falling back in the atmosphere, even if I had enough fuel to do so.

I commonly uses payload stage as upper stage, say you launch an LV-N powered spaceship to Duna, it then makes sense to do the last part of gravity turn and the circulation burn with the LV-N, just add more fuel here, use an drop tank if needed.

Yes this can easy get into your problem with TWR being to low and you don't have enough time to circulate have had problems here myself.