IN THEORY: Size/delta-v to payload

[longbyte1]

You know that little tiny 3 part rocket (pod, 1/2 1m tank, aerospike rocket)? I flew it a few days ago, but I realized something. That little rocket sure can't carry anything more than itself, can it? So its payload is virtually zero. What about that super giant rocket that you take to the Mun to make some Munar base? Its payload is probably 10 mass (what exactly is the unit for mass?). I have not made a formula yet, but in theory the more delta-v a rocket would have would affect the amount of payload it can carry. Right? I want some feedback on this, please. I can't really grip this because I am not a physicist or rocket scientist or anything like that, but I don't want to look stupid because it's an obvious fact that the more delta-v there is, the more payload you can carry.

[Altair1371]

That's not exactly true. I could have a highly fuel efficient ship that has a massive amount of delta-v, but not enough thrust to get out of the atmosphere. You need a thrust-to-weight ratio greater than 1, and 4000-5000 delta-v to enter LKO. That determines the payload you can carry up there.

[Bluejayek]

What you really want to look at is the delta-V delivered to a given payload. You could have a rocket that has 9000m/s delta-V, but the final stage that gets that speed is only a 0.8mass pod. Or you could have a rocket that also has 9000m/s delta-V but the final stage that gets that speed is 10 LFT-3200s with a mass of lots. Delta-V and payload mass are not the same thing.

What governs this is the rocket equation:

Delta V = ISP * g * ln (m0/m1)

Where delta V is your delta V delivered to final stage/payload, ISP is the specific impulse in time units, g is standard gravity 9.8m/s, m0 is the initial mass of the rocket, and m1 is the final(payload) mass.

This equation governs a single stage rocket, and the final mass would include the mass of the engine and the dry mass of the tank. Multistage rockets are more complicated, so lets stick with this idea.

As stated above, that equation says that the more starting (payload + fuel) mass you have, the higher your delta-V. However, this is a logarithmic relation, so after a certain point you hit serious diminishing returns. Below it is shown graphically what this looks like for an ISP of 400s, and a payload mass of 5. You can see that from 25 to 50 you get about an increase of 50% delta-V, but from 50 to 100 its closer to 25%. This is why you cant just continue building arbitrarily large rockets and get insanely far, there is a point where you start getting so little gain its not worth it.

Another way to look at the rocket equation is to re-arrange it for the payload mass, and assume delta-V is fixed.

m1 = m0 * e^-[delta-V/(g*ISP)]

This equation is LINEAR in m0. This means that if you want to launch a payload that is twice as big at the same delta-V, you only need a rocket that is twice as big on the launchpad. This is in contrast to getting a delta-V that is twice as large for a given payload, which can require much more then twice the fuel, as illustrated above.

I hope this helped clear some of the confusion for you. Note again that this does not apply exactly to multistage rockets: For them you have to apply the rocket equation from start to end of each stage in sequence.

Oh, and what Altair said is also quite true. When you look at launching from a planet, as opposed to just in empty space (which the above applies directly to), you have to take into account air resistance and gravity drag. This is why ion engines, despite being MUCH more efficient (read higher ISP) then chemical rockets, are not used off the launc pad: They do not have enough thrust to lift themselves or any payload off the launchpad. They are however very efficient once you get into orbit, and numerous space missions and sattelite utilize these thrusters for this purpose.

Edited September 11, 2012 by Bluejayek

[Vanamonde]

the more delta-v a rocket would have would affect the amount of payload it can carry

As I understand it, it's the other way around. The mass of the vehicle is already taken into account in the delta-v calculations, so if you change the mass, the delta-v changes. (Which is a quick and dirty version of what Bluejayek said.)

[bsalis]

I think people are over complicating things here by going over the Delta-V specifics.

A simpler way to look at this is to realise that a rocket essentially converts chemical energy into kinetic energy. Kinetic energy is a function of mass and velocity...

So a bigger rocket has more chemical energy, so you get more kinetic energy. You can have that as more mass, or more velocity (delta-v) or, typically, more of each.

[togfox]

The KGSS has a "delta-v for idiots" (like me) article in edition 3. Check my sig.