Calculating Max-Payload-Weight?

[Horman]

Hi Fellow-Kerbalnauts,

can someone tell me a way to calculate the max possible payload, for rockets?

Greetings and happy flying

Horman

[Pecan]

The two big figures ruling rockets are TWR and deltaV. Provided you have sufficient TWR to take-off in the first place, Slashy explains variations on the rocket equation (deltaV calculations) that explain max payload:

http://forum.kerbalspaceprogram.com/threads/102809-The-reverse-rocket-equation-explained

[Kesa]

The two big figures ruling rockets are TWR and deltaV. Provided you have sufficient TWR to take-off in the first place, Slashy explains variations on the rocket equation (deltaV calculations) that explain max payload:

http://forum.kerbalspaceprogram.com/threads/102809-The-reverse-rocket-equation-explained

This tell that, with sufficient margin, you're sure to take that playload into orbit. But the exact dv requierement of a rocket is quite sensitive to the ascent profile and the TWR of each stage.

What I usually do to precisely find the max playload of a craft is :

(1) launch with a playload probably to heavy, but containing fuel, that I link to the last stage engine.

(2) -If you actually used the fuel of playload, the max playload is lighter than that. See the weight of what I've put to orbit. It's approximately the max playload capacity.

-If you did not, see the weight of what I've put to orbit, ie mass of playload + mass of fuel left in the launcher (- mass of fuel needed to deorbit - safety margin, of course)

That weight is the estimated mx playload mass. This can be respectively an over/under estimation, since you used more/less fuel that you should, taking from playload. This could be an under/over estimation as well, as your TWR is lower/greater than it should be.

(3) for a better approximation, retry 1, but with a playload whose wheigh is those of the supposed max playload.

I dunno if it always converges, but it gives an idea of what your rocket can handle. If it does not converges, then try dichotomia (need more trys though) : by your first try, you now that your launcher can't handle 5t, but can handle 3t, so what about 4? yes -> 4.5? no -> 3.5?

[GoSlash27]

The two big figures ruling rockets are TWR and deltaV. Provided you have sufficient TWR to take-off in the first place, Slashy explains variations on the rocket equation (deltaV calculations) that explain max payload:

http://forum.kerbalspaceprogram.com/threads/102809-The-reverse-rocket-equation-explained

I definitely would not recommend relying on that form for launches, though. As Pecan pointed out, you need enough t/w or you're not going anywhere.

However, there is a "sorta" cure:

If you know your engine's Isp and thrust, then you can puzzle out the rest.

Say you have a KR-2L engine (T=2.5MN and Isp=280). The most total mass it can lift at T/W=1 would be 2500/9.82= 255 tonnes.

If we want to have this stage generate 1,000m/sec DV, than reversing the rocket equation (follow the link above) says:

e^[1000/(9.82*280)] = Rwd 1.44; our rocket when fully fueled will weigh 1.44 times as much as it does dry.

255 tonnes/1.44= 177 tonnes. Our rocket will weigh 177 tonnes when dry and 255 tonnes when wet. So our fuel mass is 255-177= 78 tonnes.

knowing that we are carrying 78 tonnes of fuel, we need enough tankage to hold it. Seeing as how this is a monster rocket, we'll need the Kerbodyne tank. It weighs 10 tonnes.

So...

177 tonnes of dry mass. Subtract the weight of the tank= 167 tonnes. Subtract the weight of the engine= 161 tonnes.

This is the absolute maximum mass you could lift 1,000 m/sec using a single KR-2L, assuming it is all nothing but payload. Anything additional that is not payload should be subtracted from this.

You can change the numbers as necessary for your situation, but the math works the same.

HTHs,

-Slashy

[GoSlash27]

^ Now having said that, I should point out that this is not a good way to design rockets.

You should not be asking "how much can this stage lift" and building from the pad up, but the opposite. You should be building from the top down and asking "how much rocket do I need to lift this".

Your designs will come out much more efficient that way, and you'll never have to ask this question because the most it can lift is exactly what you designed it to lift.

Best,

-Slashy

Edited December 28, 2014 by GoSlash27

[Pecan]

... You should not be asking "how much can this stage lift" and building from the pad up, but the opposite. You should be building from the top down and asking "how much rocket do I need to lift this" ...

Ideally, yes, but there is a good reason for building 'up' and asking what it can lift - we have a limited choice of parts.

For instance - if I want to launch a 3t payload I may well find optimal solutions at 2.5t and 3.7t. OK, so I take the 2.5t and add a bit of fuel or the 3.7t and tweak a bit out of a fuel tank. Close to optimal, but still sub-optimal.

On the other hand, it's valid to ask "What can I lift with one Skipper engine?" (for instance). Since the dV requirement is constant, knowing the engine ISP and max thrust the rocket equation will tell us the max payload capacity. Now, of course, we have an optimal design which may be unsuitable for any payload, doh!