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Cadet_BNSF

Booster carrying capacity

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How can the maximum payload for a given booster be found? For example, lets say I have a single stage to orbit booster, with 990 units of liquid fuel, 1210 units of oxidizer, with a swivel engine. How would I calculate the max payload?

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So the first thing you need to know here is what delta V is and how to calculate it. Delta V is the change in velocity that your rocket is capable of. So a rocket with 1000m/s delta V can go from 0m/s to 1000m/s in vacuum, or vice versa. It generally takes 4000m/s of delta V or so to reach orbit in stock KSP. More if your rocket is really draggy, or isn't accelerating fast enough.

From the 'cheat sheet' page on the wiki:

Quote
\Delta {v}=ln\left({\frac  {M_{{start}}}{M_{{end}}}}\right)\cdot I_{{sp}}\cdot 9.81{\frac  {m}{s^{2}}}
Where:
  • \Delta {v} is the velocity change possible in m/s
  • M_{{start}} is the starting mass in the same unit as M_{{end}}
  • M_{{end}} is the end mass in the same unit as M_{{start}}
  • I_{{sp}} is the specific impulse of the engine in seconds

If it's not clear, Mstart in this equation is the mass of your rocket and payload when they're fully fueled. Mend is the mass when no fuel remains in the stage you are calculating delta V for. Isp can be found in the VAB description of each different engine. Keep in mind that engines perform differently at sea level and in vacuum, and the game will show you different values for those conditions. Generally a rough average of the two will suffice for quick and dirty calculations.

Once you've done these calculations a few times, you'll start to notice what mass fraction (the quotient of starting mass divided by ending mass) will produce the numbers you want for different engines. This will let you make a pretty good guess about how much zoom your rocket has aboard without breaking out the calculator.

 

Now, if you know exactly how much engine and fuel you are using to start with, and want to calculate the maximum possible payload you can get into orbit, you have to break out some algebra. It would look something like this:

4000<ln(R1+x/R2+x)*9.81*isp where R1 and R2 are your start and end weights, and x is your max payload.

For a swivel with the fuel and tankage you mention, that would look like this, assuming nothing but engine and fuel tanks on the rocket.

Spoiler

4000<ln(13.875+x/2.875+x)*9.81*290     (a rough guess for the effective isp of the swivel over the course of the whole launch)

Divide by 9.81*290

~1.406<ln(13.875+x/2.875+x)

Take the inverse ln

~4.08<13.875+x/2.875+x

Multiply by 2.875+x and distribute

11.73+4.08x<13.875+x

Subtract 11.73 and x from both sides

3.08x<2.145

Divide by 3.08

x<~.7

 

So, about .7 tons worth of payload.

Of course, you need to keep in mind that a swivel will have a hard time lifting 14.5 tons from sea level. It just doesn't have enough thrust. You'd probably need boosters on that one.

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11 minutes ago, Cadet_BNSF said:

How can the maximum payload for a given booster be found? For example, lets say I have a single stage to orbit booster, with 990 units of liquid fuel, 1210 units of oxidizer, with a swivel engine. How would I calculate the max payload?

I am sure someone will give a better answer shortly. In the meanwhile, if you are launching from the KSC with just the one Swivel as propulsion, the limiting factor is going to be the weight that a Swivel can lift off the ground. Not much more than 16 tonnes - including fuel, rocket parts, the engine itself, payload and all.

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While theres a bunch of math stuff that can be done to find the max payload, another way to go about it is to define certain locations as general delta-v requirements, and then for said markers, add more payload until you hit the minimum dV to reach that location with your rocket, and by doing this you can look at a rockets max payload as an expression of how much tonnage it can deliver to said locations.

And generally thinking of it in this way is more accurate and precise then a singular "max payload" as the same rocket can deliver much more payload to LKO versus delivering it to Moho.

To explain that better, lets define these two locations (using fake arbitrary numbers for example purposes because I'm too lazy to look up the actual figures):

LKO  - 75km circular orbit above Kerbin.  Delta V requirement = 4000m/s2

KGSO - 2,863.3km orbit above Kerbin.  dV requirement = 4600 m/s2

So, knowing that for these two locations, we can look at our hypothetical rocket and determine the max payload for these locations. Lets say that the empty rocket, with no payload, has 10,000 dV available to it. So this rocket can effectively deliver itself to both locations nearly 3x over.  Great.

So now we add a payload to this rocket, and we keep upping the tons.  Lets say we add 100 tons to this rocket, and our dV readout shows us we're at 4000m/s2.  Great, thats our max payload to LKO. So we take off some tons, and lets say we're down to 85 tons of payload, and our dV has gone up to 4600. Great, this is our max payload to KGSO. 

And we can do this for pretty much any location to determine max payload.

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DeltaV is the main factor to consider but there is a few others(that will affect how much deltaV you need to reach orbit)

You need a TWR > 1 to lift from the ground. Also a low TWR means more time for gravity losses building up, while a higher TWR may cause drag issues.

Another possible cause of inefficience is a suboptimal trajectory. That can happen with a bulky payload or overpowered rocket (e.g. launching a satellite on top of a Thumper SRB)

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