Calculating Payload to Low Kerbin Orbit.

[davidpsummers]

I've got several lift vehicles that I match the right size for missions. I know how much they weigh and what their delta-v is without payload. Can I use that to calculate the maximum payload they can lift to Low Kerbin Orbit? It would be handier to be able to rate them by mass they can lift to LKO.

Edited April 10, 2015 by davidpsummers

[Alshain]

You can technically calculate it, yes. Do you want to? There is a test weight mod that is perfect for determining the max mass of your payload. Just raise the mass until the Delta V is at the absolute minimum you need and that will give you your max payload.

If you really want to calcualate Delta V though... http://en.wikipedia.org/wiki/Delta-v

Before you do all that work though, you should be warned in a week or two it is all going to change and you will likely have to redesign your lift vehicles.

Edited April 9, 2015 by Alshain

[UmbralRaptor]

The most straightforward approach would probably be to put your vehicles into a spreadsheet and play around with payload values until you hit the minimum (reasonable) ÃŽâ€V for various missions.

(multistage craft usually don't lend themselves to analytic solutions, especially when you need to consider TWR constraints.)

[Leszek]

If you have kerbal engineer (Or Mechjeb), you can put more stuff on the top until you have a DV of 4500. This is the required DV for getting into LKO stock. The only gotcha is make sure you have decent TWR. The total tonnage of what you put on top while still having a 1.25 TWR and 4500 DV is the max tonnage to LKO for that lifter.

[kerbiloid]

Put a fuel tank as a payload, let the last stage to use it.

When already on orbit, look at the fuel rest and calculate how much fuel from it has been consumed.

According to this value, repeat the test - decreasing fuel mass in that "payload tank" until you get to the orbit with the payload untouched.

In 2-3 attempts you will get exact value of your payload.

[Th3F3aR]

You just need to use the rocket equation

Normally you calculate with: Ve * LN(Mfull/Mdry) -> To calculate payload just add it to Mfull and Mdry => Ve * LN(Mfull+P/Mdry+P) = dV

There you go

[kerbiloid]

You just need to use the rocket equation ...

Ve * LN(Mfull+P/Mdry+P) = dV

Required dV is affected by air drag and gravity and depends on TWR, trajectory angle, craft drag, etc.

[Th3F3aR]

Required dV is affected by air drag and gravity and depends on TWR, trajectory angle, craft drag, etc.

I know This is to estimate the dV output of the rocket

[Pecan]

Most recently discussed in this thread

[davidpsummers]

Being persuaded by the issue of TWR also needing to be sufficient, I went with "take the launch vehicle and put enough weight on top until Kerbal Engineer says the amount of dV is right" approach. If I was still calculating dV's by spreadsheet, I may have calculated the weight and TWR ratios.

[capi3101]

If you want to do it by hand, try this route:

1) Since you know your rocket's thrust, set the TWR at 1.2 (generally considered the lowest acceptable value) and solve the TWR equation for mass (R=T/mg therefor m=T/Rg, where T = your booster thrust, R = 1.2 and g = 9.82). Compare the resultant mass with the known mass of your rocket. The difference between the two is the maximum payload based on TWR.

2) Now, since you know both the mass of your rocket and its mass when the tanks are dry, add that same payload mass to both the wet and dry figures and run the Rocket Equation to solve for delta-V. The result will be how much delta-V you'd get with that payload mass.

3) If the delta-V with the payload mass is less than 4500, the limiting factor on your booster is delta-V. If it is 4500 or greater, TWR is your limiting factor.

4) In the event that your determine that delta-V is your limiting factor, you're going to have to run the Rocket Equation backwards, solving for payload mass. Let me solve the equation for you there:

delta-V = Isp * Go * ln(M/Md) = 4500, where Go = 9.82 m/s^2 and Isp is the specific impulse of your engine cluster. Set Delta-V equal to 4500.

4500 / (Isp * Go) = ln(M/Md) = x (divide the 4500 delta-V by the Isp and Go, and call the result "x")

M/Md = e^x = x' (find the inverse natural logarithm of x and call it x')

M = x'Md (Solve for wet mass)

M + P = x' (Md+P) (since the payload mass is part of both M and Md, pull it out as a seperate term, called P)

Now, here's where we might have an issue: 1 meter and 2.5 meters fuel tanks (from the little FL-T100s all the way up to the Jumbo 64 orange tankls) have a wet to dry mass ratio of 9:1. For 3.5 meter tanks, the ratio is 8.2:1. Either way, you can say that the wet mass equals whatever ratio you'ure using times the dry mass. I'll assume you're using 2.5 meter tanks, and therefore I can say that M=9Md. So I plug that in:

9Md + P = x'(Md+P)

And now you solve the equation for P:

9Md + P = x'Md + x'P

9Md - x'Md = x'P - P

(9-x')Md = (x'-1)P

P = (9-x')Md/(x'-1)

You then just plug in the numbers; the result should give you the payload mass that will get you the 4500 m/s of delta-V.

Now, if you're dealing with a multi-stage rocket, you'll have to go through this process for each stage in turn. And if you're using both size-3 and size-2 tanks in a single stage and find yourself in a situation where delta-V is the limiting factor, you'll need to figure out the wet-to-dry ratio of that stage yourself (and then put that in place of the "9" in the final equation if needed.

Or you could save yourself the trouble of manual calculations and download NRAP as Alshain has suggested. Best of luck in whatever route you choose to take.