How do I calculate payload mass to orbit?

[Bluelogic32]

How do I calculate the mass my rockets can lift to orbit? For example, the Saturn 5 rocket could carry of 118,000 kg to LEO.

I'm not asking if my rocket will get to orbit or not because I know how to check that. I'm asking how were the Saturn 5's and other rockets payload mass calculated? I'm sick of designing rockets for every new craft I launch, so I just want go to rockets for a specific payload mass.(Sorry if my grammer is bad, it is 3 am)

[Francesco]

I'm sick of designing rockets for every new craft I launch, so I just want go to rockets for a specific payload mass.

Even better, you could design rockets for a payload class: one for payloads up to 5t, one for up to 10t, 20t, 50t...

So if you want to send up a 7-8 tons new shiny thingy, let's say, you pull out your 10t lifter from subassemblies, without building a custom launch vehicle specifically for that mission.

Use the excess fuel and delta-v to de-orbit a re-use the stages, maybe

[Bluelogic32]

That is what I want rockets that could carry specific payloads to orbit, but what I need to know is how do I calculate how much a rocket can carry.

Edited September 17, 2014 by Bluelogic32

[Pecan]

I've got this in a spreadsheet but as several steps, so bear with me:

Launch capactity (tonnes) = ((Launch_Ratio * Mass_Dry) - Mass_Wet) / (1 - Launch_Ratio)

Where :-

Launch_Ratio = EXP(dV_Launch / (Isp * Gravity))

EXP = the exponential function

dV_Launch = your required deltaV (eg; 4,500m/s for Kerbin launch to orbit)

Gravity = 9.81 for Kerbin

Mass_Dry = unfuelled mass

Mass_Wet = fuelled mass

(er, I think; if I've re-written that properly)

Edited September 18, 2014 by Pecan

[guitarxe]

Launch_Ratio = EXP(dV_Launch / Exhaust_Velocity)

What's the EXP mean?

[OrbitusII]

That is what I rockets that could carry specific payloads to orbit, but what I need to know is how do I calculate how much a rocket can carry.

Probably the easiest way is via experimentation. Building launchers takes time any way you look at it, so going straight to the experimental phase and designing/testing (at least in KSP) is easier and a bit quicker than doing all the math and then designing/testing.

You can certainly do the math, but depending on which direction your solution takes it can be either nice and simple or incredibly complex. I would definitely check out Pecan's stuff (above) and see how that works for you.

[Pecan]

What's the EXP mean?

I think our posts crossed, I have now edited the formula above.

EXP is the exponential function, which nearly every spreadsheet and scientific calculators should have. Funnily enough, in LibreOffice which I use, and Excel it is EXP(...)

[capi3101]

I should probably let Pecan answer this, and I'm wagering I'll get ninja'd on it, but...

1) Calculate the total thrust your booster outputs. Divide that result by 11.76 (9.8, Kerbin's Gravity, times 1.2, the generally accepted minimum TWR you can have and still expect to get into orbit). The result there is the maximum cap on your rocket's mass.

2) Work the Rocket Equation backwards for the atmospheric Isp of your rocket, setting delta-V to 4500. Plug the maximum cap in as M and solve the equation for Md

3) Subtract the mass of your engines, decouplers and anything else that ain't payload or fuel tanks from Md. Whatever is left is your maximum possible payload for the design.

Practical example: You've got a single stage booster with a KS-25x4 booster which you're separating from the payload with a TR-18A, with a set of four AV-R8s for additional control during the early part of the flight (for 0.13 tonnes "other" mass). The mass of the engine is 9.75 tonnes and its ground Isp is 320, and it outputs 3200 kN of thrust:

1) 3200 / 11.76 = 272.108 tonnes.

2) delta-V = ln(M/Md) * 9.8 * Isp, 4500 = ln(M/Md) * 9.8 * 320, M/Md = e^((4500/9.8)/320) = 4.1994, M/4.1994 = Md, Md = 64.796 tonnes

3) 64.796 - 9.75 - 0.13 = 54.917 tonnes.

So, the maximum payload for that particular booster is 54.917 tonnes. I can work through another example if you'd like, or you could wait for more help from Pecan. Or both.

Didn't get ninja'd...

EDIT: Actually, I have that wrong. You have a 207 tonnes tonne difference between the maximum mass and the dry mass, so that's 207 tonnes of fuel needed. That'd correlate to six Jumbo-64s and an X200-32 worth (roughly), which have a dry mass of 26 tonnes when combined. Subtract that from the calculated dry mass there (54.917 tonnes), and it comes down to 28.917 tonnes. So that'd be the payload mass for the booster (and no, the situation is NOT improved with the bigger fuel tanks, but rather the opposite; the new extra large tanks have an inferior mass-to-dry mass ratio as compared to the traditional tanks in the game).

Edited September 16, 2014 by capi3101

[nine_iron]

Sub Rocket_Launch

Do

If Rocket = Explode Then

MoarBoosters

Loop

Else

F5

End Do

End If

End Sub

Begin Fun

Spot the error?

Edited September 16, 2014 by nine_iron

[Bilfr3d]

Not sure if anybody realised this, but this is in the tutorials section... I don't think this is a tutorial... You should've created this in the gameplay questions section.

[mhoram]

A while back Temstar wrote a good guide on selecting and configuring engines based on payload mass.

[SRV Ron]

In Sandbox; Kerbal School of Hard Knocks. Ideal design is two stages to orbit or three stage to Kerbal escape.

1. Build your payload

2. Build the orbital insertion stage and test fly it.

3. Tweak the design as needed.

4. Add the core stage and test fly that.

5. Tweak the design as needed.

6. Use SRBs for the initial launch to lift the rocket to between 5,000 and 10,000 meters aiming for a speed over 200m/sec. Adjust their number and power output to reach that goal. 10,000 meters at about 240m/sec would be ideal for allowing the second stage to reach low orbit.

7. Tweak the second stage design so that it has the performance to place the third stage and payload into orbital insertion range. An optional design should be capable of a 75k payload orbit but is not critical.

8. Tweak the third stage design to have sufficient performance to place the payload into a 100K orbit with a comfortable reserve for recovery if desired. An optional design would have enough fuel left to push the payload to Kerbal escape.

9. Don't overbuild the launch vehicle. If it takes nearly all the thrust just to lift the boosters off the ground by themselves or you have excessive acceleration on the first 10,000 meters, you are just wasting resources.

10. Asparagus or onion designs, while not always desirable, are most efficient because all the engines are working to lift the payload to orbit during flight. They get staged when their fuel cans are empty and they are no longer needed to lift full fuel tanks for the rest of the design.

Edited September 17, 2014 by SRV Ron

[guitarxe]

I've got this in a spreadsheet but as several steps, so bear with me:

Launch capactity (tonnes) = ((Launch_Ratio * Mass_Dry) - Mass_Wet) / (1 - Launch_Ratio)

Where :-

Launch_Ratio = EXP(dV_Launch / (Isp * Gravity))

EXP = the exponential function

dV_Launch = your deltaV is at launch

Gravity = 9.81 for Kerbin

Mass_Dry = unfuelled mass

Mass_Wet = fuelled mass

(er, I think; if I've re-written that properly)

That doesn't work for me.

Example - FL-T400 X 7 with LV-T30 underneath

Mass Wet is 17

Mass Dry is 3.2

ISP is 320

dV on that stack is 5445

This gives us Launch Ratio of 5.67

Plug that back into full equation gives me -0.24.

But how can that be true? If I plop a single capsule on top, weighing 0.84 I know this can still go to space. dV comes down to 4822, and thrust is at 1.23.

[SRV Ron]

In Sandbox; Kerbal School of Hard Knocks. Ideal design is two stages to orbit or three stage to Kerbal escape.

Here is my Sandbox design for a 3 man payload with service module fully fueled in orbit. Mass 24.85 tons. Nova Punch, KW Rocketry, and Stock were used to design the conventional design rocket.

The 2 stage launch vehicle with escape tower. Mass 181.87 tons

At 5K ready for the orbital turn. Speed is ideal and at full throttle. Note, the stock NASA has the right amount of power for this design.

10K orbital turn in progress. Careful not to turn too fast or this design will flip ends at this stage of the flight.

Ready to stage. When staging takes place, the escape tower is jettisoned as well.

In orbit. Note, the second stage placed the 24.85 ton payload into a 100+K orbit with fuel to spare.

Orbital stats.

Payload in orbit ready to do further exploration and testing.

As the Odin heat shield comes with retro rockets, it can be used to deorbit the pod.

Reentry and landing;

[Pecan]

Gah - I knew I'd forgotten my own formulae; and I still can't find where on the interwebz I got it from.

Please try this;

I think my mistake was in dV_Launch. The formula can work out what the rocket has from it's wet/dry masses so what it needs is the required dV for whatever you're doing - in a normal Kerbin case that's 4,500m/s. From that (has - needs) it can re-work the remainder to give a 'spare capacity' figure in tonnes.

Maybe.

Anyway ... stick 4,500m/s in for dv_Launch and tell me if it works. In the specific case you give it leaves 1.13t but I'm way too tired (and emotional) to see if that's correct at the moment.

[guitarxe]

Gah - I knew I'd forgotten my own formulae; and I still can't find where on the interwebz I got it from.

Please try this;

I think my mistake was in dV_Launch. The formula can work out what the rocket has from it's wet/dry masses so what it needs is the required dV for whatever you're doing - in a normal Kerbin case that's 4,500m/s. From that (has - needs) it can re-work the remainder to give a 'spare capacity' figure in tonnes.

Maybe.

Anyway ... stick 4,500m/s in for dv_Launch and tell me if it works. In the specific case you give it leaves 1.13t but I'm way too tired (and emotional) to see if that's correct at the moment.

Sorry to hear about you being distraught, and thanks for taking the time to explain this.

Swapping out the dV to 4500 does indeed give me ~1.12 in launch capacity as you say.

I've also found this calculator on this forum (the calculator itself is not interesting, it's the formulas used shown on the forum post that interest me). So using that method instead, and plugging in the same values in my example gives me a launch capacity of 0.85.

I don't understand enough about rocketry to know which is more accurate, but the difference between your formula and their's is only in the final equation. They take what you have labelled as Launch_Ratio and subtract the dry mass from that to get the payload. (They also use a mass ratio to find the dry mass, but in KSP we can easily find that by just removing all the fuel (I wish you could do that with a single click...)).

Since the author does admit those calculations are "very rough", I'm leaning more on yours to be more accurate. Anyway when I come home I'll give the rocket a try and see how much it can really get into space.

My only concern, though, is that there is no where any mention of TWR for the rocket. Wouldn't that make it possible, using this equation, to design rockets that can theoretically lift certain payloads but in reality cannot due to lower than minimum TWR?

[Bluelogic32]

Thank you to every one that answerd my question, although they didn't help me in the way I expected I still appreciate your help. The reason your answers didn't help me the way I expected is because I designing my rockets before the payloads, it has to be the other way around, I can't really explain what I mean but I was confuesed about how rockets were build, and your answers helped my realize that I was building them the wrong way, so thank you

[guitarxe]

@Pecan,

I spent some of my lunch today seeing if I could use the rocket equation to come up with an equation for pay load mass. We can think of M0 and M1 in the equation as both being made up of two components - the rocket mass we know, and the payload mass that is unknown, and re-write the equation as

dV = ve * ln ( (m0 + x) / (m1 + x) )

Solving that for X gives the same formula as you had given:

X = ((Launch Ratio * M1) - M0 / (1 - Launch Ratio)

So I believe that unless we have both arrived at the wrong conclusion your formula should be spot on.

Now I'm curious to know how this can be applied to rockets with multiple stages, using different engines (that have different ISP).

[guitarxe]

Thank you to every one that answerd my question, although they didn't help me in the way I expected I still appreciate your help. The reason your answers didn't help me the way I expected is because I designing my rockets before the payloads, it has to be the other way around, I can't really explain what I mean but I was confuesed about how rockets were build, and your answers helped my realize that I was building them the wrong way, so thank you

That's not necessarily true. You can design rockets before payloads, and then use the equation provided by Pecan to find out how much payload your rocket can lift. Temstar's guide linked by mhoram above is useful if you want to design rockets to carry specific amount of payloads. Either way works, it just depends on what you're doing.

[juanml82]

If you don't want to do maths:

0) Get KER or MJ

1) Build a booster

2) Put a decoupler on top

3) Keep stacking jumbo tanks on top of the decoupler until your dV or TWR fall below 4,500/1

4) Write down how much all those jumbo tanks weight together.

5) Save the booster as a subassembly. Write down the weight of all those jumbo tanks in the commentaries.

6) Build more/less powerful boosters, rinse and repeat

That's it. The next time you build a payload, you can use KER or MJ to check it's mass. You then go to the subassemblies tab and select the lifter that has the adequate power to put it in orbit.

It's a game. You can use maths if you like. And you can play it.

[Pecan]

@Pecan,

I spent some of my lunch today seeing if I could use the rocket equation to come up with an equation for pay load mass. We can think of M0 and M1 in the equation as both being made up of two components - the rocket mass we know, and the payload mass that is unknown, and re-write the equation as

dV = ve * ln ( (m0 + x) / (m1 + x) )

Solving that for X gives the same formula as you had given:

X = ((Launch Ratio * M1) - M0 / (1 - Launch Ratio)

So I believe that unless we have both arrived at the wrong conclusion your formula should be spot on.

Now I'm curious to know how this can be applied to rockets with multiple stages, using different engines (that have different ISP).

Thank you for the verification.

As to your concern regarding TWR; yes it is possible to design a rocket with a tiny engine and lots of fuel so that it has lots of deltaV but can't actually get off the ground. The only, but simple, way to guard against that is as capi said in post #8 - total your engines' thrust, divide by (gravity * minimum TWR) and recognise that as a cap on your total mass. In a spreadsheet you'd just use a min(calculated from deltaV, calculated from TWR) function to see which satisfies both constraints best.

To apply the formulae, or indeed the rocket equation itself, to multiple stages you simply apply them to each stage in turn, using the upper stage(s) + their payload as the total payload for lower stages. There is a bit more to consider in that you may want different TWRs at different points - high at launch, low at circularisation for instance.

Oh, and by the way I wasn't distraught yesterday. "Tired and emotional" is a euphemism for 'drunk'; I went to the pub last night so I wasn't really in a fit state for debugging equations.