How to figure how many tons a launcher stage can carry into Orbit?

[Jouni]

This would seem to be a useful rule of thumb, but as several people have pointed out (myself included), you don't actually have to launch anything in order to answer this question. The inverted rocket equation I gave you will spit out the answer immediately.

The problem with this is that we don't know in advance how much delta-v a particular rocket needs to reach orbit. It's usually between 4500 m/s and 5000 m/s, but that's not good enough for any meaningful predictions about payload capacity. We can't even calculate delta-v directly, because engine efficiency depends significantly on the TWR of the rocket.

[Red Iron Crown]

These are very good points/observations. Personally, I often neglect the overall fuel usage, in favor of dV, so this was a good reminder for me to see. I may have to do a few experiments.

I noticed it while chasing lower cost, it came as a surprise to me. My comparative experiments have been with liquid fueled rockets only, though; it's tougher to compare with solids because you can't vary the engine:fuel ratio at all. Solids are definitely the way to go for lower cost, though.

[K77LostNSpace]

Sorry for not being smart enough to figure this rocket science out on my own.

I have been reviewing http://wiki.kerbalspaceprogram.com/wiki/Tutorial:Advanced_Rocket_Design

and all the help on this thread.

Aside from having to look up every math symbol or have you guys explain it. could someone post how how they figure the delta V for something simple like a RT-10 Solid Fuel Booster. And payload it could carry?

Mass Wet: 3.7475 , Mass Dry: 0.5 , atmosphere Isp: 225

maybe if i see the math in action it will start to make more sense.

I keep getting stumped on trying to figure out delta V, when i try to plug in the numbers give in that link, i come up with completely different figures. Listed example is 400isp , 3.72t Wet, 1.72t dry is suppose to be 3027.0 m/s Dv.

[GoSlash27]

K77,

I would be greatly shocked if you were able to just pick up on rocket science and run with it without any headaches. It takes all of us some time to adapt, so don't feel stupid; we all went through this.

Your rocket equation in standard form is DV= 9.81*Isp*ln(Mw/Md). Plugging in your example, DV= 9.81*(225)*ln(3.7475/.5)= 2,207*ln(7.5) = 2,207*2.014 = 4,445 m/sec. Just barely enough to make orbit without any payload whatsoever.

With good piloting and absolutely no reserves, you need 4,300 m/sec DV to reach LKO. So re-working the equation for maximum payload...

DV=9.81*Isp*ln(Mw/Md)

DV/(9.81*Isp)=ln(Mw/Md)

e^(Dv/(9.81*Isp))= Mw/Md <-- Your required wet-to-dry ratio, or "Rwd"

plugging in the numbers...

e^(4,300/(9.81* 225)=Rwd

e^(1.948)=Rwd

7.017=Rwd

Knowing that your Mw/Md must be at least 7.017 and that your payload is part of both wet and dry mass, we can continue reworking the equation.

7.017= (Mlw+Mp)/(Mld+Mp) ; The sum of the masses of your wet launcher and payload divided by the sum of the masses of your dry launcher and payload must equal 7.017.

7.017= (3.75+Mp)/(0.5+Mp)

7.017*(0.5+Mp)= 3.75+Mp

3.509+ 7.017Mp= 3.75+Mp

3.509-3.75=Mp-7.017Mp

-.241=Mp(1-7.017)

-.241=Mp(-6.017)

-.241/-6.017=Mp

.04=Mp. You can't orbit any more than .04t of payload with a single RT-10 booster. And even then, that's with good piloting and absolutely no reserve.

Using the numbers from your link,

400*9.81*ln(3.72/1.72)= 3,924*ln(2.16) =3,924*.771= 3,027 m/sec DV, which agrees with their answer.

Hths,

-Slashy

Edited August 1, 2014 by GoSlash27

[GoSlash27]

*snip* no one does exponents purely by hand -- using a calculator is much less hassle.

Back in the olden days, they used log tables for high- precision answers and slide rules for spitballing.

I still use a slide rule for KSP; Pickett #120. It's not as precise as a calculator or spreadsheet, but it shows all possible solutions for a given ratio at the same time, which makes it faster.

Best,

-Slashy

[GoSlash27]

The problem with this is that we don't know in advance how much delta-v a particular rocket needs to reach orbit. It's usually between 4500 m/s and 5000 m/s, but that's not good enough for any meaningful predictions about payload capacity. We can't even calculate delta-v directly, because engine efficiency depends significantly on the TWR of the rocket.

Jouni,

We know pretty accurately what DV will get a ship into LKO regardless of it's mass. While the T/W ratio does affect this, it's pretty negligible so long as it's within the window of 1.4-2, so not something to worry about IME. Just build the ship for 4,500 DV and make sure the T/W is correct. The rest will sort itself out.

Best,

-Slashy

[LethalDose]

With the new budgets, I've started thinking in terms of purposes for each stage (e.g. lift to orbit, transfer to Minmus, etc) instead of in terms of "overall" dV. Each stage is engineered to do it's job, and nothing more. This has led me to be more standard with my lifters, e.g. I have one lifter that I know will put 10 t up to 75 km and need ~ 200 more m/s to circularize based on experience from previous launches. The original launchers were designed with dV numbers in mind, but I need that less after some practice. I'll also tweak the thrust limiters and fuel loads in the SRBs as needed, but they're really only they're to "boost" the main stage anyway. My experience has been the same: lower initial TWRs seem to be cheaper. I'm usually launching TWRs between 1.25 and 1.5 and I'm pretty happy with my expenses.

speaking of tweaking SRB loads

I noticed it while chasing lower cost, it came as a surprise to me. My comparative experiments have been with liquid fueled rockets only, though; it's tougher to compare with solids because you can't vary the engine:fuel ratio at all. Solids are definitely the way to go for lower cost, though.

Why not tweak SRB fuel loads. That would allow you to vary the engine to fuel ratio, wouldn't it?

[GoSlash27]

I've started thinking in terms of purposes for each stage (e.g. lift to orbit, transfer to Minmus, etc) instead of in terms of "overall" dV. Each stage is engineered to do it's job, and nothing more.

That's the way I've done it also; design the mission backwards and build each stage to do it's job and nothing more. Saving a few kilos here and there at the tail end of the mission has a huge snowballing impact on the mass of preceding stages and usually spells the difference between "impossible" and "doable with a comfortable margin". The math is your friend!

-Slashy

[Seret]

It's usually between 4500 m/s and 5000 m/s, but that's not good enough for any meaningful predictions about payload capacity.

That range is about +/- 5% which is definitely close enough for a first effort. Just build for 4500ms^-1 or maybe a squidge extra. If you can fly anywhere near a decent profile that should be fine.

Edited August 1, 2014 by Seret

[Seret]

Sorry for not being smart enough to figure this rocket science out on my own.

As long as you understand what each term means there's nothing wrong with using an online ÃŽâ€v calculator to spit the answer out for you. That kind of thing is exactly what we invented computers and calculators for.

[Red Iron Crown]

Why not tweak SRB fuel loads. That would allow you to vary the engine to fuel ratio, wouldn't it?

A couple of reasons: The tweaking is one way only (you can have more engine and less fuel, but not more fuel and less engine) and its usually the opposite way from what I want to do. There is also the dry mass penalty of carrying solid fuel "tankage" that isn't used.

You're right, though, that I overgeneralized when I said, "you can't vary the engine:fuel ratio at all." Thanks for the correction.

[K77LostNSpace]

Ta du!

Thank you Slashy, laying it out step by step really helped.

After finely finding the ln button on the calculator I managed to get the same answer as you.

My second stump was getting e^ , which was hidden under the Inv button which provided more options on the calculator.

Now I feel empowered that my rockets will get to the Mun and have enough fuel for return, and launchers will be less wasteful when delivering payloads into LKO

[Jouni]

We know pretty accurately what DV will get a ship into LKO regardless of it's mass. While the T/W ratio does affect this, it's pretty negligible so long as it's within the window of 1.4-2, so not something to worry about IME. Just build the ship for 4,500 DV and make sure the T/W is correct. The rest will sort itself out.

That estimate only works within a relatively narrow range of parameters. It assumes that the rocket is small or wide, because you can't have big tall rockets with high initial TWR. It assumes that the rocket is maneuverable enough to follow a close-to-optimal ascent path. It assumes that the upper stage has high TWR, because rockets with low-TWR upper stages need steeper ascent paths to buy more time for circularization.

That range is about +/- 5% which is definitely close enough for a first effort. Just build for 4500ms^-1 or maybe a squidge extra. If you can fly anywhere near a decent profile that should be fine.

Let's take my SLS-style lifter from 0.23.5 as an example. Its nominal payload capacity is 100 tonnes, or 14.8% of the launch mass. With that payload, my spreadsheet gives it 4877 m/s of delta-v, which is probably a bit too low, because I prefer to underestimate the average Isp for the first stage. Still, because the initial TWR is below 1.1, the margin of error is quite low, if I want to reach a 120 km orbit and deorbit the upper stage.

With a payload of 120 tonnes (17.3%), the spreadsheed gives 4511 m/s of delta-v, which is probably too little to reach orbit. With 94 tonnes (14.0%) of payload, the delta-v estimate becomes 5002 m/s. The difference between the payloads is quite big.

[GoSlash27]

Ta du!

Thank you Slashy, laying it out step by step really helped.

After finely finding the ln button on the calculator I managed to get the same answer as you.

My second stump was getting e^ , which was hidden under the Inv button which provided more options on the calculator.

Now I feel empowered that my rockets will get to the Mun and have enough fuel for return, and launchers will be less wasteful when delivering payloads into LKO

Use it in good health! Didn't take you long at all to sort it out.

Best,

-Slashy

[GoSlash27]

That estimate only works within a relatively narrow range of parameters. It assumes that the rocket is small or wide, because you can't have big tall rockets with high initial TWR. It assumes that the rocket is maneuverable enough to follow a close-to-optimal ascent path. It assumes that the upper stage has high TWR, because rockets with low-TWR upper stages need steeper ascent paths to buy more time for circularization.

Let's take my SLS-style lifter from 0.23.5 as an example. Its nominal payload capacity is 100 tonnes, or 14.8% of the launch mass. With that payload, my spreadsheet gives it 4877 m/s of delta-v, which is probably a bit too low, because I prefer to underestimate the average Isp for the first stage. Still, because the initial TWR is below 1.1, the margin of error is quite low, if I want to reach a 120 km orbit and deorbit the upper stage.

With a payload of 120 tonnes (17.3%), the spreadsheed gives 4511 m/s of delta-v, which is probably too little to reach orbit. With 94 tonnes (14.0%) of payload, the delta-v estimate becomes 5002 m/s. The difference between the payloads is quite big.

Point #1, a 1.1 t/w is going to require more DV due to gravity losses, which is why I recommend keeping it between 1.4 and 2.

#2, it doesn't actually assume a high TWR for the insertion stage. I design mine to have between .5 and .7 TWR in the insertion stage and can circularize comfortably with 4500 m/sec with plenty of reserve for intercept, rendezvous, docking, and deorbit.

#3 4,300 m/sec is a good ballpark for an 80km orbit. 120Km is naturally going to require more.

#4 I really don't have any experience with 100 ton lifters, as I've never had a need to lift anything that big. I'll have to take your word for it.

Best,

-Slashy

[Jouni]

#3 4,300 m/sec is a good ballpark for an 80km orbit. 120Km is naturally going to require more.

Is that real delta-v or an estimate based on the atmospheric and/or vacuum Isp values of the engines?

#4 I really don't have any experience with 100 ton lifters, as I've never had a need to lift anything that big. I'll have to take your word for it.

That happens with smaller payloads as well. A small change in delta-v requirements results in a large change in the mass ratio. And because the dry mass of the lifter stays the same, the change in payload capacity is even bigger.