Calculating Maximum Payload to Orbit

[VincentMcConnell]

If I have a booster with a set amount of Delta-V, say, 11,000m/s.

And I want to figure out how much mass I can put on the top of it and still have the 9,000m/s of Delta-V required to get into orbit.

What is the exact mathematical equation to figure this out. There doesn't seem to be a single place on the internet that is helpful even remotely in trying to determine how much mass a booster can deliver to orbit.

If someone can help, that would be greatly appreciated.

 

[boogabooga]

[ame="http://en.wikipedia.org/wiki/Tsiolkovsky_rocket_equation"]Tsiolkovsky rocket equation - Wikipedia, the free encyclopedia[/ame]

 

[orbitingpluto]

If your not a fan of pen and paper, there's a site that will run the rocket equation for you here:

http://www.strout.net/info/science/delta-v/

That site doesn't figure multistage stuff though. This site will do the number crunching of multistage stuff, and payload shrouds and a few other effects too:

http://www.silverbirdastronautics.com/LVperform.html

Bookmark them, they sure are useful.

 

[Linguofreak]

One thing to keep in mind is that even if you have the DV, you may not have the acceleration.

 

[Urwumpe]

Also, even if you have the DV, you don't know the optimal trajectory, which depends on launch vehicle and payload. And without the trajectory, you can only roughly estimate the gravity losses, control losses, aerodynamic losses and possible plane change losses from the total DV of your launcher.

But you can solve this as well, with increasing accuracy with different methods for estimation.

 

[boogabooga]

He said he needs 9000 m/s to get to orbit, so I assume he has the losses figured out? :shrug:

 

[Loru]

He said he needs 9000 m/s to get to orbit, so I assume he has the losses figured out? :shrug:

losses depend heavily on thrust to weight ratio and trajectory - 9km/s is good estimate but if you have for example very low acelleration (slow riser) it may not be enough.

Silverbird's calculator is pretty good IMO (I usually get no more than 10% difference between calculator and orbiter vessel)

 

[Urwumpe]

He said he needs 9000 m/s to get to orbit, so I assume he has the losses figured out? :shrug:

No, 9200 m/s is the coarse estimate for getting into low earth orbit including all the losses. But it is a coarse estimate. You can get into orbit with much less DV, for example if you have a VERY high acceleration. Or you can need much more, for example if you have a very low acceleration.

 

[BruceJohnJennerLawso]

No, 9200 m/s is the coarse estimate for getting into low earth orbit including all the losses. But it is a coarse estimate. You can get into orbit with much less DV, for example if you have a VERY high acceleration. Or you can need much less, for example if you have a very low acceleration.

:hesaid:

Flat out, the minimum dv to orbit will be about 7600 m/s, the orbital velocity needed for a low-ish Earth orbit. The problem is that a lot of reaction mass is expended in directions other than horizontal; you need enough potential energy to reach a reasonable height, energy lost to air drag (probably grows the faster you try to get to orbit), propellant and/or vectored thrust to control the launchers attitude, and as has been noted, fuel to counter gravity drag during that agonizingly slow liftoff to pitch/roll phase of flight.

Generally speaking, whatever you think the dv losses are at first, estimate a little higher. I would go so far as to say 12000-14000 m/s to orbit is a fairly reasonable expectation for a medium-lowish efficiency launcher.