Calculating fuel needed to lift additional payload

[goduranus]

I am trying to determine how much additional fuel and oxidizers I need to put into a space plane, to make it carry a heavy inert payload.

What I already done is that I tested the space plane to determine the amount of fuel and oxidizers it needs to put just itself into orbit with no fuel left. From this point, I would like to find out how much fuel and oxidizer I need to put back into the plane when the plane is now lifting a 20 ton payload.

So, the space plane weights 40 tons dry, and take 60 tons of fuel and oxidizers to reach orbit.

I guess that adding a mass equivalent to half of the weight of the plane would mean adding half the weight of the fuel needed by the plane itself? plus an additional component to account for the higher gravity drag due to lowering of TWR, and another bit to account for the payload's air drag.

How would I go about calculating this extra bit? Is it usually significant?

Here are some craft numbers:

Total Rockets thrust: 1400 kN

Average Rocket ISP: 360 seconds

Rocket Start Altitude: 25 km

Orbital speed at rocket start: 1400 m/s

The target orbit: 70km x 70km

[Pecan]

...I guess that adding a mass equivalent to half of the weight of the plane would mean adding half the weight of the fuel needed by the plane itself? plus an additional component to account for the higher gravity drag due to lowering of TWR, and another bit to account for the payload's air drag.

How would I go about calculating this extra bit? Is it usually significant?...

Plus some for all the fuel you'll need to lift the fuel, and the fuel you'll need to lift the fuel to lift the fuel, etc. In general, it's the rocket equation but, as many people have asked, it's practically impossible to calculate for atmospheric work because so much depends on your ascent profile, exact TWR and different altitudes, etc, etc, etc. Being a plane just makes it even worse. Possibly not impossible but definitely improbable.

Oh, and yes, it's usually VERY significant.

[goduranus]

I think it already includes the weight of the fuel needed to lift extra fuel for the payload though.

The 60 tons of fuel needed to lift the 40 ton craft dry and empty includes the fuel needed to lift the fuel that accelerates the craft. So 30 ton extra fuel for a 20 ton load also includes the fuel that lifts the fuel which accelerates the load.

[Claw]

Well, it's hard to directly calculate how much more you need. What's also very significant for planes (in addition to fuel load) is the Thrust to Weight, intake to engine, and the Lift to Mass ratios. Everything sort of needs to scale up. Unless you already overbuilt the plane to start with, adding 50% payload (or 20% depending on the point of view)after the fact is a bit difficult.

You'll usually get better results if you start out with the payload and mission tasks as the focus of designing, then make a craft capable of that. So you want to start out making the craft capable of carrying 20t of payload, and designing to that capability.

To be honest, it sounds like you are carrying a lot of rocket fuel to start off with. Does it take all 60t to get into orbit?

[goduranus]

I got the numbers from memory and they were way off. I tested it again and wrote them down after I got home today. The craft is actually 47 tons, and fuel needed is 15 tons.

What's odd though, to add a 20 ton payload, it seem to need to an additional 40 tons of fuel, much more than the payload to craft weight ratio seem to suggest.

Edited July 10, 2014 by goduranus

[Pecan]

Again, so much depends on how much lift is being generated by wings versus thrust, how efficiently you're accelerating through different layers of the atmosphere. There simply is no straightforward way to calculate this for a spaceplane. For a rocket, yes, you broadly follow the rocket equation but the engines that efficiently lift 47 tonnes are probably not the same as you'd use for 67 tonnes so, yet again, you can't just take a working model and expect it to still work after adding just payload and fuel.