Last time around I gave some numbers for a VCLS (Venture Class Lauch Service) vehicle; today we’ll cover a bit more of the mass budget specifics.
The basis of a mass budget is the deltaV equation: deltaV = Isp * g * ln (Minitial / Mfinal). Now deltaV is our desired velocity, Isp is the engine performance, and what we are looking at today is the mass ratio of initial mass over final mass. If we only know deltaV, Isp, and g, we cannot solve this equation as we have two unknowns, but we know a bit more information than that.
Minitial = Mpayload + Mpropellant + Mdry
Mfinal = Mpayload + Mdry
PMF = Mpropellant / (Mpropellant + Mdry)
Now with all of these equations, we know the payload mass and we have to estimate PMF (propellant mass fraction). Just like Isp is a measure of performance of the engine, PMF is a measure of performance of the structure. PMF is historically around 0.93 for a First Stage and 0.89 for an Upper Stage, but obviously this is somewhat variable and a function of propellant and stage cycle.
A good reference for PMF is Propellant Mass Fraction Calculation Methodology for Launch Vehicles and Application to Ares Vehicles.
So I used 0.92 for the first stage and 0.88 for the upper stage, taking a 1% hit for the smaller scale effect (damn you cube square law and electronics actually having mass).
Once we calculate the masses, we should do a quick estimate for tanks and engines which are the major players in the mass of the vehicle. Doing this, I find that the First Stage tanks and engine are 60% of the dry mass budget and the upper stage is 75% of the dry mass budget. Just based on historical numbers and previous work, I think at this stage somewhere between 60-70% is reasonable; so that is saying that our upper stage needs to decrease its PMF estimate or improve the tanks or have a low chance of eventual success. This is why initial sizing is important: you need to to be able to understand the system and where the margins are thin to effectively build up and test the rocket.
So later this week, in continuing the VCLS, I’ll cover turbopump rocket Isp calculations.
NASA announced a draft RFP for a vehicle that launches a 60 kg payload to orbit. This is a fairly exciting prospect for the NewSpace companies that are interested in providing launch services as government funding is often seen as an effectively free investment, and I imagine that NASA is hoping to launch a new, more robust commercial small satellite marker. I just hope that the contract works a little better than the NEXT program in 2013 which hasn’t gone anywhere yet, at least as far as anything public.
I thought I might go ahead and do a bit of a quick sizing just so we could see what sort of vehicle might work for the mission. Now, first we need a DeltaV, as there is no orbit given in the draft, we will assume a slightly elliptical inclined low earth orbit so we’ll just go ahead and assume a 9400 m/s budget. And for the sake of simplicity, let’s do a 2 stage LOX/RP-1 vehicle with a pressure fed upper stage and a gas generator turbopump first stage. And we will assume aluminum 2014 propellant tanks with Ti 6AL-4V pressurant tanks. And everything else pretty bog standard for a small launch vehicle.
-First Stage – 1200 psi engine with 94% efficiency give an Isp = 282 s mission average and a 92% propellant mass factor – This has a 20% mass margin.
-Second Stage – 150 psi engine with 94% efficiency and a 50-1 expansion gives an Isp = 313 s, and a 88% propellant mass factor – This has a 10% mass margin.
Overall, the vehicle has a total mass of 11,100 lbm GTOW and an 820 lbm dry. It is also 36″ in diameter and 33′ long, or roughly 1 meter diameter and 10 meters long. This is actually a pretty convenient size to move around in a 40′ container and around a standard shop with standard tools.
The engine for the first stage has a 7″ diameter chamber and a 15″ diameter exit, 10″ to the throat and 30″ long. Just a bit big for the chamber to be 3D printed, but if you used 2 chambers, you might be able to print the chamber with a machined nozzle extension.
The engine for the upper stage has a 5″ diameter chamber and a 16″ diameter exit, 8″ to the throat and 33″ long. You should be able to print the chamber with a machined nozzle extension.
So that is just some rough sizing; I should add a little bit more about the mass budgets later this week.
Quick update here on Project Earendel: we will be switching over to focusing more on theoretical and less on testing rockets in the near future. The reason for this is that Jasmine’s job has us moving to New Zealand and I am actually posting this from Auckland right now. So posts might be a bit shaky for a couple of weeks, then we will see what I can continue working on in the new surroundings.