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.