Ok, so the project is to design a small commercial launch vehicle, again I want to stress I'm not a businessman and I don't know if such a market does or will exist, however for arguments sake lets assume there is a viable market for 'cubesat' size and style satellites (small satellites of around 1Kg each).
The rocket design I will be focusing on should therefore be capable of launching around 20Kg (a batch of one large or several small student/academia/scientific payloads) into a number of trajectories including sub-orbital, LEO and escape/TLI. This mission flexibility allows the greatest number of potential uses/customers for the smallest outlay in design, materials and tooling. It is this requirement of mission flexibility which drove me to select a modular design for the rocket. For a quick read on modular rockets take a look at the OTRAG project:
To make orbit the modules will have to be staged (as it is not yet practical to develop a single stage to orbit design), assuming each stage operates using the same propellants at a similar ISP the mission delta V will be split evenly over each stage. The minimum practical number of stages to reach LEO is 2, we want the minimum because it means less things to get complicated/go wrong. Therefore for an LEO mission we're looking at a 2 stage rocket of modules. For a LEO mission a good rule is to allow a total of 9200 m/sec delta V, you only need around 7.8 km/sec orbital velocity in LEO but the rest will be burnt up in atmospheric and gravity drag, this means a stage delta V requirement of 4600 m/sec.
Next we need to choose our propellants, I have tentatively selected hydrogen peroxide and kerosene. Why?
- I like storable propellants. LOX may be cheaper, slightly higher performing and easier to work with in some ways but it also makes ground handling more difficult, the design of tanks and plumbing more difficult and the fluid control parts such as valves much more critical and expensive. Additionally you'll end up spending more weight on insulation for tanks and plumbing.
- Hydrogen peroxide is dense, which means a small rocket with low frontal area and lower drag. Smaller tanks are lighter too. It's also relatively safe to work with assuming proper safety gear and precautions are used, toxicity is low compared to other higher performance storables such as hydrazine and nitrogen tetroxide.
- Kerosene is cheap and readily available, it's well known in rocket engine use and is again a room temperature and pressure storable propellant.
- Peroxide has a decent specific heat and its mass flow is a large percentage of total making it a good choice for regenerative cooling.
There are more reasons but those are the primary ones, the primary problem when using peroxide is getting it in the concentration needed (80% +) in any quantity for a good price. As this is currently a paper design that's not such an issue.
80% H2O2 and kerosene at a chamber pressure of 1000psi at the correct mixture ratio and expanded to sea level pressure yields an ISP of around 255 seconds. We may use the rocket equation and an iterative solver (I used the equation solver in excel) to calculate the initial (wet) mass assuming a 20Kg payload and a dry mass of 9.4% the wet mass for a delta V of 4600m/sec. 9.4% was chosen as the inverse mass fraction of the rocket based on existing designs (around the mass fraction of the Saturn 1B rocket stage). From these numbers a fully loaded mass of 305.9Kg and an empty mass (plus 20Kg payload) of 48.8Kg was calculated. Without the 20Kg payload this leaves 28.8Kg for the entire module structure, propulsion system, guidance system etc. Finally based on the density of kerosene (around 700-800Kg/m^3) and 80% H2O2 (1200Kg/m^3) the module envelope was roughly sized to 40cm diameter and 2.5m long.