Horizontal Launch
The first homework of the design series is based on the issues that some parts of Europe face, in that it is not a safe nor responsible practice to launch rockets over populated areas (AHEM China), especially when they are not allies. We see the introduction of the mobile launch. The Pegasus (NGC) and the Launcher One (Virgin Orbit) are the best-proposed solutions for this tricky situation. In essence, the rocket is loaded onto the underside of an airplane and flown to its launch altitude and direction. From there, the launch vehicle is released and takes off from that altitude, horizontally.
There are some benefits to this method, the most important one being that you would not have to go through the traditional wait time of a larger launch. Another important benefit is that you can fly to different areas to launch in different directions. For example, in the homework prompt: Israel cannot launch eastward, as there are populated, non-allied nations to its east. Israel would like to avoid launching over any populated areas, especially ones it does not have good relations with. This system offers a solution to fly out west, over the ocean to launch retrograde, or south to launch eastward. In addition, this system can be prepared and launched in as little as a few weeks (or so I've heard). One may say that this seems like it should be standard practice, but as Richard Branson and VO found out, this is not always sustainable. For this method of launch, the launch vehicle has to be smaller, to be carried by an aircraft. Less fuel would mean that farther orbits, such as GEO and MEO may not be attainable. Moreover, there is less room for larger payloads. This could increase the cost-per-kg significantly as opposed to launching from a Falcon 9, that is fully stacked with busses.
The homework focuses on the capabilities of traditional launch vehicles versus the advantages of the horizontal launch. Because a traditional launch from Israel would require a lot of steering, to avoid populated areas, which have inherent delta V losses, we realize that the cost-per-kg is lower ising the smaller unconventional vehicle.
Delta V split calculations
The second part of this homework was to go a little more in-depth with the calculations. In this part, we are to calculate the staging speeds based on a number of assumptions. We are given the orbital parameters, we choose a vehicle similar in size to estimate masses/specs. and estimate delta V of the launch site, as well as losses of drag. From the equations in the book, it is really following a series of steps. Using Excel for this is easiest, however, creating a Matlab code that does all of this is powerful later toward the end of the design class.