A More-Realistic Weight Analysis

In the last analysis, I did a simplified analysis using off-the-shelf commercial motors from ATK [http://orbitalaspirations.blogspot.com/2011/10/looking-at-solid-first-stage-booster.html]. In that earlier analysis, I used the weights of the motors without any additional weight considerations for control systems, guidance or aeroshells. I’d like to go to the next level of design detail and make a first-step attempt at including those weights.

First Stage

Starting at the first stage, although I showed an aeroshell around the upper stages, I didn’t actually include any weight for it. Therefore, I want to include that into my estimates. Without having a particular design, it’s hard to know what to put, but I’m going to make an assumption that the upper aeroshell, fins and control systems are equivalent in weight to the structure of the motor. This is obviously going to be wrong by some amount but this will give us a first-order approximation. Therefore, whatever mass I allocate for the motor casing, I will allocate equal weight for the additional components of the first stage.

Second Stage

For the second stage, I need to consider the fact that it must be mounted to the first stage and that the motor nozzle needs gimbal control. No guidance is needed since that is provided by the fourth stage. There are no aerodynamic loads that have to be figured in because it is presumed to be operating only in a vacuum. On that basis, I added a few percent (5%) of the propellant weight to account for the stage control, coupling and ejection.

Third Stage

Like the second stage, I added a small percentage (5%) for stage control, coupling and ejection.

Fourth Stage

Like the previous two space stages, I added weight (5%) to account for stage control, coupling and ejection, but I also added additional weight to account for a guidance system (0.5%).

Analysis Results

Now that I added the additional weights, the delta V available from the stages changed. Each stage weighed a bit more and its delta V was less. To account for this, I had to re-design the second stage to provide more delta V for the in-space stages. Because I am limiting myself in this experiment to considering off-the-shelf ATK motors, I had to change the motor from a Star 15G to a Star 17A. This motor has a bit more propellant and compensates for the lost delta V. However, it actually provides appreciably more delta V and is a bit larger.

Because of the weight increases of the in-space stages (stages 2 through 4), as well as the aerodynamic loss which wasn’t adequately considered in the earlier design, the first stage was no longer able to provide sufficient delta V. I had to increase the first stage motor to a larger one, from the ASAS 21-85V to an ASAS 28-185. This is a much larger motor, with a diameter of 28.5 inches.

I really didn’t like having to make these adjustments to much larger motors, but the weight drove them up to provide the necessary performance. The ¼ pound to orbit rocket went from about 2000 pounds up over 8000 pounds. As such, these represent closer to reality for the weights and weight ratios.

Here are the new rocket specifications:

And here is a comparison between the design before and after:

Comparison of Sizes before and after more enhanced weight model

Summary

In this analysis, I used a more accurate weight model. As a result, the whole rocket grew appreciably. One reason I want to establish a more reasonable weight model is that I want to use these mass ratios in future rocket design analyses. These will provide a useful baseline for comparison of various performance improvements.