# Is My Rocket Mass Distribution Formula Incorrect?

• Essence
In summary, the conversation discusses the search for a correct equation for finding the ideal mass distribution and total mass of a three stage rocket with given parameters. The formula provided yields unrealistic results, leading to the suspicion that it may be incorrect. Despite searching for alternative formulas, no satisfactory results were found. However, it is later revealed that the parameters given were not feasible, leading to a resolution of the issue.
Essence
Note: I have noted that one of the formulas I have provided does not show up on my webpage in preview mode and so have also made it as an attachment.

Quick summary: I have found two different websites that offer the equation that I am looking for in different forms, but I am starting to think that the equation is actually incorrect. So I'm really asking if any rocket engineers could assure me that the equation I am using is indeed incorrect and (if I'm lucky) point me to a reference where I can get find the actual equation. I have actually spent a long time (two days) looking for a better formula but the web has not proven very helpful and the books I have read have not gone into enough detail for actual calculations. I do not actually have a textbook (one does not exist) because this is not strictly coursework.

1. Homework Statement

Find the ideal mass distribution and total mass of a three stage rocket assuming:

1. A specific impulse of 300 seconds for all three stages
2. A ##\Delta## V of 9000 m/s
3. A dry mass fraction for each stage of 0.35
4. There are three stages
5. Payload is allowed to be left as an unknown

## Homework Equations

1.
https://www.physicsforums.com/cid:F649DCE6-2FDC-453C-830C-5D2F46A91771@guardedsystems.com

Where
M = final mass of the rocket (all three stages added together)
A = payload mass
S = dry mass fraction
Vf = final velocity: (considering the rocket starts from 0 m/s) is ##\Delta## V
C = exhaust velocity

https://math.la.asu.edu/~nbrewer/Fall2007/MAT267/RobertWagner/RobWagner%20Footnote%20181.html

- This assumes a constant inert-mass fraction throughout the rocket, which for my analysis is a given. It is clean because it uses a final formula rather than me having to partially derive one by adding up all of the stages of the rocket.

2.
## V_{exh} = I_{sp} * g_0## (For a rocket blasting off earth) (I'm using 9.8 for ##g_0## for now)

## The Attempt at a Solution

I can calculate the ##V_{exh}## to be 2940 using formula 2.
The rest is just plugging into formula 1 from which I can get a ratio between the final mass of the rocket and the mass of the payload. Here's the calculation:

## M = A \bigg( \Big((1 - .35) e^{9000/(3 * 2940)}/\big(1 - .35*e^{9000/(3 * 2940)}\big)\Big)^3 - 1 \bigg) ##

The end result is that M = 240805 A or that the total mass is 240 thousand times the payload. The Saturn V has a mass that is only roughly 17 times its payload (borrowed from mass data on Wikipedia here: https://en.wikipedia.org/wiki/Saturn_V). When I make ##g_0 ## only 9.3 I suddenly get a negative number for my mass payload ratio. This is telling me that I'm working with a very finicky formula and that it is probably incorrect.

I have done this equation in a more tedious fashion using a stage by stage analysis provided here:
http://www.projectrho.com/public_html/rocket/multistage.php#inertmass

Unfortunately this has led me to the same unrealistic answer, but prevents me from assuming my formula is incorrect (since two different sites seem to agree on the process).
Thanks for taking the time to read this.

#### Attachments

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Sorry for the trouble. Actually my assignment provider changed the dry mass fraction because he realized that the parameters we were given were not feasible. Everything is resolved now. I hope this thread did not cause any difficulties. Thanks for the time.

berkeman

## What is Ideal Rocket Mass Distribution?

Ideal Rocket Mass Distribution refers to the optimal distribution of mass within a rocket in order to achieve maximum efficiency and performance during flight. This includes the placement of the rocket's components such as fuel, engines, and payload.

## Why is Ideal Rocket Mass Distribution important?

Ideal Rocket Mass Distribution is important because it directly affects the rocket's stability and control during flight. A poorly distributed mass can result in instability and potential failure of the rocket.

## How is Ideal Rocket Mass Distribution determined?

Ideal Rocket Mass Distribution is determined through complex calculations and simulations that take into account the rocket's design, desired trajectory, and other factors such as atmospheric conditions. Engineers use computer programs and physical models to analyze and optimize the distribution of mass.

## What are some common challenges in achieving Ideal Rocket Mass Distribution?

Some common challenges in achieving Ideal Rocket Mass Distribution include the weight and size limitations of the rocket, as well as the need to balance the distribution of mass with other design considerations such as aerodynamics and structural integrity.

## How does Ideal Rocket Mass Distribution affect the success of a rocket launch?

Ideal Rocket Mass Distribution is crucial for a successful rocket launch as it ensures the stability and control of the rocket during flight. Without proper mass distribution, the rocket may experience issues such as tumbling, which can lead to a failed launch or even endanger the safety of the crew or payload.

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