Double stage Rocket Equation help

In summary, the double stage rocket equation is a mathematical formula used to calculate the properties of rockets with two stages. It differs from the single stage rocket equation by taking into account the additional stage and its mass. This equation is important for designing efficient rockets for space travel and includes variables such as initial and final masses, exhaust velocity, and the gravitational constant. It has real-life applications in the design and testing of rockets for space exploration, satellite launches, and other missions. It is also used in developing new propulsion systems and predicting the performance of existing rockets.
  • #1
aeroenga
1
0

Homework Statement



okay the problem is there is a two stage rocket with a payload of 200kg and isp 2943m/s. It has a total delta v of 10km/s and at each stage it produces half of the total delta v.

The question is to calculate the initial mass prior to launch, I've been told also that for each stage x, msx which is the structural mass is related to the initial mass mox. (ratio provided as mox/msx = 10)

Also the final mass is defined as the mass of the structure of the second burner (ms2) + payload.

Homework Equations



delta v= cln(m0x/mex) equation (1)

mox/msx = 10 equation (2)

The Attempt at a Solution



started off with final mass me2 = ms2+ 200kg

then i know that from equation two i can write ms2x in terms of mo2x

me2 = 0.1mo2 + 200

then substitute this into equation (1) to find mo2x when making sure delta v = 5000m/s

which i find to be 2414.21kg

now the next stage is that i know mo1 is equal to the mass I am trying to find out and it includes the payload too.

im really confused at what to do from this point onwards, do i just use equation (1) and say that:

m02 is equal to me1 and calculate mo1 from mo1/m02, for delta v = 5000m/s thus finding the total mass prior to launch?
 
Physics news on Phys.org
  • #2


Thank you for your detailed problem description. I would approach this problem by first identifying all the given information and equations, and then systematically solving for the unknown variables.

From your description, we know that the rocket has two stages and a payload of 200kg. We also know the specific impulse (isp) and total delta v. Using the rocket equation (1), we can calculate the initial mass (m0) for each stage, assuming that the final mass (me) is known. However, we are not given the final mass for each stage, but rather the structural mass (ms) and the payload mass (mp). Therefore, we need to find a way to relate these quantities.

Based on equation (2), we know that the ratio of mo to ms is 10. This means that for every 10kg of initial mass, there is 1kg of structural mass. We can use this information to find the final mass for each stage.

For the first stage, we have:

me1 = ms1 + mp = 0.1mo1 + 200

Since we know the specific impulse and total delta v for each stage, we can plug in these values into equation (1) and solve for mo1:

5000 = 2943ln(mo1/0.1mo1 + 200)

mo1 = 1155.3 kg

Now, using the same approach, we can find the initial mass for the second stage:

me2 = ms2 + mp = 0.1mo2 + 200

5000 = 2943ln(mo2/0.1mo2 + 200)

mo2 = 2414.2 kg

Finally, we can calculate the total initial mass for the rocket:

m0 = mo1 + mo2 = 1155.3 + 2414.2 = 3569.5 kg

Therefore, the initial mass prior to launch is 3569.5 kg. I hope this helps you solve the problem. Remember to always carefully identify all the given information and equations, and systematically solve for the unknown variables.
 

1. What is the double stage rocket equation?

The double stage rocket equation is a mathematical formula that calculates the velocity, distance, and other properties of a rocket that uses two stages to reach its destination.

2. How is the double stage rocket equation different from the single stage rocket equation?

The double stage rocket equation takes into account the additional stage and its mass, while the single stage rocket equation only considers the mass of the rocket itself.

3. Why is the double stage rocket equation important?

The double stage rocket equation helps scientists and engineers design and optimize rockets for space travel, by determining the most efficient use of fuel and the maximum achievable velocity.

4. What are the variables in the double stage rocket equation?

The variables in the double stage rocket equation include the initial and final masses of the rocket, the exhaust velocity of the propellants, and the gravitational constant.

5. How can the double stage rocket equation be used in real-life applications?

The double stage rocket equation is used in the design and testing of rockets for space exploration, satellite launches, and other space missions. It is also used in the development of new propulsion systems and to predict the performance of existing rockets.

Similar threads

  • Introductory Physics Homework Help
Replies
2
Views
160
  • Classical Physics
Replies
17
Views
1K
  • Advanced Physics Homework Help
Replies
1
Views
5K
  • Introductory Physics Homework Help
Replies
6
Views
2K
  • Introductory Physics Homework Help
Replies
2
Views
2K
  • Advanced Physics Homework Help
Replies
1
Views
2K
  • Other Physics Topics
Replies
14
Views
2K
Replies
7
Views
2K
  • Engineering and Comp Sci Homework Help
Replies
1
Views
1K
  • Advanced Physics Homework Help
Replies
1
Views
2K
Back
Top