Ideal rocket equation application help

[Jack11879]

Homework Statement

I am trying to calculate the change in velocity of the space shuttle required for a low orbit currently in use by NASA which i believe can be done from the ideal rocket equation. launch mass = 2,040,000kg external tank propellant mass=730,000kg solid rocket booster mass =504,000kgfirst stage-external tank = 455s second stage-orbiter= 316s

Homework Equations

Relevant equations[/b]deltaV=(Isp*g)ln(Mf/Me)Mf is the mass ofthe rocket fully fueledMe is the dry massIsp=specific impulse of propellants

The Attempt at a Solution

http://www.braeunig.us/space/specs/shuttle.htm3. On the above website is where i collected the data on the masses from however i may have misinterpreted as the launch mass minus both the propellant mass in the solid rocket booster and the external tank does not equate to the landing mass stated as 104,328kg on the above source, in fact it is less that it about 80,000kg. If anything i would say that it would be even lighter upon landing after using some of the orbital manouvering system's fuel. The specific impulse data was found on http://en.wikipedia.org/wiki/Space_Shuttle. Do i take Mf to be 2,040,000kg and then Me to be 2,040,000-(504,000+730,000) and the specific impulses as stated in the equation or is this completely wrong. If so can you please put me on the righ tracks. Many thanks Jack

 

[Jhero]

Dear Jack,

Thank you for your question. To calculate the change in velocity of the space shuttle, you are correct in using the ideal rocket equation. However, there are a few things to consider before plugging in the numbers.

First, the launch mass of the space shuttle includes not only the mass of the vehicle itself, but also the propellant mass in the external tank and the solid rocket boosters. So, the launch mass of 2,040,000kg already takes into account the 730,000kg of external tank propellant and the 504,000kg of solid rocket booster mass.

Second, the landing mass of the space shuttle is not just the vehicle itself, but also includes the mass of any remaining propellant in the orbital maneuvering system and the reaction control system. This accounts for the difference between the landing mass and the launch mass.

To calculate the change in velocity, you can use the following equation:

Δv = Isp * g * ln(Mf/Me)

Where:

Δv = change in velocity
Isp = specific impulse of the propellants
g = acceleration due to gravity (9.8 m/s^2)
Mf = final mass (including propellant)
Me = initial mass (without propellant)

Using the values from the sources you provided, we can calculate the change in velocity for the first stage (launch mass = 2,040,000kg, Isp = 455s) and the second stage (launch mass = 2,040,000kg, Isp = 316s):

First stage:
Δv = (455s * 9.8 m/s^2) * ln(2,040,000kg/1,536,000kg) = 2,357 m/s

Second stage:
Δv = (316s * 9.8 m/s^2) * ln(2,040,000kg/2,000,000kg) = 1,228 m/s

To calculate the total change in velocity for the entire launch, you can simply add these two values together.

I hope this helps and puts you on the right track. If you have any further questions, please don't hesitate to ask. Good luck with your calculations!