Rocket equation

  • Thread starter Biosyn
  • Start date
  • #1
114
0

Homework Statement



The following equation is known as the "Rocket Equation":

[itex]\frac{M+P}{M}[/itex]= e[itex]^{ΔV/C}[/itex] = mass ratio

M = dry mass
P = mass of propellant
C = exhaust velocity
ΔV = velocity change


e^1 = 2.72
e^2 = 2.74
e^3 = 20.4

As ΔV/C goes up, the mass of the spacecraft goes up faster than the exponential, so much so that depending on the lightness of the structural materials and the density of the propellants employed, somewhere between ΔV/C = 2 and ΔV/C = 3 the mass of a single spacecraft will go to infinity!


Please explain how and why the mass of the spacecraft will reach infinity?





Homework Equations



[itex]\frac{M+P}{M}[/itex]= e[itex]^{ΔV/C}[/itex]


The Attempt at a Solution




Shouldn't the mass ratio be equal to 1 if the mass is a really huge number?
Or, does the propellant mass have something to do with it. I know that the propellant mass needs to increase along with the dry mass of the rocket.
 
Last edited:

Answers and Replies

  • #2
haruspex
Science Advisor
Homework Helper
Insights Author
Gold Member
2020 Award
37,204
7,297
It's unclear whether the question posed refers to M or M+P. If M is fixed, then M+P goes up exponentially with ΔV/C. But I don't get the bit about going to infinity between 2 and 3. I've no idea where that's coming from. Is this the whole question, or is something left out?
Btw, the quoted value for e^2 is wrong. Looks like a typo.
 
  • #3
114
0
It's unclear whether the question posed refers to M or M+P. If M is fixed, then M+P goes up exponentially with ΔV/C. But I don't get the bit about going to infinity between 2 and 3. I've no idea where that's coming from. Is this the whole question, or is something left out?
Btw, the quoted value for e^2 is wrong. Looks like a typo.


I think it's the total mass of the spacecraft (M+P). I'm not entirely sure. This is from a USAD Science section study guide.
 
  • #4
haruspex
Science Advisor
Homework Helper
Insights Author
Gold Member
2020 Award
37,204
7,297
I think it's the total mass of the spacecraft (M+P). I'm not entirely sure. This is from a USAD Science section study guide.
Can you provide a link or is it behind a paywall?
 
  • #5
114
0
Can you provide a link or is it behind a paywall?

It's behind a paywall. :/
 

Related Threads on Rocket equation

Replies
1
Views
285
  • Last Post
Replies
13
Views
2K
  • Last Post
Replies
4
Views
8K
  • Last Post
Replies
9
Views
1K
  • Last Post
Replies
3
Views
1K
  • Last Post
Replies
1
Views
457
Replies
2
Views
141
Replies
0
Views
947
  • Last Post
Replies
4
Views
1K
  • Last Post
Replies
2
Views
714
Top