Back of envelope calculations for thurst, specific impulse, etc.

In summary, for determining the amount of thrust, power, and specific impulse needed to travel a distance of 630 million kilometers in space with a payload of 2000 kg and a desired journey time of 1 year, there are various factors to consider such as gravity, speed, and escape velocity. The simplest case involves accelerating to full speed quickly, coasting for a year, and then decelerating, while the lowest energy case involves a constant acceleration for 6 months followed by deceleration. Using the formula s = ut + 0.5 at^2 and the given values, a constant force of 2mN would be sufficient. The power required for the journey would be determined by the equation mass*acceleration
  • #1
engineer23
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"Back of envelope calculations" for thurst, specific impulse, etc.

I am working on a project that is really out of my realm of experience, so if you could give me some basics, that would be much appreciated.
How do you determine the amount of thrust, power, etc. needed to travel a distance of 630 million kilometers in space? What if the payload is 2000 kg and I want the journey to take 1 year? Don't worry about trajectories and orbital mechanics...I just want a simple calculation. The thrust calculations I am familiar with are those in which the thrust is the force necessary to overcome drag, but I'm assuming there's a more general form? How do I get the specific impulse? Power?
Suppose I'm launching from high Earth orbit as well. I guess I need escape velocity for HEO?
I really have no experience with propulsion, but I just need some ballpark figures to base a design on.
 
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  • #2
Really it all depends on the gravity, if you not near any bodies and not in orbit then it depends on how fast you want to go - and what speed you want to be doing when you get there.

Simplest case would be to accelerate the 2000kg to full speed quickly, coast for a year and then spend a similairly negligible time slowing down.
Lowest energy case would be to accelerate constantly for 6months, then turn around and decellerate at the same rate for 6 months.

s = ut + 0.5 at^2
s = 630e9 m, t = 32e6 sec
a = 2 s/ t^2 = 1.2 e-6 m/s^2
So a constant force of 2mN would do it.
 
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  • #3
Thanks!
What is the power required for the journey then? Is it just mass*acceleration*distance/time?
 
  • #4
Or you could use ke at the midpoint divided by the time to midpoint.
 

1. What are back of envelope calculations?

Back of envelope calculations refer to quick, rough estimations made using basic mathematical formulas and assumptions. They are often used in scientific or engineering fields as a first approximation or to gain a general understanding of a problem.

2. What is the purpose of back of envelope calculations for thrust?

The purpose of back of envelope calculations for thrust is to estimate the amount of force or push generated by a rocket or other propulsion system. This can be useful in the early stages of design or when evaluating the potential performance of a system.

3. How accurate are back of envelope calculations for specific impulse?

Back of envelope calculations for specific impulse are not very accurate, as they are based on simplified assumptions and do not take into account various factors that can affect specific impulse, such as atmospheric conditions or engine design. These calculations should only be used as a rough estimate and not relied upon for precise values.

4. What information is needed to perform back of envelope calculations for thrust and specific impulse?

To perform back of envelope calculations for thrust and specific impulse, you will typically need to know the mass flow rate of the propellant, the velocity of the exhaust gases, and the mass of the rocket or vehicle. Other factors such as atmospheric conditions and engine design may also be necessary for more accurate calculations.

5. Can back of envelope calculations be used for complex propulsion systems?

Back of envelope calculations are not suitable for complex propulsion systems, as they do not take into account the many variables and complexities involved. These calculations are best suited for simple systems or as a starting point for more detailed analysis and calculations.

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