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In the Analytical Graphics Inc. video Low-Thrust Space Trajectory Design and Optimization the speaker Pradipto Ghosh of AGI shows a slide at around 07:00 shown below.

On it there is a plot with the vertical axis labeled $\Delta u / v_c$ and the horizontal axis labeled $v/v_c$.

What do the variables used in these axis labels represent?

Any other explanation of how the plot should be interpreted or used is appreciated!


enter image description here

enter image description here

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  • $\begingroup$ @Paul Thanks! I wonder if that's almost a complete answer, and worth posting as such? These are normalized with respect to $v_c$, if you can find out what $v_c$ is then you're probably good to go! $\endgroup$ – uhoh Apr 2 at 4:33
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The caption in the book (Sutton) reads:

Normalized vehicle velocity increment as a function of normalized exhaust velocity for various payload fractions with negligible inert mass of propellant tanks. The optima of each curve are connected by a line that represents Eq. 17–9.

The text reads:

For a given mission, theoretically there is an optimum range of specific impulse that maximizes $\Delta u / v_c$ and thus a most favorable propulsion system design.

...This characteristic speed ($v_c$) does not represent a physical quantity but rather a grouping of parameters that has units of speed; it can be thought of as the speed a power plant’s inert mass $m_{pp}$ would attain if its full power output were converted into kinetic energy.

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