A Kerbal Nomogram (2)

[nyrath]

A Kerbal Nomogram

What's a nomogram? It is an obsolete calculating device about the same vintage as a slide rule. You do not see them much anymore because I wasn't kidding about them being obsolete. But educators on a budget might find this useful. Or not.

It is printed piece of paper optimized to do one single mathematical calculation. It is a series of printed scale that you place a ruler or other straightedge over to solve the equation. Download this and print it out. And if you spot any mistakes, let me know so I can fix them.

https://copy.com/bpqGFdh6XxUH

This particular nomogram solves the delta-V equation: dv = Ve ln®

That is, there are three variables: delta-V, Isp (or exhaust velocity), and mass ratio (or fuel percentage). Given any two variable, the nomogram will tell you the value of the third.

Example: Say your spacecraft has engines with a specific impulse (Isp) of 320 seconds. You want to do an orbital transfer from Kerbin to Dres (1,300 meters per second). Place the nomogram on the table. Lay a ruler over it so that on the Specific Impulse scale (the one on the left) it crosses the 320 second mark. Pivot the ruler so that it simultaneously crosses the Delta V scale (the one in the middle) at the 1,300 mark (labeled "Kerbin-Dres xfer 1,300 m/s). Look at where the ruler crosses the Mass Ratio scale (the one on the right), and you will see it does so at Mass Ratio 1.51 (a tad less than 34% fuel).

Now, there is one application where a nomogram has an advantage over a calculator. It allows you to visualize a range of solution. If the mission is an orbital transfer from Kerbin to Dres, you can place the ruler on the 1,300 m/s mark on the Delta V scale, and pivot it there. This allows you to see how changing the specific impulse of the engine affects the propellant fraction, and vice versa.

Remember that exhaust velocity equals specific impulse times 9.81, and propellant fraction = 1 - (1 / massRatio)

[lajoswinkler]

Nomograms aren't obsolete. They're routinely used for at least fast approximations during lab or field work in science.

Thanks for this, it looks very useful.

[Pondafarr]

Cool stuff! Thanks Nyrath!

[Tommygun]

This could be useful in the VAB when planning out a craft.