A Kerbal Nomogram

[nyrath]

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.

http://ubuntuone.com/1kD39BCoV38WP1QeG6MtO6 version 1.1

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)

Edited May 7, 2013 by nyrath

[Shrike42]

I don't know if there are any mistakes, but I really like what you're going for here. It provides an excellent visualization of numbers that casual players can use to improve their chances of success.

[nyrath]

Well, the main thing is I'm not sure the delta-V values for the various missions is correct.

The chart was plotted by a Python program I wrote using nomograph theory.

http://www.projectrho.com/nomogram/index.html

[maltesh]

You list Eve Liftoff/Land at 1,200 m/s delta-v. That's very high for landing (because the atmosphere will do a lot of slowing for you) and very low for liftoff (because the atmosphere will do a lot of slowing against you). Eve also has the highest planetary surface gravity in the game.

[nyrath]

You list Eve Liftoff/Land at 1,200 m/s delta-v. That's very high for landing (because the atmosphere will do a lot of slowing for you) and very low for liftoff (because the atmosphere will do a lot of slowing against you). Eve also has the highest planetary surface gravity in the game.

Yes, aerobraking is a problem. What would you specify as average values for liftoff and landing?

[EndlessWaves]

Yeah, Eve is around 10.5km/s for takeoff from sea level. For stopping in atmosphere, it's not much more than the amount you need to stop from terminal velocity so tends to be ~150m/s for kerbin.

It's also not at all clear what the mass ratio is refering to, is that the average ratio across the whole burn or the amount that would be required in a single stage? Neither seem to particularly match up.

[CalculusWarrior]

That's a great idea! It gives a great way of seeing how much delta-v you'll need. My only suggestion is to maybe remove some of the massively huge exhaust velocities/delta-v on the upper edge of the chart, as I don't think they're super necessary for the average player, as the nuclear engine makes it only halfway up the scale. Of course, I have no idea how you calculated this, so I don't know if you're able to chop off half of the chart and scale it.

I also don't think that Eve requires only 1.2 km/s to take off, I believe it's harder to take off from than Kerbin. I don't know specific delta-v values, but I would think that it would be pretty high, around 10 km/s?

One last suggestion, maybe colour-code the values? Maybe have different colours for different planetary systems? i.e. Purple for Eve and Gilly, blue for Kerbin, Mun, & Minmus, etc.

Regardless, I think this is a fantastic map, and it gives a good benchmark to aim for when designing rockets!

[nyrath]

Yeah, Eve is around 10.5km/s for takeoff from sea level. For stopping in atmosphere, it's not much more than the amount you need to stop from terminal velocity so tends to be ~150m/s for kerbin.

It's also not at all clear what the mass ratio is refering to, is that the average ratio across the whole burn or the amount that would be required in a single stage? Neither seem to particularly match up.

The way I understand it the mass ratio is the effective starting mass ratio, with effective meaning with multi-staging taken into account and starting meaning at the start of the burn.

I made honorable mistake in the case of Eve. The source I was using said liftoff/landing was 12000 m/s, I programmed it as 1200 m/s. My mistake.

That's a great idea! It gives a great way of seeing how much delta-v you'll need. My only suggestion is to maybe remove some of the massively huge exhaust velocities/delta-v on the upper edge of the chart, as I don't think they're super necessary for the average player, as the nuclear engine makes it only halfway up the scale. Of course, I have no idea how you calculated this, so I don't know if you're able to chop off half of the chart and scale it.

I also don't think that Eve requires only 1.2 km/s to take off, I believe it's harder to take off from than Kerbin. I don't know specific delta-v values, but I would think that it would be pretty high, around 10 km/s?

One last suggestion, maybe colour-code the values? Maybe have different colours for different planetary systems? i.e. Purple for Eve and Gilly, blue for Kerbin, Mun, & Minmus, etc.

Regardless, I think this is a fantastic map, and it gives a good benchmark to aim for when designing rockets!

The main reason for the massively huge values at the top of the Isp chart is so I could add the Ion drive (Isp 4200 seconds, exhaust velocity 41,200 m/s). The main reason for the massively huge values at the top of the delta V chart is because I thought it would be cute to list the liftoff/landing value for Jool, not that anybody could actually do that.

The main problem I have with the delta V chart is where exactly do I chop it off? You can use this chart for a "grand tour" mission, where you would add up the required delta V for each segment of the mission, and see if the spacecraft had enough delta V to do the entire mission. Right now the delta V chart is chopped of roughly at the point where the Ion drive isp is connected to a mass ratio of 10.

For that matter, what is the logical place to chop off the mass ratio scale? Keeping in mind that multi-staging can make the effective mass ratio pretty large.

I could color-code the values, but of course that makes it harder to print out. I was thinking about the poor elementary science teacher with no budget.

Thoughts?

[Specialist290]

Nicely done!

Any plans for interplanetary transfer "porkchop plots" in the near future? I know someone else was talking about an interactive program that could generate some on the forums before the Forum Kraken came through, but it doesn't seem to have made much progress lately.

[nyrath]

Any plans for interplanetary transfer "porkchop plots" in the near future? I know someone else was talking about an interactive program that could generate some on the forums before the Forum Kraken came through, but it doesn't seem to have made much progress lately.

That would be nice but it is a task way above my pay grade. It would make mission planning so much easier.

[Scoundrel]

Nicely done, even with the Eve miscalculation (how very Kerbal!). I like these sorts of old-fashioned tools because I can leave them around and fool people into thinking I'm really smart. Also they're useful. Again, well done.

[nyrath]

Thanks, Scoundrel!

I've uploaded a new version that fixes the Eve miscalculation, go back to the first post.

[kahlzun]

Link just takes me to an about:blank page..

[ethg242]

Just so you know, the link has broke because Ubuntu One has been shut down. If it's not too much trouble, I think many of us would love to see this re-hosted somewhere so we could take a look. Thanks!

[Vanamonde]

Yes, this thread is quite old and the information in it no longer seems valid. Thread closed to prevent confusion.