Calculating Huhmann Transfers

[payonel]

OOPS: Title typo, Hohmann, not Huhmann. Man, title typos are the worst!

I thought the question might have a better chance here - originally I posted on r/kerbalspaceprogram ( http://www.reddit.com/r/KerbalSpaceProgram/comments/1oxd1f/help_me_calculate_transfer/ )

I've been studying the tutorial and equations from Kosmo-not's [interplanetary How-to Guide](http://forum.kerbalspaceprogram.com/threads/16511-Tutorial-Interplanetary-How-To-Guide) but I cannot get the same answer for his first "Practice Problems".

My ejection velocity [and consequently my ejection angle] do not match.

Everything else works out fine, including the ejection angle if the ejection velocity is smudged to match.

It seems to me all you need to know to reproduce his results for just the ejection velocity is the following.

SQRT((r_1*(r_2*POWER(v_2,2)-2*μ)+2*r_2*μ)/(r_1*r_2))

where

r_1 = PARK radius (700 km)

r_2 = SOI radius (82,000 km)

v_2 = SOI exit v

// same as escape v for kerbin?, this isn't given on the site

// but the wiki says 3431.03 m/s so I used 3.43103 km/s

μ = kerbin gravity (3530 km^3/s^2)

equals

3.7909 km/s

But when I run these numbers, I get

4.67 km/s

One fake method to match his results is to use 2.09045 km/s for the SOI Exit Velocity (escape velocity)

What did I do wrong?

**PLEASE NOTE** I'm quite aware of the [interactive option](http://ksp.olex.biz/). I was doing the math as an exercise out of interest and love of science . Also, at this point in the game, I've completed many successful interplanetary missions.

Edited October 21, 2013 by payonel
use hohmann's delta v, not the escape v

[tavert]

v_2 isn't escape velocity, it's the velocity you need to have relative to the origin planet when you reach the edge of its SoI. I think you should be using what he calls delta v_1 in the equation right before.

We will need to be going that much faster than our planet of origin at the start of the Hohmann transfer. The value just calculated is the velocity we need to be at just prior to exiting the planet’s SOI.

[payonel]

EDIT: my first comment was rather negative, rewording for politeness

That is exactly it. Thank you. The equation wants the hohmann delta v. "SOI Exit Velocity" is a HORRIBLE confusing name for that. It's a delta v, not a v -- wow. Ok thank you very much. It all works out now.

Edited October 22, 2013 by payonel

[Kosmo-not]

SOI Exit Velocity is not a maneuvering burn delta-V. It is the velocity you have at the edge of the SOI. I think the name suits itself quite nicely.

[payonel]

Well hello Kosmo-not

I didn't say it is the maneuver burn delta-v, just "delta-v". I do retract part of my statement - it isn't a horrible name, it is nice rewording of what the hohmann's delta v represents. Either way, it was quite confusing as it is written. Why not just use the same naming and symbol notation of the equation just above? Using v_2 as opposed to delta_v_1 threw me way off.

[Kosmo-not]

I will look into it tonight. Thank you for your feedback.

[payonel]

I just wanted to add that the more I think about this, the more I realize that your name "SOI Exit Velocity" was quite fitting. I hadn't considered that the displayed velocity of your ship is actually your delta v of the SOI in context. Though the equation would be more obvious if the variable names were the same (e.g. delta_v_1 in both places), your description is great (though perhaps just mention in the velocity is the one just found, or is the hohmann velocity etc).

Final word: your post was fantastic and I learned a lot. Thank you.

ps: I edited my first comment to be a bit more grateful/civil for your contribution