Orbital dV calculator?

[beardysi]

Firstly, i'm not one for advanced maths, I'm sure the answer to this question could be worked out with a pen and paper but that's somewhat beyond me!

Is there an app or addon or anything what give you figures for the dV costs of landing on or launching from various bodies, and also orbital velocities at a particular altitude?

For instance, I'm planning a lander which will land from a 50km orbit of Minimus and be able to launch back into the same orbit, along with that it will need to have enough dV to alter it's orbital inclination by up to 90degrees and back again - basically it's intended to be able to land anywhere on the moon from orbit and then launch and rendez-vous with an orbiting ship where it will refuel and set off again...

I know I could do it by trial and error with a bit of fudge factor and some Kerbal gaffa tape, but I'd like to know how to come up with the proper number (as long as it doesn't involve calculus!)

Edited February 26, 2014 by beardysi

[allmappedout]

Unfortunately, it does involve calculus to calculate both the ship's dV budget, but, there are a number of mods out there, (Mechjeb, Kerbal Engineer, VOID (I think?)), which should do all the background calculations for you.

In terms of the dV requirements, again, this requires some maths to work out, but there are deltaV maps which give you very good ballpark figures to work with in terms of launch, orbit, transfer, etc. which hopefully people better than me (ie: not filtered by work firewalls!) will be able to post below.

[blizzy78]

For getting into orbit, landing, and transfers to other bodies you can consult the various delta-v maps around, for example this excellent one.

[Red Iron Crown]

Unfortunately, it does involve calculus to calculate both the ship's dV budget, but, there are a number of mods out there, (Mechjeb, Kerbal Engineer, VOID (I think?)), which should do all the background calculations for you.

No calculus required to calculate delta-V of a craft, just a bit of algebra. It is tedious, though, which is why I use the mods you mention.

[JTDismang]

I would recommend Kerbal Engineer Redux, that along with this Delta V map will do wonders on ship planning.

http://wiki.kerbalspaceprogram.com/w/images/7/73/KerbinDeltaVMap.png

So according to the chart you would need the basic 4550 dV to achieve orbit around Kerbin, 920 dV to intercept Minmus, 80 dV to get a 10km orbit around Minmus, and 240 dV to land. The map also works in reverse so 240 to take off 80 to achieve 10km orbit etc etc, with the exception of "landing" on planets with atmospheres since aerobreaking and chutes can be used. Assuming all of your maneuvers are optimal this is the amount of dV you will need, but there are times where course corrections are needed so always pack a little extra so you don't end up stranded. As you mentioned you want to land from a 50km orbit it wont really save you dV it will end up being close to the dV maps estimations if not a little more, the fuel you saved achieving a higher orbit will be spent on landing so it doesn't really save any dV.

Here is another helpful tool I use http://ksp.olex.biz/

[capi3101]

KER is awesome. There's also another mod that would automatically set up your existing command pods to use KER without having to add parts, so its something that could be applied in the event that you're talking about a craft that's already up and running.

As for delta-V maps, I recommend blizzy78's over JTDismangs; blizzy's map is newer and more complete (including data such as delta-V for plane changes).

Now, as far as a 50k orbit of Minmus to landing is concerned, you need only to calculate the orbital velocity at that height - dependent on this formula:

V = sqrt(mu/R), where V is the orbital velocity, sqrt is "square root", mu is the Gravitational Parameter - the Gravitational Constant (6.67 *10^-11) times the body's mass (information already calculated for you on the wiki), and R is the radius from the center of the body.

So we go to the wiki: Minmus's mu is 1.7658*10⁹ m³/s² and its radius is 60,000 m. We're wanting a 50 kilometer orbit, so R in this case is 110,000 (60,000+50,000)

Now we just plug in the numbers:

V = sqrt (1.7658*10⁹ / 110,000) = sqrt(16052.727 m²/s²) = 126.699 m/s

Your velocity when you've landed is zero, of course. So optimally, you'll need 126.699 m/s of delta-V to complete the manever.

Naturally it'll take a bit more than that if your piloting is not up to snuff, but you can make plans for it.

[Red Iron Crown]

Don't forget that Minmus is rotating, so your orbital velocity when landed is not zero. It will take a bit less dV to achieve the desired orbit if you launch in the direction of rotation, a bit more dV if you launch opposite the direction of rotation.

[beardysi]

Cheers for that folks, seems the maths is less daunting than I'd feared! I reckon I can manage that

I was just going to build a dirty great fuelling station which would have met all my needs (and then some) but I just couldn't lift the bugger up at my current stage in the tech tree... Rather than going for the overkill I'll consider my needs and plan appropriately!

[JTDismang]

After looking at the map blizzy posted I agree.

[capi3101]

<snip />but I just couldn't lift the bugger up at my current stage in the tech tree... Rather than going for the overkill I'll consider my needs and plan appropriately!

Where exactly are you at in the tech tree?

Here's a trick: You can build a Mainsail equivalent from 6xLV-T30s, 1xLV-T45 and Modular Girder Adapters (Starting Tech). This configuration will result in more parts and more mass, but will give you comparable thrust and have a higher Isp; change it up to eight LV-T30s and you'll have greater thrust than a Mainsail (1920 kN). Set the girders parallel to the sides of a large tank (X200-8, X200-16 or X200-32 depending on what you've got available), stick the LV-T30s on the bottom and the LV-T45 centerline. The Girders allow fuel flow. Slap two X200-8s on top of one another, put another six radially around them, run fuel lines to the center from the outboard tanks and put the faux Mainsail engine configuration on them, and you've got the equivalent of an orange tank/Mainsail. All you need for that to work is Fuel Systems, picking up General Construction and General Rocketry along the way (no more than 160 Science points total from the start of your career game).

Edited February 25, 2014 by capi3101

[Padishar]

Now, as far as a 50k orbit of Minmus to landing is concerned, you need only to calculate the orbital velocity at that height - dependent on this formula:

V = sqrt(mu/R), where V is the orbital velocity, sqrt is "square root", mu is the Gravitational Parameter - the Gravitational Constant (6.67 *10^-11) times the body's mass (information already calculated for you on the wiki), and R is the radius from the center of the body.

So we go to the wiki: Minmus's mu is 1.7658*10⁹ m³/s² and its radius is 60,000 m. We're wanting a 50 kilometer orbit, so R in this case is 110,000 (60,000+50,000)

Now we just plug in the numbers:

V = sqrt (1.7658*10⁹ / 110,000) = sqrt(16052.727 m²/s²) = 126.699 m/s

Your velocity when you've landed is zero, of course. So optimally, you'll need 126.699 m/s of delta-V to complete the manever.

This doesn't allow for the velocity you gain as you descend (your gravitational potential energy is converted to kinetic energy). You would need 126.7m/s to "stop" in your orbit but that still leaves you 50km above the ground. If you then fall vertically to the ground you will be going at a substantial speed and will need that much extra deltaV to actually land. This is why your number has come out way too low.

I believe that for the theoretical best landing from a circular orbit you need to lower your periapsis to 0 by burning retrograde at apoapsis and then stop all your orbital speed when you are at periapsis. So, you need to be able to calculate the burn required to drop your periapsis from 50km to 0km (this is just half of a hohmann transfer so the equations are explained in lots of places) and then add the orbital speed at the surface (this needs a different equation to the above as the orbit is not circular, you will be going faster then you would for a circular 0km orbit, but it basically amounts to the other half of the hohmann transfer and then killing your circular orbit speed of 171.5m/s) . This will come out to a value much closer to the values given in the deltaV maps.

In practice the actual value you will need to land is quite a bit higher than this as your burns will not be instantaneous and you generally burn more to come in at a steeper angle (otherwise mountains can ruin your day real quick) meaning you are still descending quite quickly when approaching the surface...

Edited February 25, 2014 by Padishar

[beardysi]

Interesting.... Have always been a big fan of cluster motors but as yet I don't seem to have the little girder cubes needed to make them. Hadn't though of using the bigger girder segments on the sides of a large tank! Must give it a shot later on!

[capi3101]

Follow Padishar's line of thought with the delta-V; he's absolutely correct.

[PlonioFludrasco]

Maybe little OT, but I suggest to put your refueling ship in a low minmus orbit (around 20 km), for the simple reason that your lander needs less delta v to land from 20 km orbit than to 50 km orbit and back.

That means that your lander could be smaller and carrying less fuel, so you can fly more missions before your refueler runs out of fuel.

Edited February 25, 2014 by PlonioFludrasco

[beardysi]

Cheers folks, the 50km orbit was just a figure pulled out of the air, I agree, 20km is more than sufficient for Mimimus!

Turns out it's all a little academic as the smallest lander I built to meet the mission spec holds enough fuel for about three round trips and it's light as a feather to boot!

[Kryxal]

I like just over 30 km on Minimus, it gives lots of space to sit in a "catch-up" orbit and is just above a time-warp boundary.