How to calculate a DeltaV Map?

[Snafu]

Hello,

Could someone can explain how to calculte the deltaV required on a deltaV map? For exemple, We need 4500M/s to arrive on the low Kerbin Orbit. What is the method to find this number?

Thanks.

[Floule]

Welcome to the forums!

Here is a good map:

As you can see, from "Kerbin" to "Low Kerbin Orbit" there is the number 4550. Well ,that's it

[blizzy78]

In general, you just add up all the numbers from your origin up to your destination.

Be aware that some numbers may be an extreme minimum, so always pack some reserves.

[Jasmir]

Guys, he want to know how to make such a map, not how to use it...

Unfortunately, i also don't know. But i'am very interersted in that, also.

[blizzy78]

Hmm, I don't think the question made that very clear.

[Traches]

I'm no expert on the subject, but here's what I know--

Launching to orbit from atmospheric bodies is determined experimentally AFAIK.

Launching to orbit from non-atmospheric bodies would require orbital velocity at your chosen altitude, plus whatever it takes to get there. I'm not sure about the math to figure that part.

Transfers from one body to another are assumed to be hohmann transfers, explained here:

http://en.wikipedia.org/wiki/Hohmann_transfer_orbit

The map that floule linked doesn't add extra for plane changes along the way, but some of them give a "maximum plane change dV".

If you want to calculate your own dV map, I'd start by spending time reading about orbital mechanics on wikipedia.

[Commissioner Tadpole]

Welcome to the forums!

Here is a good map:

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

As you can see, from "Kerbin" to "Low Kerbin Orbit" there is the number 4550. Well ,that's it

Is that dV map really right? It says I need 14260dV to land on Laythe. So you're telling me that you need 28.520dV for a round trip to Laythe.

[blizzy78]

Is that dV map really right? It says I need 14260dV to land on Laythe.

Where do you see that number? It says it takes 2800 m/s to land on Laythe from low Laythe orbit.

Edit: Ah, I see it now, you added everything together. So, why is that not correct? The map numbers are for powered descents, not using parachutes and/or aerobrakings.

Edited January 7, 2014 by blizzy78

[Floule]

Is that dV map really right? It says I need 14260dV to land on Laythe. So you're telling me that you need 28.520dV for a round trip to Laythe.

The map is from the official wiki, so I'm pretty sure it's right.

[Commissioner Tadpole]

Where do you see that number? It says it takes 2800 m/s to land on Laythe from low Laythe orbit.

Edit: Ah, I see it now, you added everything together. So, why is that not correct? The map numbers are for powered descents, not using parachutes and/or aerobrakings.

Ah, I see. But what about dV to *return*?

[Floule]

Ah, I see. But what about dV to *return*?

I would be interested in that too! How can I calculate the dV for return, with this map?

[Rhomphaia]

Is that dV map really right? It says I need 14260dV to land on Laythe. So you're telling me that you need 28.520dV for a round trip to Laythe.

The numbers for atmospheric bodies are to take off, landing takes a lot less since the atmosphere will slow you down.

you can also shave a lot off between intercept and orbit around an atmospheric body by aero-braking. The map doesn't take these thing into account.

[capi3101]

So how does one go about calculating the numbers to place on the map? I assume that NASA had some notion of the delta-V requirements to make a full trip from Earth to the Moon, or to make a trip to LEO. Hell, I imagine the Soviets had some notion of what they needed for Sputnik I...

Seriously, does anybody know the methodology involved? I'm with the OP - I'd like to know how it's done.

[Kasuha]

First you decide which points you want to have in your map. Surface, low orbit, SOI boundary ("intercept") etc. Then you calculate dv needed for optimal transfer between each two points for which you want to have a line in the map.

[sciguyCO]

Here's a delta-V map I use from reddit, and in the comment thread the poster goes over the methods used to get the numbers.

From my understanding, when you ignore atmospheric drag, the launch number is basically just a hohman transfer from zero height to orbital radius, plus circularization, plus what "orbital speed" is at height 0, minus the rotational speed of the body.

So for the Mun, a transfer from radius 200,000 (Mun's radius) to 210,000 ("low orbit" on that map is defined as height where you get 50x time accelleration) is about 10 m/s. Circularization is another 9 m/s. Orbital speed at 200,000 is 571 m/s. Rotational speed is 9 m/s. 10 + 9 + 571 - 9 =~ 580 m/s delta-V required to launch from the moon and settle into a 10km orbit.

Numbers are from a spreadsheet I put together to use KSP body information and the equations from here

Similar methods were used to get the escape numbers (transfer orbit from start to edge of SOI) and interplanetary transfers.

When launching through an atmosphere, there's drag to take into account, which requires more delta-V. I'm guessing this has to be done experimentally. It might be possible to figure out with KSP's simplified drag model.

[capi3101]

Then you calculate dv needed for optimal transfer between each two points for which you want to have a line in the map.

And you do that.........how? I'm not trying to be smart; I genuinely would like to know how to do this.

Let's go with the demo. Kerbin, Mün, Kerbol. On my map, I want:

a) delta-V required to make Kerbin orbit

delta-V required to transfer to the Mün

c) delta-V required for Münar orbital insertion at 14 kilometers

d) delta-V required to land on Mün.

Now, I assuming the Hohmann Transfer and Orbital Velocity equations in the wiki's Advanced Rocket Design tutorial have something to do with this, and so what you would need is the distance between the two bodies, the radii and their respective gravitational parameters. Some other factor is involved with Kerbin launch though (the atmosphere, I'd wager), which is why it takes ~4550 to make orbit instead of ~2250.

Is that even remotely close to being correct? Can anyone walk me through the calculations?

[Jean Deaux]

Don't expect these numbers to be spot on either, I think those numbers are for "perfect maneuvers" for every move of the trip. For example, I planned a trip with well over double the dV required for the trip in plans of returning, and I didn't have enough fuel to even make orbit. Piloting would seem to also play a major play in the number crunch.

[regex]

Some other factor is involved with Kerbin launch though (the atmosphere, I'd wager), which is why it takes ~4550 to make orbit instead of ~2250.

Yep, it's the pea soup dragging you down. First line item here also applies to KSP. The rest of the calculations depend on a combination of required orbital speed for a given altitude, and drag (if applicable) and gravity losses on the way up/down. I'm not sure how to handle gravity and drag losses... For transfers to other planets, you would calculate the optimum Hohmann transfer delta-V, which ends up being pretty optimistic given that they are optimum rather than average. Therefore, a delta-V map can really only give you values for the best possible transfer (as stated above).

You might also take into account escape velocity for a body in order to get the little delta-V steps that aren't readily apparent.

In truth, though, I've never bothered delving into the equations myself, so take them with a grain of salt.

[Jasmir]

Ok, i've read a little abut it, and try something out in KSP.

First Point: The map that Floule has show above, seems to be a -more or less- rough estimation of the needed dV-Requirements for launching/landing. The dV-requirements for transfers between Body-Orbits seems to be calculated using formulars like http://en.wikipedia.org/wiki/Hohmann_transfer_orbit#Calculation. But: These seems not include the dV, that is needed for plane changes. In case of Moho, thats a lot dV that is missing in this chart.

@Commissioner Tadpole: The dV needed for return is the same as getting to the destination.

[capi3101]

Still can't find the original posting of the new delta-V map, so I'll put it up on my imgur. If the original creator will let me know where it is, I'll take my copy down and replace it with the proper attribution/link. Meantime:

Note that this one has the plane change delta-Vs.

@Regex: haven't had time to review your post yet; I'll probably have questions when I do.

There's probably some substantial rounding going on...I calculated the ten kilometer orbital velocity for Mün at 556.94 m/s; that could be rounded up to 560 easily. Precision isn't exactly required for a delta-V map; it is just a planning tool after all.

Of course, it says 580. So I wonder what's up with that.

Edited January 7, 2014 by capi3101

[regex]

In case of Moho, thats a lot dV that is missing in this chart.

It's not as much as you think. The chart there says 3880m/s to get to Moho orbit from LKO, the best transfer I can find from Alex Moon's tool is 4066m/s. Of course, the chart won't help you with higher-energy transfers (Moho transfers vary quite a bit), but it's mostly accurate for the best case scenario.

[Kasuha]

Alexmoon's planner does not calculate optimal trajectories and minimum dv needed. It calculates optimal solutions only for the class of maneuvers it supports and minimum dv only in the window for which it looks for solution.

[regex]

Alexmoon's planner does not calculate optimal trajectories and minimum dv needed. It calculates optimal solutions only for the class of maneuvers it supports and minimum dv only in the window for which it looks for solution.

And? It's a better tool for planning than a delta-V map since the map doesn't tell you what sort of maneuver is needed for that optimal transfer or when to do the burn(s). A map is good for best case estimation, and that's about it. In the end, though, if you really want to plan correctly you do the math yourself.

[sciguyCO]

And you do that.........how? I'm not trying to be smart; I genuinely would like to know how to do this.

Let's go with the demo. Kerbin, Mün, Kerbol. On my map, I want:

a) delta-V required to make Kerbin orbit

delta-V required to transfer to the Mün

c) delta-V required for Münar orbital insertion at 14 kilometers

d) delta-V required to land on Mün.

Now, I assuming the Hohmann Transfer and Orbital Velocity equations in the wiki's Advanced Rocket Design tutorial have something to do with this, and so what you would need is the distance between the two bodies, the radii and their respective gravitational parameters. Some other factor is involved with Kerbin launch though (the atmosphere, I'd wager), which is why it takes ~4550 to make orbit instead of ~2250.

Is that even remotely close to being correct? Can anyone walk me through the calculations?

Let's take those in reverse order:

d) delta-V required to land on Mün.

To land on the Mun from 14km requires basically the sum of two maneuvers:

1) Hohmann transfer from 214 km orbit to 200km (where 200km is the radius of the Mun)

2) Zeroing out horizontal surface speed at periapsis to come to rest.

#1 can be calculated from the "delta V1" equation in the Calculating Transfer Maneuvers section of the KSP wiki page you linked to. Since you're orbiting the Mun, you use its gravitational parameter (6.51x10^10). r1 will be 14,000 m, r2 will be 0 m, and R will be 200,000m. This works out to just over 9 m/s.

#2 will be your "orbital" speed at periapsis with a 200 x 214km orbit plus or minus the Mun's rotational speed of 9 m/s. Orbital speed is sqrt(mu * (2/a - 1/r) ). In that equation, "mu" is the gravitational parameter of the Mun, "a" is the semi-major axis (PE + AP)/2 and "r" is the current radius (PE in this example).

That works out to 580 m/s. If your ship is coming down west-to-east (counterclockwise orbit), the 9 m/s rotational speed of the Mun is subtracted to get the delta-V required; since you're going in the same direction, you have to decelerate less to "match" it. Coming the other direction would require adding the rotational speed.

In the case of the Mun (and that orbit height), the rotational speed matches the de-orbit delta-V pretty closely, hence the "580" on that first map.

As an important note, this gives you the minimum delta-V for a landing. We can't do instantaneous velocity changes, and surface variability means that we can't come in perfectly horizontal at PE. You can get a little closer to these numbers at launch (which is basically a landing in reverse). At launch you don't have the "oh god the ground is coming at me!" factor which always causes me to brake too soon / often, adding to gravity drag.

c) delta-V required for Münar orbital insertion at 14 kilometers

Um, after a bunch of typing / editing, I don't think I understand this leg enough to explain it. From the Mun's frame of reference, you're on a parabolic orbit that you need to circularize, there's gravitational acceleration going on that I'm messing up somewhere, and you're entering the SOI with some relative speed that I'm not accounting for right when I try to work it out. Let's move on...

delta-V required to transfer to the Mün

Simple Hohmann transfer from 700km orbit to 12,000km orbit (both numbers include Kerbin's radius, PE reported in game will be 100km, AP will be 11,400km). Since this is done within Kerbin's SOI, you use its gravitational parameter in the equation.

a) delta-V required to make Kerbin orbit

Ok, you know how I said a launch is a reversed landing? Let's start from there and ignore atmospheric drag. The maneuvers this time (starting at the launch pad moving at 174m/s east relative to Kerbin's center)

1) Go from 174m/s to the PE speed of a 600 x 680km orbit (where 600km is the radius of Kerbin)

2) Circularization burn at AP to go from 600 x 680 km orbit to 680 x 680 km

The speed at PE for a 600x680 orbit around Kerbin is 2501 m/s, so you need to gain 2501 - 174 = 2327 m/s horizontal. The circularization delta-V works out to be about 73 for a total of about 2400 m/s. That's obviously way lower than you see during real launches because (1) That calculation assumes you've already gained the horizontal speed in step #1 and (2) drag.

The atmospheric drag (plus some buffer) adds the extra 1100 m/s requirement to get to the magic 4500 number needed to get to space. There really isn't any way to calculate this from other constants, since it depends on things like TWR (which determines how long you stay in atmosphere), timing of your gravity turn (turning sooner = more time in atmosphere = more drag), throttle management (pushing past terminal velocity increases drag) and probably size of your craft (since KSP calculates total drag by summing up each part).

[Kasuha]

And?

And nothing. I was just providing more detailed explanation why it shows higher values than what are in delta-v maps.

[JDobs]

The dV numbers are calculated using the vis-viva equation. http://en.wikipedia.org/wiki/Vis-viva_equation

You plug in the values of the equation to find the required change in velocity to alter your orbit parameters to meet the other body.