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Help is needed from experienced pilots about calculating orbital inclination before launch.

Question

Hello, kind sirs and ladies. Does anybody know of any way to launch your vessel into orbit in a pre-calculated, non equitorial, non polar orbit?

You see, I'm running Real Solas System, but the reason I chose not to submit this topic into the mods' discussions, is because this question is one about the technicals of ksp.

The problem is, the moon in the RSS setup is rotating in a highly inclined orbit. So, to reach it, the most efficient way is to launch into an inclined orbit to begin with. Thus, here's the question: Is there any way for me to pre-calculate the inclination of the orbit I'm gonna launch into, without randomly pointing towards different directions during ascend and watching what the orbit is doing?

Any help or advice is strongly appreciated.

Cheers!

Edited by TheMonkeytect

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Well I'll call members from the Real Space Program who works on these calculations. @Dman979 @Mad Rocket Scientist .

My personal suggestion is to wait for the moon to pass directly overhead the KSC and launch towards it. Lots of extra DV to go direct, but it works :/ .

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Unlike what many people say, launching straight up takes very little, if any, extra DV -- so that solution works well, if you can wait until KSC and the moon are both at a node. If you don't want to wait that long, you can just wait until the node, which happens twice a day. If the moon's orbit is inclined 10 degrees from Kerbin's equator, then you aim your heading to either 80 degrees or 100 degrees, depending on whether it's a descending or ascending node. This should put you into an LKO orbit with the proper inclination for a transfer.

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1. Get KER
2. Send a probe in LEO with a lot of dV in the approximate inclination of the Moon (use KER's relative inclination readout under Rendez-vous for that)
3. Adjust inclination of the probe until it is perfectly aligned with the Moon
4. Now, to get to the Moon, wait until your launch site is perfectly under your probe's orbit, and launch your rocket.
5. If you keep relative inclination minimal during ascent, you should achieve orbit with an orbit aligned with the Moon's
6. Place a node, and burn for the Moon

Now, if you don't know how to launch a rocket in a rough defined inclination in the first place, I suggest you train in the stock system which is a lot more forgiving than RSS in terms of dV costs (for orbits and inclination changes).
Put a probe in a random inclination in Kerbin orbit, and with another rocket, try to follow the direction of the target marker to get in a similarly inclined orbit.
You should be able to match inclinations pretty well in a few launches.

Note that if your launch site is past the 28th parallel (I think) N or S, this doesn't work and you can't match inclination in a single burn launch (not without changing direction in the middle of the ascent).

Though I'm not really sure what you mean by "pre-calculate", could you explain what you exactly want to do ?

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@Gaarst has the major gist of it. I've found it very useful to park three probes in lowish orbit around Earth for aiding in launching into inclinations: one in equatorial, one in the same plane as the Moon, and one in the plane of the ecliptic. Then I just wait for the desired probe's orbit to be directly over the launch site and launch directly into that plane. There's not really any calculation necessary.

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1 minute ago, Red Iron Crown said:

@Gaarst has the major gist of it. I've found it very useful to park three probes in lowish orbit around Earth for aiding in launching into inclinations: one in equatorial, one in the same plane as the Moon, and one in the plane of the ecliptic. Then I just wait for the desired probe's orbit to be directly over the launch site and launch directly into that plane. There's not really any calculation necessary.

^ This.

The first (or zeroth) mission of any of my Moon/interplanetary program is to put a probe in LEO with the inclination required for the mission (lunar orbit or ecliptic) to know when and in what direction to launch.

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1 hour ago, bewing said:

Unlike what many people say, launching straight up takes very little, if any, extra DV -- so that solution works well, if you can wait until KSC and the moon are both at a node. If you don't want to wait that long, you can just wait until the node, which happens twice a day. If the moon's orbit is inclined 10 degrees from Kerbin's equator, then you aim your heading to either 80 degrees or 100 degrees, depending on whether it's a descending or ascending node. This should put you into an LKO orbit with the proper inclination for a transfer.

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This is actually fairly trivial bit of trig to figure this out.

You probably know how long it takes to get into orbit... so if it takes 5 minutes to get there, then you want to launch a little less than 5 minutes before the launch site passes under the orbital plane you're trying to get into.

Next, you need the orbital velocity you need to reach. I don't know about RSS, but whatever that Vo is... have it handy. You also need the ground speed of the planet... (check orbital speed on navball when you're still on the ground if in doubt)

From the equator, you'll want an initial heading near the inclination of your orbit, N or S from 090. So if your inclination is 20 degrees, you'll want to be looking at heading towards 070, or 110. But then you need to be looking a little further west to neutralize the ground speed... and that's where the trig comes in. It's actually easiest to draw it out. But basically, if you had 3000m/s for Vo, and 300 m/s for ground speed, you'll be looking at up to around 6 degrees further (for polar orbits)... so 064 or 116... probably more like 068 and 118... but whatever.

If you have a launch site at a different lattiude, the main differences is that you won't need to steer as severely to get into the orbital inclination... ie if you were at 20N Lat and wanted a 20 degree inclination, you'd have to launch at 090! And the ground speed will be less, the further north you go.

This is an older video using stock, but the principle and math is the same... around the 5 minute mark, it'll take you through step by step.

If you really don't want to do the math... you can simply launch and set your gravity turn a couple degrees west of your inclination heading, and watch the orbital prograde marker on your navball. When it's on the right heading (070 for a 020 inclination for example, in orbit mode) then you're probably pretty close to what you need.

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3 hours ago, bewing said:

Unlike what many people say, launching straight up takes very little, if any, extra DV -- so that solution works well, if you can wait until KSC and the moon are both at a node. If you don't want to wait that long, you can just wait until the node, which happens twice a day. If the moon's orbit is inclined 10 degrees from Kerbin's equator, then you aim your heading to either 80 degrees or 100 degrees, depending on whether it's a descending or ascending node. This should put you into an LKO orbit with the proper inclination for a transfer.

By all means I encourage the OP to test this himself. If he builds reasonable rockets with typically low TWR, then he will soon see for himself how wrong this is. If he moars his boosters to Kingdom Come and back, then he will see how true it is.

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I remember using these formulas a lot in my Orbiter days to compute the launch azimuth.
Not sure how it translates to KSP + RSS though...

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I wrote a little spreadsheet just for deciding when to launch from the major launch sites in RSS to fly to Earth's Moon. It is down near the bottom of the first post in my FF for RSS thread, it's called "MoonfinderB".

This gives the details:

I haven't verified the rotation speed for the Earth in the latest version of RSS (the one for KSP 1.1.x) though the config says it is the same as the previous version so I think it is good. The Earth's rotation period changed a few times over the various versions of RSS so I put a method to check each new version on page 2 of the spreadsheet. Note the one place it doesn't always work for is Kourou since that is at a lower latitude than the Moon's inclination, but from Kourou you should just launch when it passes directly under the Moon's orbital plane. Of course then you have the trick of figuring out what launch azimuth to use...

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On 23/5/2016 at 4:20 AM, 5thHorseman said:

By all means I encourage the OP to test this himself. If he builds reasonable rockets with typically low TWR, then he will soon see for himself how wrong this is. If he moars his boosters to Kingdom Come and back, then he will see how true it is.

Yeah, even in Science mode and with SpaceY Heavy Lifters AND KW Rocketry, actually shooting for the moon is a no-go for now.

Thank you all for your time, people! I think the solution of putting a "pin" probe in LEO with the correct inclination is the best for me. I'll also check the video, to be sure I have some idea about launching in the wanted inclination.

On 23/5/2016 at 4:05 AM, purpletarget said:

you can simply launch and set your gravity turn a couple degrees west of your inclination heading, and watch the orbital prograde marker on your navball. When it's on the right heading (070 for a 020 inclination for example, in orbit mode) then you're probably pretty close to what you need.

That's the thing I've been doing and I don't like it that much

Oh, I also noticed: Launching from Australia near noon, gets you in the perfect inclination.

On 22/5/2016 at 1:21 AM, Gaarst said:

Though I'm not really sure what you mean by "pre-calculate", could you explain what you exactly want to do ?

I wanted to somehow know the best direction of the gravity turn before hitting the space bar. A "pin" probe in LEO in correct plane seems like the best solution.

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2 hours ago, TheMonkeytect said:

I wanted to somehow know the best direction of the gravity turn before hitting the space bar. A "pin" probe in LEO in correct plane seems like the best solution.

Yes, a probe is definitely very useful.

To know which direction to follow, set the probe as target, and do not follow the target marker, but draw an imaginary line passing through the target marker (or anti-target) and zenith, and this will be the heading you will have to follow.
Note that this only works if your target's orbit is directly over your launch site. (This is also a reason to set a probe in LEO: while you can directly set the Moon as a target, it is a lot easier to see when a probe's orbit is over your launch site than when the Moon's is).

Spoiler

EDIT:

2 hours ago, TheMonkeytect said:

Yeah, even in Science mode and with SpaceY Heavy Lifters AND KW Rocketry, actually shooting for the moon is a no-go for now.

If you want to get to the Moon and like SpaceY HL, you should definitely give SpaceY Expanded a try, you'll need these 7.5m parts.

Edited by Gaarst
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3 hours ago, Gaarst said:

Yes, a probe is definitely very useful.

To know which direction to follow, set the probe as target, and do not follow the target marker, but draw an imaginary line passing through the target marker (or anti-target) and zenith, and this will be the heading you will have to follow.
Note that this only works if your target's orbit is directly over your launch site. (This is also a reason to set a probe in LEO: while you can directly set the Moon as a target, it is a lot easier to see when a probe's orbit is over your launch site than when the Moon's is).

Reveal hidden contents

EDIT:

If you want to get to the Moon and like SpaceY HL, you should definitely give SpaceY Expanded a try, you'll need these 7.5m parts.

I did, I just din't mention it. I also had 7.5 m parts. No use there. I'm doing something wrong.

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You have to fly very, very clean:  There's no such thing as "plenty" of dV in RSS - though you can do the Moon with 3.75m parts if you engineer super-light and aren't opposed to assembling transfer stages/landers in LEO.

But yes - "pilot" satellites are the easiest solution to matching inclinations on launch

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To attain a particular orbit inclination from a particular launch site, what we want is a method to compute the required launch azimuth.  For instance, if we are launching from a latitude of 28.6o and we want to insert into an orbit with an inclination of 33o, then in what direction do we want to fly when coming off the launch pad?  The equations used to compute this are,

β = βI – γ

where,

sin βI  = cos i / cos L

tan γ = (Veq cos L cos βI) / (Vo – Veq cos i)

β is the launch azimuth (measured clockwise from north), i is the orbit inclination, L is the launch site latitude, Veq is the velocity of the planet’s rotation at the equator, Vo is the velocity of the space vehicle immediately after launch, βI is the inertial launch azimuth, and γ is a small correction to account for the velocity contribution due to the rotation of the planet.  When using RSS, Veq = 464.58 m/s and, for the Florida launch site, L = 28.608333o.

For example, let's say i = 33o and Vo = 7810 m/s.  Therefore, we have

βI  = arcsin[ cos(33) / cos(28.608333) ] = 72.80418o

γ = atan[ (464.58*cos(28.608333)*cos(72.80418)) / (7810–464.58*cos(33)) ] = 0.93096o

β = 72.80418 – 0.93096 = 71.87322o

Note that we can't insert into an orbit that has an inclination lower than the latitude of the launch site.  For instance, we can't insert into an orbit with an inclination of 20o from the Cape Canaveral.  If a lower inclination is required, a plane change must be executed after orbit insertion.

Also note that if we are trying to match the orbit of a particular target, we must not only match the inclination of the target, but also its longitude of ascending node.  This means that we must carefully time the launch so that we end up in the correct plane.

Edited by OhioBob
correct value of Veq
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1 hour ago, OhioBob said:

To attain a particular orbit inclination from a particular launch site, what we want is a method to compute the required launch azimuth.  For instance, if we are launching from a latitude of 28.6o and we want to insert into an orbit with an inclination of 33o, then in what direction do we want to fly when coming off the launch pad?  The equations used to compute this are,

β = βI – γ

where,

sin βI  = cos i / cos L

tan γ = (Veq cos L cos βI) / (Vo – Veq cos i)

β is the launch azimuth (measured clockwise from north), i is the orbit inclination, L is the launch site latitude, Veq is the velocity of the planet’s rotation at the equator, Vo is the velocity of the space vehicle immediately after launch, βI is the inertial launch azimuth, and γ is a small correction to account for the velocity contribution due to the rotation of the planet.  When using RSS, Veq = 464.58 m/s and, for the Florida launch site, L = 28.608333o.

For example, let's say i = 33o and Vo = 7810 m/s.  Therefore, we have

βI  = arcsin[ cos(33) / cos(28.608333) ] = 72.80418o

γ = atan[ (464.58*cos(28.608333)*cos(72.80418)) / (7810–464.58*cos(33)) ] = 0.93096o

β = 72.80418 – 0.93096 = 71.87322o

Note that we can't insert into an orbit that has an inclination lower than the latitude of the launch site.  For instance, we can't insert into an orbit with an inclination of 20o from the Cape Canaveral.  If a lower inclination is required, a plane change must be executed after orbit insertion.

Also note that if we are trying to match the orbit of a particular target, we must not only match the inclination of the target, but also its longitude of ascending node.  This means that we must carefully time the launch so that we end up in the correct plane.

Dude. I was JUST now studying for my exams, in material science university. I absolutely appreciate your time and effort in showing me these steps, but if I have to do all this, I think I'll get an indicator probe or just... you know. Launch and see

Edited by TheMonkeytect
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54 minutes ago, TheMonkeytect said:

I absolutely appreciate your time and effort in showing me these steps, but if I have to do all this, I think I'll get an indicator probe or just... you know. Launch and see

It would be pretty easy to put the formulae into a spreadsheet so that all you have is a couple input variables.  Provided you're using only one launch site, you could input orbit altitude and inclination and it would spit out the launch azimuth.

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20 hours ago, OhioBob said:

It would be pretty easy to put the formulae into a spreadsheet so that all you have is a couple input variables.  Provided you're using only one launch site, you could input orbit altitude and inclination and it would spit out the launch azimuth.

Actually, that's a lot less terrifying. Thanks!

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32 minutes ago, TheMonkeytect said:

Actually, that's a lot less terrifying. Thanks!

Just note that the equations previously given use Vo rather than orbit altitude.  If you input altitude, the value of Vo is calculated using the following:

Vo = SQRT( 3.986004418E+14 / (z + 6371000) )

where z = altitude.

Note that the above equation is for Earth in RSS.  If anybody wants to use these equations to compute launch azimuth for stock KSC, then use the following:

L = -0.096944o
Veq = 174.94 m/s
Vo = SQRT( 3.5316+12 / (z + 600000) )

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