# As liftoff proceeds, the desired inclination of your rocket equals the lattitude from which you are lifting off.

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Hi KSP colleagues,

The guideline during liftoff of a rocket is to get your spacecraft inclined to the same degree as the complement of your latitude on the planet, and also head due East.  Thus, at the Kerbin Space Center, which is on Kerbin's equator (0 degrees, of course), soon enough you want to get your rocket inclined to 90 degrees.  Hypothetically, therefore, if we were lifting off at 30 degrees North latitude (or 30 degrees South latitude, for that matter), the spacecraft should get to an inclination of 30 degrees.  And for one last example, if we were lifting off from Kerbin's North or South Pole -- obviously, highly less than desirable -- you would point your rocket ship straight up, and thus with zero=degrees inclination.

We all understand that this method takes the most advantage of Kerbin's counterclockwise rotation.  Moreover, the same principle applies on Earth, in the real world.

When I first heard this, it sounded so strikingly simple that I was skeptical.  But when I thought about the extreme case of a rocket's lifting off from the North or the South Pole, I realized that the guideline was true.

But I would please like to see proof that it is true.

Could one of you knowledgeable ISP forum readers kindly show a proof.

Stanley

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Yep, if you launch from Baikerbanur and head due east, you will end up in a 20 degree orbit because Baikerbanur is at 20 degrees latitude.

An important thing to note is that your range of inclinations get more limited as your launch site moves toward the poles. If you're at the equator, you can get into any inclination by changing your direction. If you're at Baikerbanur, you can only get into 20 degree or more orbits. Launching from the north pole, every direction is due south and you will be in a 90 degree orbit no matter what.

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You wouldn't launch your rocket "straight up" though. Inclination doesn't mean the inclination of your launch trajectory in regard to the ground, but the inclination of the resulting orbital plane to the equator.

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I think there is a misunderstanding from the OP about the orbit inclination versus the pitch angle versus the heading of the rocket during launch.

Edited by mikegarrison
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6 hours ago, mikegarrison said:

I think there is a misunderstanding from the OP about the orbit inclination versus the pitch angle versus the heading of the rocket during launch.

I guess I don't understand this, but I am always trying to learn.

Could you or someone else please be so kind as to define these three terms -- and in particular the difference among them?

Stanley

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8 hours ago, cubinator said:

Launching from the north pole, every direction is due south and you will be in a 90 degree orbit no matter what.

Just had a 'no durrr' moment.  This kind of info makes the rest of it make sense.

Tango Yankee

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9 minutes ago, MetricKerbalist said:

I guess I don't understand this, but I am always trying to learn.

Could you or someone else please be so kind as to define these three terms -- and in particular the difference among them?

Stanley

Orbital inclination - the angle of the orbital plane to the plane of the equator.

Pitch angle - the angle of the rocket with respect to the virtual horizon (to the rocket's current horizontal plane with respect to earth).

Edited by RCgothic
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Hi KSP colleagues,

13 minutes ago, RCgothic said:

Orbital inclination - the angle of the orbital plane to the plane of the equator.

Pitch angle - the angle of the rocket with respect to virtual horizon (horizontal plane tangent to earth's surface drawn through the rocket's current location).

I agree with everything that RCgothic just said.

When the rocket sits on the launch pad, its orbital inclination is actually 90 degrees.  By convention, however, rocketeers call this zero degrees, don't they?  Next, once the rocket gains some speed -- usually between about 50 m/s and 100 m/s -- you start to tip the rocket over, oh, let's say 3 degrees.  Its pitch angle then should be called 87 degrees, but by convention rocketeers call this 3 degrees.

Let's just define our terms.  When the rocket sits on the launch pad straight up, are we going to say that the pitch angle is zero degrees or 90 degrees?

Stanley

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36 minutes ago, MetricKerbalist said:

Hi KSP colleagues,

I agree with everything that RCgothic just said.

When the rocket sits on the launch pad, its orbital inclination is actually 90 degrees.  By convention, however, rocketeers call this zero degrees, don't they?  Next, once the rocket gains some speed -- usually between about 50 m/s and 100 m/s -- you start to tip the rocket over, oh, let's say 3 degrees.  Its pitch angle then should be called 87 degrees, but by convention rocketeers call this 3 degrees.

Let's just define our terms.  When the rocket sits on the launch pad straight up, are we going to say that the pitch angle is zero degrees or 90 degrees?

Stanley

If it was an airplane, we would say 90 degrees in a standard Earth reference frame, so I think I would stick to that. (I actually think it might be -90 because of the right hand rule) So when the rocket is horizontal its pitch angle would be 0 degrees.

When studying a vehicle's motion we use an Earth-fixed frame with xyz dimensions, and a body-fixed frame which is oriented along the axes of the rocket/plane/etc. The motion is determined by finding the differences in position, velocity, acceleration between these frames. Technically you can choose whatever you want for these frames, but certain frames are easier or more useful to use.

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Hi @cubinatorand everyone else,

27 minutes ago, cubinator said:

If it was an airplane, we would say 90 degrees in a standard Earth reference frame, so I think I would stick to that....  So when the rocket is horizontal its pitch angle would be 0 degrees.

When the rocket sits on the launch pad, I would also like to call its inclination 90 degrees.

However, I am a member of the National Association of Rocketry, and I know for a fact that the NAR calls it zero degrees.  For example, NAR rules state that, for a high-powered rocket, "the maximum launch angle, measured from vertical" is 20 degrees, and I am citing Section 7 of the NAR High Power Rocket Safety Code.  I myself would prefer to call it 70 degrees, and apparently so would you.

All of us rocketeers need to come to some agreement on this issue, which should be easy enough to do.

35 minutes ago, cubinator said:

I actually think it might be -90 because of the right hand rule.

Using the right-hand rule -- which makes a lot of sense -- the angle would be +90 degrees, I believe.  Right?  The tip of your thumb would be the nose of the rocket.

Stanley

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That wording from NAR always bugged me. They have to throw in the "from vertical" qualifier for it to make any sense. In general, most terms in aviation, and by extension spaceflight, originate from nautical terms...and thinking logically, 0 degrees must be when the keel is parallel with the surface of the water. There is no reason to make a reference point for a ship when it is standing on end like a skyscraper aside from "How quickly did it sink?"

Another way to think about it is 0 degrees is the human point of view. You are standing upright on the surface of the earth and your eyes are your "reference point", aimed parallel to the ground. 0 degrees is generally a "resting" reference point.

"All of us rocketeers need to come to some agreement on this issue, which should be easy enough to do. "

If you look at the FDAI's in NASA videos (basically the equivalent of the navball in Kerbal), when they are on the launchpad, the ball is solid blue indicating 90 degrees. Now this might sound elitist, but I'mma go with how NASA rolls rather than the guys who make rockets from waxed paper towel tubes.

Edited by Meecrob
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12 hours ago, cubinator said:

Yep, if you launch from Baikerbanur and head due east, you will end up in a 20 degree orbit because Baikerbanur is at 20 degrees latitude.

An important thing to note is that your range of inclinations get more limited as your launch site moves toward the poles. If you're at the equator, you can get into any inclination by changing your direction. If you're at Baikerbanur, you can only get into 20 degree or more orbits. Launching from the north pole, every direction is due south and you will be in a 90 degree orbit no matter what.

However as I read launching for an polar orbit its better to be more north. One startup launch for Alaska and Norway has tried to sell Spitsbergen as an launch site as its very far north and still accessible by ships most of the year.  Yes they want more industry there

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When discussing orbits, pitch relative to virtual horizon is more generally useful.

The KSP Navball also uses this convention.

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Hi everyone,

This is interesting.

I have a rocket on the launchpad right now, and I am looking at the Orbit Info Panel.  The inclination reads 0.1 degrees (I don't know why it's not exactly 0.0 degrees).  Moreover, the NavBall is solid blue with the orange dot centered at zero degrees.

So perhaps Kerbal Space Program also considers the initial inclination to be zero degrees, and not 90 degrees.

Stanley

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Inclination is a different measurement than pitch angle. your inclination is 0 because you are on Kerbins equator. You can point any direction and still be at 0 because your position relative to the rotational axis of the planet is the same. Pitch angle is the measurement of the angle your rocket's longditudinal axis makes relative to the ground.

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11 minutes ago, Meecrob said:

Inclination is a different measurement than pitch angle. your inclination is 0 because you are on Kerbins equator. You can point any direction and still be at 0 because your position relative to the rotational axis of the planet is the same. Pitch angle is the measurement of the angle your rocket's longditudinal axis makes relative to the ground.

Thank you, @Meecrob.  That makes sense.

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Glad I could help, its always nice to see people interested in space!

By the way, your sig reminds me of an NDT quote...to paraphrase "drug dealers are fully into the metric system!"

Edited by Meecrob
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Hi everyone,

Actually, this discussion clarified a few things in my mind.

Let me summarize, and get things nailed down.

Let's say that we were at Kennedy Space Center, and let's agree to call its latitude 28 °.

Case 1: A rocket is standing upright on the launchpad

Inclination: 28 °
Pitch: 90 °

Case 2: A rocket is lying on the ground with its nose pointed towards Tallahassee

Inclination: 28 °
Pitch: 0 °
Heading: 300 ° or North 60 ° West

Case 3: A rocket is lying with its aft side on the ground and its nose propped up 30 ° pointed towards London

Inclination: 28 °
Pitch: 30 °
Heading: 40 ° or North 40° East

Case 4: A rocket is suspended vertically from its aft side and its nose pointed straight down

Inclination: 28 °
Pitch: -90 °

Could anyone please confirm the three parameters for all four cases.  Note, however, that I have a question mark regarding the heading on Case 1 and Case 4.

Thank you.

Stanley

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Pretty much right.

I'll change "Heading" into "Azimuth" however - heading changes as the rocket goes downrange, but it remains on the same azimuth* as viewed from the launch point, except if a dogleg maneuver is carried out.

* now technically it doesn't since the launch site itself is located on a rotating body, but let's presume the parent body is non-rotating.

Edited by YNM
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1 hour ago, MetricKerbalist said:

Hi everyone,

Actually, this discussion clarified a few things in my mind.

Let me summarize, and get things nailed down.

Let's say that we were at Kennedy Space Center, and let's agree to call its latitude 28 °.

Case 1: A rocket is standing upright on the launchpad

Inclination: 28 °
Pitch: 90 °

Case 2: A rocket is lying on the ground with its nose pointed towards Tallahassee

Inclination: 28 °
Pitch: 0 °
Heading: 300 ° or North 60 ° West

Case 3: A rocket is lying with its aft side on the ground and its nose propped up 30 ° pointed towards London

Inclination: 28 °
Pitch: 30 °
Heading: 40 ° or North 40° East

Case 4: A rocket is suspended vertically from its aft side and its nose pointed straight down

Inclination: 28 °
Pitch: -90 °

Could anyone please confirm the three parameters for all four cases.  Note, however, that I have a question mark regarding the heading on Case 1 and Case 4.

Thank you.

Stanley

Correct. In cases 1 and 4 the heading/azimuth is undefined.  The rocket is not pointing in any compass direction.

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Hi everyone,

Thank you very much.

Back to the NAR rule to which I referred above, it would be better if it said that, for a high-powered rocket, "the minimum pitch" must be 70 degrees.

Stanley

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13 hours ago, MetricKerbalist said:

Hi everyone,

Actually, this discussion clarified a few things in my mind.

Let me summarize, and get things nailed down.

Let's say that we were at Kennedy Space Center, and let's agree to call its latitude 28 °.

Case 1: A rocket is standing upright on the launchpad

Inclination: 28 °
Pitch: 90 °

Heading referenced to Earth surface is not defined. If you think in inertial coordinates heading is to east (I do not remember what definitions of zero and direction is used in this case). Orbit of standing object is very narrow ellipse and object is in apoapsis point. Inclination is equal to latitude and periapsis near the center of Earth. Or center of Earth if object sits on pole.

Both coordinate systems are relevant in ascent. For example KSP changes from surface referenced frame to inertial frame during ascent (typically soon after 1000 m/s, I do not know if altitude or speed triggers the change).

13 hours ago, MetricKerbalist said:

Could anyone please confirm the three parameters for all four cases.  Note, however, that I have a question mark regarding the heading on Case 1 and Case 4.

I did not check those values of Heading but they seem to be correct.

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OP, you are confusing several different coordinate systems.

Heading and pitch are relevant with respect to local horizon. Inclination is an orbital element. You shouldn't be mixing these together. And neither is inherently tied to your geographical location, which is yet another coordinate system. A rocket taking off from 20°N latitude will end up in an orbit with an inclination of no less than 20°. And to achieve exactly 20° the ascent will begin with rocket pitching over to head East, 90°. In general, the optimal ascent will always begin by heading directly East regardless of where you take off from and will put you in minimal possible inclination. The only time you might want to launch in a different direction is if you are targeting inclination greater than your latitude. In general, relationship between initial heading and final inclination is quite complex. For example, if you take off from 20°N and wish to establish an orbit that has inclination of 30°, the heading you should be aiming for is 108.6° or 71.4° (via considerable amount of trig). So roughly East by South East or East by North East, depending on how close to ascending node you want to be. You're still going mostly East, though.

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Hi @Hannu2,

8 hours ago, Hannu2 said:

Orbit of standing object is very narrow ellipse and object is in apoapsis point. Inclination is equal to latitude and periapsis near the center of Earth. Or center of Earth if object sits on pole.

I don't understand the sentence that I quoted.  Would you mind explaining further.

Hi @K^2

7 hours ago, K^2 said:

... via considerable amount of trig ...

Would it be burdensome for you to show this trig?

Stanley

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Hi @K^2 or anyone else,

Wow!  I am getting overwhelmed.  I didn't realize how much I didn't know.

May I please ask you this?  Let's say that a rocket were lifting off from Kennedy Space Center, which is at roughly 28 degrees North latitude.  Could you kindly show on a map or on Google Earth or on something what one complete orbit around Earth would look like?

Stanley

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