The automated stock circumnavigation of Kerbin

[Wjolcz]

It just struck me literally seconds ago.

So now we have those pilot skills. What if you got a probe to orbit, waited for it to get over the horizon, took off with a plane, targrted the probe and left it there to go around the planet on its own? The only problem is figuring out what orbit it should be on.

[Starwhip]

Unless you're going at orbital velocity, the probe will continue to dip below the horizon, and you'll slam into the ground.

Good try, though.

Me forgot me maths. Sorry.

Edited January 5, 2015 by Starwhip

[Wjolcz]

Unless you're going at orbital velocity, the probe will continue to dip below the horizon, and you'll slam into the ground.

Good try, though.

Depends on its orbit. If its on a lower one it will go below the horizon faster. If its higher itll go slower, not at all(geostationary), or from east to West(higher than geostationary).

[Starwhip]

Depends on its orbit. If its on a lower one it will go below the horizon faster. If its higher itll go slower, not at all(geostationary), or from east to West(higher than geostationary).

I is sorry, vacation made me lose my maths.

Yes, if you could get the plane to fly at a constant speed, and the satellite to move at that speed relative to Kerbin and stationary compared to the plane, it should* work.

*Provided you've actually got the time for that.

I'd suggest looking up the equations for orbital velocity vs. altitude.

EDIT:

Here we go:

Velocity = sqrt((G*M)/r)

Where G*M is the Gravitational Parameter of the planet (G is the gravitational constant, M the mass of the planet) and r is the radius of the orbit (from the center of the planet.)

For Kerbin it's

Vo = sqrt(3.5316000×10E12 / r)

Say you put the satellite in a 600km orbit. (Realize that Kerbin is also 600km in radius, you add the radius of the orbit to this.)

Vo = sqrt(3.5316000×10E12 / 1200000) = 1715.52 m/s

Kerbin rotates once every 6 hours. It's circumference is 3769911.184 meters. Thus, the surface moves at:

3769911.184 / 21600 = 174.53 m/s

So the plane would need to move at 1541.0 m/s to keep it's position relative to the satellite. This is doable.

Let's try 1000km.

1485.68 m/s is the orbital velocity.

Thus, the plane needs to move at 1311.2 m/s to keep up with the satellite.

These two assume a sea level altitude (I think, right? ).

If you wanted to do this for real, designating two altitudes first would be the easiest plan of action. I will attempt to find you an example.

Edited January 5, 2015 by Starwhip

[zarakon]

I think you'd have trouble creating a stable system this way.

The feedback response you'll get from going too slow or too fast is pretty much the opposite of what you'd want. If you're going a bit too slow, you'll end up aiming lower, which will reduce your altitude, which will further reduce your speed. If you're going too fast, you'll end up aiming higher, which will increase your altitude, which will further increase your speed (until you stall out and end up in the too-slow problem).

[Starwhip]

I think you'd have trouble creating a stable system this way.

The feedback response you'll get from going too slow or too fast is pretty much the opposite of what you'd want. If you're going a bit too slow, you'll end up aiming lower, which will reduce your altitude, which will further reduce your speed. If you're going too fast, you'll end up aiming higher, which will increase your altitude, which will further increase your speed (until you stall out and end up in the too-slow problem).

Neither of us said it was easy. Just possible.

- - - Updated - - -

Ack, I did it wrong.

You need to compare the times of the "orbits" so that they are the same.

Okay. We'll put the sat in a 2400 km orbit.

Vo = sqrt(3.53160000x10E12 / 3000000) = 1085.0 m/s

The circumference of this orbit is 18849555.92 m

Thus, the orbital period is 17372.86 seconds.

We'll put the plane at 10,000 meters.

It needs the same orbital period as the sat. It's "orbit" circumference is 1916371.52 meters.

It needs to move at 110.3 m/s, which at 10km is no easy feat.

Aagh, it's hard to balance. Maybe set up the airplane first? Yeah, I'll do that.

NO, IT'S NOT! GAH!

Circ = 3832742.04 m

Speed = 220.62 m/s

Still funky. Right, airplane first time.

Edited January 5, 2015 by Starwhip

[StevenRS11]

To make the system stable, you could have a backwards facing probe control the plane, and have the target probe orbit behind you. Going too fast, you go down. Going too slow, you go up!

[numerobis]

I'm getting very long-distance flights just from going prograde with an appropriate plane. Then I can set it on autopilot going prograde at 2x acceleration, and leave for dinner. I haven't circumnavigated like this, but that's because I was flying to a destination to do surveys; the longest run I did was KSC to the north pole without touching controls.

The plane is a basic jet, large wings tilted so that in flat flight they have positive angle of attack. Also tilt them so they rise as they get further from the fuselage, which makes roll self-limiting (roll left; the left wing will gain lift and the right one will lose lift, so you'll level out without touching the con). I make it so that when full of fuel, the plane flies flat at 50 m/s at about 2-3km altitude (higher than most hills, but maybe aim higher if you have mountains in the way). I fly up to there, set the throttle appropriately, then leave. SAS will keep the pitch perfectly flat, since you're neither rising nor dropping. Roll is self-limiting, so you won't get much turning. As you burn off fuel, the plane will slowly rise and gain speed; SAS going prograde can make this oscillate a bit, but my experience is that it dampens out pretty quickly when you're flying slowly.

This doesn't work as well with a turbojet because you'd be flying much higher, where the self-damping features wouldn't be as effective.

[zarakon]

To make the system stable, you could have a backwards facing probe control the plane, and have the target probe orbit behind you. Going too fast, you go down. Going too slow, you go up!

I think you'd actually have the same problem.

If you're going too fast, the satellite will fall lower behind you. That means the BACK of your plane will tilt downward, but the front will go up and you'll end up climbing and going faster.

[Starwhip]

Airplane Altitude: 10km

Airplane Speed: 1000 m/s

Circ = 3832742.04 meters.

Period = 3832.7 seconds. (63.87 minutes, just over an hour, which sounds about right.)

Now we need to solve for the radius of the satellite's orbit.

The formula for orbital period is this:

Time = 2pi * sqrt(a^3 / u)

where a is the semi-major axis of the orbit. Which in a circular orbit, is the radius.

And where u is the gravitational parameter: GM.

So T = 2pi * sqrt(r^3 / GM)

We need to solve for r.

T / 2pi = sqrt(r^3 / GM)

(T / 2pi)^2 = r^3 / GM

GMT^2 / 4pi^2 = r^3

cubert(GMT^2 / 4pi^2) = r

Plug-n'-chug:

cubert((3.5316000×10E12 * 3832.7^2) / 4pi^2) = 1095318.631 m

Which on the orbital display would read 495318.631 m, or 495.318 km

(Geosyc is ~2800 km)

There you go. Now all you need to do is position the sat so that when you reach altitude and speed with the plane, tracking the sat will keep your nose up just enough to stay level.

Good luck!

[numerobis]

Another option: a plane where you don't have enough control authority to change your angle of attack more than a few degrees, and which has enough lift even at the most-negative pitch that you can't land without reducing throttle.

As the satellite orbits, sometimes you pitch up, sometimes down. With pitch up, you'll climb some, no worries. With pitch down, you'll drop, but eventually the lift will pull you back up.

This only works with an equatorial orbit of course (inclination 0 or 180).

[Dr-Drunk]

The plane you designed for this would have to be quite stable and have virtually no roll or deviation but if you could pull that off then yea in theory it would be possible to do this. Assuming you fly up to the upper atmosphere and could hold a stable flightpath there the speeds required to keep up with an orbital target aren't unheard of.

[numerobis]

The minimum speed required to keep up with an orbital target is zero, if that target is in geostationary orbit.

[Starwhip]

The plane you designed for this would have to be quite stable and have virtually no roll or deviation but if you could pull that off then yea in theory it would be possible to do this. Assuming you fly up to the upper atmosphere and could hold a stable flightpath there the speeds required to keep up with an orbital target aren't unheard of.

Airplane Altitude: 10km

Airplane Speed: 1000 m/s

Circ = 3832742.04 meters.

Period = 3832.7 seconds. (63.87 minutes, just over an hour, which sounds about right.)

Now we need to solve for the radius of the satellite's orbit.

The formula for orbital period is this:

Time = 2pi * sqrt(a^3 / u)

where a is the semi-major axis of the orbit. Which in a circular orbit, is the radius.

And where u is the gravitational parameter: GM.

So T = 2pi * sqrt(r^3 / GM)

We need to solve for r.

T / 2pi = sqrt(r^3 / GM)

(T / 2pi)^2 = r^3 / GM

GMT^2 / 4pi^2 = r^3

cubert(GMT^2 / 4pi^2) = r

Plug-n'-chug:

cubert((3.5316000×10E12 * 3832.7^2) / 4pi^2) = 1095318.631 m

Which on the orbital display would read 495318.631 m, or 495.318 km

(Geosyc is ~2800 km)

There you go. Now all you need to do is position the sat so that when you reach altitude and speed with the plane, tracking the sat will keep your nose up just enough to stay level.

Good luck!

I didn't go through all of that for no reason. 1000 m/s is possible.

Now, I've built planes that go at Mach 6, over 2000 m/s, but those are hard to keep stable.

The slower and lower you go, the more control you'll have.

[merendel]

It might be easier to just tell the probe to point prograde and ever so slighty angle the probe core so when its pointed at prograde the rest of the craft is actualy pointed a few degrees upwards. If you get the alignment right for a specific speed/altitude you'll fly strait indefinitely. If you get going too fast or have the angle too high you'll eventualy climb till you start to stall, prograde will drop below horizon and you'll fall go down for a bit. However because the probe core naturaly angles the craft up it will pull out of the dive as it gets lower and the wings generate more lift and engine more thrust. The hard part will be keeping it from rolling.

[numerobis]

It's only the wings, maybe the engines that you want to have an angle of attack -- the rest of the airframe is usually best left pointing straight into the wind, either in FAR or, in stock, for the Mk2 parts.

Roll control I already discussed above.

[Wjolcz]

I guess I migh've overcomplicated it a bit with the pilot skills

Maybe a plane fast enough and pointing prograde would actually weork better?

[mknote]

Actually, there is a further complication that nobody has pointed out: as you burn fuel, the mass of the aircraft will decrease, causing the velocity to increase over time. Without manual input, this will throw out the balance and the aircraft will try to climb out of the atmosphere.

[Engineer of Stuff]

Actually, there is a further complication that nobody has pointed out: as you burn fuel, the mass of the aircraft will decrease, causing the velocity to increase over time. Without manual input, this will throw out the balance and the aircraft will try to climb out of the atmosphere.

That is a good point.

[aleis]

So I am not an engineer and haven't tried playing kerbal with math. However from what I am to under stand about orbital mechanics is that your orbit is defined by your speed.

There for if you are trying to use a probe in orbit ad your target that you are keeping at a constant distance (distance would relate to angle over the horizon). You will be going the same speed, thus end up in the same exact orbit simply behind it.

Maybe I'm wrong

Edited January 7, 2015 by aleis

[merendel]

Actually, there is a further complication that nobody has pointed out: as you burn fuel, the mass of the aircraft will decrease, causing the velocity to increase over time. Without manual input, this will throw out the balance and the aircraft will try to climb out of the atmosphere.

Kinda why I suggested a prograde following plane with the probecore slightly tilted so it would pitch up. Yes its slightly more efficent to just give the wings an AOA but you can split the difference a bit. if you need a 10 degree AOA can do 5 on the wings and 5 on the core. You'll still have the issue of the plane wanting to climb higher as fuel load drops but when you get too high you'll start to stall and drop. the probe will follow the prograde down but because its angled slightly off it will actualy be pulling out of the dive naturaly. I'm just concerned that pure AOA on the wings wont always be enough to pull out of the dive while the tilted probe will force a bit of steering correction as well as your tricking it into aiming your direction of travle a bit above prograde. It will experience more extreme oscillation as the aircraft lightens but it should keep going till out of fuel.

[vexx32]

Actually, in KSP there isn't really any 'stalling' mechanism. You'll have your engines dying on you if you don't get them enough air higher up, and your wings will slowly produce less lift than they would at lower altitudes, but you'll never actually stall like you would in real life.

Unless you have FAR installed. I think it simulates stalling.