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The Best Relay Orbit | KSP Let's Do The Math
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- Опубліковано 14 лис 2019
- What is the best orbit for your relay satellites?
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Yea! I managed to work this one out for myself, well most of it. I was not only surprised I could do it, but that I was playing a computer game and actually wanted to "do the maths". Isn't KSP great!
It certainly is! I love the feeling of having puzzled something out for myself. It's why I get into the whys in these videos, not just what to do.
One small thing that no one ever seems to mention: You don't HAVE to go to 2/3rds orbital period for insertion. It might be cheaper and easier to go to 4/3rd or even 5/3rd, seeing how that would be a much higher Ap, meaning less dV needed in the carrier stage.
Excellent point! Thanks. It would be fun to look at the different options in more detail. You would need less delta-v for the transfer vehicle, but would you be offloading the cost onto the individual probes? I don't know.
Diving orbits vs accending orbits, some food for thought
You could also do ie 5/6 or 7/6, but you'll have to wait two orbits between deploying
@@canaDavid1 299/300ths!
@@kdaviper you'll have to wait 100 orbits for each insertion, but yes, it would work.
This is the best KSP videos I've ever found. Thank You Mike so much for making these videos
Wow! High praise indeed. Thanks.
@@MikeAben I won't say it's the best KSP video ever, we can't risk swelling the man's head, so it was... average! 😉
in early carrer stock game, this is pure gold
love this series its just what we all were probably looking for. thats why we play kerbal
Doh. When figuring out the 2/3 radius for the orbital insertion, I never even considered calculating the radius of the Mun. I was just using the altitude numbers. Haha. No wonder it didn't work.
It's an easy mistake to make. I certainly have done it.
mike you're a life saver, I thought this was impossible for me to do but with all these calculations I finally created a relay orbit..
That's precisely the video I needed to watch. Thank you!
This is the first time math has been fun.Thank you so much for the well paced explanation! I wish you were my math teacher back then ;)
Amazing video and excellent explanations. Love the clean graphical presentation too. This one is going in my KSP playlist for all eternity.
I brought this up in chat, but in my most recent game, I never deliberately built a comsat network around the Mun or Minmus. Instead, I set up the upper transfer stages of my launches to double as communications relays, so over time a constellation just sort of happened.
Also, with a kOS script to execute maneuver nodes and landings, the most critical needs for a communications network sort of went away.
... but look at all the pretty triangles.
Seriously, though, reusing upper stages that way is a great idea. In previous campaigns, I took my probes from those "put a satellite in a specific orbit" contracts and added a relay and some extra fuel. Then, after they satisfied the contract, I would shuffle them over to the Mun or Minmus as relays. It was rather fun (well, I found it fun) to shuffle the satellites around into what I would consider good orbits.
@@MikeAben Building a proper communications network is worth doing for the fun of it. But designing vessels to work as relays once their primary missions are over is also an effective strategy, just because you eventually get so many dead missions orbiting the Mun and Minmus that you can retain very reliable communications that way as well.
better than deorbiting :D
I needed that thanks ! Very pedagogic explanation.
You're very welcome.
Bro you explained this better than my AP trig teacher
Good shit, man. Just started working on my relay network in KSP, so your explanations have been helpful. Wish my math teachers in school had been as clear as you.
Thanks. Love the nic.
There's another method I just discovered for getting equidistant relays around ANY body, and its actually simplifies things a lot. (TLDR at the bottom)
So I was number crunching seeing if I could come up with a simplified formula that didn't require you to target specific altitudes or orbital periods. With the idea that I don't have to memorize/lookup a handful of data and tables to make the right relay orbit, something that would be easy to remember...which would make things a lot more flexible. I started with the formula that finds a semi-major axis, "x" with the given Orbital period: (apologies for the excessive parenthesis upcoming in the formulas, writing formulas in UA-cam is not the best)
x = (GM * (T^2)/4pi^2)^1/3, where x is the semi-major axis of the phasing orbit
I then substituted T with the Orbital Period of the phasing orbit which is the 2/3rds the duration of the larger relay orbit:
T = 2/3 * (2pi/GM * y^3)^(1/2), where "y" is the semi-major axis of the larger, circular orbit
giving the formula:
x = (GM * (2/3 * 2pi*(y^3/GM)^(1/2))^2 / 4pi^2) ^(1/3)
Most of the variables like the gravitational standard parameter mu and pi and the exponents cancel out. heres how it looks simplified:
x = (2/3)^(2/3) * y
Moving the leftover (2/3)^(2/3) into variable "o" (which I initially called the phasing orbit modifier, this simplifies things later).
o = ((n-1)/n)^(2/3), where "n" is the number of relays you want in the orbit
I then substitute "x" with the semi-major axis formula (P+A)/2 , and y as A (since its both the phasing orbit's apoapsis and is also a circular orbit). then simplify further
(P+A)/2 = 2*o * A - A =>
P = A* (2o - 1), where "P" is the phasing orbit's periapsis, and"A" is apoapsis of the phasing orbit
Great so if we know the apoapsis of the relay orbit we can also easily find the target periapsis needed for the phasing orbit using this phasing orbit modifier.
BUT WAIT THERE'S MORE!!
While crunching for a "simplified formula" I had a hunch that eccentricity may be the thing I needed.
I didn't recall seeing the formula for Eccentricity ever posted in the video series so I had to look it up. The formula is as follows:
E = 1-2/(A/P+1), where A is the orbits apoapsis and P periapsis. (this formula doesn't apply to escaping orbits, i.e. parabolic/hyperbolic)
I had these two numbers up next to each other and quickly noticed that this also holds true:
E = o-1
The phasing orbit mod is directly related to the phasing orbit's eccentricity!
This means that since KSP shows you the eccentricity, you don't need to plan for an explicit period or attitude(within reason, apoapsis still needs to be within the min/max bounds as mentioned in the video), you just burn for an explicit eccentricity and you'll get the perfect phasing orbit, which works on ALL CELESTIAL BODIES.
Its also possible to burn from periapsis, but only if the apoapsis is in the correct range. If the periapsis is very low the apoapsis can end up under the minimum bounds and thus get occluded from other relays by the body it's orbiting. Also like normal, after the relays have been deployed and circularized you still may need to do minor correction burns so that the sibling relays sync their orbital periods.
TLDR;
Keep your apoapsis anywhere above 2x the body's radius but below the SOI (or for me, my upper bound is also the relays range / 25 for strong ground signal). Then burn for an eccentricity of 0.310371 (for 3 equidistant relays). If your eccentricity is less than this, burn retrograde. if its greater, burn prograde.
That is very cool!!! I'll go through the math when I have more of a chance. Thanks. 😀
I just went through and verified the math (sorry, I have to write it out). This is awesome! I'll have to give it a go in game. I may work it into a video sometime in the future if you don't mind. I'll give you the credit for it.
@@MikeAben Sure! I'd be delighted. Also I don't mind that you double-check my work, I actually find it refreshing haha.
I'm confused as to how you got 0.310371? if you want 3 relay sats you said o = ((n-1)/n)^(2/3) = (2/3)^(2/3), and E = o-1 so E = 0.76314 - 1 = -0.23685 when it should be 0.310371?
@@redpug5042 Because the original post had a typo. The actual formula is E = 1/o-1, not E = o-1. If you took the original formula I posted for for eccentricity, E = 1-2/(A/P+1), and then substituted P for my simplified formula of P = A* (2o - 1), you would see the expanded formula, E=1-2/(A/A*(2o-1)+1), which when simplified becomes, E = 1-1/o. however since this would always return the negative counterpart the signs are switched, becoming E= 1/o-1
I noticed the typo moments after I posted and submitted an edit with the correct formula. and thats the formula Mike likely saw and checked. however it seems that when youtube archived my comment its showing back the original post.
Thank you, this rules! I love having reasons to use geometry! Also, I came up with my own delivery method for the three relays. Rather than stacking them one on top of another, I put a size 18 engine plate on the TOP of my delivery stage, set the engine plate to have triple nodes and attached my relays to these three nodes with a junior docking port each. The great thing about this is that my mun craft was tiny and I didn't even need to use a tall fairing
I am definitely going to use this next time I launch a relay network
Watching this as my (now ex-) fiancé just moved out. I take a lot of comfort in learning from these videos. Very well explained indeed
The RA-2 is a *VASTLY* better relay antenna than the HG-5. It weighs almost the same as two HG-5s, but its signal is stronger than *2,947* HG-5s.
Even when connecting to the very weak 5k antenna built into pods and probe cores, the RA-2 gets a 3,162 km range. (Ten times that range when connecting to a Communotron 16.) So you can set a high relay orbit anywhere in the Mun's SOI, and then you can not only get science from any craft capable of transmitting data, you can also control vessels that don't have an attached antenna, or whose deployable antenna is currently not deployed.
One reason the increased range matters is that a higher relay orbit has less signal dropout for landers. With a low orbit, one relay will be close to the horizon when the next one rises, possibly obscured by terrain like crater rims for a while. Higher orbits aren't as easily obscured.
The RA-2 is bigger than the HG-5, and best mounted inline rather than radially, but the extra height turns out not to be a concern: three satellites, each topped with an RA-2, just barely manage to fit in the interstage nodes provided by a standard 1.25m fairing.
The RA-2 is further up the tech tree than the HG-5, but the satellites pictured here already assume Precision Engineering, for the HECS core.
The only disadvantage of the RA-2 is power: if you want your relay to also carry a science experiment and transmit data, the RA-2 is very power hungry for transmission per Mit. But in that case, you can just slap on an additional lightweight non-relay antenna like the Communotron 16. You then click that antenna to have it, rather than your power-hungry relay, transmit your data.
amazing i love it
Damn! Had to pause to avoid you blowing my mind oO
My heart sank when you started talking about proofs. I have PTSD from doing proofs from my upper-division Linear Algebra and Analysis courses.
Sorry to hear that. Hopefully mine weren't too bad.
@@MikeAben Haha, no you were good.
That "smaller and cheaper" satellite at 1:25 looks like a GPS IIF, which was a pretty expensive milsat flying at MEO. :D
interesting and useful
Great video! Even a few years later, this video still rocks and is still useful. I was wondering if there is any benefit to using more than three satellites in a relay network. Am I correct in thinking that using more satellites allows you to have a lower minimum orbit to maintain connectivity? If I'm thinking about the geometry correctly, using 6 sats instead of 3 would lower your minimum altitude by half.
That would give you a bigger range in which you can pick your relay orbit. So instead of adding antenna (or upgrading to more powerful antenna) to increase the min-max orbital range, you could add satellites.
However, it's probably cheaper (certainly easier) to just add more antenna (or upgrade antenna) than it is to add more satellites. And as you say in the video, this only really matters for the Mun.
Yes, more satellites brings down that minimum orbit and the max distance you would be from a relay which, potentially, means the relays need to be less powerful. Another advantage is that the satellites can drift more from their ideal positions without affecting the functioning network. I tend to find three satellites is enough, but others may disagree.
Wow you explained this better than my math teacher lol
Bad ass!
Me at 0:10 - seems alright.
Me at 1:10 - wft.
Great videos @mikeaben keep it up! Do you have a background in Maths to be able to do all these calculations? I am the reason for the extra 20 views in the last 3hrs lol. Now to fight with excel to get the equations onto my KSP helper spreadsheet
I'm a retired high school math teacher.
@@MikeAbenthat's really interesting. Your videos are great. I'm not good at maths, (or ksp) but with your videos I'm making good progress. Thank you.
Great video, i love the explanation, one question though, why does the period has to be dividable by 3? Can it not be 2 or 2.5 ad long as the period is exactly the same for all relays?
The divisible by three has to do with wanting three satellites in that orbit. If you want to deploy all three from the same vehicle, you can put that vehicle into an orbit that is two-thirds or four-thirds the preiod of the final orbit. You can then drop a relay on each orbit and they will be a third of N orbit apart.
I explain this in more detail in the video linked under the info tab.
I love that the max range has a period of pretty much π hours (it's only out by 10 seconds). I think i might strap bigger relays on to get that period anyway.
Edit: you need an Ap of 395,378.78m, with Pe of 113,339.3m to put 3 satellites into an orbit around Mun with an exact orbital period of π hours, but you need 3 HG-5's to achieve the slightly higher overall power of 11.3975, which is good up to 492km above Mun :D
p.s. I've just signed up as a Patreon, same name :D
I wanted funni space game.
Instead I get math
Thanks for the video, it helped a lot
You say that like it's a bad thing. 😉
Great tutorial videos! I spent a few hours last night using what I learned from your videos to design a mission to position 3 relay satellites in orbit around kerbin, with 99.99% signal strength between each pair of relays and more on the hop to KSC. It should give me at least 85% signal on the first hop with any single communotron 16 inside the relay orbit, so the overall signal strength would be >82% easily.
I also used your math videos to calculate the period of my chosen orbit, which I adjusted to the nearest multiple of Kerbins sidereal rotation period, so the relays should be in the same position above the surface once every 5 rotations. I calculated the periaps for a 2/3 period phasing orbit for insertion.
Then I used your math videos on hohmann transfers and elliptical transfers to calculate the dV I needed for each relay to circularise, for the inserted to get into the phasing orbit, and for the inserter to deorbit.
Finally, I learned from you about how to design the craft. How to use the interstage nodes in the fairing to install 3 payload craft. How to use subassemblies to save the payload and the boosters and reusable chunks. How to tune the booster subassembly for a particular carry weight (4.8t in my case).
Your videos have helped me do so much that I never thought I would have found fun but it is! Thanks for your great tutorial series.
mike how do you compute the ratio for 3, 4, 5, 6...satellite resonant orbits for both Dive orbits where AP is the final AP and non-dive orbits where PE is the final AP? I want a 4 sat network and forget how to computer the ratio of the PE for a resonant orbit? For 3 sats the ratio for the dive resonant orbit is 2/3. What's the ratio for 4, 5, 6, ...?
The number of satellites is the denominator of the fraction. The numerator is one down for dive orbits, and one up for non-dive. So for four satellites, the possible fractions are 3/4 and 5/4. For five satellites, 4/5 and 6/5, etc.
Thx Mike I recalled it after thinking about it a bit.@@MikeAben
It seems blindly firing satellites at the minimum orbit size or kerbin wasn’t the best idea
I feel like an ape now
I'm assuming this won't give you coverage on the poles (especially if in a crater or behind hills or whatever). Would perfect mun coverage require adding an extra three in polar orbits? Is there a way to do it with less?
Perfect coverage would require three satellites arranged in the same way but a polar orbit. There's no way to do it with less.
I was just thinking of a tetrahedral array, which would put a satellite ALWAYS above the horizon at every point on the planet.
Conceptually simple, but a significant challenge to one's piloting skill -- one polar circular orbit, three 30-degree inclined orbits of the same altitude. Set it up so the inclined satellites are at longitude 0, 120, and 240 in the southern hemisphere at the same time the polar satellite is over the North pole on a heading of 0, 120, or 240.
I'm certainly not that good a pilot -- might be an interesting challenge for those who are.
So, the antenna rating (500k, 5M, 2G, etc.) is just the max range?
Remember there is always two antennas. If both antennas are identical, then yes, but that's not usually the case. The max range is the square root of the product of the individual ranges.
I know this is an older video but I'm only getting into this now, in Wolfram alpha I'm getting around 0.71 if I input this sum "2x³*3x³=0.8" and if I input the sum in the video "2x³*3x²=0.8" I get around 0.67. Am I using Wolfram alpha incorrectly or is the sum written down incorrectly? Thanks.
The equation is -2x^3 + 3x^2.
Please do a "let's do the math" on a tetrahedral constellation. I don't understand why they don't use circular orbits when it seems like circular orbits would be fine. They also seem like they would give better coverage than a planar constellation like you set up with 3 satellites. I worry about this because I like to put science labs at a planet's poles, and I worry whether they'll really alway be able to see a planar constellation, especially if the labs aren't perfectly placed at the top of a mountain.
That's an interesting idea, but not something I intend to explore anytime soon. The reason they aren't in circular orbits is because it's unavoidable that the four satellites won't all be in the same plane at some moment. Making the orbits elliptical puts that moment at periapsis when the satellites are moving the quickest, this minimizing the time spent in this orientation. Here's a neat animation I found.
www.vttoth.com/GIT/TETRA/index.html?init=2
There are people that have worked out the appropriate orbits for KSP, but as each satellite's orbit has to be in a different plane, it's a lot of work to set up. If you're concerned about your polar stations, you could put three relays into an inclined orbit (there's no reason they need to be equatorial). That'll cover the poles. Or, if you'd rather, you could launch three additional relays into orbits perpendicular to the first three. Yes, that's six relays instead of four, but it's much easier to set up.
@@MikeAben I was able to "see" this in Unity, and it seems no matter what I do all 4 points eventually intersect a common plane at some point I guess that's what you were trying to tell me "because it's unavoidable that the four satellites won't all be in the same plane at some moment." :) That took me a while to see (and I admit I still don't really understand it). Thanks for your patience.
Also thanks for the poles advice - yeah 6 total definitely will cover everything, and I've never seen loss of coverage at the poles with just the 3 configuration. I tried to make the orbits relatively large just to help line-of-sight at the poles, though I think the radio waves can bend over the horizon somewhat even without line of sight.
Any special reason why we want a signal strength of 80%?
I found some answers, someone took measurements - really non linear science boost, varying in jumps at some parts. Minimum signal strength 82% gives full bonus, with a big drop in the bonus at 81%
@@matthewp4046 Good to know. I just pulled 80% out of the air.
Nice explanation, but i have problem in equation signal=- 2x^3+3x^2, can you explain why?, can I using this equation on remote tech mod
In short, no and no. I have no idea as to the origins of the equation. I suspect it was invented by the devs, though if someone knows otherwise please let me know. As for Remote Tech, the last I played it (which would be 3 or 4 years ago) it worked on a completely, and simpler, principle. It is possible they may have changed since then.
@@MikeAben Thanks for answering💯👍
At 11:20 I do not see any equation for computing the phasing orbit to compute the PE of 103.85km with a period of 2 hr and an AP of 377.35km. Please explain as throw to a five-year-old how you take the 377.35AP and a desired phasing orbit period of 2hr and get 103.85.
I have been googling to the point where I am ready to go play Sunny Happy Prancing Unicorn Island instead of KSP in frustration!!! I just want to make a spreadsheet and this is the only remaining calculation I need to make.
This is a follow up to some previous videos, so I didn't go over it again. There are links, but you may have missed them. Here's what you're looking for.
ua-cam.com/video/xNiFcI-fcmA/v-deo.htmlsi=DR9dGMshC83cHpFM
@@MikeAben thanks Mike.
Hi Mike, first I love your videos! they're amazing. Second, I have a question. In my career game I'm trying to put a Relay Comm on Kerbin (because I only have connection with KSP), so I follow your videos and put on each relay sat two HG-5 and the orbit period are 12h (so the orbit altitude is 4.906.298m) but I have one problem, the relay satellites don't communicate with each other. Trying to know the reason, I found the distance between each other is 8.497km (please correct me if I'm wrong, I found it because in a right triangle the short side (orbit altitude) is 4906km and the ang is 60° so tang 60 x 4906 = 8497km x 2 -> 16994km). So, what i'm doing wrong? How can I know if the power of the antennas are enough to communicate between each other?.
Thank you for this class of videos, they are amazing.
You know, I thought the Mun was the easy one to mess up, but I didn't even consider around Kerbin as I always use the ground stations. Anyway, don't use the altitude, but the orbital radius which is 4906+600 = 5506 km. You also need to use sine in your calculation. You should find the distance between your satellites is 9537 km, which is two far apart for two pairs of HG-5s to talk to each other. Looks like I need another video.
Anyway, here's my video on calculating signal strength.
ua-cam.com/video/hVd-WhL4tZ8/v-deo.html
And here's an awesome spreadsheet (not by me) that might help.
goo.gl/r4b6uo
You should find a pair of RA-2's will work nicely at that altitude.
@@MikeAben only one hour to answer me! thank you Mike! I have another question. I was using tan because in 4:38 I see the large axis of the triangle (I don't know how you call in English) is the opposite side of the angle of 60°, so having the short side of the triangle (my orbit radius, now 5506km) and the angle I can find the large side of the triangle with tan 60° x 5506. What is wrong in my point of view?.
And again thank you very much Mike!
And another question if I can. The signal of one antenna need to reach the relay satellite or need to reach the edge of the signal of the relay satellite?
@@iMSn20 I captured the image from the video and annotated it a bit.
photos.app.goo.gl/a7yK2M9A1kXF9pZN7
What might be confusing is the 'r' in the diagram, but here it is representing the radius of the parent body, not the orbital radius. The 5506 km is the longest side of the right triangle, which is called the hypotenuse. We want the side that is opposite the 60 degrees, and the function that connects these two sides together is sine.
@@iMSn20 The signal has to reach the other satellite, but it's a bit more complicated than that when the two antennas trying to communicate have different powers. Here, you multiply the two powers and take the square root of the result to get the maximum range.
Keep in mind this is the very outside of the range where the signal strength drops towards zero. You typically want to be quite a bit closer than that.
Someone may have asked this already, but why did you chose 80% as your minimum effective strength? Is that the minimum signal strength it takes to get your +40% bonus when transmitting science?
I think I more or less pulled out of my back end. I'll have to check to be sure.
That would be great to know. Also I wonder if there is a minimum effective strength for full probe control?
@@jaredmh90 That, I know, is just an on/off thing. You have a signal, you have full control.
@@jaredmh90 I couldn't find any good info on exactly how the bonus is calculated, but in the signal strength video that's referred to above, I got the full 40% bonus with a signal strength of 84%.
@@MikeAben good to know about the control. I have an idea to test the other. Pick a body outside the communatrons range of KSC. Put in a relay network that has 100% effective strength to KSC. Then have a craft orbit outside the relay orbit where it’s effective strength varies, then run an experiment repeatedly as the strength changes to find where you get the 0% to 40% bonuses at. I may test this on my own and report back to you since I just put up my first relay network, thanks to your tutorials!
Mmmmmmmmm
Maph
Math went over my head :/
I do go pretty quick. Where did I lose you?
There are a few previous videos that build to this one. Links are in the cards.
@@MikeAben So I was "with" you when you determined the signal range of two HG-5s was 595km, but I was lost in how you found the altitude 395km as the maximum orbit.
If 595km corresponds to the maximum range of a Communotron 16 talking to two HG-5 antennas with 80% signal strength, then wouldn't the maximum altitude for your relay network be 595km?
@@Heresy488 Don't forget the radius of the Mun is 200 km. So an orbital radius of 595 km is an altitude of 395 km above the surface, and that's what's measure in game.
@@MikeAben That makes sense, and also answers another question about how you got 258 km w only 1 HG-5 antenna. Thanks! Loving your videos.
Dude this was just way too fucking much. All i did was make a swarm of cubesats, only one cubesat had enough power and range to communicate with eloo from kerbin.