Atmospheric Landing Charts: Pinpoint landings! [NEW UPDATE: No Protractor Required!]

[alterbaron]

New, protractor-free landing method!

A new, easier way of targeting landings in-game, without any external tools. Starting from a circular orbit, simply burn to lower your periapsis directly over your target.

If you know what periapsis to use, you can land near your target, every time!

Below is a plot of the landing periapsis that you need to put directly above your target to land there.

The blue curve is the required periapsis height.

The green curve is how much your landing site changes for every 1m change in the periapsis. This gives an estimate of how much precision is required to hit the target.

I tested these results in-game, and got pretty good results. Here's an album of some test results:

http://imgur.com/a/tKq8l

Since the final landing site is so sensitive to small changes in the periapsis, the graph's hard to use for anything more than an overview.

For actually using these results to land, here's the hard numbers:

Landing PE Values for Kerbin
===================================================
Orbit Altitude (m)	Landing PE (m)	Error per m (m)
===================================================
70000				48901			53
80000				45550			49
90000				43898			46
100000				42778			44
110000				41938			42
120000				41272			41
130000				40727			40
140000				40270			40
150000				39878			39
160000				39539			39
170000				39242			39
180000				38979			39
190000				38744			38
200000				38534			38
210000				38345			38
220000				38173			38
230000				38017			39
240000				37874			39
250000				37743			39
260000				37623			39
270000				37512			39
280000				37410			39
290000				37315			40
300000				37227			40
310000				37145			40
320000				37069			41
330000				36999			41
340000				36932			41
350000				36871			42
360000				36813			42
370000				36758			43
380000				36707			43
390000				36660			44
400000				36615			44
410000				36572			45
420000				36532			45
430000				36494			47
440000				36459			46
450000				36425			47
460000				36393			47
470000				36363			48
480000				36335			49
490000				36308			49
500000				36282			50
510000				36258			50
520000				36234			51
530000				36212			52
540000				36191			53
550000				36171			53
560000				36152			54
570000				36134			55
580000				36116			56
590000				36099			56
600000				36083			57
610000				36068			58
620000				36053			59
630000				36039			60
640000				36025			61
650000				36012			61
660000				36000			62
670000				35987			63
680000				35976			64
690000				35964			67
700000				35953			66
710000				35943			67
720000				35933			68
730000				35923			69
740000				35913			70
750000				35903			73
760000				35894			73
770000				35885			74
780000				35877			75
790000				35868			76
800000				35860			77
810000				35852			79
820000				35844			80
830000				35836			81
840000				35828			82
850000				35821			84
860000				35814			85
870000				35806			88
880000				35799			88
890000				35792			89
900000				35785			91
910000				35778			92
920000				35772			94
930000				35765			95
940000				35759			97
950000				35752			98
960000				35746			100
970000				35739			102
980000				35733			103
990000				35727			105
1000000				35721			107

Using RCS for fine adjustment should make this landing method really easy!

Charts for other bodies.

Using this method along with minor correctional burns in atmosphere allows for extremely precise landings. Such corrections are best made before dipping into the thickest part of the atmosphere. On kerbin, I've managed to land only a few steps from a flag using this method!

---

Protractor Method

Have trouble landing at your base from orbit? Want to transfer Kerbals from your Duna or Laythe station to the surface with precision?

Then this is the chart for you!

Big Version

Imgur Album With Tutorial

Here's how to use the chart:

Start off in a circular orbit. (You must be more or less in a circular orbit before using the chart.)

Look up your orbital altitude on the x-axis. The corresponding y-coordinate gives you your "landing phase angle".

Basically, you want to burn so that your periapsis is at as close as possible to 0 meters, and at the given angle AHEAD of your target.

(Make sure to view full resolution, or you'll never be able to read it! Also note that the x-axis is in 10^5 meters.)

Take a peek at the Imgur album for a walkthrough! It's actually really easy.

Let me know what you think!

Edit: Updated plot with data for lower orbits.

Edited September 11, 2013 by alterbaron
New and improved landing method!

[pebble_garden]

This is awesome. Thank you!

[togfox]

Wicked.

[Mr Shifty]

Very nice; will use.

[stoani96]

Pretty good, but i've two things that could be better:

1. i think it would be better if you could calculate the periapsis-height above the target, because how do you want to messure for example 52.3°? i think its better if you know your periapsis has to be for example 10km and has to be above the target.

2. what formulas did you use?

because, if you look at the formula for drag = (density * S * Cw(Cd in english??) * v^2)/2 you can see, that density/2 and v^2 is a constant for a planet, but S and Cw(Cd??) depends on the craft and is maybe already multiplicated in this strange drag-value of a part.

What i want to say is, that this graph depends on the drag-value of the craft you use. --> the formula would be helpful to be really accurate

(or is there something i missed, and that makes it the same to all drag coefficients?)

[numerobis]

The drag coefficient is almost the same for all rockets. The chart will be off if you have a lot of aerospike or solid rocket mass. If you have wings, the chart is completely off, but that's what you would expect.

[stoani96]

okay, and what formula was used?

[alterbaron]

Hi stoani96,

There are many formulas that went in to making this plot.

The curves on the plot were calculated by a computer program. The program is a straightforward modification of this source code: LINK

[Couchonaut]

Hi

Downloaded charts but my angles are funny when I try to use a paper drawn protractor. However, I noticed that you use a nifty on-screen protractor in your screen shots. Can you tell me where to get it so that I can use it with your charts?

Thanks

[Cashen]

Hi

Downloaded charts but my angles are funny when I try to use a paper drawn protractor. However, I noticed that you use a nifty on-screen protractor in your screen shots. Can you tell me where to get it so that I can use it with your charts?

Thanks

I'd like to know this as well as it looks amazingly useful.

One way around it though, if you have a base or target already on the ground, and you have MechJeb/Kerbal Engineer/something that can tell you what your coordinates are, you can find the target's longitude, add the periapsis offset as calculated by the chart, and then find the spot 180 degrees from that, and that's where your craft needs to de-orbit.

[alterbaron]

I used a program called "screenscales". You can get it here: http://www.talon-designs.net/screen_scales.htm

Mentioned on the forums here: http://forum.kerbalspaceprogram.com/showthread.php/21255-Screen-Scales-Freeware-%E2%80%93-Orbit-Transfer-Angles-made-(a-little)-easier

It's an adobe air app, so click the "install now" button to download and install it.

Side-note: As a future project, I'll look into making a chart where you set your periapsis directly above your target, and it spits out what periapsis height you need to land there.

This could make planning landings even easier, no protractor required.

[Couchonaut]

Ah cool! This is most appreciated.

[togfox]

Side-note: As a future project, I'll look into making a chart where you set your periapsis directly above your target, and it spits out what periapsis height you need to land there.

This could make planning landings even easier, no protractor required.

Yes please!

[Jodo42]

I hate to semi-necro this, but OP, would it be possible to make a similar chart for use on non-atmospheric bodies that takes into account the rotation of the body? If so I'd love to see it, as I'm sure would others.

[alterbaron]

a similar chart for use on non-atmospheric bodies

The problem with doing this for non-atmospheric bodies is that there's no atmosphere to slow you down. As a result, how & when you execute your burns makes all the difference. And how long your burns will take depends on the craft, making it near impossible to make a useful plot. (Luckily, at this time atmospheric drag doesn't depend much on the craft, making a universal plot possible in that specific case.)

I don't want to leave you with nothing though, so here's a method you can use to quickly estimate how far the planet will rotate while landing.

You only need a simple desktop calculator and a small table of values from the wiki:

Calculating How Much a Planet Will Rotate During Landing (Easy)

1) Perform your landing burn.

2) Make sure you've passed your Apoapsis.

3a) If your trajectory is suborbital (no PE marker), read the time to apoapsis by mousing over the AP marker, and divide this by 2.

3b) If your trajectory is orbital (PE marker is there), read the time to periapsis by mousing over the PE marker.

4) Grab the so-called "sidereal rotation period" for the body from the wiki.

5) The angle the planet will rotate is given by:

RotationAngle = 360 degrees x [Time from Step 3 in Seconds]/[sidereal Rotation Period]

That's it, pretty straightforward. If you write down the "Sidereal Rotation Period" for each body in advance, it's easy to work this out in-game.

Have fun!

Edited July 30, 2013 by alterbaron

[brusura]

Thanks for the necro or I would not have found this usefeul tutorial!

[brusura]

Side-note: As a future project, I'll look into making a chart where you set your periapsis directly above your target, and it spits out what periapsis height you need to land there.

This could make planning landings even easier, no protractor required.

I would do the math myself but I am not that good , it's very much easier, because using the protactor or the talon software is very difficult you can not be much accurate and this kind of landing is very sensitive to little drift, I found, empiric way, that periapsis at 43 km over target for a circular 100km orbit is the magic number to land ( kerbin ).

You have some speed left after the areobraking to adjust the landing, so far I managed to get closer as 600m from my target, while with the angles I managed to get as close as 10km

[Diche Bach]

Sweet! Sweet!

[alterbaron]

Here's a sample of what's to come: a landing chart without the need for protractors:

Brusura, you said a landing PE (periapsis) of ~43km worked well for a 100,000m orbit. This is consistent with these preliminary calculations!

I'll do some testing, and post the completed chart soon!

---

EDIT: I looked into this a little be further.

It seems that, theoretically, the "place PE over target" approach to landing is VERY difficult to do, since the final landing site is extremely sensitive to small changes in the landing PE.

Here's a plot that shows just how bad the problem might be:

The green line is an estimate of the landing site error for each meter your landing PE is off by. My calculations suggest that an error of a few hundreds of meters can send you tens of kilometers off target.

My first attempts to land using this approach seemed to support this as well.

Edited August 4, 2013 by alterbaron

[alterbaron]

Well, I think I've got this new type of landing figured out.

Below is a plot of the landing periapsis that you need to put directly above your target to land there.

I tested these results in-game, and got pretty good results. Here's an album of some test results:

http://imgur.com/a/tKq8l

Since the final landing site is so sensitive to small changes in the periapsis, the graph's hard to use for anything more than an overview.

For actually using these results to land, here's the hard numbers:

Landing PE Values for Kerbin
===================================================
Orbit Altitude (m)	Landing PE (m)	Error per m (m)
===================================================
70000				48901			53
80000				45550			49
90000				43898			46
100000				42778			44
110000				41938			42
120000				41272			41
130000				40727			40
140000				40270			40
150000				39878			39
160000				39539			39
170000				39242			39
180000				38979			39
190000				38744			38
200000				38534			38
210000				38345			38
220000				38173			38
230000				38017			39
240000				37874			39
250000				37743			39
260000				37623			39
270000				37512			39
280000				37410			39
290000				37315			40
300000				37227			40
310000				37145			40
320000				37069			41
330000				36999			41
340000				36932			41
350000				36871			42
360000				36813			42
370000				36758			43
380000				36707			43
390000				36660			44
400000				36615			44
410000				36572			45
420000				36532			45
430000				36494			47
440000				36459			46
450000				36425			47
460000				36393			47
470000				36363			48
480000				36335			49
490000				36308			49
500000				36282			50
510000				36258			50
520000				36234			51
530000				36212			52
540000				36191			53
550000				36171			53
560000				36152			54
570000				36134			55
580000				36116			56
590000				36099			56
600000				36083			57
610000				36068			58
620000				36053			59
630000				36039			60
640000				36025			61
650000				36012			61
660000				36000			62
670000				35987			63
680000				35976			64
690000				35964			67
700000				35953			66
710000				35943			67
720000				35933			68
730000				35923			69
740000				35913			70
750000				35903			73
760000				35894			73
770000				35885			74
780000				35877			75
790000				35868			76
800000				35860			77
810000				35852			79
820000				35844			80
830000				35836			81
840000				35828			82
850000				35821			84
860000				35814			85
870000				35806			88
880000				35799			88
890000				35792			89
900000				35785			91
910000				35778			92
920000				35772			94
930000				35765			95
940000				35759			97
950000				35752			98
960000				35746			100
970000				35739			102
980000				35733			103
990000				35727			105
1000000				35721			107

Using RCS for fine adjustment would really make this landing method easy!

[brusura]

Wow wonderfull Alterbaron, thanks a lot for you work

[Sauron]

I bow down to your numbers and shiny graphs. Thanks!

[Diche Bach]

Excellent stuff!!

[intidragon]

Sir I do believe that you science a lot. xD Nice charts though, very well-done.

[alterbaron]

Thanks!

I just realized that I forgot to add a link to the charts for other atmospheric bodies. I've added it to the main post.