Challenge Rescue in Antartica (paper, pencil and a calculator)

[dgatsoulis]

I was refreshing my DGIV skills today, going through the mission scenarios folder. Then i remembered that back in the DGIII, there was an extra mission, that appears to no longer be a part of the mission scenarios. I think the name was "Rescue in Antartica" or something similar. The general idea was that a DGIV had crash-landed somewhere in Antartica and you had a limited amount of time to go and save the crew, using only the data from the AE-35 antenna.

So here is the challenge. (Default DGIV settings).

You are in a DGIV sitting on Lpad1 of KSC with a heading of 90 degrees.
You turn on the AE-35 antenna to locate the disabled craft.
The data you receive from the antenna is: Rel. heading 110.495 degrees and distance 11799 km.

1.Find the true heading, true distance and the disabled ship's longitude and lattitude.
2.Calculate the launch azimuth for the suborbital flight.
3.Use the scenario editor to place a DGIV on Lpad1 of KSC (heading 90) and another at the coordinates you found.
4.Take off and land within 50 km of the target and pick up the crew.
5.Take off and land back at KSC.

Help/Hints:
#1 The first part is a trigonometry problem. You can find all the formulas you need [ame="http://en.wikipedia.org/wiki/Law_of_cosines"]here[/ame] and here.
#2 The second part is a bit trickier. You need to know your ship and take the planet's rotation into account.
#3 I'm not posting a scenario, because it will be interesting to see and compare the coordinates and launch azimuth(s) that will be found, by those that try the challenge.
#4 AerobrakeMFD is your friend, but since there is no base to target, you'll have to keep an eye on the Pe/landing position coordinates.
#5 For the fifth part, you'll need to calculate a new launch azimuth for the suborbital flight back to KSC. Fuel will be very limited. (And the launch azimuth might surprise you).

Post your step by step calculations here and if you manage to make the flight, a succesfull playback.

Have fun, happy (sub)orbiting

 

[Grover]

could someone please post a scenario with the two craft placed? although i could probably work out the positions myself, im too lazy, but the flight sounds rather challenging; ive never flown the DGIV suborbital before, and seeing antarctica is a new one for me (lets hope my hover engines dont melt too much ice below me on final approach... else Al Gore will have another inconvenient truth: "you split Antarctica up"

 

[Napalm42]

Wow, I will really be hard pressed on this one.

I think I might add a personal challenge thanks to Grover, and limit the amount of time I can use hover/low attitude thrust before the ice begins to suffer severe melting.

That'll probably be a 20 m/s descent quickly reduced to 1 or 2 just before touchdown, should be fun.

 

[Spacethingy]

Penguins and hydrazine don't mix well, just thought you should know...

Sounds fun, I'll give it a go!

 

[Notebook]

Penguins, just follow the...
http://www.orbiter-forum.com/showthread.php?t=8555&highlight=penguin+droppings

N.

 

[RisingFury]

could someone please post a scenario with the two craft placed? although i could probably work out the positions myself, im too lazy,

#3 I'm not posting a scenario, because it will be interesting to see and compare the coordinates and launch azimuth(s) that will be found, by those that try the challenge.

The point is to make your own scenario.

The only thing that could be posted would be the starting scenario: DGIV sitting on pad 1 at Cape Canaveral, facing east.

 

[Tommy]

Just to save people a bit of time, the coordinates for KSC L-Pad 1 are 28.522764 (Lat) X -80.675896 (Lon).


I've had a chance to do the math, but won't have time to try the flight til next week probably. Second DG seems to be somewhere south of Australia - I won't say exactly where my figures show!

 

[Tommy]

Had just enough time to set up a scenario and give it a quick try. I had been hoping that I could use the antenna to verify my crash co-ordinates, but no luck there. On the DGIV trying to target the crashed vessel yields an "axis error".

I also found that DockMFD can target the crashed DGIV if you use the TGT button - and that told me the distance (no real heading info) of 11.8M, so I'll take that as a clue that my math was OK.

None of the other stock MFD's will target a landed vessel, it seems.

Just had time for a short "test flight" to try and get familiar with the DGIV again - been a while since I've flown one. The test showed that I need to re-think my ascent, etc, if I'm going to make the round trip without an extra fuel cargo. I used half the fuel, and I'm not sure I had enough energy to get to the crash site. After I had spent more fuel landing I wouldn't have had enough fuel to get back.

I'll try the flight again sometime this week, and we'll see what happens.

 

[dgatsoulis]

I had been hoping that I could use the antenna to verify my crash co-ordinates, but no luck there. On the DGIV trying to target the crashed vessel yields an "axis error".

That's odd, you should get a "pitch limit" msg, but the antenna should return rel. heading and distance values.
From your previous post "...south of Australia..." and the verification from DockMFD, i'd say that you have the right coordinates.

Just had time for a short "test flight" to try and get familiar with the DGIV again - been a while since I've flown one. The test showed that I need to re-think my ascent, etc, if I'm going to make the round trip without an extra fuel cargo. I used half the fuel, and I'm not sure I had enough energy to get to the crash site. After I had spent more fuel landing I wouldn't have had enough fuel to get back.

With the "PRO904SPECx" ascent autopilot (for both take-offs), my fuel usage was ~57-58% (main) to get to the disabled craft and after cross-feeding from the RCS tank, i landed back at KSC with about 150 kg of total fuel.

 

[Tommy]

That's odd, you should get a "pitch limit" msg, but the antenna should return rel. heading and distance values.
From your previous post "...south of Australia..." and the verification from DockMFD, i'd say that you have the right coordinates.

Well, one of the delays in flying this is due to problems with my 2010P1 install - I get CTD's when trying to transfer from one vessel to another, etc. It's not a clean install, so I need time to diagnose the problem and find out what I installed that is messing things up.

Also, as I said it's been a while since I used the DGIV, so it's possible that it is showing the rel heading and distance - just not where I expect to see it? I was short on time, so I didn't see if there was a FC mode that displayed that - just saw the axis error message and moved on.

I'm fairly confident in my math - even though my math-fu is weak. I used a fairly "blunt object" approach that relies on very basic geometry and trig - so it's not elegant but it should get the job done. I also relied heavily on the second page you linked to - especially the section about halfway down that calculated a Great Circle path based on starting location, initial heading , and range. The only part that was even a little bit "tricky" was converting the chord length to the arc length ... (don't want to give up to many hints yet).

With the "PRO904SPECx" ascent autopilot (for both take-offs), my fuel usage was ~57-58% (main) to get to the disabled craft and after cross-feeding from the RCS tank, i landed back at KSC with about 150 kg of total fuel.

This is the heart of my current problem. I can get a DGIV into orbit quite a bit more efficiently than the AP - but I need to tailor that ascent profile for a suborbital flight. I haven't done a suborbital in an DGIV, and I've gotten used to the XR series - which uses a different ascent profile and has a much higher glide ratio.

I think it's just a matter of getting used to the DGIV again, so I can set up a survivable skip to get me to the target. It seems that the DGIV is a bit less forgiving on 2010 than it was on 2006 - when most other vessels seem to be more forgiving on 2010. I just need to find enough Orbiter time to adjust - rather than having Real Life force me to be in a hurry and trying to force the issue. Hopefully sometime this week - but no promises what with all the Thanksgiving obligations this week.

At any rate - it's nice to have a challenge that isn't easily solvable simply by my IMFD skills alone. Even though I use IMFD to help account for planetary rotation!

 

[dgatsoulis]

I 'll go ahead and place another "hint" here, that may or may not be so obvious.
Everything on Earth's surface, moves from West to East, at a rate of 360 degrees/day ~ 0.25 degrees/minute.

You are trying to hit a moving target.

If you know how much time it will take you, to get to your destination, then you know by how much you have to aim ahead of it.

 

[Tommy]

Well, I've completed the flight. Or should I say flights - the recorder doesn't handle UMMU transfers, so I made two recordings. Even the gear status isn't recorded - the viewer will have to press the "g" key at the appropriate times during playback to raise and lower the gear.

BTW, how did you get the ascent autopilot to accept a heading with over 2 digits?

Anyway, I'll put together a little PDF with my math and explanations, then pack it with the flight recordings, and post it in a couple days.

 

[dgatsoulis]

BTW, how did you get the ascent autopilot to accept a heading with over 2 digits?

Easy, i launched at the correct heading, and then i waited untill the speed was over 500 m/s. Then I used the autopilot.

Anyway, I'll put together a little PDF with my math and explanations, then pack it with the flight recordings, and post it in a couple days.

Looking forward to seeing that! I've done something similar, myself! It will be nice to compare notes.

 

[Napalm42]

For all of my experience, I can't for the life of me hit that target. I'll just wait until some instructions come out. I can do any sort of interplanetary mission, but when you tell me suborbital, don't expect a fing.

 

[Tommy]

Easy, i launched at the correct heading, and then i waited untill the speed was over 500 m/s. Then I used the autopilot.

I see. I used a very different profile - but since I'm quite out of practice with the DG-IV I sort of "missed" the optimum and figure I wasted about 4 -5 kg of fuel on the first ascent. Second was a bit better - but still not great.

It would be interesting to know how long it took you to complete this, I took 1:45, with 7 minutes on the ground at the crash site. With a bit of practice I could easily shorten that up with more aggressive braking.

For all of my experience, I can't for the life of me hit that target. I'll just wait until some instructions come out. I can do any sort of interplanetary mission, but when you tell me suborbital, don't expect a fing.

There will be a couple of "tricks" in my pdf, ways of using MFD's in ways they weren't really designed for, that will help you with that. The first flight is still pretty tricky.

 

[dgatsoulis]

BTW, how did you get the ascent autopilot to accept a heading with over 2 digits?

I'm sorry, I probably didn't understand the question very well, in my previous reply. The PRO904SPECxxx (hover take-off) and the PRO903... (normal take-off) autopilots, accept a 3 digit format for the heading. Writing PRO904SPEC090 is the same as PRO904SPEC90.

then i waited untill the speed was over 500 m/s

My comment was about the slight correction that was needed after the take off.

It would be interesting to know how long it took you to complete this, I took 1:45, with 7 minutes on the ground at the crash site. With a bit of practice I could easily shorten that up with more aggressive braking.

Very similar to yours. I think it was about 97 minutes, with 3 minutes on the ground at Antartica.

There will be a couple of "tricks" in my pdf, ways of using MFD's in ways they weren't really designed for, that will help you with that. The first flight is still pretty tricky.

This will be very interesting to see. I have tried to use IMFD for suborbital flights, but my results were not very good.
The way I go about it, is to try and make a relatively accurate estimate of how much time the flight will take me (in minutes) and then multiply that with 0.25 to see how many degrees to the east my target will "move", by the time I get there. (360 degrees/day ~ 0.25 degrees/minute).
Then I add the result to the target's longitude and find the bearing for the new coordinates.

 

[Tommy]

When I tried to use the AP for the ascent it didn't seem to accept more than 2 digits - it's possible I have a different release of the DG-IV, or just don't know how to use it!

My "trick" with IMFD didn't work as well as I'd hoped - but another MFD from the same guy (hint, hint) proved very useful for directional corrections.

My launch heading adjustments were "seat of the pants", based on experience - and the heading was fudged "to the right" on both ascents! I also used a lower altitude "skimming" flight so minor corrections were possible.

Should be posting the files in this week sometime.

 

[Tommy]

So, I haven't had a chance to put together that pdf, and now I can't find the paper with all the math on it, etc.

Still, I'll post the flight recordings, and explain the process I used to figure out the position of the crash site, etc.

ABOUT THE RECORDINGS: The DGIV doesn't record animations, so you will have to operate the landing gear. A note will tell you when. The turbo pump is also not recorded, so more fuel is used on the actual flights. Mission is broken into two flights, and I allowed 7 minutes on the ground at the crash site.

The DGIV's panel doesn't respond to the mouse during playback. You can use glass cockpit mode to set MFD's, etc. Shortly into the second flight (TommyReturn) the low fuel warning is triggered - and you won't be able to shut it off!

THE MATH:

My math-fu is weak, so while I'm sure there is a more elegant and efficient way to do this, I just took a hammer to the problem. The second page that dgatsoulis gave (to movable-type.co.uk) was very helpful. A little ways down the page is a calculator that takes a starting location, direction, and distance, and finds the destination.

Starting location is easy. I fire up Orbiter, open the scenario editor, and place a DGIV on Pad one at KSC. Set the heading to 90, and take note of the latitude and longitude.

Direction isn't hard either. I simply add the relative direction provided to the current heading and get 200.495.

Distance is a bit trickier. I have a straight line distance (11799 km), but the calculator wants a geographical distance. I'm sure there's a simple way to convert a chord distance to an arc length - but can't remember how. I'll have to use an intermediary stage - convert to angular distance first.

Imagine, if you will, a circle. I'll place point A the the center. I'll place two more points on the circle (B and C) to represent my starting and ending destinations. It doesn't need to be perfectly to scale, so I'll place them on each side, about a third of the way up. I draw radial lines from A to B and from A to C, and draw a straight line from B to C. This makes an Isosceles triangle. Sided AB and AC are equal to the radius (6371 km) and BC is 11799 km). I need to determine the angle of A.

I suppose I could have googled up a site like this one: http://ostermiller.org/calc/triangle.html - but I didn't. I added a fourth point (D) in the middle of line BC, then add a line from A to D. This creates two right triangles. Looking at triangle ABD I see that I know the hypotenuse (side AB) and the side opposite (side BD, length is 1/2 the length of BC), and sine = opposite over the hypotenuse. My calculator converts that to an angle, which I double to get my angular distance. Then, Angular Distance is divided by 360, then multiplied by the circumference of the Earth to yield the arc length.

At long last, I can input the distance into that calculator we mentioned earlier, and it provides up with the coordinates of the crash site. It also provides our "Final Heading", which I also take note off. Later, I subtract 180 from that and use it for my initial heading on the return trip.

I'll also hit the "view map" link, so I can see my target and course on a map - how nice!

THE FLIGHTS:

The headings that I have don't account for the Earth's rotation. I could make calculation, like dgatsoulis, or I could be lazy and just guess. The crash site is pretty close to the pole, so it won't move that far. I'll aim about 5 degrees to the right - maybe less, call it 205 degrees even. For the return I'll need a larger offset, about 15 degrees.

It's been quite I while since I drove one of these, so my ascents were far from perfect. I was also rather timid with the braking, and could easily shave at least 5 minutes or more off each leg.

As for navigation, the first leg is a bit tricky. There is no base to target, and the only stock MFD that can target a LANDED vessel is DockMFD! This at least provides us with a distance. AerobrakeMFD isn't much help without a target, but I know about where the site is on the map, so it can help a bit with energy management, but won't be very accurate. As for direction, the solution is BaseSyncMFD. It has the ability to target a co-ordinate, not just a base. One we are up to speed it will help us fine tune our heading. I'll use a skip re-entry method (rather than a single ballistic hop) to allow for heading corrections.

As you can see, I could have been much aggressive and delayed braking - saving time and fuel on the first leg, and more time on the second leg. The first landing (hover) took longer than it should have, and I screwed up a bit on the return trip - let myself get under the glideslope during the alignment turn and had to use a bit of power on final.

Still, it got the job done!
View attachment TommyRescue.zip

 

[dgatsoulis]

Great job Tommy! :thumbup:

As the maths go, we did pretty much the same thing. Starting location and bearing were straightforward to find, but distance was trickier. I also used the pythagorean theorem, first finding half the angle and then doubling it to find the true distance. Any difference in our calculations is from roundoff errors and nothing else.

Once you have starting point-bearing-distance, it's not too difficult to calculate the target's coordinates. (link with the equations and shortcuts on post #1 of this thread).

For the launch azimuth, I tried to make a good estimate for my TOF and then see how much my target will move, by the time i get there. (Everything moves to the East at 0.25 degrees/min)
On the PDF attached here, I explain my reasoning and also give some examples of different ships and different departure/arrival sites. The first part may seem a little complicated at first, but with that equation, one can make a somewhat accurate estimate of how long the flight will take.

For the TOF, I got 50.67 minutes, multiplied it with 0.25 and added the result to my target's longitude. Then I calculated the bearing for the "new" coordinates. This would be my launch azimuth. The result was 204.25 degrees.

As for the flight, I took off with the PRO904SPEC204 autopilot and after reaching 500 m/s, I made a small correction to try and get that 0.25 degrees to the "right". - Important note: Must have the correct azimuth, before the ship reaches ~800-900 m/s speed.

I already knew the coordinates of my target and had a pretty good idea where it was on the map. I trusted my launch azimuth calculation so I let the AP burn the engines untill the groundtrack on MapMFD was above it. Then I pitched the ship to about 40 degrees AoA and used AerobrakeMFD to see if i needed more or less thrust to get to my target. The difficulty here is that there is no base to target.
I used the "map" page of AerobrakeMFD to see on what coordinates i was going to land and made the slight adjustments that were needed. DockMFD was on the other panel and after the reentry, I landed a few hundreds of meters away from the disabled DGIV.

The journey home was easier. I used the same method to calculate the launch azimuth, but this time, there was a base to target. Fuel was tight but enough to make it. To my surprise the same AP that I had used to get here, got me to a higher ApA than before, making my reentry more aggressive at first, but the DGIV could easily handle it.

I hope that the ones that tried this challenge enjoyed it, even if they were not successfull.

Playback attached. Remember to raise your gear right after the take offs and press "Backspace" to engage the turbo-pumps, ~40-50 secs later. Also lower the gears before the landings.

Have fun, happy (sub)orbiting

 

[Gr_Chris_pilot]

I think this PDF can be really useful!

http://www.freelancepilot.nl/ATPL summary.pdf
Page 3 General navigation :thumbup: