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Tricky14

Is a one day, solar polar race possible?

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I've been tinkering on ever faster,  stabler rovers for a while and I am starting to wonder if I can do it. Starting at the KSC from the very crack of dawn (on empty batteries), the further north I get, the longer it takes for the sun to set. The start is slow, but it picks up quickly. If I can just hit a sweet spot, can I 'follow' the sun all the way to the North pole? Average speed on flat terrain is about 57 m/s (FAR installed). Presume a straight route up to the north, I found a path that doesn't veer far from it.

Edited by Tricky14
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Kerbin is 600km in radius so you need to go 2*pi*600/4 or about 942km, or let's say 1000 for easy math and to account for deviations.

You have 3 hours from sunup to sundown.

To travel 1000km in 3 hours, you need to go 333km/hr or 5.55km/m or 92.5m/s.

That's about 1.6 times your max speed.

I don't know how much more time you get at the poles due to the sun taking longer to set, but don't think it's that much? If it gave you an entire extra hour you'd need to go 250km/hr or 4.17km/m or about 70m/s, which is still not doable.

Also you'd have to drive a rover for 3 (or 4, or 5) hours non-stop without making a single mistake, or multiple quicksaves that eat into your average speed.

Edited by 5thHorseman
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3 hours ago, 5thHorseman said:

I don't know how much more time you get at the poles due to the sun taking longer to set, but don't think it's that much? If it gave you an entire extra hour you'd need to go 250km/hr or 4.17km/m or about 70m/s, which is still not doable.

That's the whole gimmick. As you aproach the north pole, the available time approaches infinity. You should gain increasingly more time, much more than one hour if you can progress fast enough.

 

What I *should* probably do is create a little plane that flies stable at about 57 m/s and see if I can reach the north pole with that before sundown... something for next weekend maybe.

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4 minutes ago, Tricky14 said:

That's the whole gimmick. As you aproach the north pole, the available time approaches infinity. You should gain increasingly more time, much more than one hour if you can progress fast enough.

I think that's a very minor thing until you're at the ice cap though. I'd place a station about the size of a rover at various latitudes and see how many hours of light you get. I suspect it's 3 hours (+/- a little for mountains and the tallness of your base, plus whatever the game considers where sunlight comes from).

4 minutes ago, Tricky14 said:

What I *should* probably do is create a little plane that flies stable at about 57 m/s and see if I can reach the north pole with that before sundown... something for next weekend maybe.

I hope you have an autopilot. That's a shade over 4 1/2 hours of work.

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@Tricky14

Why only solar?

Isn't the whole idea of driving there by any means possible a achievement in and of itself?

Using fuel cells and or jet engines will get you there guaranteed. 

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12 minutes ago, Tricky14 said:

You must be new here. :wink:

Not sure what made you say that. Is it something I said?

I don't think it's possible to do what you want and 5thhorsemen explained why. Electric rovers can't get the speed required so I gave advice in reconsidering the challenge rules.
But for some reason I'm new here :/ Newish at best but I think that includes yourself also.

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Posted (edited)

The primary KSP question is never why. It's why not.

I have reached the north pole in a few (quite) different vehicles already, including solar. But I've never managed to do so in one solar day, so I just want to challenge myself. What better reason is there?

The speed required **may** be sufficient if I can get enough of an advantage on the decreasingly slower moving/setting sun as I travel north. The advantage is constantly increasing and eventually reaches infinity. I've done some test drives up to about one hour this weekend (without plotting an optimal course) and I was able to make sufficient progress toward my intended half-way marker at 1.5 hours.

I think I have a fair shot at this. Will definitely record and publish the final attempt it if I manage it.

Edited by Tricky14
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Would the differential steering exploit work? I've never used it, but I've heard it can be get a rover to around 80 m/s

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4.7 hours / 4 for physical time acceleration is just under 1.2 hours. Totally doable amount of time. Of course that means you've gotta be able to drive a rover that's going 280m/s as far as your reactions are concerned.

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Posted (edited)

TL;DR: Arc your path eastward and 57 m/s should be just barely enough.

Kerbin's full day is 6 hours. I.E. There are 3 hours of sunlight at any given location. That's 10800 seconds. Kerbin's sea level radius is 600 kilometers.

So the question is, can you get to the north pole before you run out of daylight?

What is the distance to the pole? The diameter of a circle is 2*pi*r, and r is 600 km, but you only need to go 1/4th the diameter of the circle in order to reach the pole. That is 942,477 meters.

The minimum speed required to reach the pole before dark, going directly north, is therefore, is 87.27 m/s.

Based on this, I shall say that, no, you cannot reach the pole before the sun sets on the KSC in your current rover, which would take 4.6 hours.

That being said... you can go eastward to extend the daylight on your rover's location.

For example, once you're north of latitude 70.938 degrees, 57 m/s is enough to keep the sun constantly in view. If you can reach 71 degrees and the sun hasn't set, that's enough to reach the pole, even though you're still 199,613 meters away. So how long does it take to reach this point at 57 m/s?

Sadly, about 3 hours, 37 minutes, and 13 seconds at 57 m/s, which is slightly too long.

But wait, we can delay the sunset even if we can't delay it indefinitely.

The question is, what is the optimal angle at any given latitude to gain the most latitude for a given amount progress of the sun towards setting?

The equation for ground speed is G=cos(L)*pi*600,000/10800 where G is ground speed and L is the latitude.

The equation for westward speed is W=V*cos(H) where W is westward speed, V is speed, and H is heading.

The equation for sun progression rate is: P=(1 + W/G) * pi/10800, where P is progression rate in radians/sec, G is ground speed at that latitude, and W is westward speed. P=(1 + W/G) * 180/10800 for degrees/second.

The equation for northward speed is N=V*sin(H) where N is northward speed, V is speed, and H is heading.

It should be clear, then that our goal is to optimize northward speed over sun progression rate, N/P, which, broken into constituent parts, looks like: N/P=(V*sin(H))/((1 + W/G) * pi/10800)

Which becomes: N/P=(V*sin(H))/((1 +(V*cos(H))/(cos(L)*pi*600000/10800)) * pi/10800)

Which simplifies down to:  N/P=5400000*V*sin(H)/(9*V*cos(H)*sec(L) + 500*pi)

Thus, you should NOT start heading due north. This only achieves a steady N/P = 195152 meters/radian of sun movement, or about N/P = 3406.0 meters/degree of sun movement.

Instead, turn to a heading of 109.06 degrees. 19.06 degrees off from true north. This maximizes your initial N/P at 207319 meters/radian, or 3618.4 meters/degree. It achieves by slowing the sun progression by 10.7% while northward movement is only slowed by 5.5%.

You need to turn gradually more eastward:
Here is a chart I made indicating where the sun will be in degrees, how efficient your movement will be, and what direction you must be facing for optimal efficiency.

LAT    LAT/sun prog    Total sun prog    Heading
0         0.383925    0                              109.061943345
10       0.384639    26.0467539233    109.367329850
20       0.386997    52.0451576213    110.337347397
30       0.391800    77.8851512130    112.154769523
40       0.401156    103.408377349    115.234990630
50       0.421303    128.336335550    120.535996151
55       0.441414    140.204278574    124.707128899
60       0.479224    151.531513324    130.781054485
62.5    0.513307    156.748280431    135.014066676
65       0.571735    161.618660145    140.603269967
67.5    0.695173    165.991315309    148.584572053
68       0.740794    166.710560734    150.669565470
68.5    0.799589    167.385512205    153.010671021
69       0.881379    168.010833464    155.687529840
69.5    1.005080    168.578126308    158.835932924
70       1.221740    169.075599146    162.721732691
70.5    1.754090    169.484851524    168.061126383
71                            169.769899612

As you can see, the sun progression will get quite far, BUT it is doable. Your rover should eventually be able to reach the north pole without the sun ever quite setting on it. You may have to go almost due east for quite some time, but with enough persistence, a 57 m/s rover can make it to the pole on sunlight alone. Maybe not "in a day" because it will involve a considerably longer journey, but certainly without the sun setting if you can indeed follow that path pretty reasonably.

Edited by Pds314
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Although TBH you're better off, especially in FAR, making an electric prop. Why go 57 m/s when you can go 200?

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I'm starting to think the "solution" is to add 4 hours of battery to the rover.

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16 hours ago, Pds314 said:

eastward

Westward. Sun rises in the East and sets in the West. The big problem of course being that northwest of KSC is where all the water is, which will make roving a bit problematic.

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On 9/30/2018 at 9:10 PM, Tricky14 said:

I've been tinkering on ever faster,  stabler rovers for a while and I am starting to wonder if I can do it. Starting at the KSC from the very crack of dawn (on empty batteries), the further north I get, the longer it takes for the sun to set. The start is slow, but it picks up quickly. If I can just hit a sweet spot, can I 'follow' the sun all the way to the North pole? Average speed on flat terrain is about 57 m/s (FAR installed). Presume a straight route up to the north, I found a path that doesn't veer far from it.

I did a solar pole challenge, I found "sailing" with extended solar panels very effective, I could charge while driving.

Have a look (warning, long blog)

 

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Posted (edited)

@Tricky14 Does only solar permit the use of batteries? Remember that real life solar cars got them. They require batteries when it's cloudy during solar race challenges so it should be part of a solar car.

If you stack a bunch you can get quite a few km extra. Top speed is mostly determined by drag and remember that you also go down quicker when you weigh more. With batteries you can begin your journey when its still very, very dawn (still night) to get some distance on battery power and then do the rest on solar. I'm not sure if it pays off in the end as the battery weight slows you down a tiny bit and a bit more uphill. You may allow yourself to stage them after dawn and do the rest on solar power from there on.

edit: I tested a quik rover with only batteries. It used 1/20th the amount of stored EC and did 52m/s average (200kph) but that is without solar panels and cockpit. It traveled 12.5km so could do 250km. Expect 150-200km for a fully equipped solar rover.

520dW59.jpg

Edited by Aeroboi
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You should pack some batteries for head start (preferrably for 2-3 hours of driving) at early dawn using battery power, and after the sun is able to charge your battery, start accelerating in bursts. Remember, battery power is only consumed when you press W, so you can save battery power by accelerating and let the momentum/ downward slope move your rover while your battery is continuously being charged. Accelerate only when going on upward slope or maintaining momentum to avoid going too slow. When the sun sets, hit the gas (by this point your battery should have plenty of electricity) to go all the way to north pole

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Posted (edited)
On 10/1/2018 at 1:57 PM, roboslacker said:

Would the differential steering exploit work? I've never used it, but I've heard it can be get a rover to around 80 m/s

I may be wrong, but I think that only works for the very large wheels? Not sure how easily they break in this current version, but I used to have to go out and repair them all the time even without the steering exploit.

On 10/2/2018 at 5:17 AM, joshudson said:

4.7 hours / 4 for physical time acceleration is just under 1.2 hours. Totally doable amount of time. Of course that means you've gotta be able to drive a rover that's going 280m/s as far as your reactions are concerned.

I should have made a pod racer.

On 10/2/2018 at 1:08 PM, Pds314 said:

TL;DR: Arc your path eastward and 57 m/s should be just barely enough.

Kerbin's full day is 6 hours. I.E. There are 3 hours of sunlight at any given location. That's 10800 seconds. Kerbin's sea level radius is 600 kilometers.

So the question is, can you get to the north pole before you run out of daylight?

What is the distance to the pole? The diameter of a circle is 2*pi*r, and r is 600 km, but you only need to go 1/4th the diameter of the circle in order to reach the pole. That is 942,477 meters.

The minimum speed required to reach the pole before dark, going directly north, is therefore, is 87.27 m/s.

Based on this, I shall say that, no, you cannot reach the pole before the sun sets on the KSC in your current rover, which would take 4.6 hours.

That being said... you can go eastward to extend the daylight on your rover's location.

For example, once you're north of latitude 70.938 degrees, 57 m/s is enough to keep the sun constantly in view. If you can reach 71 degrees and the sun hasn't set, that's enough to reach the pole, even though you're still 199,613 meters away. So how long does it take to reach this point at 57 m/s?

Sadly, about 3 hours, 37 minutes, and 13 seconds at 57 m/s, which is slightly too long.

But wait, we can delay the sunset even if we can't delay it indefinitely.

The question is, what is the optimal angle at any given latitude to gain the most latitude for a given amount progress of the sun towards setting?

The equation for ground speed is G=cos(L)*pi*600,000/10800 where G is ground speed and L is the latitude.

The equation for westward speed is W=V*cos(H) where W is westward speed, V is speed, and H is heading.

The equation for sun progression rate is: P=(1 + W/G) * pi/10800, where P is progression rate in radians/sec, G is ground speed at that latitude, and W is westward speed. P=(1 + W/G) * 180/10800 for degrees/second.

The equation for northward speed is N=V*sin(H) where N is northward speed, V is speed, and H is heading.

It should be clear, then that our goal is to optimize northward speed over sun progression rate, N/P, which, broken into constituent parts, looks like: N/P=(V*sin(H))/((1 + W/G) * pi/10800)

Which becomes: N/P=(V*sin(H))/((1 +(V*cos(H))/(cos(L)*pi*600000/10800)) * pi/10800)

Which simplifies down to:  N/P=5400000*V*sin(H)/(9*V*cos(H)*sec(L) + 500*pi)

Thus, you should NOT start heading due north. This only achieves a steady N/P = 195152 meters/radian of sun movement, or about N/P = 3406.0 meters/degree of sun movement.

Instead, turn to a heading of 109.06 degrees. 19.06 degrees off from true north. This maximizes your initial N/P at 207319 meters/radian, or 3618.4 meters/degree. It achieves by slowing the sun progression by 10.7% while northward movement is only slowed by 5.5%.

You need to turn gradually more eastward:
Here is a chart I made indicating where the sun will be in degrees, how efficient your movement will be, and what direction you must be facing for optimal efficiency.

LAT    LAT/sun prog    Total sun prog    Heading
0         0.383925    0                              109.061943345
10       0.384639    26.0467539233    109.367329850
20       0.386997    52.0451576213    110.337347397
30       0.391800    77.8851512130    112.154769523
40       0.401156    103.408377349    115.234990630
50       0.421303    128.336335550    120.535996151
55       0.441414    140.204278574    124.707128899
60       0.479224    151.531513324    130.781054485
62.5    0.513307    156.748280431    135.014066676
65       0.571735    161.618660145    140.603269967
67.5    0.695173    165.991315309    148.584572053
68       0.740794    166.710560734    150.669565470
68.5    0.799589    167.385512205    153.010671021
69       0.881379    168.010833464    155.687529840
69.5    1.005080    168.578126308    158.835932924
70       1.221740    169.075599146    162.721732691
70.5    1.754090    169.484851524    168.061126383
71                            169.769899612

As you can see, the sun progression will get quite far, BUT it is doable. Your rover should eventually be able to reach the north pole without the sun ever quite setting on it. You may have to go almost due east for quite some time, but with enough persistence, a 57 m/s rover can make it to the pole on sunlight alone. Maybe not "in a day" because it will involve a considerably longer journey, but certainly without the sun setting if you can indeed follow that path pretty reasonably.

I'll take your very calculated word for it. Plotting out that route is going to be hell though. Need more time to investigate.

On 10/2/2018 at 3:37 PM, Pds314 said:

Although TBH you're better off, especially in FAR, making an electric prop. Why go 57 m/s when you can go 200?

Well here's the thing about that. I already use lifting surfaces to extend the wheel base, make it stable to drive at high speeds. If I add a propellor as well, I've basically build a plane, defeating the point of the exercise.

On 10/3/2018 at 5:22 AM, joshudson said:

I'm starting to think the "solution" is to add 4 hours of battery to the rover.

I did that once, pre 1.2. Gigantic rover. It's perfectly doable, but it takes away some of the challenge.

On 10/3/2018 at 5:35 AM, 5thHorseman said:

Westward. Sun rises in the East and sets in the West. The big problem of course being that northwest of KSC is where all the water is, which will make roving a bit problematic.

b8TtXw1.jpg
12 hours ago, Triop said:

I did a solar pole challenge, I found "sailing" with extended solar panels very effective, I could charge while driving.

Have a look (warning, long blog)

 

Neat. I did this pre 1.2, but they kept breaking.

45 minutes ago, Aeroboi said:

@Tricky14 Does only solar permit the use of batteries? Remember that real life solar cars got them. They require batteries when it's cloudy during solar race challenges so it should be part of a solar car.

If you stack a bunch you can get quite a few km extra. Top speed is mostly determined by drag and remember that you also go down quicker when you weigh more. With batteries you can begin your journey when its still very, very dawn (still night) to get some distance on battery power and then do the rest on solar. I'm not sure if it pays off in the end as the battery weight slows you down a tiny bit and a bit more uphill. You may allow yourself to stage them after dawn and do the rest on solar power from there on.

edit: I tested a quik rover with only batteries. It used 1/20th the amount of stored EC and did 52m/s average (200kph) but that is without solar panels and cockpit. It traveled 12.5km so could do 250km. Expect 150-200km for a fully equipped solar rover.

520dW59.jpg

Fuel cells quickly become the better option because fuel at least loses mass. Tried this a while back, was fairly easy because weight limitation wasn't really a problem. I could basically add as much fuel, fuel cells and rover wheels as I wanted.

30 minutes ago, ARS said:

You should pack some batteries for head start (preferrably for 2-3 hours of driving) at early dawn using battery power, and after the sun is able to charge your battery, start accelerating in bursts. Remember, battery power is only consumed when you press W, so you can save battery power by accelerating and let the momentum/ downward slope move your rover while your battery is continuously being charged. Accelerate only when going on upward slope or maintaining momentum to avoid going too slow. When the sun sets, hit the gas (by this point your battery should have plenty of electricity) to go all the way to north pole

I'm actually starting with completely empty batteries. The first trickle of energy being absorbed from the rising sun is the moment the race begins. With solar panels set up the right way, it doesn't actually take that long for it to pick up speed. Just gotta be careful with the first few hills, as wel as the shadows they cast. I find that the 'oberth effect' also helps. When you're between two hills, accelerate only at the bottom when craft is going at its fastest. Air resistance puts an upper speed limit to how useful this is though. It does works great at the start.

Someone will tell me this is not how the Oberth effect works, or that I'm using the wrong term. This is fine. :lol:

Edited by Tricky14
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This is the craft I've been working on for the past week and a half. It's fairly resistant against accidental spin, tends to recover from it provided it's moving fast enough. Top speed is about 57 m/s, weight is about 2.4 tons, mostly due to the ridiculous wing setup I have currently to stretch the wheel base. Different, less aerodynamic configurations actually bring the weight down to around a ton and a half.

TcVOLzF.jpg

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^if the above craft seems like it uses maybe too many solar panels, that's likely due to Kerbalism which changes some things. I intend to use that mod at a later point to add resource management to different challenges.

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Had my first go at this this evening. Reached the halfway point 25 minutes behind schedule, which I figure I can get down to 10 with further route optimizations. The thing is that beyond that, the 'final' waypoint at the edge of the ice sheet is already visible on my gimbal. It feels close.

I crashed a bunch of times around the middle, mountainous area of the map, so a single run won't happen until I get more used to driving there. However, the rover drrives better at high speeds than I had hoped. Particularly downhill around 60-80 ms it is surprisingly self-stabilizing.

I feel like I can do it. It will be tight for sure, but I'm already noticing I'm gaining on the sunset. I'll try the 'straight' run from the half-way point to the ice sheet tomorrow. I'm a little worried about a mountain range that casts pretty long shadows near the end, so if it doesn't work out I'll continue with Pds314's suggestion to take more of a north-westward approach, starting about 30 km north from where I am now, the point where the ocean gets closest to my route. It's only from there, a little over 1/2 the entire way that I can start heading west. I hope it is enough.

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2 hours ago, Tricky14 said:

I feel like I can do it.

YES YOU CAN !

I'm following this, some pictures would be nice though. :cool:

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uB2rhOg.jpg

 

A little past halfway point I spoke of, close to the ocean.

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Posted (edited)

My first attempt (straight North past the halway-point route) has failed, but I got close enough to entice me to try a few more times.

  • At the 3:00:00 marker I still had light, as anticipated.
  • Around 3:05:00 the shadows started becoming a problem, but I could still quite easily dodge them by staying on the left side of hills and such.
  • By 3:15 the sun was still up *but* higher distant hills began blocking it. By my best estimate the sun actually set roughtly 10 minutes later.
  • I coasted on my remaining battery charge for something like 30 minutes. The challenge was lost at that point, *but* to my own surprise I only ended up 42.7 km away from my second to final marker, the narrow 'glacial passage', a land bridge that connects the ice sheet with the main continent. At my average cruising speed of about 200 kph that would've only taken me about 15 minutes to drive.

 

y2zC5mW.jpg

 

PdcEsSe.jpg

 

I got sooo close to the edge of it!

 

Things I can still optimize:

  1. Route. I think -15 minutes is achievable here, but I'm in an optimistic mood and hoping for -20
  2. Craft weight. An earlier, less aerodynamic rover weighed a full ton less than this current one does.
  3. @Pds314 suggestion to take a westward approach is something I can only take advantage of past the halfway point, due to the ocean. Even if it doesn't gain me time, it will help me avoid those early shadows of the taller hills in the middle of that continent.
  4. Possibly re-arrange the solar panels. I thought the vertical ones were well clear of the rover wheels, but I saw 'blocked by vehicle' maybe 15 minutes before I saw the 'blocked by celestial body' notification.
  5. Spin. With the airplane-like aerodyniamics the rover is really stable at higher speeds, but at lower speeds (below 40 m/s) I do sometimes end up in an unrecoverable spin. While I don't lose too much time getting back on track, near the end the electricity cost becomes a bit too high. Traction contol and further wheel balancing will need to be looked into. Is there a downside to having too much traction control?

 

Edited by Tricky14
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