Longest Hover Challenge

[Petabyte]

Well, it's pretty simple. Try to get the longest hover time on a spacecraft.

This is my first post on the KSP forums. I have been playing the game for a few years though.

Rules:

• Must be between 10-1000m
• Can't touch the ground during hover
• No jet engines, only solid/liquid rocket fuel
• No use of aerodynamics/wings to fly
• Be honest :-)
• A video isn't required but it would be better.
• No parallel staging
• No engine more than once

Leaderboard:

vyznev - 9.5 minutes

Edited April 2, 2020 by Petabyte

[vyznev]

By "spacecraft", I assume you mean a rocket-powered one? Because I'm pretty sure I could build a solar and/or RTG powered helicopter than can hover forever. Possibly even without using DLC parts, although it'd certainly be much easier with the Breaking Ground motors.

Also, I assume this should be done on Kerbin, and that the altitude is to be measured from the surface and not from sea level. (If you wanted, you could specify an airless celestial body like the Mun or Tylo instead to definitely rule out any non-rocket solutions. But you do need to require a specific body, or everyone will choose Gilly.)

[Petabyte]

2 hours ago, vyznev said:

By "spacecraft", I assume you mean a rocket-powered one? Because I'm pretty sure I could build a solar and/or RTG powered helicopter than can hover forever. Possibly even without using DLC parts, although it'd certainly be much easier with the Breaking Ground motors.

Also, I assume this should be done on Kerbin, and that the altitude is to be measured from the surface and not from sea level. (If you wanted, you could specify an airless celestial body like the Mun or Tylo instead to definitely rule out any non-rocket solutions. But you do need to require a specific body, or everyone will choose Gilly.)

Yes, it should be on Kerbin, with a liquid fuel engine. I wasn't very clear on that. It also can't take advantage of wings + aerodynamics.

It also can not use jet engines.

Edited March 4, 2020 by Petabyte

[Pds314]

Is staging allowed?

[vyznev]

...and I assume staging is also not allowed?

Anyway, with those restrictions, I figured the optimal craft ought to be fairly simple: take the engine with the highest sea-level specific impulse, which turns out to be the Mammoth.* Stack enough fuel on it to put the sea-level thrust-to-weight ratio just over 1.0 and add the lightest probe core available. Then just turn on SAS, launch at full throttle and slowly throttle down as the fuel is depleted and the TWR goes up.

*) The Vector engine has the same sea-level Isp as the Mammoth, but the Mammoth produces 4 times as much thrust as the Vector while weighing slightly less than 4 times as much, so using the Mammoth saves a bit of dead weight.

And it worked. This was really supposed to be just a test run, so I didn't bother recording video, and I did go briefly above 500 m at the beginning because I didn't throttle down soon enough. But this thing hovers beautifully.

Spoiler

 

I noticed I was drifting slowly west, so I decided to see if I could fly over the VAB and maybe even land on it.

Still plenty of fuel left. Can I get over the astronaut complex too?

Yep, easily. I wonder if I can reach the helipad?

Nope, not quite. I decided to aim for a landing on the admin parking lot instead.

This is the last screenshot I managed to grab before landing. The mission timer says 09:28, and the remaining burn time estimate is 3 seconds, so I figure I probably just about hit the 09:30 mark before touching down.

Here's a final postcard shot taken after landing. As you can see, I even managed to touch down without breaking anything.

 

So, yeah, pretty nice flight, if I may say so myself. Nine and a half minutes is way longer than I expected.

In fact, I was quite surprised that my hover time was longer than the Mammoth engine's Isp of 295 seconds (i.e. just under 5 minutes), since I originally assumed that this should be the theoretical upper limit. However, I realized my mistake afterwards: the Isp gives the maximum time that the engine could theoretically support its initial fuel load while hovering in normal Earth (or Kerbin) gravity, assuming that the weight of the engine itself and any fuel tanks etc. was negligible. But since the craft gets lighter as the fuel is depleted, and that allows the engine to be throttled down, the actual maximum possible hover time is longer.

 

[ralanboyle]

Okay, so rocket power only, no props or jets. You might want to add that to the list of rules.  

[Petabyte]

I'm raising the max height to 1000m. 500 is just too little.

[vyznev]

BTW, I worked out the actual theoretical upper limit on the hover time. It turns out that I got very close to it. 

For those interested, let me briefly explain the math:

Spoiler

At a perfect hover, the thrust of the engine should be exactly equal to the weight of the rocket at all times. In other words, ƒ(t) = 9.81 m/s² • m(t), where ƒ(t) is the thrust force and m(t) is the mass of the rocket at time t.

The thrust of the engine ƒ(t) is equal to its specific impulse I_sp times the fuel consumption rate –ṁ(t), which equals the rate at which the mass of the rocket decreases over time. Thus, we get a simple differential equation:

ṁ(t) = –9.81 m/s² • m(t) / I_sp

(where the standard gravitational acceleration of 9.81 m/s² is sometimes subsumed into the definition of I_sp, giving it units of seconds instead of m/s). Now, differential equations might seem like arcane magic if you haven't studied them, but this is the very simplest kind of them all, and has a simple and well known solution:

m(t) = m(0) • exp(–9.81 m/s² • t / I_sp)

where m(0) is the total (wet) mass of the rocket at launch (or, more precisely, at the start of the hover). Now, when the remaining mass m(t) equals the dry mass m_dry of the rocket, then the fuel runs out and the rocket cannot hover any longer. This happens when:

t = –ln(m_dry / m(0)) • I_sp / 9.81 m/s²

To obtain the maximum possible hover time, we thus need to maximize I_sp and minimize the ratio of dry to wet mass. So how do we do that?

Let's first figure out what the optimal dry/wet mass ratio is. Obviously, the dry mass includes the mass of the engine m_E and of any other non-fuel-containing parts on the rocket, which at a minimum means a single OKTO2 probe core with mass m_P = 0.04 t. The rest of the rocket will consist of fuel tanks, of which we'd like to choose the type with the lowest dry/wet mass ratio. In KSP, it turns out that there's not much difference between the various types:

Quote

Their mass fully fuelled with liquid fuel and oxidizer is between 8 and 9 times higher than the dry mass. The lower ratio of 8 applies to all fuel-containing Mk2 and Mk3 fuselages and adapters, along with the C7 brand adapters (2.5 m to 1.25 m). All other tanks have the higher ratio of 9.

OK, so as long as we avoid the Mk2/Mk3 parts and the C7 adapters, all other LF+Ox tanks in stock KSP have the same dry/wet mass ratio of 1/9. This means that:

m_dry = m_E + m_P + 1/9 • (m(0) – m_E – m_P) = 1/9 • m(0) + 8/9 • (m_E + m_P)

and thus:

m_dry / m(0) = 1/9 + 8/9 • (m_E + m_P) / m(0)

Now all we need to know is the initial wet mass or the rocket m(0). For optimal hovering, this should be equal to the maximum mass that the engine can lift at full thrust. Looking at the original equation ƒ(t) = 9.81 m/s² • m(t), this implies that m(0) = ƒ(0) / 9.81 m/s², where ƒ(0) is the maximum atmospheric thrust of the engine. Thus:

m_dry / m(0) = 1/9 + 8/9 • 9.81 m/s² • (m_E + m_P) / ƒ(0)

BTW, it's worth noting here that, as the mass m_P of the probe core is basically negligible, (m_E + m_P) / ƒ(0) is approximately the inverse of the thrust-to-weight ratio ƒ(0) / m_E of the engine. Thus, to minimize the dry-to-wet mass ratio of the rocket, we need to choose the engine with the highest TWR. Looking at the list of stock KSP liquid fueled rocket engines, the Mammoth both has the highest sea-level TWR and is tied with the Vector for highest I_sp. So my intuition was right — it is indeed the best stock LF rocket engine for this task.

So, with the engine choice made, let's plug in some numbers. The Mammoth's mass is m_E = 15 t, it produces ƒ(0) = 3746.03 kN of thrust at sea level and consumes 1294.88 kg/s of fuel and oxidizer to do it, for a sea-level I_sp = 3746.03 kN / 1294.88 kg/s = 2892.96 m/s. So we get:

m_dry / m(0) = 1/9 + 8/9 • 9.81 m/s² • 15.04 t / 3746.03 kN = 0.14612

t = –ln(0.14612) • 2892.96 m/s / 9.81 m/s² = 567.2 seconds

So that's the maximum amount of time that a rocket with a Mammoth engine (and an OKTO2 probe core) could hover in place at sea level on Kerbin.

So it turns out that the theoretical maximum time a rocket with a single Mammoth engine (which should be the optimal choice among the stock engines) can hover at Kerbin's sea level is 567.2 seconds, or 9 minutes 27.2 seconds. In principle, we could do slightly better by sticking together multiple Mammoth engines and fuel tanks with just one probe core. But all this achieves is spreading the tiny 0.04 t mass of the OKTO2 probe core over multiple engines. In the limit, this would be equivalent to just removing the mass of the probe core from the equation, which turns out to increase the hover time by less than 0.2 seconds.

But wait, how was my rocket still hovering at 9:28 seconds into the flight, then?  Well, the reason is because I wasn't hovering at sea level. Even a couple hundred meters of extra altitude is enough to slightly decrease the air pressure and increase the thrust that the engine produces for a given fuel consumption rate. For example, a quick check using the delta-v menu in the VAB shows that at 500 m above sea level the maximum thrust of the Mammoth engine increases from 3446.03 kN to 3766.9 kN. Plugging that improved thrust into the formulas above gives an I_sp of 2909.07 m/s and a maximum hover time of 570.9 seconds, or 9 minutes 30.9 seconds.

Of course, I clearly didn't quite manage to reach that theoretical optimum. Besides imperfect flying, one reason is that my rocket was slightly underweight at only 375.04 t of wet mass at launch,  almost 7 tonnes short of the optimal sea-level m(0) = 381.858 t, which is enough to drop my rocket's theoretical maximum hover time (at 500 m ASL) down to just 569.06 seconds. Adding a few more fuel tanks (say, an FL-T800 and an FL-T400, for a total launch mass of 381.79 t) could've maybe allowed me to squeeze out that extra second or two of hover time.

OK, so can this magic limit of nine and a half minutes be beaten? Well, maybe, sort of:

• We could try using DLC parts. The Mastodon engine from Making History has a better sea-level TWR than the Mammoth, although its I_sp is worse. Alas, a quick calculation suggests that, even clustered, it can only hover for 559.65 seconds at sea level, which is slightly worse than the Mammoth.
• Obviously, if the altitude limits are to be measured from the ground, then we could haul the rocket to a mountain top and hover there. This would not only increase the rocket's thrust, but also (very slightly) reduce the force of gravity. Off the top of my head, I'm not sure what the Mammoth engine's thrust would be 500 m above Kerbin's highest mountain top, and I've spent way too much time researching this already to bother trying to find out, but just plugging in the engine's vacuum thrust of 4000 kN gives a theoretical hover time of 610.66 seconds. It might be possible to break the 10 minute limit this way.
• We could go full Kerbal and try using SRBs instead! Alas, it would seem that, despite their impressive sea-level TWR, they all lose to LF engines both in I_sp and in their dry/wet mass ratio (which is fixed, since all the fuel comes with the engine and you can't add more). FWIW, the Clydesdale would probably be the best of the lot, with a theoretical hover time of 404.17 seconds at sea level. In any case, since you can't throttle SRBs (and since stock KSP won't even let you adjust the thrust curve), the only way to hover with them would be to cluster multiple engines with different burn rates and fire them in a carefully planned sequence.

(I'll leave adjusting the figures above for the new 1 km height limit as an exercise for now. You can probably squeeze out a couple more seconds of hover time from that.)

Edited March 6, 2020 by vyznev

[EveMaster]

Well, this challenge has been solved and analyzed thoroughly by vyznev now. I like the idea of hovering for a challenge, so I was thinking what could be done to still make it interesting.

Propeller driven crafts can hover indefinitely if they have RTGs as an energy source. So these should not be allowed. Solar power is not available during night so it would be interesting to see how long after sunset a craft can continue hovering on battery power. Can it even make it to the next moring? I doubt it. Especially if you don't allow for wings/aerodynamic surfaces. There could be two categories for this challenge: with and without wings.

Another type of hovering craft could be a rotating hovering craft. Jet engines will get no intake air if you are just hovering without movement. If you mount air intakes on the tips of a rotating craft they should get some intake air. It would be interesting to see how long you can hover using this intake air and jet engines. The rotation can be caused by reaction wheels or by jet engines. Optionally, only a part of the craft could rotate.

[vyznev]

1 hour ago, EveMaster said:

Well, this challenge has been solved and analyzed thoroughly by vyznev now. I like the idea of hovering for a challenge, so I was thinking what could be done to still make it interesting.

Actually, I had an idea for a spinoff challenge. I won't spoil it quite yet, but it feels interesting (and way more challenging that just hovering in place). I'll just need to record a video to show that it's doable… 

Edit: Here we go…

 

Edited March 7, 2020 by vyznev

[Petabyte]

I am allowing staging now. This should allow for a much more interesting challenge.

[kspnerd122]

I used Microtanks to get a huge amount of fuel in a small space, then I just lit the singular vector engine and asparagus staged the tanks, this got me a total time of just under 13 minutes.

[sevenperforce]

On 3/6/2020 at 6:13 PM, EveMaster said:

Jet engines will get no intake air if you are just hovering without movement.

The jet intakes all have suction at zero forward airspeed.

On 3/8/2020 at 1:02 PM, Petabyte said:

I am allowing staging now. This should allow for a much more interesting challenge.

On the other hand it becomes a "whose computer can handle the highest part count" challenge, which is not as interesting.

To make it more interesting you could do a "no parallel staging and no engine more than once" rule which would be very interesting.

[Petabyte]

On 3/30/2020 at 12:57 PM, sevenperforce said:

The jet intakes all have suction at zero forward airspeed.

On the other hand it becomes a "whose computer can handle the highest part count" challenge, which is not as interesting.

To make it more interesting you could do a "no parallel staging and no engine more than once" rule which would be very interesting.

Thanks. I'll add that.

[EveMaster]

6 hours ago, Petabyte said:

Thanks. I'll add that.

You can add that. I'm not sure with the zero air intake at zero forward speed, however.

I just assumed that it is the case and that the initial air in the intakes is to overcome this.

I found no clear information about this and have not performed tests myself.

A hint that I might be wrong is the following post:

On 3/30/2020 at 7:57 PM, sevenperforce said:

The jet intakes all have suction at zero forward airspeed.

[kspnerd122]

I used 1 vector engine for the flight along with liberal part clipping part count is 200 Oscar tanks

[sevenperforce]

2 hours ago, kspnerd122 said:

I used 1 vector engine for the flight along with liberal part clipping part count is 200 Oscar tanks

Why would you clip? Oscars are denser than any other case but their mass ratio is the same as every other tank. Clip them if you need to avoid drag, but this is a hover test where drag is nonexistent.

3 hours ago, EveMaster said:

I'm not sure with the zero air intake at zero forward speed, however.

I just assumed that it is the case and that the initial air in the intakes is to overcome this.

I found no clear information about this and have not performed tests myself.

Take a spaceplane into a suborbital flight until intake air is exhausted. Close the intakes. Re-enter and glide to a landing; stop. Open the intakes and restart. You'll note that there is intake air at zero forward airspeed.

[kspnerd122]

the reason why i clipped is because otherwise it would not fit on the launchpad