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Serious Scientific Answers to Absurd Hypothetical questions


DAL59

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Have been into some debates with some guys on the Children of a Dead Earth forums of late. Many different themes, but one of them that I'm a bit baffled by: laser, reflectance and space warfare.

Game portrays lasers in the 13 MW to 100MW ballpark as being fairly effective in space combat. The list of materials that can be used to armor ships is probably about 75% complete: meaning, out of all the actual elemental, alloy and composite materials one could conceive using to armor a spaceship in the near term, the game includes a large fraction of them I'm guessing.

But here is the thing: reflectance is treated as being utterly irrelevant. I find this rather difficult to believe given that the LIGO 1MW lasers are blasting away at the mirrors in those machines for months or years now and may well function without having to be shut down and repolished or replaced for many years.

What do you guys say? Are space ships with reflective armor to foil lasers impossible or highly probable?

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8 hours ago, Green Baron said:

Airliners are not "routinely" tested at supersonic flight. If you browse the web you'll find out that trying so would most probably have fatal consequences. Engines choke out, profiles stall, control surfaces loose flow and fly off, frames get overloaded. Pick one (if you had enough power to cross the sound barrier, which an airliner does not have). Vne/Mmo is usually around Mach 0.9.

Edit: Vne = never-exceed-speed ... or exceed-once-speed :-)

Not really disagreeing here, but VNE and MMO are not really equivalent (even though they are both speed limits). MMO is due to Mach buffet, and is basically a limit for controllability. VNE is essentially a limit on dynamic pressure and is a structural concern.

Also, these are certification speeds. They don't really mean the airplane will fall apart or go out of control if you exceed them, but they do mean that it might! Basically, you are guaranteed that it won't happen if you stay under those limits, but there are no guarantees above them. As a pilot, you have no idea how big the margin is (if any) -- all you know is that the FAA (or EASA, etc.) has guaranteed that if you do stay below them you will be OK.

Edited by mikegarrison
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58 minutes ago, Diche Bach said:

Have been into some debates with some guys on the Children of a Dead Earth forums of late. Many different themes, but one of them that I'm a bit baffled by: laser, reflectance and space warfare.

Game portrays lasers in the 13 MW to 100MW ballpark as being fairly effective in space combat. The list of materials that can be used to armor ships is probably about 75% complete: meaning, out of all the actual elemental, alloy and composite materials one could conceive using to armor a spaceship in the near term, the game includes a large fraction of them I'm guessing.

But here is the thing: reflectance is treated as being utterly irrelevant. I find this rather difficult to believe given that the LIGO 1MW lasers are blasting away at the mirrors in those machines for months or years now and may well function without having to be shut down and repolished or replaced for many years.

What do you guys say? Are space ships with reflective armor to foil lasers impossible or highly probable?

There have to be some limits to reflectors. They aren't 100% perfect, so they must absorb some photons. I would guess that as they do that, they heat up. If you dump enough energy into them quickly enough, I imagine you will overwhelm them and they will simply explode/vaporize rather than reflect.

My guess is that a mirror that could reflect a 1MW laser all day long might be nearly-instantly destroyed by a 100 MW laser. But you would have to test it.

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1 minute ago, mikegarrison said:

There have to be some limits to reflectors. They aren't 100% perfect, so they must absorb some photons. I would guess that as they do that, they heat up. If you dump enough energy into them quickly enough, I imagine you will overwhelm them and they will simply explode/vaporize rather than reflect.

My guess is that a mirror that could reflect a 1MW laser all day long might be nearly-instantly destroyed by a 100 MW laser. But you would have to test it.

So in short: reflectance SHOULD matter in a game that bills itself "the most realistic space warfare simulator ever made." Perhaps a ships surface reflectance is a factor which (like whipple shielding) offers only brief mitigation of damage, but that is more than simply "Reflectance is irrelevant" and not modeled.

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14 hours ago, mikegarrison said:

What's your source for this?

Decades-ago reading, probably of the exact article you linked.  My memory isn't perfect, but I'd have sworn the DC-8 "supersonic" (actually, just high transonic) dive was something that was repeated multiple times.  I might, however, be conflating that incident with something else involving another design.

2 hours ago, mikegarrison said:

My guess is that a mirror that could reflect a 1MW laser all day long might be nearly-instantly destroyed by a 100 MW laser. But you would have to test it.

A 100 MW laser would heat your near-perfect mirror 100x faster than the 1 MW beam.  The limit to what you can reflect is whether you can keep the substrate under the reflective layer cool enough that the layer isn't disrupted.  Further, even without any kind of active cooling, it'll take time to apply enough heating to the mirror/substrate combination to cause damage.  A ruby laser pulse that will burn through a razor blade will reflect off an aluminum-on-glass first-surface mirror without incident, but a similar power level in a continuous beam will destroy the mirror fairly quickly.

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1 hour ago, DAL59 said:

If all land on Earth was replaced with water, what would happen?  

(and all water was replaced with land)

If all the land on the planet is flattened equally across the world to allow the water to spread equally too, then the entire planet earth will be covered by water, a plametwide ocean with uniform depth of 200 meters deep

If all water is replaced by land, then global climate would be messed up. Wind and weather patter would no longer following their regular pattern and desertification might spread since there's no water anymore

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13 hours ago, Green Baron said:

Airliners are not "routinely" tested at supersonic flight. If you browse the web you'll find out that trying so would most probably have fatal consequences. Engines choke out, profiles stall, control surfaces loose flow and fly off, frames get overloaded. Pick one (if you had enough power to cross the sound barrier, which an airliner does not have). Vne/Mmo is usually around Mach 0.9.

Edit: Vne = never-exceed-speed ... or exceed-once-speed :-)

Don't you have to at least test some fudge factor?  Googling around says that a 757 flies less than mach .8, so a bit less than mach 0.9 is probably fast enough (although I don't think any test pilot will want to be a few hundredths from Vne).  I'm pretty sure one needed to be rated to something like mach 0.85 and the requirements including testing past mach 1.0, that may have been what was remembered.  Modern planes seem to fly slower than those designed nearer to the Concorde.

And then there are issues about *measuring* Vre (releative airspeed.  Since Vne is measured relative to air it doesn't help to know what ground control or GPS thinks  you are going).  And in small craft it is said to be "the gauge that lies".  Hopefully airlines pay for non-lying Vre meters.

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5 minutes ago, wumpus said:

Don't you have to at least test some fudge factor?  Googling around says that a 757 flies less than mach .8, so a bit less than mach 0.9 is probably fast enough (although I don't think any test pilot will want to be a few hundredths from Vne).  I'm pretty sure one needed to be rated to something like mach 0.85 and the requirements including testing past mach 1.0, that may have been what was remembered.  Modern planes seem to fly slower than those designed nearer to the Concorde.

And then there are issues about *measuring* Vre (releative airspeed.  Since Vne is measured relative to air it doesn't help to know what ground control or GPS thinks  you are going).  And in small craft it is said to be "the gauge that lies".  Hopefully airlines pay for non-lying Vre meters.

The airplane is certified to be safe within those speed limits. It's not certified to be safe outside them. That's really all that an operating pilot needs to know, generally speaking.

I really don't know for sure the exact details of how it is tested. And I probably couldn't go into detail on a forum if I did, to be blunt. But I do know that the manufacturers and the NAAs (airworthiness authorities) agree on a test plan in advance, then conduct the testing to verify it.

As for measuring airspeed, this is quite simple with modern instruments. Since we are talking about large civil transports, it's a given that they have accurate knowledge of their airspeed. The only time this is ever really a problem is if the pitot tubes somehow get blocked.

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5 hours ago, Diche Bach said:

Have been into some debates with some guys on the Children of a Dead Earth forums of late. Many different themes, but one of them that I'm a bit baffled by: laser, reflectance and space warfare.

Game portrays lasers in the 13 MW to 100MW ballpark as being fairly effective in space combat. The list of materials that can be used to armor ships is probably about 75% complete: meaning, out of all the actual elemental, alloy and composite materials one could conceive using to armor a spaceship in the near term, the game includes a large fraction of them I'm guessing.

But here is the thing: reflectance is treated as being utterly irrelevant. I find this rather difficult to believe given that the LIGO 1MW lasers are blasting away at the mirrors in those machines for months or years now and may well function without having to be shut down and repolished or replaced for many years.

What do you guys say? Are space ships with reflective armor to foil lasers impossible or highly probable?

The simple calculation we use to determine a laser's effectiveness is to divide the laser's energy by the surface area of the spot at the target, then find out the depth of the cylinder created if all of the laser's energy is used to vaporize the target material. Lasers do not penetrate opaque materials so we only deal with the top-most millimeter layer at a time. 

The calculation is sufficient for most cases, but fails at extremely high or extremely low laser intensities.

Reflectance comes into play at the lower intensities. If the target reflects 95% of the laser beam, it is absorbing 5% of the laser energy. From that 5%, we must deduct the energy that is dissipated through conduction into the surrounding material. What remains heats up the material. 
All materials are only reflective within a specific range of temperatures. Some degrade at rather low temperatures and become charred and black. Reflectivity decreases as the temperature decreases. By the time the material melts, it can be considered a perfect blackbody absorbing all radiations. 

With weapons grade lasers, the intensity of the beam at the target is so high that no material can get rid of its heat through conduction and it heats up very quickly even if it is only absorbing 5% of the beam or less. Here is an example:

A 10MW UV beam focused by a 2m wide mirror is focused on a target 1000km away. 
The spot radius is 0.061m and the surface area is 0.0117m^2. The beam intensity is 855MW/m^2. 
If the target material is aluminium, we can expect 90 to 95% of the laser to be reflected away. The target only absorbs 1MW at an intensity of 85.5MW/m^2. 
Aluminium has a thermal conductivity of 209W/mK. A 0.0117m^2 area a millimeter thick heated to room temperature can conduct 667.6kW to the surrounding material. It radiates an additional 0.5W. So, the millimeter thick layer gets heated up at a rate of 332kW. 

Aluminium has a heat capacity of 0.91kJ/kg.K and a density of 2700kg/m^3. A 0.0117m^2 layer of 1mm thick aluminium masses 31.6 grams. 334kW is enough to raise 31.6 gram of aluminium from a temperature of 273K (freezing) to 993K (melting) in about 0.06 seconds.

In practice, this figure is even lower. As the aluminium heats up, it loses reflectance and absorbs more of the laser's energy. This means it starts melting even faster. Once it is molten, it absorbs nearly 100% of the laser beam's energy, so our simple calculation becomes accurate again. 

With even more megawatt, reflective surfaces are even less of a worry. 

Their only use is to keep armor safe at extreme distances. For example, if the laser beam was being focused from a distance of 10000km, the laser spot covers a 1.17m^2 area instead. The thermal conductivity is now 66.7MW at room temperature. Absorbing only 1MW of the beam's energy means the aluminium remains safe. 

4 hours ago, mikegarrison said:

There have to be some limits to reflectors. They aren't 100% perfect, so they must absorb some photons. I would guess that as they do that, they heat up. If you dump enough energy into them quickly enough, I imagine you will overwhelm them and they will simply explode/vaporize rather than reflect.

My guess is that a mirror that could reflect a 1MW laser all day long might be nearly-instantly destroyed by a 100 MW laser. But you would have to test it.

Yes. 'Weapons' grade lasers simply means that they overwhelm any target's material properties. 

Pulsed lasers are even more dangerous. A short pulse might deliver energy at GW or TW rates, even if the average beam power is a million times lower. This short pulse is enough to vaporize the surface of the target, leaving behind a rough and hot scar. This scar is not very reflective... 

4 hours ago, Diche Bach said:

So in short: reflectance SHOULD matter in a game that bills itself "the most realistic space warfare simulator ever made." Perhaps a ships surface reflectance is a factor which (like whipple shielding) offers only brief mitigation of damage, but that is more than simply "Reflectance is irrelevant" and not modeled.

As demonstrated above, reflectance is a factor... but for tenths of a second at most. The lasers in CoaDE are not accurate enough to be used at distances where reflectance matters either, so it is not a great loss to the game's accuracy if it is left out altogether. 

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9 hours ago, Diche Bach said:

Have been into some debates with some guys on the Children of a Dead Earth forums of late. Many different themes, but one of them that I'm a bit baffled by: laser, reflectance and space warfare.

Game portrays lasers in the 13 MW to 100MW ballpark as being fairly effective in space combat. The list of materials that can be used to armor ships is probably about 75% complete: meaning, out of all the actual elemental, alloy and composite materials one could conceive using to armor a spaceship in the near term, the game includes a large fraction of them I'm guessing.

But here is the thing: reflectance is treated as being utterly irrelevant. I find this rather difficult to believe given that the LIGO 1MW lasers are blasting away at the mirrors in those machines for months or years now and may well function without having to be shut down and repolished or replaced for many years.

What do you guys say? Are space ships with reflective armor to foil lasers impossible or highly probable?

Apparently reflectance is factored in, it just stops being relevant very quickly. I’ve seen QSwitched cite aluminium outer armour as being dirt-cheap and light-coloured, hence more resistant to lasers than its thermal properties alone would suggest... but not by much.

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8 hours ago, wumpus said:

Don't you have to at least test some fudge factor?  Googling around says that a 757 flies less than mach .8, so a bit less than mach 0.9 is probably fast enough (although I don't think any test pilot will want to be a few hundredths from Vne).  I'm pretty sure one needed to be rated to something like mach 0.85 and the requirements including testing past mach 1.0, that may have been what was remembered.  Modern planes seem to fly slower than those designed nearer to the Concorde.

And then there are issues about *measuring* Vre (releative airspeed.  Since Vne is measured relative to air it doesn't help to know what ground control or GPS thinks  you are going).  And in small craft it is said to be "the gauge that lies".  Hopefully airlines pay for non-lying Vre meters.

Well, i have been a little drastic, an airliner might not immediately disintegrate once it goes transsonic, but it isn't healthy at all. A few airliners actually have accidentally been in that area and afaik most of them recovered without serious damage, some with damage. But doing so voluntarily like in a full power steep dive at 35000ft might end in a disaster.

Fortunately the thrust an airliner can produce is not enough to push the whole thing near soundspeed in level flight, so there is that. Look at the profiles and cross section of a 747 from the front and compare it to the Concorde for example. Also flight computers, if unmanipulated and engaged, will keep a pilot from being so stupid as to try a steep dive.

Engines fade out because they aren't constructed for that regime, laminar flow around the lifting surfaces tears off, control surfaces loose efficiency, vibrations might loosen them.

Airliners, their airframes, wing profiles, configurations, are all constructed for economic flight and safety.

Edited by Green Baron
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1 hour ago, Green Baron said:

Airliners, their airframes, wing profiles, configurations, are all constructed for economic flight and safety.

With this, I can completely agree.

Back to the original question, of whether you could (with a hand-waved "adequate engine") push a B-52, 737, or DC-8 into orbit , well, of course you could.

IFF you keep speed low enough to avoid breaking up the airframe until the air is thin enough not to matter, and can support the weight by other than aerodynamics for a while during the period when stall speed exceeds maximum safe speed and air is still thick enough to cause damage (i.e. too thin to hold you up, too thick to ignore).  A simplistic flight profile, given TWR => 1, would be to pull into vertical climb from normal flight, and stay vertical until air is no longer a big concern, then tilt gradually into horizontal to "transition" (more or less like a VTOL) from vertical to orbital flight.  If TWR < 1, you'll never get there with an airframe that can't take high Mach numbers.

Getting the aircraft back down will be left as an exercise -- I don't want to be anywhere near a B-52 during reentry.

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On the topic of supersonic airliners:

Could an airliner reach Mach 1? Yeah sure, but so can a rock, doesnt mean you'd want to fly one.

Take a look at a supersonic fighter jet. Look at the horizontal stabilisers. They are slab-like, all-moving affairs, ie: there is no seperate "elevator" flap.

This is because in the transonic region, shockwaves are set up across wing surfaces. These shockwaves interfere strongly with the airflow over the trailing edge, almost completely removing all control authority from elevators, and in the early days of supersonic research, there were many "unexplained" incidences of aircraft falling out of the sky for no apparent reason. Only later was it discovered that this (amongst other things and other incidents) was the likely cause.

Combine this with the "Mach Tuck" phenomenon (and a 0.85Mach-rated airliner may not have the capacity to alter its centre-of-mass enough to compensate even just for that) and aircraft have to be carefully designed to operate in/around the trans/supersonic regime.

Modern airliners are however designed with transonics in mind, many obvious design features are there to improve performance in the transonic region, but there are many features appropriate to the supersonic regime that are conspicuously absent, eg: the all-moving slab tailplanes.

I certainly wouldnt bet my life on any airliner surviving anything other than a brief foray to just above the sound barrier.

Gross structural integrity should not be ignored either, the dynamic pressure on the front surfaces of the aircraft will rise significantly with speed. With the square of speed, even. As will temperature, which will in turn, also affect structural properties.

 

FunFactTM: the "bulge" at the front of a 747 actually reduces transonic drag by smoothing cross-sectional area changes, just like wasp-waisted fighter jets (see: area rule). Same goes for those aerodynamic bodies you see under the wings.

main-qimg-793fcfb4a678f4962ddecda36ddbee

Edited by p1t1o
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1 hour ago, p1t1o said:

FunFactTM: the "bulge" at the front of a 747 actually reduces transonic drag by smoothing cross-sectional area changes, just like wasp-waisted fighter jets (see: area rule). Same goes for those aerodynamic bodies you see under the wings.

main-qimg-793fcfb4a678f4962ddecda36ddbee

It's a little more complicated than that. Wave drag is only part of the drag, the upper deck on the 747 was not designed for area rule but rather to allow the nose loading for the freighter, and you have to put the flap actuators somewhere.

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41 minutes ago, mikegarrison said:

It's a little more complicated than that. Wave drag is only part of the drag, the upper deck on the 747 was not designed for area rule but rather to allow the nose loading for the freighter, and you have to put the flap actuators somewhere.

All true, but they do reduce drag :)

I believe the "bulge" was extended specifically to take advantage, and the anti-shock bodies which house flap actuators are far wider than they would otherwise be.

"One interesting outcome of the area rule is the shaping of the Boeing 747's upper deck.[9] The aircraft was designed to carry standard intermodal containers in a two-wide, two-high stack on the main deck, which was considered a serious accident risk for the pilots if they were located in a cockpit at the front of the aircraft. They were instead moved above the deck in a small "hump", which was designed to be as small as possible given normal streamlining principles. It was later realized that the drag could be reduced much more by lengthening the hump, using it to reduce wave drag offsetting the tail surface's contribution. The new design was introduced on the 747-300, improving its cruise speed and lowering drag, with the side effect of slightly increasing capacity on passenger flights."

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17 hours ago, MatterBeam said:

 . . . SNIP . . .

As demonstrated above, reflectance is a factor... but for tenths of a second at most. The lasers in CoaDE are not accurate enough to be used at distances where reflectance matters either, so it is not a great loss to the game's accuracy if it is left out altogether. 

Interesting stuff! Thanks for answering :)

So, to see if I get this by putting it my laymans terms:

The 1 MW LIGO laser does not incinerate its mirror (even though it would incinerate a human head) because . . .

(a) it is only 1 MW not 10MW

(b) its wavelength (or other characteristics) is tuned for the properties of the mirror

(c) the mirror (and or other aspects of the mechanism) is made of exactly the right materials that it can always disssipate more heat than it absorbs and thus stay cool despite being bombarded by photons for months and years at a time

(e) some combination of some or all the above

 

ADDIT: to put it another way: It is quite obvious one can build a functioning laser + mirror pair in which the mirror will REFLECT the laser, and not be damage, for a very long time (if ever)--at least up to 1MW.

Why would it NOT be possible to device general purpose mirrors that could reflect combat lasers, and not be damaged--at least up to a certain laser power?

Edited by Diche Bach
grammar
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5 hours ago, p1t1o said:

"One interesting outcome of the area rule is the shaping of the Boeing 747's upper deck.[9] The aircraft was designed to carry standard intermodal containers in a two-wide, two-high stack on the main deck, which was considered a serious accident risk for the pilots if they were located in a cockpit at the front of the aircraft. They were instead moved above the deck in a small "hump", which was designed to be as small as possible given normal streamlining principles. It was later realized that the drag could be reduced much more by lengthening the hump, using it to reduce wave drag offsetting the tail surface's contribution. The new design was introduced on the 747-300, improving its cruise speed and lowering drag, with the side effect of slightly increasing capacity on passenger flights."

I still think that's not really correct. It does show that the original design, with the shorter hump, does not really "area rule" properly, because it gets big and then small again before the area starts expanding around the wings. And this shorter hump has always been maintained for the purpose-built freighters. When they expanded the upper deck and called it the -300, the reduction in wave drag was something of a bonus. The main purpose was just to fit in more seats. But somehow a whole mythology grew up around this little wave drag effect until people started believing that the whole design had been about area ruling.

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9 hours ago, p1t1o said:

On the topic of supersonic airliners:

Could an airliner reach Mach 1? Yeah sure, but so can a rock, doesnt mean you'd want to fly one.

Take a look at a supersonic fighter jet. Look at the horizontal stabilisers. They are slab-like, all-moving affairs, ie: there is no seperate "elevator" flap.

This is because in the transonic region, shockwaves are set up across wing surfaces. These shockwaves interfere strongly with the airflow over the trailing edge, almost completely removing all control authority from elevators, and in the early days of supersonic research, there were many "unexplained" incidences of aircraft falling out of the sky for no apparent reason. Only later was it discovered that this (amongst other things and other incidents) was the likely cause.

Combine this with the "Mach Tuck" phenomenon (and a 0.85Mach-rated airliner may not have the capacity to alter its centre-of-mass enough to compensate even just for that) and aircraft have to be carefully designed to operate in/around the trans/supersonic regime.

Modern airliners are however designed with transonics in mind, many obvious design features are there to improve performance in the transonic region, but there are many features appropriate to the supersonic regime that are conspicuously absent, eg: the all-moving slab tailplanes.

I certainly wouldnt bet my life on any airliner surviving anything other than a brief foray to just above the sound barrier.

Gross structural integrity should not be ignored either, the dynamic pressure on the front surfaces of the aircraft will rise significantly with speed. With the square of speed, even. As will temperature, which will in turn, also affect structural properties.

 

FunFactTM: the "bulge" at the front of a 747 actually reduces transonic drag by smoothing cross-sectional area changes, just like wasp-waisted fighter jets (see: area rule). Same goes for those aerodynamic bodies you see under the wings.

main-qimg-793fcfb4a678f4962ddecda36ddbee

Makes sense, and as an safety feature avoiding coffin corner and RUD if you get into issues diving fast because of cabin pressure fail or other issues. 
You would however not want to break the sound barrier with an 747. I assume that would call for major service overall. 
I was in an small 4 seat plane with an friend as pilot, he few over an cliff and the downdraft got us to decent very fast. 
I was nervous trying to avoid bumping into the right seat stick getting pulled forward in the seat, the guy in the back was just screaming :)
The pilot later explained that he was so nervous during the decent, not because we could crash but because we was close to pass the max allowed speed for the plane. 
If that happened it would need major overhaul and he would get serious issues as it belong to the club and he did an noob mistake. 

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1 hour ago, mikegarrison said:

I still think that's not really correct. It does show that the original design, with the shorter hump, does not really "area rule" properly, because it gets big and then small again before the area starts expanding around the wings. And this shorter hump has always been maintained for the purpose-built freighters. When they expanded the upper deck and called it the -300, the reduction in wave drag was something of a bonus. The main purpose was just to fit in more seats. But somehow a whole mythology grew up around this little wave drag effect until people started believing that the whole design had been about area ruling.

That the freighters version was not updated point that the drag reduction was not significant. An longer upper deck is more expensive but pretty redundant on freight planes and using the lower upper deck on freighter then qualified for passenger flight would be easy  
Redundant as you don't need so much crew transfer and using it for passengers would not be easy as you had to register it as an passenger planes. (yes its cheating with this, selling crew or military tickets on the black marked)
On the passenger version an long upper deck is nice for first class 

Flew an weird 474 once there the back part was for cargo. That they they loose the nice nose loading but guess it matched their mission profile, we should be allowed extra luggage however 

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13 minutes ago, magnemoe said:

Flew an weird 474 once there the back part was for cargo. That they they loose the nice nose loading but guess it matched their mission profile, we should be allowed extra luggage however 

That's known as a "combi". Some combi airplanes have the freight in front and the passengers in back. Others have the reverse.

A "convertible" airplane is another way to share passengers and freight on the same airframe (but not at the same time). In the case of a convertible the passenger cabin is palletized. So you can slide the passenger cabin out the cargo door and you have a freighter. If you want to carry passengers again, you just slide the passenger cabin back in.

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how few gs does a planet have to have before you can place a golfball in orbit with a typical drive. assume the drive takes place atop a mountain so that periapsis is roughly at position of the ball atop the tee.

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1 hour ago, Nuke said:

how few gs does a planet have to have before you can place a golfball in orbit with a typical drive. assume the drive takes place atop a mountain so that periapsis is roughly at position of the ball atop the tee.

A pro drive is about 200 mph, that's 90 m/s using a system that makes sense.

Orbital velocity is v2 = GM / r. Using density makes is more useful here because we don't know the mass of the planet, so M = (4/3)*pi*r3*rho.

Put everything together using density about 2000 kg/m3 (average density for a large asteroid), and you find that your planet should have a radius of about 150 km.

That's a very large asteroid which would have a mass of 2e19 kg and a surface gravity of 0.06 m/s2 (1/150th of a g).

Edited by Gaarst
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1 hour ago, Nuke said:

how few gs does a planet have to have before you can place a golfball in orbit with a typical drive. assume the drive takes place atop a mountain so that periapsis is roughly at position of the ball atop the tee.

Not a matter of how many or how few G at surface; it's what the orbital velocity is.  A "typical" drive, good for 250+ meters (I'm no Tiger Woods, and neither are you) leaves the tee at around 70-80 m/s.  Periapsis, in this case, will always be at the location of the tee, though rotation of the body will drag the whole surface under the periapsis over one rotation.

Well, what bodies have an orbital velocity around 70-80 m/s?  Minmus is fairly close, Gilly's too small, Ike may be closer than Minmus (IIRC Minmus has an low circular velocity under 50 m/s).

However: keep the surface gravity constant, and expand the body (like running a rescale mod in KSP) and the escape and orbital velocities both increase, because the larger surface radius gives a slower gravity reduction (remember, gravity drops off as the square of radius).  One example: Kerbin's orbital velocity is close to 2300 m/s; Earth's, with the same surface gravity, is just over double that figure.

So: you could have a body with 1 g at surface and drive a golf ball into orbit, if the body was small enough -- it'd be roughly 18% the size of Kerbin (1/30 the velocity requires square root of 1/30 radius).  Better delete the atmosphere, or your ball will still show as "suborbital" and it'll come down before it's gone all the way around...

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