Impulse Drive: What do we know? (Non-canon speculation)

[John O.]

There is no reason that a warp engine cannot operate at sublight speeds, if the Alcubierre type field is roughly how things work in the Star Trek.

I agree in principle, but it's at least conceivable that there is some minimum velocity associated with the energy output necessary to generate spatial compression, analogous to minimum ionization energy.

I agree that "Warp Drive" and "Impulse Drive" are probably broad umbrella terms for different types of engines that use similar principles. It would sort of be analogous to the terms "Nuclear Powered" and "Conventionally Powered" used today.

I think it's almost always implied by the context that there's a fundamental difference in the physics going on, though, between impulse and warp. It might be more of an appropriate contemporary analogy to refer to subsonic versus supersonic flight. Assuming the 'superluminal barrier' is in fact just an engineering barrier as the sound barrier was, the analogy holds.

That's completely backwards, since a jet engine can work just as well at subsonic as well as supersonic speeds. "Conventional" and "nuclear" powered engines WOULD be consistent with two completely different physical processes, enough to fit the analogy between impulse and warp drives in the same way. That impulse engines can be used at FTL velocities would also reflect this, much the way a nuclear-powered aircraft can probably achieve hypersonic velocities alot more effectively than an ordinary turbojet.

You'd have to be more familiar with the history of the development of supersonic flight to understand my analogy. I'm sorry if that comes off as arrogant, but let me explain - because the reference you're making is to modern day jets with converging-diverging nozzles (which, yes can work at both supersonic and subsonic flight). But before it was discovered that supersonic flows behave differently through a nozzle to subsonic flows, it was impossible to generate supersonic effective exhaust velocities - and therefore impossible to generate supersonic airspeed.

There's probably a couple other ways I could make the analogy relating to normal shocks and how the aerothermochemistry going on kind of changes paradigmatically on the leading surfaces when you approach the speed of sound, but the nozzle area thing is really what I was referring to.

To explain better why I didn't think the analogy between nuclear/conventional worked - yes, the energy generating process going on is different physics - chemical combustion for rockets versus nuclear fission or fusion for nuclear - but in reality, when people talk about "nuclear propulsion" they're usually talking about a nuclear hybrid rocket without really saying it. I'm not telling you anything you didn't know I'm sure, Iim just pointing out that in a nuclear rocket, all you're doing is finding a reaction mechanism that's capable of producing more heat and pressure in the combustion products prior to exhausting them (nuclear) than chemical can. But in essence, a chemical rocket and a nuclear rocket work the same - nuclear just dumps massive heat into the exhaust products that they can disseminate into kinetic energy of the jet (exhaust velocity) which turns into momentum transfer. If you're talking about "nuclear propulsion" in a difference sense like pulsed nuclear sails or RTG-driven ion engines or Prometheus ion engines or VASIMIR or something like that, obviously we're on a completely different topic then but I assumed you were referring to nuclear rocket propulsion.

 

[Crazy Eddie]

when people talk about "nuclear propulsion" they're usually talking about a nuclear hybrid rocket without really saying it.

Actually, in the context of the statement, they're talking about the difference between a pressurized water reactor and chemically fueled engines like oil-fired boilers, diesel engines or gas turbines. IOW, the difference between the USS Long Beach (nuclear powered) and the USS Ticonderoga (conventionally powered).

There's some very different physics going on in these two systems, and a nuclear-powered vessel can be several times faster than a conventionally powered one (epsecially submarines; the Virginias have top speeds upwards of 40 knots, while smaller diesel-electric boats putz around at 10 to 15 knots).

I assumed you were referring to nuclear rocket propulsion.

It wasn't me, it was AtoZ. And the implication was "nuclear powered" vs. "conventionally powered" in the context of naval vessels. The distinction doesn't really exist in space applications since no nuclear propulsion system has ever been flown in an actual launch vehicle.

 

[Mister_Atoz]

Actually, I never meant to make any suggestion of a nuclear powered propulsion system in space. I was simply saying, that from a writer's standpoint, one could make the analogy between an impulse engine and a conventional powered naval vessel. That is to say, Impulse, however it works, is very much a "conventional" spacecraft propulsion system, similar to one we might develop today, only much more advanced. Whereas "warp drive" would be a revolutionary breakthrough in space craft propulsion, with little to no resemblance to anything we might develop today, just as the first nuclear powered naval vessels were quite different from pre-nuclear vessels.

I was referring mostly to Scotty's line in 'Balance of Terror" about the Romulan vessel using "simple impulse". I could see a similar discussion in the cold war era setting, with the captain of a nuclear powered submarine comparing his ship's capabilities against that of an old style diesel electric submarine.

I simply don't have the engineering background to make any analogies in an engineering context.

 

[Crazy Eddie]

"No question. Their power is simple diesel."

 

[Timo]

Many real space craft do mount their orbital engines significantly off-axis from the center of gravity. Those engines are angled so that they fire through the center of gravity regardless of their position; on the space shuttle, they're even gimballed for fine control.

The end result in such setups is that the spacecraft doesn't move bow first, yet bow-first movement is an established Trek fact. Or then there are multiple thrust units angled so that net movement is bow first (say, the angled RCS of the shuttle orbiter allowing for direct X, Y and Z translations), which the Trek ships in turn prominently lack.

"Asymmetric" thrust is something engineers can get away with when thrust overall is not particularly important - say, in spacecraft that may use it for just a fraction of their operational lives. Extremely few aircraft have ever been built with even angled-but-balanced thrust (say, Martin Seamaster), and fewer still with truly asymmetric thrust arrangements (mainly Rutan's funnies), as thrust in aircraft is actually a fairly important thing and thus literally doesn't get shoved aside. Anything else can and will be displaced to silly and cumbersome positions, including weapons, pilots, landing gear and in some cases wings.

Is impulse drive indeed so nonessential for a starship that a thrust nozzle would be located far away from the optimal position, and something seemingly superfluous like a shuttlebay installed in that position instead?

Timo Saloniemi

 

[Santaman]

Heh? The grillework on the impulse engine looks nothing like the warp nacelles. It's a porous grid, in fact it's almost identical to the exhaust vent on the HiPep ion thruster.

Except that there's absolutely nothing exhausted

What about that "fusion reactor exhaust" you mentioned earlier? Or do you want to walk that one back too?

Just going with what you pointed out, tsk tsk there's no talking with you, discuss against something and its no good, try and go along and its no good either, make up your mind damnit!

 

[John O.]

It wasn't me, it was AtoZ. And the implication was "nuclear powered" vs. "conventionally powered" in the context of naval vessels. The distinction doesn't really exist in space applications since no nuclear propulsion system has ever been flown in an actual launch vehicle.

I'm a pretty far reach from a naval engineer, but I was under the impression that nuclear powered submarines and carriers housed nuclear reactors that heated steam as a working fluid and pumped it through turbines to power the propellers? Isn't that exactly what a diesel vessel does, except burns diesel in a gas combustion reaction?? There aren't "very different physics going on in these systems" - there's different physics going on to produce the heat of reaction, yes, but I was referring to "the same physics" going on in actual production of propulsive force - in the turbines. Or in the case of what I thought you were talking about, a rocket nozzle.

I would argue that the distinction between chemical and nuclar does exist in spacecraft. First of all, you have RTGs that count as 'nuclear propulsion', and even more strictly according to the analogy, the distinction still exists because even non-RTG nuclear propulsions system designs exist, regardless of never having been flown.

 

[Saquist]

Oh really?

What is that?

Since when? Fuel consumption of most MODERN rocket engines has practically nothing to do with their nozzle size and everything to do with chamber pressure.

That's not true. The nozzle size is just as important as the combustion chamber to accelerate, constrict and concentrate the out gassing.

 

[Santaman]

"That" is a linear aerospike nozzle.

http://en.wikipedia.org/wiki/Linear_aerospike

 

[BK613]

My take on Impulse Tech

 

[Crazy Eddie]

Many real space craft do mount their orbital engines significantly off-axis from the center of gravity. Those engines are angled so that they fire through the center of gravity regardless of their position; on the space shuttle, they're even gimballed for fine control.

The end result in such setups is that the spacecraft doesn't move bow first

Close enough not to matter, at the very least. The angle of attack for the space shuttle is something like ten degrees negative pitch for the oms engines.

OTOH, space craft will "move" in any direction they want under inertial flight, there's no reason for them to move bow first while orbiting a planet, which Trek ships invariably APPEAR to anyway. I think we can take either with a bit of artistic license.

"Asymmetric" thrust is something engineers can get away with when thrust overall is not particularly important - say, in spacecraft that may use it for just a fraction of their operational lives. Extremely few aircraft have ever been built with even angled-but-balanced thrust (say, Martin Seamaster)

Or the F-4 Phantom, and to a lesser extent the A-6 intruder. In both cases it was intentional, not something they hoped to "Get away" with; the Phantom's engines are low and angled to provide a bit of extra upward thrust during carrier takeoffs.

Is impulse drive indeed so nonessential for a starship that a thrust nozzle would be located far away from the optimal position

In space craft, ANY position is optimal as long as the nozzle can be aimed through the ship's center of gravity.

 

[Crazy Eddie]

It wasn't me, it was AtoZ. And the implication was "nuclear powered" vs. "conventionally powered" in the context of naval vessels. The distinction doesn't really exist in space applications since no nuclear propulsion system has ever been flown in an actual launch vehicle.

I'm a pretty far reach from a naval engineer, but I was under the impression that nuclear powered submarines and carriers housed nuclear reactors that heated steam as a working fluid and pumped it through turbines to power the propellers? Isn't that exactly what a diesel vessel does, except burns diesel in a gas combustion reaction??

No, diesel engines use internal combustion engines to generate mechanical torque; in an old-style diesel, the diesel engine directly turns a propeller shaft, while in the newer/quieter designs the engine turns a generator that provides electricity to the electric motors. In the latter configuration, the same motors can run on power from diesel engines or batteries.

Nuclear reactors use high-temperature steam to turn a turbine which turns either a propeller shaft or a generator or both.

There aren't "very different physics going on in these systems"

Yes there are. In the former, the prime mover is an internal combustion engine releasing energy from an exothermic chemical reaction. In the latter, the prime mover is pressurized water reactor releasing energy from a the splitting of atomic nuclei. It's literally the difference between chemistry and nuclear physics.

I was referring to "the same physics" going on in actual production of propulsive force - in the turbines.

Diesel engines do not power turbines, if that's what you mean. But to be sure, ANY drive system that uses a nuclear reactor as a prime mover--whether steam to turbine to shaft or steam to turbine to generator to motor or steam to turbine to generator to MHD drive--falls under the umbrella term "nuclear reactor." Any drive system that uses diesel engines, gas turbines, oil-fired boilers, etc, uses a chemical reaction in its prime mover and therefore falls under the blanket term "Conventional power."

I would argue that the distinction between chemical and nuclar does exist in spacecraft. First of all, you have RTGs that count as 'nuclear propulsion'

No, because RTGs are not part of the propulsion system.

nuclear propulsions system designs exist, regardless of never having been flown.

There are several terms for those systems, but the distinction is made between the competing theories. Nuclear thermal rockets use heat directly from the reactor to accelerate a working fluid (usually liquid hydrogen) at high velocities. Nuclear-electric rockets use a nuclear reactor to power some other propulsion system, like an ion drive or a VASIMR.

Since when? Fuel consumption of most MODERN rocket engines has practically nothing to do with their nozzle size and everything to do with chamber pressure.

That's not true. The nozzle size is just as important as the combustion chamber to accelerate, constrict and concentrate the out gassing.

Not exactly. Fuel consumption is a constant for a given chamber pressure, the only variable is exhaust velocity. Different nozzle shapes and sizes can alter exhaust velocity at different ambient pressures and altitudes and that affects the relationship between thrust and specific impulse; the same engine that develops high thrust and low ISP at sealevel may develop high ISP and low thrust at orbit altitude; fuel consumption is the same in either case.

It's true that if you fuck up your nozzle design then your rocket will have both low thrust AND low ISP for its flight regime, but it will still burn the same amount of fuel for a given chamber pressure. The only difference is how much more fuel you have to burn in order to achieve the necessary delta-v. So a rocket with a better designed nozzle uses less fuel TO ACHIEVE THE SAME PERFORMANCE, but two identical engines with no meaningful differences other than nozzle design will have the same fuel consumption, but one will have slightly higher performance.

 

[Timo]

In space craft, ANY position is optimal as long as the nozzle can be aimed through the ship's center of gravity.

Yet in starships, it is not. Bow-first movement is an absolute design criterion for starships, and one will get nothing even coarsely approximating that from the offset impulse windows of the Miranda. Not if one expects to get it from the Constitution as well, because balancing this hero ship on its impulse window requires heavy nacelles, and it's unreasonable to assume the nacelles somehow become significantly lighter when installed on the Miranda.

It's clear that warp nacelles can be placed without concern of thrust axes or the like - that indeed there are few if any rules concerning placement, because so many competing schemes are in evidence. Since impulse windows are similarly placed on unlikely and wildly varying locations, it's not unreasonable to assume that impulse engines are based on the same principles of motion as warp engines!

Timo Saloniemi

 

[John O.]

Not exactly. Fuel consumption is a constant for a given chamber pressure, the only variable is exhaust velocity. Different nozzle shapes and sizes can alter exhaust velocity at different ambient pressures and altitudes and that affects the relationship between thrust and specific impulse; the same engine that develops high thrust and low ISP at sealevel may develop high ISP and low thrust at orbit altitude; fuel consumption is the same in either case.

It's true that if you fuck up your nozzle design then your rocket will have both low thrust AND low ISP for its flight regime, but it will still burn the same amount of fuel for a given chamber pressure. The only difference is how much more fuel you have to burn in order to achieve the necessary delta-v. So a rocket with a better designed nozzle uses less fuel TO ACHIEVE THE SAME PERFORMANCE, but two identical engines with no meaningful differences other than nozzle design will have the same fuel consumption, but one will have slightly higher performance.

mass flow rate is NOT constant at a given chamber pressure - as far as nozzle design parameters it's a function of chamber pressure and throat area.

Some of these statements are irrelevant because of flight realities you're not acknowledging:

1. yes, back pressure will cause underexpansion at off design altitudes, lowering thrust - but it doesn't make sense to talk about thrust and ISP being different between SL and 120,000 ft as a result of the difference in pressure thrust because chances are at 120,000 ft you're on stage 2, you're using a completely different rocket motor with entirely different nozzle characteristics and exhaust velocity, so everything is different, probably even the area ratio. So yes, thrust and Isp are different, but for much more complicated reasons than just changing pressure thrust.

2. mass flow rate is not constant throughout a flight on any rocket period, at all, for probably many reasons - only 2 that I can think of right away - for one, it's necessary to maintain a constant felt acceleration to the payload; and two, that change in the back pressure invariably leads to over expansion at high altitude operation, and most nozzles are designed to experience controlled flow separation and when that happens, all our nicely laid out isentropic flow relations go to hell and you have to CFD that shit - and the mass flow rate's all over the map

 

[Crazy Eddie]

In space craft, ANY position is optimal as long as the nozzle can be aimed through the ship's center of gravity.

Yet in starships, it is not. Bow-first movement is an absolute design criterion for starships

No, it is a critereon for SPECIAL EFFECTS. Again: starships still move bow first even while in orbit, when there is absolutely no physical or technical reason for them to do so. This is simply artistic license that is universal to science fiction in general: the audience knows which way is forward, so the ship always moves forward over any significant distance. If the ship under impulse power is constantly accelerating towards a point 15 degrees off its centerline, we would never notice it, nor would the FX shots have any reason to reflect this since it would require an extra amount of explanation that doesn't factor into any storyline.

Not if one expects to get it from the Constitution as well, because balancing this hero ship on its impulse window requires heavy nacelles, and it's unreasonable to assume the nacelles somehow become significantly lighter when installed on the Miranda.

Why not? If nothing else it gives us a valid reason why the Miranda is designed the way it is, with a blocky monohull and low-slung deflectors instead of a pod-mounted drive section; the ship may simply have a lighter warp drive and therefore considerably different engineering requirements.

It's clear that warp nacelles can be placed without concern of thrust axes or the like - that indeed there are few if any rules concerning placement, because so many competing schemes are in evidence. Since impulse windows are similarly placed on unlikely and wildly varying locations, it's not unreasonable to assume that impulse engines are based on the same principles of motion as warp engines!

The point being, of course, that if this were true then there would be no reason at all to HAVE impulse engines, you could simply use the warp drives as that. And even if a separate set of HARDWARE was required, mounting the equipment in a completely separate component with little or no physical connection to the warp core--with their own power systems to boot--would be doubly unnecessary, since the impulse engines could just as easily be mounted on the backs of the warp nacelles and use the same power supply as the main drives.

Really, it's like a naval vessel with two different sets of propellers, one powered by a diesel engine and one powered by a nuclear reactor. If the only difference between them is power and transmission, what's the point of having two different propellers?

 

[Crazy Eddie]

mass flow rate is NOT constant at a given chamber pressure - as far as nozzle design parameters it's a function of chamber pressure and throat area.

If you want to be overly pendantic about it, it's actually a function of mixture ratio, ambient temperature, injector size, the cooling characteristics of the combustion chamber, etc.

But I'm talking about the way you calculate these for any specific engine design, which assumes a combustion chamber whose properties have already been defined (and the only way to know THAT is to test the hell out of it). So combustion chamber pressure would be a constant here.

Some of these statements are irrelevant because of flight realities you're not acknowledging:

Those flight realities are a RESULT of those statements, so I'm not sure what point you're making. Specifically:

1. yes, back pressure will cause underexpansion at off design altitudes, lowering thrust - but it doesn't make sense to talk about thrust and ISP being different between SL and 120,000 ft as a result of the difference in pressure thrust because chances are at 120,000 ft you're on stage 2, you're using a completely different rocket motor...

And the REASON you would do this is, as I said, if you fuck up your nozzle design then your engine will have poor performance for its flight regime. It isn't that a better designed nozzle will reduce your fuel consumption, it's that a better designed nozzle will give you a higher exhaust velocity per unit of propellant expended; you burn the same amount of propellant in either case, the only difference is how much thrust you get from it.

2. mass flow rate is not constant throughout a flight on any rocket period, at all, for probably many reasons - only 2 that I can think of right away - for one, it's necessary to maintain a constant felt acceleration to the payload; and two, that change in the back pressure invariably leads to over expansion at high altitude operation

Over-expansion has very little to do with mass flow since, again, that is mainly a function of chamber pressure. Another reason you forgot is that chamber pressure is also not a constant during the boost phase, especially for pressure-fed systems without turbopumps (and even pump-fed systems will require more and more fuel to run the compressors as the tank's ambient pressure drops). Constant acceleration is a non-issue as well, since nearly ALL rockets have a peak acceleration period, and this can be varied depending on the limits of the payload.

 

[John O.]

mass flow rate is NOT constant at a given chamber pressure - as far as nozzle design parameters it's a function of chamber pressure and throat area.

If you want to be overly pendantic about it, it's actually a function of mixture ratio, ambient temperature, injector size, the cooling characteristics of the combustion chamber, etc.

lol... how is throat area an "overly pedantic" characteristic of a nozzle? I just pulled out my rocket propulsion notes and there's mdot, directly proportional to A* under isentropic assumptions...

And the REASON you would do this is, as I said, if you fuck up your nozzle design then your engine will have poor performance for its flight regime. It isn't that a better designed nozzle will reduce your fuel consumption, it's that a better designed nozzle will give you a higher exhaust velocity per unit of propellant expended; you burn the same amount of propellant in either case, the only difference is how much
thrust you get from it.

I'm not even sure which wrong assertion you're making:

1. that staging is performed ... because a nozzle design is flawed??? (Which is wrong - staging is done because it increases overall payload fraction)

2. that nozzle design is somehow asymptotic and you can continue to "design a better nozzle" and keep getting higher exhaust velocities and .: higher thrust (Which is wrong - there's an optimal nozzle design for ONE altitude, or in the case of the SRBs, an average optimal altitude range.)

or 3. that back pressure and underexpansion that causes thrust loss is a result of "poor nozzle design". (It's NOT. Underexpansion at off-design altitudes is inevitable, it's a physical reality, it always happens. "off design altitudes" doesn't mean somebody screwed up. Ae/At ALONE determines the exit mach # and the pressure drop (isentropically), which determines the pressure thrust loss or gain. Ordinary bell nozzles with fixed area ratios physically cannot generate optimal thrust at seal level AND 120,000 feet, it's not physically possible.

Over-expansion has very little to do with mass flow since, again, that is mainly a function of chamber pressure. Another reason you forgot is that chamber pressure is also not a constant during the boost phase, especially for pressure-fed systems without turbopumps (and even pump-fed systems will require more and more fuel to run the compressors as the tank's ambient pressure drops). Constant acceleration is a non-issue as well, since nearly ALL rockets have a peak acceleration period, and this can be varied depending on the limits of the payload.

What ARE you talking about? Pressure fed systems don't use PROPELLANT to feed the pressure into the lines, they use some inert gas! And they use regulators all over the place with a set pressure below line pressure so that fuel pressure stays (relatively) constant.

There are more than enough places on a fully assembled rocket engine from tip to tail to identify sources of mass flow rate fluctuation in the nozzle, but the entire point of a regulator is to make sure that fluctuation doesn't actually make it to the combustion chamber, otherwise you can have some serious in flight instabilities. No real rocket motor that flies actually sees variable combustion pressure as a result of upstream fluctuation.

I didn't say "overexpansion is related to mass flow rate", I said mass flow rate is dependent on over expansion and -yes- it is. Do you know what flow separation is? Eddies, shocks, boundary layer, shear layer shedding, vortices? Instability inside the rocket nozzle caused by separation ABSOLUTELY lowers the effective exhaust velocity, of which mass flow rate IS a function. If you don't think mass flow rate is affected by turbulent boundary layer separation, eddy formation or non-axysimmetric boundary layer separation along a nozzle wall, seriously, just open a compressible turbulent flow book.

As a side note, mass flow rate isn't just affected by separation because of variable geometry - it's also affected by it because the flow separates from the wall and you get very complex interactions between the thermal boundary layer and the viscous boundary layer, so under more realistic non-adiabatic conditions, the heat flux between the wall and flow changes dramatically, and in a completely non-linear fashion.

To re-emphasize my point - overexpansion has absolutely nothing to do with chamber pressure. It's a result of the difference between exit pressure and ambient pressure. And before you go and say that exit pressure is a function of chamber pressure -no-, it's not. The RATIO of the exit pressure to the chamber pressure is a function of the exit mach# and the propellant choice (via the propellant gamma and molecular weight), which is a function of the area ratio and the propellant choice (gamma and MW).

I promise you I'm not just making this up as I go. I had a midterm exam in my graduate rocket propulsion course last Wednesday, I'm pretty up on compressible nozzle flow.

 

[Crazy Eddie]

mass flow rate is NOT constant at a given chamber pressure - as far as nozzle design parameters it's a function of chamber pressure and throat area.

If you want to be overly pendantic about it, it's actually a function of mixture ratio, ambient temperature, injector size, the cooling characteristics of the combustion chamber, etc.

lol... how is throat area an "overly pedantic" characteristic of a nozzle?

It isn't, it's a characteristic of the combustion chamber. The ratio of the throat to the volume of the combustion chamber, the flow rate and temperature of the injectors are all factors affecting mass flow. Once that's established, then we're talking about nozzle shape/size.

I'm not even sure which wrong assertion you're making...

Sigh...

Let's try it this way: when you're trying to design a rocket engine, you start with your combustion chamber configuration--fuel injection, temperature, volume, etc--and then work on a nozzle configuration ideal for the engine's flight regime.

As in, for example, the Kestrel engine: you would start with known properties for a combustion chamber with a particular size and shape, injector geometry and feed system. Once you have chamber pressure, you can figure out the exhaust velocity at the throat area, and then compute the needed nozzle shape based on ambient pressure at flight altitude.

Mass flow for the Kestrel engine is independent of nozzle shape or ambient pressure, it's a constant. But a Kestrel engine without a nozzle will produce very little thrust. Put a divergent nozzle on it, then you get more thrust for the same exhaust velocity. Put a nozzle extension on the back of it and you might get even more. Neither of these effect mass flow, only the amount of propellant mass you wind up using for your required d-v.

What ARE you talking about? Pressure fed systems don't use PROPELLANT to feed the pressure into the lines, they use some inert gas!

I never said they did. In fact, I believe I specifically said they DIDN'T. Pump-fed systems do, though.

There are more than enough places on a fully assembled rocket engine from tip to tail to identify sources of mass flow rate fluctuation in the nozzle, but the entire point of a regulator is to make sure that fluctuation doesn't actually make it to the combustion chamber, otherwise you can have some serious in flight instabilities. No real rocket motor that flies actually sees variable combustion pressure as a result of upstream fluctuation.

Right, only from fuel-flow fluctuation, and most engines are designed to take this into account.

Instability inside the rocket nozzle caused by separation ABSOLUTELY lowers the effective exhaust velocity, of which mass flow rate IS a function.

Over-expansion doesn't occur INSIDE the nozzle, though, and can be prevented by adding a properly shaped nozzle extension. Effective exhaust velocity is measured at the nozzle end, not the throat of the combustion chamber, so a nozzle extension that increases exhaust velocity by redirecting exhaust downstream.

To re-emphasize my point - overexpansion has absolutely nothing to do with chamber pressure.

So... why did you bring it up?

 

[blssdwlf]

Not if one expects to get it from the Constitution as well, because balancing this hero ship on its impulse window requires heavy nacelles, and it's unreasonable to assume the nacelles somehow become significantly lighter when installed on the Miranda.

Why not? If nothing else it gives us a valid reason why the Miranda is designed the way it is, with a blocky monohull and low-slung deflectors instead of a pod-mounted drive section; the ship may simply have a lighter warp drive and therefore considerably different engineering requirements.

There is no way those impulse engines on the back of the Reliant could be balanced against anything on the ship unless the torpedo pod itself was the mass of the lower portion of the monohull AND the nacelles combined. Lighter nacelles got nothin' to do with it They are just too high up to work in a conventionally balanced way.

http://movies.trekcore.com/gallery/albums/twokhd/twokhd0116.jpg

 

[Crazy Eddie]

And I again point you to the space shuttles OMS engine pods which are proportionally even higher above centerline.