Friday, February 24, 2023

Critter Funny


My wife ran across this on her Facebook.  I thought it was too funny not to post here. 

Sunday, February 5, 2023

Thoughts On the Chinese Spy Balloon

Updates have been added to this article,  appended below.  These are for 8,  13,  and 14 Feb. 2023.  Also,  one photo was added at the end 18 Feb. 2023.


I see a lot of activity on the internet about the Chinese balloon that flew over the US.  Most of that crap is just that:  “uninformed speculation” is just a long-winded way of saying “crap”.  Informed speculation (“not crap”) is far better.

Some informed speculation from me:

1. This thing had a forest of antennas and other equipment under it,  about the size of two school buses,  which is why they wanted to delay shooting it down until it was over the ocean.  That's a serious falling debris hazard over inhabited land. 

Speculation:  could this thing have been harvesting data from the Tik Tok software that they have infiltrated into us over the last few years?  Or the Chinese-made microchips that are in just about everything we use today?  Or both?

2. Everybody here wanted to see the thing shot down.  Question is,  how do you actually do that?  Our air-to-air missiles are not designed to track targets of that type.  The gas bag itself would have little or no radar signature,  and little if any infrared signature. 

Such missiles would be more likely to home-in on the equipment hanging underneath the gas bag.  That would have some radar and infrared signatures.  In that event,  it would be more difficult to recover the equipment and determine what it was doing.  The missile would have blown it all to pieces,  not to mention the further damage from impact with the surface.

Puncturing the gas bag with simple gunfire would be a better choice,  but who has airplanes that fly that high anymore?  This thing was reportedly at or above 66,000 feet. Only the U-2 and SR-71 spy planes flew that high.  Neither was ever armed.  Both are now long-retired.

Supposedly this thing was shot down by an F-22 using an AIM-9 Sidewinder.  The aircraft was reportedly flying at 58,000 feet,  which would be just about the top of its flight envelope.  Climbing from there to 66,000 feet would be just about the limits of what a Sidewinder would be able to do.  It would be way out of range vertically for a gun shot,  even if the F-22 had guns.  (Actually it does,  but they may or may not have loaded gun ammo on board for this mission.)

3. Supposedly this is the 4th such incursion by balloon in recent years.  It was just the first seen by the public,  thus making the news and causing a commotion.  But there is a pattern here!  The Chinese would not be doing this to spy on our missile silos and bomber bases.  They do that with satellites.  It's hard-to-impossible to steer a balloon where you want it to go,  anyway.

Speculation:  they were trying to acquire information that is spread diffusely across America,  not any particular point targets.  That lends credence to the notion of intercepting internet information generally,  and Tik Tok or microchip-acquired information specifically.  Such would be preparation for waging cyber warfare.

4. The "right" interceptor for high-altitude balloons like this would resemble the old NF-104.  That would be a modified jet fighter craft with a rocket engine,  an attitude thruster control system,  and air-to-air guns to punch holes in the balloon and let the lifting gas out.  It's been 50 years since we had a thing like that,  and the NF-104 had no guns back then,  being instead a trainer for rocket plane pilots.  It flew multiple times to altitudes in the 90,000-to-125,000 feet range.  Some less heavily loaded weather balloons fly that high.

My suggestion:  modify some F-16’s with a simple rocket engine in the tail like the old NF-104,  plus an attitude control thruster system.  It doesn’t need the heavy radar in the nose anymore,  that weight allowance can go to the modifications.  It already carries missiles,  just make sure it has guns and ammo on board.  (Most of the F-16’s had an M61 Vulcan 20 mm cannon in the left wing root.)

Just keep it simple,  stupid! (“KISS”).  Such a craft can take off within minutes,  and climb to meet the balloon threat within just minutes more.  You can fire at the balloon on the way up past it,  and again on the way back down.  Way cheaper than a surface-launched interceptor missile!

One additional suggestion:  the gas turbine main engine is going to starve for air on the way up in rocket power.  Make sure the modifications include a sure way to restart it on the way down,  and make sure there is no loss of hydraulic power to the flight controls while the engine is not turning.  Those were serious flaws seen with the old NF-104.

This is not a high-tech development.  There is no excuse for not having one flying within just several months.  And it should not be expensive,  either.  After all,  it was fast and inexpensive 50 years ago with the NF-104!

One last thing to worry about:  US spy planes flying near China are unarmed.  They have been subject to Chinese fighter harassment that includes some very unsafe flying practices.  The next step for the Chinese is to start shooting those US spy planes down,  international airspace notwithstanding.  It’s my opinion that those planes need to be armed or escorted,  and the rules of engagement should be to shoot before the enemy gets too close.

Update 8 Feb 2023 Reports now indicate there was another one over Latin America during this incident,  an earlier one over the US during Biden's term,  and 3 during Trump's term.  These earlier ones were not detected until after-the-fact,  which explains why Trump administration figures say this didn't happen,  when the actual military records say it did.  

What that really indicates is that NORAD did not detect or recognize these balloons for what they were,  until very recently.  Yet detecting intruders over the US is exactly what NORAD is intended to do!  It would appear that nobody expected such an obsolescent technology as a threat,  so nobody was watching for it.  These things don't have much in the way of radar or infrared signatures,  and are visually apparent only in broad daylight,  so they really are a sort of semi-stealth platform.

The mission here may be as much about political ends as anything to with gathering surveillance information.  China has been infamous ever since its communist revolution for bullying behavior to intimidate other nations into submitting to Chinese will.  Now they have a track record of flying surveillance balloons over the US unopposed,  until this last one.  That may explain their outraged reaction to its being shot down.  

The "open skies" precedent set by Sputnik 1 in 1957 applies to satellites and spacecraft considered to be flying in space,  that being defined as above 62 miles (100 km) altitude,  above the sensible atmosphere.  That is why nobody has been trying to destroy other countries' spy satellites.  It very most definitely has never applied to balloons or any other kind of aircraft flying below that altitude,  down in the atmosphere!  Airspace violators have always risked being shot down!  

It does make moral sense to determine if an intruder is a hostile threat or not,  before deciding to shoot it down.  Spy missions intruding into territorial airspace have traditionally been considered hostile threats.  Airliners strayed off course would not be,  although Russia shot one down for straying over its territory at Sakhalin Island a few years ago.  Dictatorships tend to do ugly and immoral things like that,  as we have seen.  

Science missions like a weather balloon straying off course would be hard to identify as such,  but the ground team managing the mission need merely contact the country where it strayed,  to avoid it being taken as a hostile.  That did not happen with any of these Chinese balloons.  So,  that excuse is as flimsy as a straw house in a hurricane.  Do not believe it!

These things apparently had as their prime mission the political end of seeing if they could get away with intruding into US airspace at high altitude unopposed.  Any actual intelligence they could gather would just be gravy.  It would be diffuse information spread across the country,  likely from the internet and the chips that enable so many devices these day.  It would help enable better cyber warfare against us.  Things that connect to the internet can always be hacked!  That's just an ugly little fact of life!

The way for a balloon to avoid being shot down by fighters like the F-22 would be to either increase gas bag size for a given payload,  or reduce payload weight for a given gas bag size,  or both.  That would enable the balloon to fly at significantly higher altitudes,  even above 100,000 feet,  where fighters (and nearly all missiles) cannot reach.  They may try that before they give these missions up.  But like any bully,  they won't stop bullying until smacked in the nose.  

Therefore,  we are going to need a way to shoot these things down at altitudes above 100,000 feet!  Which is exactly why I suggested a mixed-power F-16 as a reprise of the NF-104's capability to conduct vertical zoom flights to altitudes above 100,000 feet.  You don't even need explosive gun rounds,  simple solid slugs will punch holes in a thin plastic gas bag.   

Lasers might work,  except that accurate pointing is required,  and the difficulty and expense of doing that increases exponentially with the range.  The slant range to a balloon target is going to be a few dozen miles.  That's long range,  and it will be difficult and expensive to do.  Besides,  radar and infrared guidance for pointing the laser is not going to work,  and visible light guidance will only work in broad daylight on a relatively clear day.  There is nothing else to use.  That puts us right back to a manned interceptor airplane. 

Solid slug ammo,  even at 20 mm cannon size,  would be cheap at a few bucks each.  Explosive rounds are a few hundred bucks each.  An air-to-air missile is a few hundred thousand bucks (or more),  and a surface launched SAM is a few million bucks.  One capable of hitting targets at over 100,000 feet up,  will be several million bucks or more.

It's a cheap intercept because you recover the plane!  You are only out the price of the fuel,  a payment to the engine overhaul kitty,  the pilot's hazardous duty pay,  and the price of the ammunition used.  The planes I suggested are obsolescent anyway,  and will eventually be going to the boneyard otherwise.  The modifications needed are all well-known,  no development required.  There is no excuse for such a capability requiring a large budget or a long time to emplace.  

You build one or two,  test them,  make the indicated changes and test those to verify them,  then you build a few more examples and field them.  We don't need very many,  but once your mods are verified and you have drawings,  you can always build a few more if you find you need them.  

Plus,  they can serve a dual purpose.  They can help train space plane pilots,  just like the old NF-104 did.  Sierra Nevada may need that,  if they get their manned version of their Dream Chaser space plane flying.   If they do,  others will follow.

Update 13 Feb 2023:  As of this writing,  since the downing of the big Chinese spy balloon 8 days ago,  there have been three more shootdowns:  over Alaska (10th) and the Yukon (11th) of much smaller objects at much lower altitude (near 40,000 feet),  plus a small object at 20,000 feet over Lake Huron.  The Alaska and Yukon objects appear to be cylindrical,  and about the size of a small car,  and appear to be floating with the wind.  The Lake Huron object was described as “octagonal with strings hanging from it”.  There is no indication yet of what they really were,  or who put them up there.

What I think we are all seeing is the chaos of NORAD realizing these small radar anomalies that it used to ignore,  really are intruding stealthy objects of some sort.  Suddenly the skies seem to be full of them.  A lot of public figures,  and some military leaders,  are saying noncommittal and sometimes-contradictory things about this issue.  Complicating this further are the recent news stories about investigating other unidentified objects often seen by military pilots.  Refer again to the yellow-highlighted paragraph in the previous update just above.

I don’t think anybody on our side realized just how stealthy a such balloon platform can be for purposes of spying.  But the Chinese,  and maybe some others,  seem to have understood this.  It does make the spy balloon a “cheap” alternative to the spy satellite.  These are the lower altitudes from which better photography can be obtained than from satellites hundreds of miles up,  the main reason we once fielded the U-2 and SR-71 spy planes. 

Higher is more invulnerable from intercept.  Both the Air Force and the Navy have had fighter aircraft capable of reaching 58,000 to 65,000 feet,  for a long time now.  But large balloons,  if lightly loaded for their size,  can fly very high indeed!  The balloon from which Joe Kittinger parachute-jumped in 1960 testing high-altitude bailout equipment,  was flying at about 103,000 feet.  The persons who broke his parachute jump record just a few years ago,  jumped from balloons flying at about 130,000 feet.  The airplanes and air-to-air missiles that we have today simply cannot reach those altitudes. 

If the target identification and beam guidance problems can be handled,  it would be far less expensive to “pop” these balloons with a laser beam.  However,  the slant range to target from the surface is multiple dozens of miles.  Doing this laser shot thing from an airplane near 50,000 or 60,000 feet reduces those beam guidance difficulties,  with a weapon that could still reach a really high-altitude balloon,  when the airborne missiles we have cannot reach such targets.  That does assume the well-guided laser system is a payload light enough,  that the airplane carrying it can still reach 50,000-60,000 feet.  But if the laser system is too big,  the airplane carrying it cannot reach such altitudes. 

Spy craft are traditionally considered to be “hostiles”,  and traditionally subject to being summarily shot down.  It is just as possible to send a small weapon payload by balloon as it is to send a spy payload:  the Japanese tried sending incendiary fire bombs to the US by balloon in World War 2.  It would not be all that easy to tell a scientific payload from a spy payload,  or some kind of weapon payload,  even if one could “eyeball” the thing fairly close up.  That means you have to “eyeball” it really close up!

Many weather balloons are small objects intended to reveal the winds,  with little or nothing in the way of payload suspended beneath.  Others could be very large balloons with large scientific payloads.  Even companies and private individuals can launch such things.  Ethics requires target identification before shooting the thing down.  Dictatorships may ignore ethics,  democracies should not.

My point is that target identification,  required for a yes or no answer to the shootdown question,  may well be the real reason we need an aircraft capable of reaching the balloon at its altitude,  no matter how extreme,  for a close look.  If the balloon is flying nearer 100,000-150,000 feet than 60,000 feet,  then we currently have no airplanes capable of doing that mission,  regardless of any laser or other weapon we might use for the shootdown.  We might not want to shoot it down after all,  depending upon what it turns out to be,  upon close inspection. 

Which dilemma puts us right back to my suggestion of reprising the vertical zoom flight capability to the edge of space,  that we had in the NF-104 decades ago.  That’s currently the only imaginable way to get human eyeballs close to one of these intruders,  for target identification purposes,  at the more extreme altitudes well above 65,000 feet.  The stay time close-by isn’t very long,  but it is much better than nothing!  It might take two flights sequentially,  one to evaluate the target visually for the shootdown decision,  the other to shoot it down,  if that is the decision. 

If you can get that close,  a gun (or a short-range laser) is all that is needed.  Guns we have had for decades.  Airborne lasers,  well,  maybe,  and maybe not.  Gun rounds are cheap compared to missiles,  even small airborne missiles.  I would further suggest using standard 20 mm ammunition,  except replacing the projectiles with scattershot loads,  like a big shotgun shell.  That way,  there would be very little risk to people and things on the ground,  from falling ammunition,  only from the balloon payload itself.

As to the chaos we have seen recently,  consider this.  What we have been watching for all these years,  is intruding airplanes and missiles (or drones).  If stealthy,  the radar return will barely be distinguishable in terms of signal-to-noise ratio.  The doppler would show the higher speeds of aircraft or missile flight.  The radar anomalies previously ignored would show barely-perceptible low radar return and a low doppler-derived velocity,  comparable to wind speeds.  Unless you are actually looking for balloons,  you would ignore targets like this.  And apparently,  we did.

Now that we are looking for such targets instead of dismissing them as “anomalies”,  we are suddenly seeing a lot of them!  Odds are,  most of these are neither spies or other threats.  Quite a lot of them might be things sent up for commercial interests or even private-individuals-for-fun.  Distinguishing the real spies and threats from the harmless stuff so many miles in the air is what will require sending a real pair of eyes very close by. 

If you seriously want to reprise the mixed-propulsion vertical zoom aircraft capability,  here are the design requirements I suggest.  The rocket thrust to aircraft weight ratio needs to be such that thrust equals or exceeds the aircraft weight plus its drag.  Use the lift/drag ratio L/D for high-altitude lift equals weight cruise,  to rough-estimate this as Fth/W = 1 + 1/(cruise L/D).  Use the max gross takeoff weight of the aircraft for this.  You should probably have a turndown ratio equal to,  or exceeding,  3 to 1 . 

Assuming you are zooming upward under rocket thrust at roughly the speed of sound in cold air (about 960 ft/sec),  the vertical distance you need to traverse is target altitude less the altitude at which you start the zoom climb (perhaps 35,000 feet as a guess).  For a target at 150,000 feet,  that would be about 115,000 feet.  The rocket burn time requirement is then roughly 115,000/960 = 120 sec = 2 minutes of burn.  That sets your propellant quantity Wprop required,  from the rocket specific impulse Isp and the design thrust Fth,  as a total impulse requirement:  Itot = Fth * tburn = Isp * Wprop.

The zoom aircraft will not need the typical radar and associated avionics for fighting with radar-guided air-to-air missiles.  Removing those gives you the weight allowance you must have,  in order to install the rocket engines and propellant tankage that you need,  plus the attitude thrusters and associated propellant,  that you will also have to install. 

For shooting down the threat,  use the guns or infrared-guided air-to-air missiles (or a laser installation,  if you can afford the weight).  If you cannot afford the weight of the laser on your zoom craft,  your laser installation will have to work from a lower altitude where it actually can be carried. That’s a different airplane design from the zoom craft.

There,  I’ve told you exactly how to get started on reprising a mixed-propulsion vertical zoom aircraft capable of reaching extreme balloon altitudes.  It’s an aircraft modification,  not a new development!  You scab on the rocket engines,  and replace the on-board radar with the propellants and the attitude thrusters.  You keep the gun if it has one,  and any launchers for Sidewinder missiles.  There’s no excuse to spend years and $billions doing this!

Update 14 Feb. 2023:

This is what it looks like to rough-size the items for a mixed-propulsion modification to an F-16C aircraft.  The aircraft weight statement rough-size calculations look like Figure A,  which is the spreadsheet image where I iterated these numbers.  What I assumed for the rockets was IRFNA-jet fuel propellants for the pressure-fed main rocket engines,  and IRFNA-UDMH for the attitude thrusters.  Both IRFNA and UDMH are materials the military has handled in the field previously. 

The pressure-fed main engines are not hypergolic,  and will require something like TEB injection for their ignition.  The thrusters are hypergolic and pressure-fed.  Since the main engines use aircraft jet fuel,  the added propellants include a little bit of UDMH for the attitude thrusters,  and a lot of IRFNA for the main engines and the attitude thrusters.   Part of the rocket systems package is a pump to take the unpressurized aircraft fuel and pressurize it to around 2000 psia for pressure-feeding the rocket chambers.

Figure A – Rough-Sizing the Weight Statement Numbers for a Mixed-Propulsion F-16C

Supporting these numbers are the ballistic sizing results for the main engines (Figure B) and for the attitude thruster “engines” (Figure C).  The main engines have a thrust sizing requirement more-or-less determined by the aircraft weight rough-out in Figure A.  The thrust requirement I used for the attitude thrusters is an arbitrary 500 lb force for any one single thruster.  I assumed the total thruster impulse requirement to be equivalent to one thruster continuously for the entire main engine burn time.  

Figure B – Roughed-Out Ballistic Sizing for the Main Rocket Engines (2)

Figure C – Roughed-Out Ballistic Sizing for Attitude Control Thrusters (Multiple)

The specific impulses I obtained for the main engines and thrusters are close enough to the 300 sec values that I assumed for them in the aircraft weights sizing,  that I did not need to revise those inputs to the aircraft weights sizing.  There are larger uncertainties here than just those values of specific impulse.

The dimensions of the main engine units are not all that large,  and should easily fit as scab-ons to the upper strake surface,  on either side of the vertical fin.  The plumbing and storage vessels for the TEB (tri-ethyl borane) ignition fluid should probably just be a part of each main engine unit.  That allows very easy access for TEB load and unload,  enhancing safety.  TEB is also a material the military handles in the field,  the most recent example being the SR-71 engine/afterburner igniter fluid.

That gets us to the illustration in Figure D of what these aircraft modifications look like,  and where they are located. 

First,  there are considerable avionics equipment items to remove from the nose,  this craft not being expected to ever use radar-guided air-to-air missiles,  or to ever need countermeasures in combat.  Those include the AN/APG-68 radar,  the AN/ALR-56M radar warning receiver,   and the AN/ALQ-213 electronic warfare suite.  Some of my numbers are for “similar equipment”,  and I rounded up slightly to cover removal of countermeasures and countermeasure dispensers elsewhere on the airplane. 

The rocket “pressure plumbing and controls” that replaces the avionics in the nose includes the pressure pump and surge chamber that takes jet fuel from the aircraft tanks and pressurizes it to about 2000 psia for the pressure-fed main rockets.  There’s crudely a 500 lb allowance for all of that in the nose.

The main rocket propellants are stored pressurized in two payloads mounted to the inboard store pylons under the wings,  specifically to be near the aircraft center-of-gravity.  These custom items resemble 500-gallon drop tanks,  much smaller than most stores usually carried on these stations.  Each carries about 450 US gallons of IRFNA oxidizer to support both main rockets and the attitude thrusters,  plus about 3 US gallons of UDMH to support the attitude thrusters.  

Figure D – What the Aircraft Modifications Are,  And Where They Are

I would anticipate (for redundancy) 2 thrusters for nose-up pitch,  2 for nose-down pitch,  2 for nose-left yaw,  and 2 for nose-right yaw,  all located right at the vehicle axis on the nose,  and perpendicular to the surface.  However only 1 such of each pair is actually used.  I would anticipate 4 tangential thrusters for left roll as two opposed pairs (achieving redundancy),  and 4 tangential thrusters for right roll,  also as two opposed pairs.  I would anticipate using all 4 for any given roll impetus.  None are needed for vehicle axial acceleration or deceleration.  That’s a total of some 16 of these small thruster units.

The mission that such a modified aircraft might execute is illustrated in Figure E.  The aircraft operates as a normal jet aircraft until reaching the geographic coordinates of the intercept zone,  whereupon it executes a brief dive to accelerate,  followed by a sharp pullup into vertical ascent,  with immediate rocket ignition.  The jet engine needs a controlled shutdown during this ascent.  The aircraft remains powered by the rockets in the vertical ascent until it reaches the extreme-altitude target,  with the attitude thrusters maintaining its attitude control above about 65,000 feet. 

Time adjacent to the target is only several seconds,  but the range is close enough to make detailed observations with human eyes right outside the canopy.  These would support a shoot-down or no-shoot-down decision,  more-or-less in real time upon arrival near the target.

The aircraft then falls back unpowered,  using the attitude thrusters to put its nose down,  and to maintain attitude control.  Once dense-enough air is reached (probably around 65,000 feet for the F-16C),  the jet engine is restarted,  and the aerodynamic flight controls will again function.  The aircraft then operates as an ordinary jet aircraft,  pulling out of the dive,  cruising back to its base,  and landing.  

Figure E – The Basic Mission This Modified Aircraft Can Execute

The observation flight that supports the shoot-down-or-not decision is not also the shoot-down flight!  There is a second aircraft needed to perform the shootdown function.  If air-to-air laser technology will support it,  this could be a laser-equipped aircraft,  of any suitable type,  operating as a wingman to the mixed-propulsion observation aircraft. 

If laser will not serve adequately,  a second mixed-propulsion vertical zoom aircraft could perform the shootdown,  using either a heat-seeking air-to-air missile (AIM-9X Sidewinder),  or its 20 mm gun,  or both.  It could actually zoom up past the target,  firing two times:  first on passing the target in ascent,  then second on passing the target in descent. 

Again,  the F-16C has a Vulcan M61 20 mm 6-barrel cannon in its left wing root,  and Sidewinder missile stations on its wingtips.  These would not be changed in the zoom modifications.  I would suggest using custom 20 mm ammunition in the gun.  The idea is to make each round a “shotgun shell”,  by replacing the standard projectiles with a scattershot load.  Such spherical scattershot falling back is small enough (and therefore slow enough) to pose almost no hazard to anybody or anything on the ground. 

Update 18 Feb. 2023photo added as humor pertinent to recent events.

Saturday, February 4, 2023

Rocket Nozzle Types

I have corresponded with multiple friends recently over the merits of using an aerospike engine versus a conventional bell nozzle engine for flying from Earth’s surface into low Earth orbit.  I conducted a design analysis using such nozzles,  without pushing the state-of-the-art right to the edge,  and I found even the sea level conventional bell to be much superior in vacuum. 

What I uncovered during my design sizing analyses was:  (1) not only was unconfined streamline divergence a very serious problem for aerospike designs,  as I have maintained for some years now,  but also (2) there is a strong effect favoring lower chamber pressures!  Unless one sharply reduces design chamber pressures,  the streamline divergence problem degenerates into complete infeasibility at very low altitudes indeed.  That chamber pressure reduction has a big negative effect upon the thrust and specific impulse that one can achieve,  including the effects of somewhat lower chamber c* velocity.

I did in fact confirm that my “roughly 60,000 foot altitude” point,  beyond which aerospike performance falls while conventional bell performance does not,   is indeed correct!  While still a rather fuzzy boundary,  my analyses do show poor aerospike performance not far above that critical altitude.

Here Is Where I Started

I had done some nozzle evaluations and published an earlier article on this topic (ref. 1).  The free-expansion designs I evaluated for that article were a twin-spike single-throat approach,  not an annular or linear aerospike,  but the behavior and physics are quite similar.  That is the genesis of Figs. 1 and 2.

Figure 1 – Basic Flow Physics of Conventional Bell Nozzles

Figure 2 – Basic Flow Physics of Aerospike Nozzles and Other Free-Expansion Designs

The fundamental lessons as I initially understood them are:

#1. Conventional bells have inherently-limited streamline divergence effects,  with a fixed (locked-in) momentum term in thrust;  plus an exit pressure term in thrust that differences expanded pressure and ambient atmospheric pressure acting on the fixed exit area.  If the ambient pressure is too high for the expanded pressure,  bell flow separates and “kills” the momentum and pressure terms. 

#2. Free-expansion designs,  including the aerospikes,  have ever-increasing streamline divergence as ambient atmospheric pressure drops,  while the expansion Mach number increases.  This leads to an ever-increasing potential momentum term (and there is no pressure term) in thrust.  However,  the streamline divergence angles quickly lead to low cosine-components of the streamtube momentum vectors in the axial thrust direction.  At higher altitudes,  this divergence inefficiency effect completely overwhelms the larger momentum effect,  with the result that performance actually falls with altitude. 

This Is What I Did

For the conventional bell cases,  I used “typical” chamber c* = 5900 ft/sec for LOX-RP-1 at 1000 psia Pc,  from ref. 2,  a modest modern max Pc = 3000 psia,  a modest pressure turndown ratio (TDR) of 3,  and a massflow bleed fraction of 5% to drive the turbopumps.  I did not change the c* for the min Pc value,  as it is a small effect over that small a Pc range.  The other variables were much more important.   

I used the sea level chamber and throat design as the basic common gas generator,  by forcing the design thrust levels for two higher-altitude designs (60,000 feet and 30,000 feet) to produce the same throat area At and flow rate values as the sea level design.  That produces a very fair comparison,  conceptually just substituting one bell design for another onto the same chamber,  throat,  and pump assembly,  while also operating at the same chamber pressures and propellant flow rates. 

I used a simple empirical equation to estimate separation pressure ratios from the bell’s average half angle.  It works very well for conical nozzles,  and runs slightly conservative with curved bells:

Psep/Pc = (1.5 * Pe/Pc)0.8333 

For the aerospike nozzle,  I started with that same Pc = 3000 psia gas generator,  and sized low in the stratosphere,  but the streamline divergence effects were infeasibly extreme at 28 x 2 degrees.  The numbers simply made little sense.  I did notice a definite improvement at the min Pc over max Pc! 

Therefore,  I revised the gas generator design to a max Pc = 300 psia,  c* = 5700 ft/sec (reflecting the drastically-lowered pressure range),  TDR = 3 as before,  and the same 5% bleed fraction.  I sized for 100,000 lb thrust at 10,000 feet,  using an aerospike that started at 56 degrees to axial,  to zero the fan angle at design.  That gave me numbers that actually made sense,  and looked very realistic. 

I selected that design point thrust so that the sea level thrust was comparable to the sea level bell design at 100,000 lb.  That gave me flow rates somewhat higher than the fixed-bell designs,  primarily because of the lower c* associated with the order-of-magnitude-lower range of chamber pressures. 

I used the Prandtl-Myer flow model of supersonic expansion around a corner to estimate the flow divergence angles at the edge of the plume,  based on the expected expansion Mach number as determined by the Pc/Pa ratio.  The equations for Prandtl-Meyer expansion come from Ref. 3

The orientation of the gas generator throat axis is the same as the slope of the aerospike at its forward end,  so that the attaching stream starts out parallel to the adjacent surface.  If it were to impinge more directly,  that would induce a strong shock wave train on the aerospike surface,  as it turns toward the axis direction,  with corresponding large pressure losses,  disrupting the expansion.

I finally picked a 56 deg x 2 deg shape for the aerospike,  with the ring of thrusters 56 deg off axis at its start.  The Prandtl-Meyer angle gets that 56 deg subtracted off,  because of thruster orientation,  to determine the actual lateral divergence fan angle of the plume relative to the thrust axis.  Below design altitude,  you get negative fan angle data,  because the plume geometrically contracts due to the changing shape of the aerospike.  The end of the aerospike is a small angle whose cosine is always near 1.  Nozzle kinetic energy efficiency is just the average of the cosines of the inner and outer angles. 

At design,  I used straight axial and the aft aerospike angle to calculate the effective nozzle kinetic energy efficiency.  Both below and above design altitudes where the plume edge is off axial,  I used the average of the fan angle cosine and the 2 deg aerospike cosine,  for my effective nozzle kinetic energy efficiency.  This efficiency is just a cosine component correction to the plume momentum. 

I needed a nonzero ambient pressure at 300 kft altitude,  instead of just using zero representing vacuum.  That zero works fine for conventional bells,  but is inappropriate for estimating free-expansion designs.  It drives the expanded area and Mach numbers to infinity.  Accordingly,  I looked up a “standard atmosphere” model in ref. 4 that extended all the way up to 300 kft geometric altitude.  It’s not an exact match to the standard atmosphere table from ref. 2 that I used,  but it’s still “in-the-ballpark”,  and gave me realistic numbers.  The ref. 2 data only extended up to 200 kft.

Here Are The Results I Found

I selected relevant data for comparison of the conventional bell designs,  and arranged those as 3 plots versus altitude on a single figure for each design.  I created the same plots for the aerospike,  but needed a second figure to display the variable expansion data and the streamline divergence data. 

Figure 3 shows the baseline sea level conventional bell,  Figure 4 a bell sized at 60,000 feet as if it were a “vacuum” design,  and Figure 5 a bell sized at 30,000 feet,  representing a “compromise vacuum” design that could actually be static-fired at sea level without separating.  Figures 6 and 7 show the results for the aerospike design,  with 6 showing the same content in the same format as the conventional bells. 

The sea level conventional bell in Figure 3 does not separate at full power or min power,  at any altitude.  The exit pressure term on thrust shows significant effect on thrust coefficient,  thrust,  and specific impulse up to around 60,000 feet,  and almost no effect above that.  The change from sea level to vacuum thrust and specific impulse (Isp) is quite modest,  as would be expected from the very limited expansion available for the fixed momentum term of thrust. 

The same gas generator fitted with a “vacuum” bell (the 60,000 foot design in Figure 4) shows a potential for very significant thrust increase with increasing altitude (due to the pressure term acting on a larger exit area,  along with a larger momentum term).  This obtains up to about 60,000 feet.  There is very little effect from there to vacuum.  The problem is that much of this potential is unrealizable for launch,  due to flow separation in the bell near sea level,  even at max Pc,  as noted in the figure. 

The “compromise vacuum” design sized at 30,000 feet in Figure 5 shows behavior intermediate between the other two extremes.  It has an intermediate momentum term and an intermediate exit area.  The thrust increase with altitude due to the pressure term is realizable at full power,  but not at min power due to flow separation,  as shown in the figure. 

The results for the aerospike design are given in Figures 6 and 7.  More detail is required to understand the expansion and flow divergence phenomena,  which is why Figure 7 is included.  As a reminder,  the data in Figure 6 are the same content and format as that presented for the bell nozzles. 

The thrust coefficient,  thrust,  and specific impulse data increase to peak values in the stratosphere,  then decrease from there into vacuum!  The peak is near 50-60,000 feet at full Pc,  and nearer 80-90,000 feet at min Pc,  so there is a strong pressure effect favoring lower chamber pressures!  That is why I had to reduce the Pc range to 300-to-100 psia,  from 3000-to-1000 psia for the conventional bells.

The main difference between the aerospike and the conventional bell designs is the effective nozzle kinetic energy efficiency data that is shown in the same plots with thrust coefficient versus altitude.  The conventional bells all have constant kinetic energy efficiency,  at a rather high value,  all the way out into vacuum.  This reflects the confined plume following bell angles,  right to the exit point (last point of contact).  The exiting plumes suddenly spread wide,  out in vacuum,  but since that occurs downstream of the last point of contact,  it does not affect the exit flow condition results.

The aerospike plume is unconfined laterally,  and spreads very wide as altitude increases.  This shows up as an initially-high effective nozzle kinetic energy efficiency,  that starts decreasing about 50-60,000 feet.  It falls to drastically-low values as altitude increases into space!  The details in Figure 7 show why:  the fan-out angles get very large,  and simply overwhelm the increasing expansion,  quite rapidly.  

Figure 3 – Analysis Results For Sea Level Bell With Common Gas Generator Design

Figure 4 – Analysis Results For High-Altitude Bell With Common Gas Generator Design

Figure 5 – Analysis Results For Modest-Altitude Bell With Common Gas Generator Design

Figure 6 – Analysis Results For Low-Altitude-Sized Aerospike With Reduced-Pressure Gas Generator

Figure 7 – Analysis Results Details For Aerospike

The only thing that I found that I did not really expect initially,  was just how sensitive the aerospike is to the aggravation of plume spreading effects at higher chamber pressures!  I could not get a feasible design until I reduced the chamber pressures from thousands to only hundreds of psia.  That’s a factor-10 reduction required!  Otherwise,  what I thought going into this analysis turned out to be true.  The list of revised lessons follow (#3 Is the new one,  no change to #1 or #2):

#1. Conventional bells have inherently-limited streamline divergence effects,  with a fixed (locked-in) momentum term in thrust;  plus an exit pressure term in thrust that differences expanded pressure and ambient atmospheric pressure acting on the fixed exit area.  If the ambient pressure is too high for the expanded pressure,  bell flow separates and “kills” the momentum and pressure terms. 

#2. Free-expansion designs,  including the aerospikes,  have ever-increasing streamline divergence as ambient atmospheric pressure drops,  while the expansion Mach number increases.  This leads to an ever-increasing potential momentum term (and there is no pressure term) in thrust.  However,  the streamline divergence angles quickly lead to low cosine-components of the streamtube momentum vectors in the axial thrust direction.  At higher altitudes,  the divergence inefficiency effect completely overwhelms the larger momentum effect,  with the result that performance falls with altitude. 

#3. Aerospikes,  and presumably all the free-expansion designs,  benefit strongly from reducing gas generator chamber pressures by around an order of magnitude below modern rocket practice.  This acts to somewhat-limit the adverse plume spread laterally,  at higher altitudes approaching vacuum.  You want that fan angle to be zero at your design point,  which sets your forward spike and thruster angle.

Final Remarks

Bear in mind that I already know how to optimize the designs of conventional bell nozzles.  I used to do that for a living,  long ago.  I do not yet know how to optimize the design of free-expansion nozzle configurations,  including specifically the aerospike nozzles examined here. 

The aerospike configuration I came up with “worked”,  but can hardly be said to be optimal!  I had to compromise it severely by lowering chamber pressure by a factor of 10 to match up plume boundary expansion effects at the design point,  with the requirement that the plume boundary fan angle be zero.  That also forced a very large initial spike angle and mounting angle for the gas generator chambers adjacent to it.  And it lowers chamber c*,  and thus specific impulse.

Therefore,  do not put much credence in the lower specific impulse I got near design at low altitudes,  lower than with any of the conventional bell nozzles.  That is very likely an artifact of my not knowing how to optimize the design of aerospike engines. 

Put your credence into the strongly-decreasing performance trends at higher altitudes as you fly out into vacuum!  That is real,  and even an optimized design will show a similar trend!  It is inherent that the plume boundary will spread straight out to the side as you fly an aerospike into vacuum,  and it is also inherent that this phenomenon will affect the thrust level that can be achieved. 

The plume inherently spreads laterally precisely because of the physics embodied in Prandtl-Meyer expansion around a corner.   It does not matter if that model needs modification to tailor it to this application or not,  it will still show the same basic plume-spreading trend. 

Because this plume spreading takes place upstream of the last point of stream contact with the engine hardware,  it inevitably must affect the thrust!  It is nothing more than velocity vector component effects at off-axis angles.  That’s just the physics of compressible flow.  No one can argue otherwise.  But it takes place while the expansion is still occurring,  which in turn is what creates the thrust,  which must be measured at that last point of contact. 

As a result,  the effective nozzle kinetic energy efficiency,  the achieved thrust for the flow rate,  and the delivered specific impulse,  will inherently show downward trends as one flies out into space.  Whether I got the exact right numbers is irrelevant.  That downward trend,  and the physics underlying it,  are real!

Aerospike nozzles show excellent fluid mechanical performance from the surface up to the stratosphere,  probably better than with bell nozzles,  if they can be correctly optimized.  But,  the free-expansion nozzles will always show severe performance degradation as you fly from the stratosphere out into vacuum!  It is inherent,  and it is unavoidable.  It is a big effect!

The most important take-away:  aerospike nozzles are simply NOT good vacuum nozzles,  despite what is often claimed.  They inherently cannot be. 

The better application for aerospikes is between the surface and the stratosphere.  That is where the ambient atmospheric pressures are high enough to limit the plume lateral expansion,  which greatly improves the effective nozzle kinetic energy efficiency.   I rather suspect that is true of any free-expansion design approach that lets the plume boundary adjust prior to last point of contact with engine structure. 

The only thing I can think of to investigate further is to add some nozzle expansion past the sonic throat of the gas generator chambers,  in an effort to limit the Prandtl-Meyer fan expansion effect to lesser values,  at least initially.  This might also allow an increase in chamber pressure,  that being a lesser effect per Figure 7 above.  About the largest expansion to add would be a sea level expansion.  This does raise the risk of compression shocks on the spike,  as the Mach number at impingement is higher. 


As an aside,  the aerospike nozzle is in fairly wide use in some aircraft turbine engines that lack afterburners.   Those would be the ones with a conical spike sticking out past the “turkey-feather” exit.  These work from sea level to the lower stratosphere.  Stream pressures approaching the nozzle are much lower than they are in typical modern rockets.  All of that is favorable to aerospike behavior.

When the turkey feathers form a convergent nozzle,  and the internal stream pressures are high enough to more-than-just-barely-choke that exit,  this rig functions very well as an aerospike nozzle facilitating a supersonic plume expansion to the last point of contact:  the tip of the exit spike.  That increases engine overall thrust and performance by increasing the nozzle thrust term in the airbreathing thrust equation.

My Qualifications to Say These Things

My original college and graduate school education was in high-speed compressible aerodynamics and thermodynamics/heat transfer,  much of it oriented toward propulsion.  I spent 20 years in aerospace defense work doing compressible flow mechanics,  including specifically the operation of all kinds of nozzles for rockets,  ramjets,  and other propulsion items,  some rather unconventional because of throat area modulation devices.


#1. G. W. Johnson,  “How Propulsion Nozzles Work”,  posted on “exrocketman” 12 November 2018.

#2. Pratt and Whitney “Aeronautical Vest-Pocket Handbook”,  12th edition,  21st printing,  December 1969;  from “Theoretical Rocket Engine Propellant Summary” page 92,  for LOX-RP1 at 1000 psia;  and from “U.S. Standard Atmosphere – 1962” pages 4 – 9 for pressure ratio versus altitude. 

#3. Ames Research Staff,  National Advisory Committee For Aeronautics (NACA) Report 1135 “Equations,  Tables,  and Charts For Compressible Flow”,  1953;  specifically “Prandtl-Meyer Expansion”, page 14.

#4. Chemical Rubber Company (CRC) “Handbook of Chemistry and Physics”,  53rd edition 1972-1973,  published by CRC Press;  section F page F-171,  metric or English abbreviated tables of the US Extension to the ICAO Standard Atmosphere,  for the pressure ratio at 300 kft geometric altitude.

Related Articles

There are lists of articles on this site,  organized by the topic areas they pertain to.  These are given in an article titled “Lists of Some Articles By Topic Area”,  dated 21 October 2021.  Related topic areas might include “ramjet”,  “aerothermo”,  and “rocket performance”.  I have added this article to those lists.

The fastest way to access any given article on this site is to jot down the dates and titles you want,  and use the fast navigation tool on the left side of this page.  Click on the year,  the month,  then the title if need be (if there was more than one posted that month). 

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Here are images of the spreadsheet worksheets I used to generate the plots given above,  except that I did not include the worksheet-generated plots in these images.  The name of the spreadsheet file is “nozzles.xls”.  Figure 8 is the worksheet for the sea level bell design.  Figure 9 is the 60,000 foot bell as “vacuum engine”,  and Figure 10 the 30,000 foot bell as the “compromise vacuum engine.  Figure 11 is the worksheet used for the aerospike.  It has to be laid out differently,  as the expansion is not geometrically fixed.   Figure 12 shows exactly how nozzle efficiencies were computed,  and what assumptions were made to do the analyses,  for both the bells and the aerospikes.

Figure 8 – Sea Level Bell Worksheet

Figure 9 – 60,000 Foot Bell Worksheet

Figure 10 – 30,000 Foot Bell Worksheet

Figure 11 – Aerospike Worksheet

Figure 12 --  Nozzle Efficiency Calculations and Assumptions Made

Update 6 Feb 2023:          

Doing exactly what was suggested above,  I designed a revised aerospike nozzle that uses some bell-confined supersonic expansion out of the gas generator,  before doing the free expansion on the spike from there to ambient.  This actually did reduce the expanded plume fan angles at high altitude,  enough to raise the design altitude,  and to re-raise the gas generator chamber pressure from 300 psia back to 3000 psia.   These changes were beneficial enough to restore much of the compromised off-design performance seen with the sonic-only gas generator design. 

Results for thrust coefficient and nozzle efficiency,  thrust,  and specific impulse are given in Figure 13,  which one should compare to the sonic-only gas generator design in Figure 6 above.  Results for expanded Mach number,  expanded area ratio,  and the plume fan angles are given in Figure 14,  which one should compare to the sonic-only gas generator values in Figure 7 above.  Formats are identical.

The best of the three fixed-bell designs was the one designed for perfect expansion at a modest altitude,  which gets a lot of improved vacuum performance,  while still being testable at sea level in the open air,  without flow separation in the bell.  Those performance numbers are given in Figure 5 above. 

In Figure 15,  data are plotted for direct comparison of the best fixed bell design,  and the best aerospike design,  for both at max Pc = 3000 psia.  In Figure 16,  the same comparison plots are given with both operating at min Pc = 1000 psia.  Bear in mind these are LOX/RP-1 designs that I arbitrarily roughed out.  The “best bell” was sized to perfect expansion at 30,000 feet so that it could be fired in the open air at sea level,  at full Pc.  At min Pc,  it must be at or above almost 30,000 feet in order not to separate.  It was sized with Fth = 106,230 lb.  The best aerospike was the revised spike with the supersonic-bell gas generators,  sized for an axial plume boundary at 60,000 feet,  and a nominal thrust Fth = 100,000 lb.

There is still performance degradation with the revised aerospike below fixed-bell levels,  while flying out into vacuum,  but it is not nearly as degraded as with the earlier sonic-only gas generator aerospike design described above.  This improvement in performance was afforded by the limited supersonic expansion bell on the gas generator,  which limits how adversely-lateral the plume angle can spread at lowest backpressures.  The aerospike itself is a little less extreme in its initial angle,  as well.

That this revised aerospike is a near-optimal design is confirmed by its specific impulse performance very slightly exceeding the best fixed bell,  from sea level to about 200,000 feet.  For ascents,  this aerospike might be competitive in terms of performance,  since the specific impulse advantage in the stratosphere offsets the specific impulse deficit out in vacuum,  as long as it is not used for too much impulse delivery out in vacuum.  For routine use out in vacuum,  the fixed bell is still better.

The original conclusion above that aerospikes are not good vacuum nozzles really is confirmed in this update.  However,  the vacuum shortfall definitely can be made more modest than was originally indicated in the sonic-only gas generator version.  One does that by fitting a sea level bell upon the gas generator,  allowing a reduction in initial spike surface angle off of axial.  The mechanism of the fan angle reduction is the direction-confining action of the modest bell,  limiting the further Prandtl-Meyer expansion angle from there to ambient,  and which then also allows higher chamber pressure.

The higher chamber pressure raises both c* and thrust coefficient,  which in turn acts to raise specific impulse.  The more-limited plume fan-out angle in vacuum raises the effective nozzle kinetic energy efficiency,  which acts to raise thrust and specific impulse.  Of the two effects,  the fan angle dominates.

Figure 13 – Basic Results for Aerospike with Supersonic-Expanding Gas Generator

Figure 14 – Detail Results for Aerospike with Supersonic-Expanding Gas Generator

Figure 15 – Comparison of Best Bell and Best Aerospike at Max Pc

Figure 16 --  Comparison of Best Bell and Best Aerospike at Min Pc

As before,  the better measures of relative performance lie in the nondimensional factors like thrust coefficient.  The differences in sized thrust show up in the sized throat areas (a sum of multiple gas generators in the aerospike case),  which directly affect thrust and flow rate in the same way.  These areas are close but not equal,  in the comparison given here.  That’s why one should put less credence in the calculated thrust trends as a direct measure of comparison.  However,  one can put full credence in the specific impulse trends,  because the throat area effects on thrust and massflow rate divide out.

The basic message here is that by sizing the throat areas correctly,  the thrust shortfall evident even in the stratosphere in Figures 15 and 16 can be eliminated!  This will not really change the thrust coefficient and specific impulse trends!  Those show the revised aerospike (with combined supersonic bell and free-expansion spike) can equal or exceed the performance of the “best” fixed bell up to the outer stratosphere (around 200,000 feet),  but will inevitably fall short of fixed-bell performance from the outer stratosphere on out into vacuum! 

Those statements are made for a “modest vacuum bell” design,  sized to operate over-expanded at sea level up to its design perfect expansion altitude of 30,000 feet.  From there it operates under-expanded all the way to vacuum,  at the highest expanded-momentum term available.  That design selection is limited by being able to test fire in the open air without flow separation at sea level and full power.  It cannot be test-fired at sea level like that,  at min throttle.

The ”full vacuum bell” can equal aerospike performance in the stratosphere,  as indicated in Figure 17,  but cannot be operated at sea level.  However,  note that out in vacuum,  even a sea level bell outperforms the aerospikeAerospikes are quite simply not good vacuum engines!

Figure 17 – 3-Way Comparison In Terms of Specific Impulse