Sunday, January 8, 2023

Border Emergency

The current border emergency is a real emergency,  but the nature of it is NOT what you are being told,  especially by the politicians you have elected!   Most of the news media are failing you,  too,  because they also lie to you,  or at least they are not really pointing out the things that I point out in this article.

 Defining Terms

I'm going to use the term "migrant" (or the other form "immigrant") to include most everybody that comes to,  or across,  our southern US border.  There is a big-enough surge of these recently,  that our border towns (El Paso for one) are declaring humanitarian emergencies.  And migrant lives are being cruelly (and criminally?) endangered,  for the political stunt of busing them to non-border states.

Immigrants are not all the same.  There are people who want to be "guest workers",  meaning they want to fill some sorts of jobs up here in the US.  There are people who are "refugees",  meaning those who are fleeing for their continued existence,  perhaps even their very lives.  There are people who want to move here and “become Americans”.  And there are the "smugglers",  meaning those who bring across both guest workers and refugees,  and those who bring across illegal drugs.  See the figure,  and read on. 

Guest workers

The guest worker problem dates back to the end of WW2 and the end of the "Bracero" program,  when we sent all the guest workers (mostly agricultural) home to Mexico,  and set guest worker visa quotas rather low,  expecting our returning soldiers to return to the farms,  but they did not!  The Mexican guest workers actually want to be legal,  but that demand is an order of magnitude or more higher than the guest worker visa quotas,  and this has been true since then.  Statistically,  these people,  illegal or not,  are more law-abiding than most US citizens,  and they do pay taxes,  despite what you've been told!  And,  they are an integral and productive part of our economy,  there is no denying that!

The jobs are here,  the workers are there,  and they must feed themselves and their families.  If not legally,  then they must cross and do the work illegally.  Congress has ignored this since 1945,  which is why about 5 years ago it was estimated that the “illegal alien” population (then mostly illegal guest workers plus their families) was about 11 million in this country.  Fixing this ends the “DACA problem” in 1 generation,  but it requires staffing-up to track a lot more visas!   Congresses and Presidents have utterly failed in their duty to fix this,  for some 7 decades now,  by not staffing up and issuing more visas.


Refugees are different.  We have a very long history under federal law of supposedly treating refugees very similarly to the way we treat lost people found at sea:  it doesn't matter who they are or where they came from,  you just pick them up and tend their ills,  and then get them where they need to go.  In particular,  refugees are entitled under federal law to a timely hearing before a real immigration judge for admission to the US.  That is long-established law,  and it does not care how they crossed,  to ask.

There are no guarantees about being granted entry,  but that timely hearing is guaranteed under those laws.  Anyone who denies them this right is committing a serious federal crime.  Refugees,  like guest workers,  statistically tend to be more law-abiding than most US citizens,  at least up to now.  The data on the ground so far say that the real terrorists and criminals are coming in elsewhere,  sometimes through the northern US border,  and mostly through the international US airports inside the country.  

The refugee problem used to be a small one,  which is why the low quotas for it were possibly sort-of appropriate long ago.  That has changed with so many failed,  and failing,  states in Central and South America,  in the Caribbean,  and also now around the world.   That situation is not under our control!  It never was,  and it never will be,  despite what your preferred political candidates may tell you!  All we can really do is respond properly. 

There are now roughly as many refugees as there are guest workers,  in any given year.  Yet the quotas and the number of immigration judges never rose,  and Congresses and Presidents have refused to staff up to meet the higher demand in recent years!   So,  hearings take years,  instead of the weeks that are appropriate,  thus violating the clear intent of established federal immigration law!  

The "remain-in-Mexico" policy violates that law,  because in all practicality,  you can't attend your hearing if you aren't inside the country,  since the border guards are unlikely to let you in. 

"Title 42" violates that established law in its entirety:  refugees get turned away with no hearing at all (fear of contagion is actually now known to be a bullshit excuse,  just now used as a political vote-getter). 

These are violations of federal law that were actually ordered by the very Congresses and Presidents charged with fixing this, of both parties.  They are at fault for letting these violations persist so long, unaddressed.  Plus numerous border-state officials,  doing evil for political advantage.  Oath breakers all!

People Wanting to Become Americans

There are people who just want to move here and become Americans.  Some of these are guest workers,  some refugees,  and some just want to come here and become citizens without either of those other two reasons.  I did not choose a word by which to label them,  although others have used “immigrant”,  which confuses needlessly with the other categories I named. 

Those numbers were often (but not always) fairly small long ago,  but they are much higher now.  Statistically,  these have mostly been good people,  who become positive assets to our society.  We are in fact a nation originally built of such people!  These are,  and always have been,  people that we should want to admit.  Although,  we have not always done so,  usually for racist reasons.   And THAT needs to change!

Smugglers and Related Criminals

As for the smugglers and related criminals,  there aren’t,  and never were,  very many of them.  Our border patrol agents are,  and for many years have been,  completely tied up chasing illegal guest workers and illegal refugees,  when those people are illegal only because multiple Congresses and multiple Presidential administrations,  of both parties,  have not done their jobsFix the guest worker and refugee problems properly,  and our border patrol agents are freed-up to deal with the smugglers.  And they can,  and they will!

How to Properly Fix the Problems

Walls and fences on the border don't fix this problem.  National guard troops on the border don't fix this,  either.  Those are political lies to get your vote based on fearing all migrants as criminals,  when they are not!  Truly fix the guest worker and refugee problems by staffing up properly and setting realistic quotas,  and most of this "migrants-at-the-border problem" inherently goes away,  leaving our border patrol able to catch the smugglers and criminals.  Simple as that.  And the cost will be worth it,  in the long term far cheaper than any of those political lie “solutions”!

But it does require that we have Presidents and members of both houses of Congressthat will actually do the jobs they swore to dowhen they took their oaths of office!  That is something I have not seen in decades!  Such oath-breaking should be a crime!  (If it already is,  it is clearly unenforced.)

In lieu of that,  I generally do not vote to re-elect incumbents,  unless I can verify that they did a good job (most do not).  That's the “term limits” that we have always had,  and too many folks do not use it!  Which in turn is exactly why we have so many idiots in public office,  not doing their jobs properly.

I would also favor criminalizing political lies,  limiting sources of campaign funding,  and limiting the intervals in which campaigning can be done.  Billions spent on mostly-lies for a midterm election (or any other election) is preposterously ridiculous!  So also are big-money interests buying the offices of elected officials for them!  And all these campaigns for re-election throughout the holder’s term-in-office are just abysmally wrong!

Regarding My Proposed New Crimes

Oath-breaking:  officials take an oath of office quite similar to the oath taken by those who join the military.  Breaking that oath by failing to do the job properly,  should have very serious consequences,  as it does in the military:  oath-breakers in elected office need to go to jail.  I think everybody understands that.  Not fixing the immigration crisis properly is oath-breaking.  (And it is not the only thing they do that is oath-breaking.)  We all saw the recent President break his oath of office by fomenting an insurrection,  instead of heading it off or putting it down,  as was his sworn duty! We also all saw the danger to the country that particular oath-breaking episode did.

Political lies:  there are limits to the right of free speech:  it is not absolute,  and never was.  One may not yell “fire” in a theater when there is not a fire,  because it is both untrue and it endangers people!  There are serious consequences for doing such,  and rightly so.  Political lies are not just untrue,  they also endanger people (as we saw Jan. 6, 2021 because of the “stop the steal” lie).  Thus,  there need to be serious consequences for political lies!  

If something is offered to the public at large as “true”,  it really does need to be true!  I think everybody understands that.  And this applies to outlets on social media and cable TV,  as well.  It applies to talk radio.  And it applies to candidates running for office:  their qualifications cannot be based on lies,  as is true in the recent self-admitted case from New York.

Campaign contributions not identifiable to the public:  we need a codified law to make such things criminally illegal,  since the Supreme Court wouldn’t rule correctly about this.  We could even take this further,  and give all candidates an appropriate campaign budget out of tax funds.  Then we jail those who campaign with funds from outside that budget!  I would vote for that,  as long as no other sources were allowed.  That’s one of the few things they do in the UK that I think we should adopt,  adapt,  and improve here.

Campaigning outside an allowable interval:  elected officials out on the campaign trail are simply not at work doing their sworn jobs!  For an official to be out campaigning for 80+% of his term in office,  is patently ridiculous,  to the point of criminal fault for not doing his sworn job!  We need a law to limit campaigning to a defined short interval appropriate to the office and the constituency,  and we really need to jail violators.  That’s the other thing they do in the UK that I think we should adopt,  adapt,  and improve here.  (As for most of the rest of what they do in the UK,  that’s why we had a revolution.)

Final Comments

The politicians we elect are quite clearly not going to fix our very serious immigration problems,  until we the voters eliminate their ability to ignore us by throwing them out of office!  Campaign rallies,  party agendas,  and political slogans are all bullshit!  The way you actually do this is to routinely vote them out of office,  no matter who they are or what party they claim.  Period! 

That won’t happen until all you voters out there ignore party,  and stop re-electing incumbents.  You do this again and again,  until you find somebody willing to adopt and enforce the laws we actually need.  That’s actually what the Founders had in mind when they wrote our Constitution! 

Then,  once you find a candidate for office who will try to do the right things,  you keep that one for only a short while (a term or two),  until he/she shows signs of corruption (and they all eventually do,  if left in office long enough).  Then you go looking for new ones willing to do what is right.  Simple as that.

The words “political party” are NOT in the Constitution (go look for yourself)!  Think about THAT!  George Washington warned us in his Presidential farewell address NOT to go the political party route,  and I think he was right.  All of which is EXACTLY why I have been a lifetime independent voter!

By the way,  if a political party told you what “the right things to do” are,  then you can bet your very life those are lies!  (That applies to both parties,  and most everything that is on social media and the internet,  and also what is on most cable TV and talk radio.)  Hear what they say,  but DARE NOT BELIEVE ANY OF IT!  You need to decide FOR YOURSELF what is the right thing to do.  Period!  End of issue!

That being said,  I hope my “exrocketman” internet site is one of those very few who attempt to tell you the truth.  This site is not monetized or funded.  I am beholden to no one.  THAT should tell you a lot! 

The most nearly reliable sources I can find are the 3 major TV broadcast networks,  the PBS broadcasts,  and some (but not all) of the newspapers,  here in the US.  They at least attempt to self-police themselves to standards of accurate journalism.  Some are more successful than others at this. 

This “standards of journalism” stuff gets thrown off a bit by trying to “balance both sides for fairness”,  instead of just pointing out the obvious lies and wrongdoing of individual powerful politicians or political organizations,  the way they really should.  There is no “fair balance” of reporting to be had,  if one side is misbehaving more than the other.  But,  even so,  we still do need to know about it,  including the asymmetry of the misbehavior

The other problem that I see,  even among the best sources out there,  is too much focus on the bottom line instead of the public-service aspect of news reporting.  This is less of a problem with PBS,  which is not commercially funded.  The others really do suffer from this,  more so in recent decades.  The last third of a half-hour news broadcast on the commercial networks,  is now more commercial time than time spent actually reporting the news.  Time it yourself,  if you don’t believe me.  That’s just not right!

If you are aware of those two shortcomings,  then you can otherwise trust those sources.  You probably want to hear from more than two of them,  before you decide for yourself about any particular story.

Related Prior Articles (all on this site,  all written by me):

To find other articles on this “exrocketman” site quickly,  jot down titles and dates that you want to see.  Then use the navigation tool on the left side of this page.  Click on the year,  then the month,  then the title if need be (if more than one article was posted that month).  Here the list of other articles that are closely related to this article: 

#1. “Invasion At the Border?  No,  I Don’t Think So!”,  7 December 2022

#2. “Border Crisis?  Nope”,  17 January 2019

#3. “Immigration Politics and the Nazification of America”,  7 July 2018

#4. “Forget the Stupid Wall”,  4 March 2018

#5. “Why So Many Illegal Immigrants?”,  23 September 2017

#6. “More Troops and Fences on the Border Won’t Fix Our Troubles”,  10 September 2010

As for more technical topics,  I have an article on this site with lists of other articles in multiple topic areas.  That one is “Lists of Some Articles By Topic Area”,  dated 21 October 2021.  Topic areas include “ramjets”,  “aerothermodynamics and heat transfer”,  “rocket propulsion and vehicles”,  “space suits and atmospheres”,  “radiation hazards”,  “pulsejets”,  “ethanol and blends in vehicles”,  “automotive care”,  “cactus eradication”,  ”forensic analyses”,  and “towed decoys”.  More may get added in the future.

Thursday, January 5, 2023

It’s All In the Punctuation!

Misplacing your punctuation sometimes changes the meaning entirely.  This effect is illustrated in the figure,  where both of the girls are pointing up at the sky,  the essence of astronomy without telescopes.  The words are exactly the same,  only the hyphen moves!  These cases are “naked-eye astronomy”,  and “naked eye-astronomy”.  However,  one of these cases promises to be rather more fun than the other.  I’ll give you one guess as to which. 

Sunday, January 1, 2023

Towed Hardbody Decoys

Protecting aircraft against missiles and ground fire is an old need.  Deceiving radar with chaff goes back to World War 2,  although it wasn’t originally called “chaff” then.  Flares came to be,  with the advent of infrared (IR) guided missiles in the mid-1950’s.  Chaff and flares are the original aircraft decoys.

The problem with these is that they depart quickly behind the aircraft,  so you have to carry and dispense a lot of them.  They have gone too far away to do any good,  in about 1 second or so at modern jet aircraft combat speeds.  And when they run out,  so does your luck,  if the threats are still at hand. 

The notion of the towed decoy was originally “towed chaff” and “towed flares”.  One replaces the many small items with just one (or a very few) somewhat-larger items that would stay in the right place close by the aircraft,  but for a much longer time (essentially throughout the engagement and beyond). 

There are two quite-different concepts regarding the towed radar decoy application:  the towed hardbody decoy and the towed ribbon decoy.  There is only the towed hardbody concept currently available for the towed IR decoy application. 

Towed ribbons are a different “beast” entirely,  and the available radar reflection technology only supports their use for protecting extremely low-observables aircraft.  Even that application has severe limitations.  Towed ribbons are not covered here!

Some History

The original successful towed decoy concept demonstrator was designed by my friend Byron Hinderer at what was then Tracor Aerospace,  in Austin,  Texas.  He did this before I ever reached Tracor. 

That decoy featured a dorsally-attached towline (termed “cg tow”) on a very simple body with an aft-mounted ram air turbine (RAT).  The RAT supplied the electric power to make the radar receiver and transmitter aboard the decoy function.  There was no power-down-the-towline.  It successfully deceived all radars in flight tests before the Navy,  despite all sorts of “experts” saying it could not possibly work. 

I spent a little over 3 years at Tracor,  working on (among several other things) towed hardbody decoys,  towed ribbon decoys,  and one IR signature generation technique that might fly aboard one of the towed hardbody decoys.  This included extensive ground tests, wind tunnel tests,  and flight tests.  That testing led to some very successful flight tests of various test articles,  and a prototype design for possible acquisition by the Navy,  featuring power-down-the-towline.   That last became ready a year or so after I left Tracor.

The Navy initially bought a competing design from Raytheon instead.  There were severe “teething troubles” with tow stability initially,  because Raytheon was using an incorrect design approach:  nose tow like a gunnery target,  producing both an uncontrollable rolling motion,  and a cone of no protection directly behind the aircraft.  That last reflected a decoy located behind the aircraft at its same altitude. 

What really works is quite unlike towed targets:  one does a “cg (center-of-gravity) tow” from a dorsal lug,  which produces a decoy tow point that is both behind,  and somewhat below,  the aircraft.  The cone of no protection (where decoy and aircraft line up in the threat’s sight picture),  is thus depressed below horizontal.  Thus,  there can be effective protection from a threat in a tail chase from above.  Because this works so well,  towed radar decoys are now common among many countries’ armed forces.

This same hardbody tow scheme could also be used as an “airframe” for a towed IR decoy.  If airbreathing combustion is used to produce the IR signature,  then fuel does not necessarily have to be carried on board the decoy.  It might instead come down the towline,  as an option.    

Engagement Scenarios

There are some things necessary to understand about the characteristics of engagements between threats and aircraft.  The air-to-air and surface-to-air scenarios are different,  but the critical features are grossly the same.  There’s basically head-on attacks,  attacks from the side,  and tail-chase attacks. 

Because the missile threats all use one or another form of what is called “3-D proportional navigation” for their guidance,  the head-on and side attack geometries have the tendency to convert toward the tail chase scenario.  How close to a tail chase these scenarios become varies,  but it does point out the need to have decoy protection in the tail chase scenario!  This is illustrated with crude sketches in Figure 1. 

Figure 1 – How the Various Engagement Geometries Tend To Convert to Tail Chases

All these engagement aspects use the same basic 3-D proportional navigation guidance.  That guidance has built into it something termed “gee bias” that more-or-less eliminates the downward pull of gravity as a disturbing influence on the missile.  The usual implementation overcompensates somewhat.  That has two effects:  (1) the trajectory is bowed upward,  and (2) the thinner air at the higher peak altitude increases the missile range,  to whatever extent is possible.  This is also illustrated in the figure.

The basic sight picture seen by the missile is then from somewhere behind and slightly above the aircraft.  One wants significant separation between aircraft and decoy,  as viewed in that missile sight picture!  If the decoy lines up with the aircraft,  then it can afford no protection.  That is the definitional concept behind the term “cone of no protection”.  What that really means is that you want that cone of no protection to be depressed below horizontal,  as shown in Figure 2.  The exception is shoulder-fired IR,  which is still coming up from below as it turns into a tail chase.  Straight tow is better for that. 

Figure 2 – Threat Sight Picture and Cones of No Protection

What is shown in the figure applies directly to non-imaging threats (radar or reticle-based IR).  Radar sees reflected energy in this or that pixel,  within its narrow field of view (FOV).  The seeker itself steers in such a way as to center that “bright” pixel in its sight picture.  It is the off-angle position of the seeker (plus the range information) that allows the guidance to lead the target,  to a calculated intercept point in space.  If more than one pixel has reflected energy,  the seeker tends to use the “power centroid” of the multiple “bright” pixels as its aim point at the center of its narrow FOV. 

Reticle-based IR is somewhat similar (in not forming an image),  but lacks range information,  so the estimate of the intercept point in space is somewhat cruder.  The seeker still steers itself toward centering the power centroid of all the hot spots it sees,  in the center of its sight picture.  Seeker deflection angle generates the information for leading the target.  Like radar,  it has a very narrow FOV.  There’s just no individual pixels (which there are,  once you start using imaging IR).

Here’s the key thing for any decoy:  as the missile closes upon the aircraft,  its sight picture of aircraft and decoy becomes larger and larger.  Eventually,  that whole picture cannot fit within the FOV.  If the decoy is “brighter” than the aircraft,  it will be nearer the power centroid.  The more remote aircraft then drops out of the FOV first.  After that,  the only target seen by the seeker is the decoy,  and the missile steers toward it rather than the aircraft,  causing the miss.  Its warhead may (or may not) fuse,  since the decoy is so small compared to the aircraft that the missile designers expected.

So,  two things become clear at this point:  (1) you want a lower tow for a widest-possible sight picture,  while also depressing the cone of no protection below the line-of-sight to the descending (or at least co-altitude) threat,  and (2) the decoy’s signature (whether radar or IR) must be “brighter” than the aircraft. 

The great benefit here is that 1 decoy serves for the 1 engagement.  If it is shot away,  you can dispense another one,  but you need not dispense multiple dozens per engagement,  the way you do with chaff and flares.   You do not need to carry anywhere near as many towed decoys,  as you do chaff and flares,  which means the typically-larger sizes of the towed decoys are no obstacle.

What I have said about threat guidance and engagement characteristics so far is stuff that has been in the open literature for a very long time.  I cannot say much more about that,  without getting into ITAR and classified information.  That is the realm of counter-counter measures:  the missile guidance recognizing decoy from aircraft,  and then acting upon that information.

About Towed Hardbody Decoy Design Approaches

There’s low/straight tow,  side tow,  and high tow,  as possible places to locate a decoy (which moves the cone of no protection).  These are illustrated in Figure 3.  Only low/straight tow requires no automatic flight controls for stability.  Having to develop the flight controls to make side or high tow stable and reliable,  is another big development effort beyond just getting the decoy to emit signature. 

Accordingly,  the simplest,  easiest,  and least expensive option is to do low/straight tow.  You do want as low a tow as possible,  for enhanced stability reasons,  as well as depressing the cone of no protection well outside the engagement sight picture.  That low/straight tow is the only topic I cover here.

Figure 3 – Possible Tow Locations and the Associated Considerations

How This Rough-Out Design Analysis Is Done

Start with the decoy itself:  first size its tail for high “arrow stability”,  then second select a trimmed-out angle of attack that gets high downforce,  and then finally size a tow lug height for net zero-moment about the cg at your desired trim point.  Such a decoy rough-out design results in a tow force at an angle,  which also applies as a tension to the tow cable end,  and as an angle boundary condition.  See Figure 4.  The details of exactly how to do this are discussed below.

Figure 4 – The Design Analysis Sequence for Roughing-Out a Towed Hardbody Decoy

Next,  you do the curved portion of the towline.  The entire tow line is modeled as a short straight length and a much-longer curved length.  For simplicity in a design rough-out,  I just use a circular curved shape.  The angles at its two ends are the tow cable angle at the decoy,  and zero where it joins the straight section. 

Ignoring towline weight,  the curved towline lift force must exactly balance the total decoy downforce,  and the curved towline drag adds to the total decoy drag for the line tension where it joins the straight section.  This is an inherently iterative process:  you simply change the length of towline in the curved section,  until the vertical forces balance to zero.  Exactly how to compute those forces is described below.

The drag of the short straight section adds to the tension applied to its end,  for the tension as felt at the aircraft.  That’s the largest tension in the towline,  steady state.  The size and shape of the curved portion determine its horizontal and vertical dimensions.  These plus the length of the straight section of towline determine just how far back,  and how far below the aircraft,  the decoy is actually located.  That in turn determines the depression angle of the line-of-sight from aircraft to decoy,  which is the axis of the cone of no protection.    Accordingly,  it is wise to keep the length of the straight section short.

Recommended Towed Body Geometry

We want the decoy to fly as low as we can,  to depress the cone of no protection well below horizontal.  Square or rectangular cross sections generate more body lift at a given angle of attack than round cross sections.  So,  the square cross section is the best recommendation.  Those corners can be slightly radiused without changing that effect.  See Figure 5.

Streamline bodies generate very destabilizing moments about their putative centers of gravity (cg),  particularly those with boat-tails or pointed rear ends.  The effect is reduced a little with a bluff rear end,  which reduces the sizes of stabilizing tail fins needed.  Hence,  the bluff rear end is recommended.

In the wind tunnel,  there was a rolling instability with a cross fin pattern that was simply not seen with an X-fin pattern.  This was thought to be related to a sort of alternating vortex shedding off the two horizontal fins in the cross pattern.  The X-fins are always slanted,  and thus the shed vortex positions seemed to be far more stable.  Hence X-fins are recommended,  even if the body has to be round in cross section for any other reason. 

Putting fin trailing edges flush to the bluff rear of the body,  positions those fins farthest from the cg,  which reduces their required size a little.  Thus aft-edge-flush fins are recommended.

Any downlift fins added to the decoy should be positioned with their center of pressure (cp) at the decoy cg.  This minimizes downlift fin moment contributions about that cg,  while maximizing their downlift effect,  which added downlift would be the only reason for having them.

The tow lug is located axially at the cg,  and on the dorsal side of the body.  The towline force component parallel to the body axis,  at the lug height,  is the means to trim-out the body to fly at the desired angle of attack.  Otherwise,  the stabilizing tail makes it want to fly at zero angle of attack.

The figure shows a really odd-looking recommended nose shape for the square cross section body that is recommended.  There is a good reason for that: 

In the pitch plane,  the rounded nose helps delay flow separation to a point well down the ventral surface.  This maximizes the forward ventral surface suction component of the body downlift,  which downlift we greatly desire.  In the yaw plane,  the edges are sharp,  leading to flow separation on the lee side in yaw,  right at the nose.  This diminishes the yaw-inducing side forces created by lee-side suction,  thus diminishing the response to any yaw disturbances while towing.

At best,  this sort of asymmetric nose shape is difficult to do with a round body cross section.  A pointed cone or ogive nose shape is pretty much all that can be done.  Such will have equal propensities for lift and yaw forces.  This is something we saw in the wind tunnel:  at the higher speeds (higher drag/weight ratios),  the round bodies were much less stable in yaw than the square bodies with the odd nose. 

The opposite was true at very low speeds (low drag/weight ratios).  But it is the higher speed range that is of interest for jet aircraft that might need towed decoys!  If you must do a round body,  put a sharp cone on it,  and let the flow separation induced by the cone-cylinder joint kill the yaw forces.  That also kills body downlift forces,  so you will need to add the downlift fins to get the tow position you desire.

That being said,  on the square body section,  you put any downlift fins at the upper chine line,  positioned axially with their ¼-chord points at the axial cg station.  Those downlift fins see cleaner air there (remember,  we are flying with the nose pitched down,  not up) and are thus maximally effective. 

On the round body,  you put them straight out from the sides at the cg.  They see cleaner air there,  than anywhere else. 

Figure 5 – Recommended Geometry for Towed Hardbodies

About the Aerodynamic (And Other) Forces

There are the forces from the body alone,  the forces from the tail fins,  and the forces from any downlift fins.  All of these induce moments about the decoy cg.  At zero tow force,  we want that moment sum about the cg to pitch the nose up rather strongly.  That is how we obtain “arrow stability”.  Adding in the moment of the towline force about the cg,  should create zero net moment at the desired downward angle of attack.  That is how we “trim-out” the decoy to fly the way we want it to,  on that towline.

Body lift and drag are located without any moment at all,  at the axial position of the body center of pressure (cp).  As indicated in the figure above,  I recommend measuring axial position from the nose of the decoy.  This cp position is denoted as body xcp,  which varies very strongly in location.  At zero angle of attack,  it is typically way out in front of the nose,  for just about any imaginable streamline body shape.  As angle of attack increases (up or down),  xcp moves quickly to some position interior to the body.  Here,  positive angle of attack is down,  and positive moment acts to increase that angle of attack.

The amount of body lift varies nonlinearly with angle of attack,  differently for each possible streamline body shape (airship hulls,  bombs,  etc.).  The xcp position also varies quite nonlinearly with angle of attack,  differently for various shapes.  The best thing here is to select old plotted data for an appropriate shape,  and curve-fit it;  which is exactly what I did.

Tail fin lift and drag forces are located at the tail cp,  which for uncambered flat plate fin shapes,  is pretty much fixed at the ¼-chord point,  with a zero moment value about that point.  That means the tail xcp is at a definite location from rear edge of the body (and thus from its nose). 

The same is true for any downlift fins,  you just locate them with their ¼-chord points at the decoy cg.

That’s three sets of lift,  drag,  and cp data:  body,  tail,  and downlift fins.  Thus there are 6 aerodynamic forces,  each contributing moments about the decoy cg.  The seventh is the towline force,  and the eighth is the decoy weight.  These forces and locations are shown in Figure 6.  For these 6 aerodynamic forces,  the relevant moment arm geometry in the wind axis coordinates uses body axis moment arms and the appropriate sine and cosine values of the angle of attack.  The towline force component parallel to the body axis,  times the lug height,  is that moment,  using the sum of towline angle and decoy angle of attack.  The weight acts through the cg by definition,  and thus generates no moment. 

Figure 6 – Locations and Moment Arm Data for All 8 Forces

               More About the Body Forces

An old reference had a multitude of plotted curves of the body forces for a variety of shapes.  Among them,  the square section lift curves had roughly twice as much lift as the round section lift curves.  The variation is quite nonlinear,  which is why I selected a cubic polynomial for my curve fit. 

The same reference had a relatively simple model for the body induced drag,  one peculiar to streamline bodies alone.  I used that.  The body zero-lift drag is just a “typical value” one can obtain from a variety of sources,  including the ones I used.

At low angle of attack,  the body cp is way out in front of the nose,  and moves aft as angle of attack increases.   Bodies with bluff rear ends showed reductions in just how far ahead of the nose the xcp is,  at zero angle of attack.  The correlated variation for bluff-ended bodies was also quite nonlinear,  so I used a cubic polynomial curve fit for that,  too.   All of this is illustrated in Figure 7,  with the curve fits given in Figure 8,  along with the reference whose data I used.

Figure 7 – What All the Body-Only Forces Look Like

               More About the Fin Forces

The fin forces are easier to deal with,  since the centers of pressure are essentially fixed in location at the 1/4-chord point.  Tail fin or downlift fin,  the fundamental single-panel geometry and data are shown in Figure 9.  These are simple flat plate airfoils with rounded edges.  Post-stall behavior is simply assumed,  just to have “gross ballpark” data. 

For the tail fin group,  I assumed that the leading edges could be swept,  if desired.  They do not have to be.  The trailing edges I assumed straight,  unswept.  For the downlift fins,  I presumed a constant chord,  unswept.  These are to be lifting wings,  after all.  All these fin designs will behave as low,  to very low,   aspect ratio surfaces.

Figure 8 – Curve-Fitted Plots of the Data for Square-Section Bodies with Bluff Rear Ends

Figure 9 – Basic Fin Aerodynamic Data

Figure 10 – How I Handled the Twin-Tail Effect of the X-Fin Configuration

The X-fin tail is a little different than in the usual aircraft design practice.  Because of the angles,  there is a cosine component to apply,  for a panel’s projected area.  But,  there is also a sort of twin-tail effect that increases the effective area beyond just the projected area (where one side masks the other).  This opens the door to aerodynamic interference,  so I did not double it for the twin effect,  as indicated in Figure 10.  You could use a round body,  but you still put X-fins on it,  per the wind tunnel experience.

               Towline Aerodynamics

The towline is an essentially-cylindrical shape,  which in the curved section has some local angle of attack in every segment.  The aerodynamics came from the old indicated reference shown in Figure 11 with the data,  for a cylinder in crossflow.  The reference area used for the aerodynamic coefficients in that old reference calculates as Lseg*dia,  which is a sort of “planform” area for the segment.   

These are very old results,  but they are still quite useful.  The drag coefficient is simple indeed at zero angle of attack,  for the lift and drag coefficients equations shown in the figure.  It is just the additive constant in the CD equation.

I modeled the curved portion of the towline as 10 finite segments,  and simply added the lift,  drag,  and geometry contributions of each segment to estimate the result of the entire curved section of the towline.  The local angle of attack at the decoy end is identical to the decoy towline angle determined from that analysis.  It is zero where the curved section joins the straight section.  Being circular,  the angle at each segment is quite easy to determine,  using a constant change from segment to segment.

I did not include the weight of the towline in my analysis.  If I were to do so,  I would need data on the weight per unit length of the towline material,  and reduce each segment’s lift by the amount of its weight,  before adding everything up.  Most cords are rather light,  so it seemed a rather inconsequential effect,  compared to the other assumptions being made for this design analysis. 

However,  that might not be as inconsequential,  if electric power or fuel were to be delivered down the towline.  That’s a change I might add to the spreadsheet in the future. 

Figure 11 – Aerodynamic Model Used For The Towline                  

Running Example Cases

Two things needed to be addressed.  First,  a guessed drag coefficient for the zero-lift body drag was not sufficient.  Second,  online research revealed that operational towed radar decoys that did not feature large drops behind the aircraft,  but did feature shapes that would actually enhance drag.

To address the drag coefficient,  I used Hoerner “drag bible” again,  this time going to his chapter 3,  regarding the pressure drag,  skin friction drag,  and base drag of a variety of shapes.  The pressure drag is primarily the drag of the nose shape.  His Figure 20 offered useful data,  as sketched in Figure 12.

For the square body decoy,  I used the average of the indicated drag coefficients for the hemispherical nose (0.01 on body cross section),  and the flat-ended bluff nose (0.80).  That’s a 0.405 contribution for the nose,  and using the body cross section area reference that I wished to use.  

The same figure has a nose drag coefficient of 0.20 for a rather bluff nose,  but with a small radius transition to the basic cylinder.  I used that for 90% of the nose drag,  and 10% of the flat-ended shape (0.80) to represent the effect of the presumed igniter for an IR decoy.  That produced a nose contribution of 0.260 for the round-body decoy.

Hoerner offers a close approximation of the Schoenherr turbulent skin friction model that is quite easy to use,  and within about a percent of the Schoenherr value.  His equation 26 from chapter 2 for that is:

1/Cfwet^0.5 = 3.46 log10(ReL) – 4.6,  where Cfwet is based on the wetted area,  and L is the wetted length

To convert Cfwet to a cross section area basis,  one simply uses the ratio of areas:

CfB = Cfwet Swet/Ax,  where CfB is the skin drag coefficient referenced to body cross section Ax

For the 2.5 x 2.5 inch square body decoy,  the wetted length is the full decoy length of 18 inches.  Evaluated at 800 ft/sec at 5000 feet altitude on a US 1962 standard day,  the Reynolds number per foot is 2.826 million per foot. Cfwet calculates as 0.00333,  and it converts to CfB = 0.0959. 

For the 3-inch diameter round-body IR decoy,  the situation is much more complicated,  there being a more-or-less cylindrical body about 10 or 11 inches long,  followed by a smaller diameter blast tube to the tail,  and a final full diameter short spoiler to hold the pyrotechnic flame in place behind the decoy.  The blast tube is largely in a base-drag wake zone,  with flow attachment around the periphery of the spoiler,  behind which there is another base drag wake zone. See Figure 13

I used 0.9 feet for the skin drag calculation of the forward full-diameter portion,  which produced a Cfwet of 0.00365,  which converted to a CfB of 0.0535.  I used half the body cross section as the wake zone area behind the forward body around the blast tube,  plus the entire body cross section for the wake zone behind the spoiler. I also treated the reattachment on the spoiler as the same blunt-but-radiused nose drag,  on half the body cross section.

According to Hoerner,  the base drag is related to the skin friction drag ahead of the wake separation,  by his equation 34 in chapter 3:

Added CDbase (on body cross section Ax) = 0.029/CfB^0.5

For the square body,  this figured as added CDbase = 0.050,  and for the base drag behind the forward body on the round decoy,  0.1253.  I use half of that for the first wake on the theory it is about half the area,  and all of it for the spoiler wake,  it being full size.  The reattachment pressure drag on the spoiler is half that of the nose drag,  that being about half the cross section. 

The zero-lift body-only drag buildups are:

Item                                                    square body                      round body

Nose (pressure) drag                         0.405                                   0.260

Skin friction                                      0.0959                                 0.0535

Fwd base drag                                 NA                                        0.0627

Reattachment pressure                     NA                                        0.100

Final base drag                                0.050                                   0.1253

Total on Ax                                       0.551                                   0.602

The zero-lift drag of the fins get added to that of the body in the spreadsheet.  That sum is the actual estimate of the zero-lift drag of the decoy. 

To address towing with or without large drop,  I took a clue from the tangent of the cable angle being the ratio of decoy total downforce (which includes its weight) to net decoy drag (which could be reduced by its thrust,  if any). I ran 1 degree AOA cases square and round,  with and without downlift,  to get a min tow lug height.  I also ran 6 degree AOA cases,  for something halfway to fin stall.  These analyses were loaded into a spreadsheet worksheet for easy iteration.  I created separate worksheets for the square body decoy,  and for the round body decoy.  The square body setup is given in Figure 14,  and the round body in Figure 15.  

Figure 12 – Nose Drag Contributions Data From Hoerner

Figure 13 – Square Body and Round Body Example Cases

Figure 14 – Square Body Setup in the Worksheet

Figure 15 – Round Body Setup in the Worksheet

Determining Tow Positions

It proved possible to generate decoy tow point and towline equilibrium characterizations versus AOA with the square and round body decoys,  each with and without any downlift fins.  These data were plotted for comparison,  as shown in Figure 16 for the square body,  and Figure 17 for the round body.    

Figure 16 – Square Body Results Vs AOA

Figure 17 – Round Body Results Vs AOA

One of the surprises was the occurrence of cable angle theta plus AOA exceeding 90 degrees for both square bodies,  and with the downlifter round body.  You cannot actually reach that condition in actual tow,  it is simply an artifact of the arbitrary calculation tables used in the two spreadsheet worksheets.

From these results,  I learned that tow lug exposed heights were acceptable at small values,  for the 1 degree AOA data that I had generated.  Higher AOA will require either an inappropriately-tall tow lug,  or else we must have added aerosurfaces to produce additional nose-down pitch moment.  Not knowing what might be appropriate as a trim angle,  I used 6 degree AOA data as “about halfway to fin stall”. 

I did this design analysis at a speed and altitude “typical” of a ground attack scenario,  with a high-subsonic weapons-release constraint.  Such a constraint is actually rather typical.  The hope is that there is sufficient excess stability embodied in the tail sizing,  that the effects of higher speeds and higher altitudes are also covered adequately,  for any reasonable engagement scenario.

The risk at higher speeds is that aerodynamic forces exceed the weight so much that the decoy no longer passively “knows” where “down” is.  The risk at higher altitudes is that,  in the thin air,  inertia coupling overcomes stability,  a problem well-known in high-speed jet fighters.  That is,  the control accelerations afforded by the tail fin aerodynamic forces,  in comparison to the decoy inertia,  are simply too small to effect a timely recovery from any sort of disturbance.

Ultimately,  I did the towline equilibrium calculations in the worksheets for the square body at 1 and 6 degrees AOA,  with and without downlift.  And I did exactly the same spread for the round body.  The resulting drops below the aircraft,  distances behind the aircraft,  and depression angles for the cone of no protection are all a function of total towline length.  So I ran multiple lengths for these 8 cases,  collated,  and plotted the result data as depression angle vs total towline length,  for the 8 cases.  Those plots are given in Figure 18.  Three times a “typical aircraft length” would be a towline 150 feet long. 

Figure 18 – Tow Positions Vs Towline Length,  All Cases

This is where the design solutions become very judgmental.  For the square body at 1 degree AOA,  the exposed tow lug heights are right-at about half an inch,  which is quite realistic.  Adding downlift has more effect with a shorter towline,  but that is not very advantageous toward aircraft protection.  The “right” towline length seems to be about 3 aircraft lengths,  or about 150 feet,  based on what little open-source information there is on the existing towed radar decoys.  At that distance,  adding downlift fins depresses the cone of protection to 5 degrees from 4,  which is not much change at all. 

Adding downlift has a lot more effect at 6 degrees AOA and 150 feet:  about 21 degrees vs 12.  Intuition suggests we only need about 9 degrees,  so we don’t need the full 6 degrees of AOA.    Interpolating linearly,  it would appear the no-downlift square body needs about 4 degrees AOA,  while the downlifter square body needs about 2 degrees AOA. 

For the round body,  the picture is quite similar,  but the numbers are different,  because there is less body lift available.  For no downlift,  the 6 degree AOA point generates just about 9 degrees of depression,  no interpolation necessary.  For downlift,  interpolation yields an estimated 3 degree AOA. 

The net result is 4 potential decoy designs,  two square body,  two round body,  each with and without downlift,  all at 150 feet total towline length,  and all targeting 9 degrees of depression.  Plus,  there are two more configurations (square and round) that tow with little depression at 1 degree AOA,  and which need no downlift.  That spread is:

The towline equilibria and tow position data for these 6 configurations are given in Figures 19 – 24.  Bear in mind that for all trimmed AOA values exceeding about 1 degree,  the exposed tow lug heights become unreasonable,  requiring the decoys to be fitted with additional aerosurfaces to add down-pitch moment.  That affects both total downforce and net drag,  and the results have to be recomputed in response to that design change.  Adding downlift reduces that trim requirement.

Now,  if the decoy represents totally passive protection,  you need to depress the cone of no protection well below the line of sight to the approaching threat,  which should be at least co-altitude,  and maybe a little above.  In other words,  you need the most “low” of the “low/straight tow” that you can get.  That means adding downlift for the min trim aerosurface requirement,  whether square or round.

But,  if the decoy is not passive,  then you have information about from what direction the threat approaches.  In that case,  you turn across the approaching threat at high gee,  to prevent it from achieving a tail chase.  You must know whether it approaches from the left or right,  so that you can turn across it:  left if on the left,  right if on the right. For those scenarios,  little or no depression doesn’t matter.  So no added downlift or trim surfaces are required,  whether square or round.

Towline strength:  some of these are still marginal at best,  failing the old strength/load criterion.  

Figure 19 – Results for Square Body,  No Downlift,  AOA 4 Degrees,  Target 9 Degrees Depression

Figure 20 – Results for Square Body,  Downlift,  AOA 2 Degrees,  Target 9 Degrees Depression

Figure 21 --  Square Body,  No Downlift,  AOA 1 Degree,  Target “Low Depression”

Figure 22 – Round Body,  No Downlift,  AOA 6 Degrees,  Target 9 Degrees Depression

Figure 23 – Round Body,  Downlift,  AOA 3 Degrees,  Target 9 Degrees Depression

Figure 24 – Round Body,  No Downlift,  AOA 1 Degree,  Target “Low Depression”

Discussion of Results

The interpolated trimmed AOA results for the round-body decoy designs with significant trimmed AOA hit the target depression pretty close at the selected total towline length.  The square body designs with significant trimmed AOA are in the ballpark,  but fell a bit short of the target depression,  indicating that linear interpolation is not very appropriate.  Further iterations would be required to hit the target depression values,  and to account for the drags of the necessary trimmed-AOA aerosurfaces.  But for illustrative purposes,  these results are close enough,  just as they are.

If depression of the cone of no protection is important,  both body shapes benefit from adding downlift surfaces,  as these reduce either the tall tow lug requirement to trim,  or they reduce the size of any added aerosurfaces necessary to trim out the AOA.  These decoys have lower tow points behind the airplane.  That would be the downlift-equipped square body at 2 degrees,  or the downlift-equipped round body at 3 degrees.  They do fail the towline strength criterion at least somewhere along the towline,  for the presumed towline material,  which was simple nylon mason’s twine.

If significant depression of the cone of no protection is not deemed necessary,  then very short tow lugs,  no downlift surfaces,  and no added trim aerosurfaces become feasible.  These decoys have smaller drops behind the airplane.  However,  these shapes are easier to package into a dispenser.  That would be the no-downlift square body at 1 degree,  and the no-downlift round body at 1 degree.  These do achieve about 4 degrees depression,  on the same 150 foot towline.   Both meet the old towline strength criterion with the presumed nylon mason’s twine material.

The square body options identified here meet all of the old criteria for stable towed decoys.  Such designs would likely require few changes in experimental development testing to perform adequately.  The round body options identified here fail the L/D and tail volume criteria,  but not by very much.  But it is a risk:  some changes might become very necessary during experimental development testing.

Results are summarized in Figure 25

Figure 25 – Results Summary


Deployment is an entirely separate issue,  as noted briefly in Figure 26This topic was not covered here,  except in summary on that figure.  There are 2 options:  slow reel and fast-braked.  Slow reel could be reeled back in and reused,  but it takes long time to deploy.  Fast/braked is 1-shot non-reusable,  but can deploy very fast at need.  These are very difficult design considerations indeed,  involving large engineering development efforts.  None of those issues were considered here.  

Figure 26 – About Deployment,  The Separate Issue

Final Remarks

A square body flight mechanics-only test article built to these criteria,  using these design methods,  was flight tested during 1987 at Flight Systems,  at the Mojave Airport,  on an F-4 “Phantom” aircraft.  Flight test speeds were up to Mach 1.4,  while flight test maneuvering gees were up to 6,  in defensive-break maneuvers.  The test pilot tried to break the tow line,  but could not.  That towline was Kevlar,  with very little elongation capability to absorb line shock!  That alone demonstrates just how practical the towed hardbody decoy can be if designed correctly!  This is summarized in bullet form in Figure 27.

Practical deployment design is an entirely separate issue,  which is its own topic.  That is not covered here.  The experimental test article was slowly reeled out.

Towed ribbon decoys,  while covered by another worksheet in the same spreadsheet file,  are also an entirely separate issue.  Those are not covered here.  

Figure 27 – Overall Conclusions

The US military is currently flying towed radar decoys.  These include the AN/ALE-50 decoy for the FA-18 and B-1B,  the AN/ALE-55 fiber optic towed decoy for the FA-18E/F (Super Hornet),  and a version of the fiber optic decoy that is being developed as the AN/ALE-70 for the F-35. Adding an IR option to the AN/ALE-55 is also an option being considered.

The earliest one of these was the AN/ALE-50.  It is the one that suffered “teething problems”,  until its manufacturer Raytheon finally invented these same aeromechanics tow rules for themselves.  A different manufacturer (BAE Systems) makes the AN/ALE-55 to fit the AN/ALE-50 dispenser,  and is developing the AN/ALE-70,  which requires a different dispenser not externally exposed on the aircraft.

As for chaff and flares,  there is only one producer of chaff,  and two producers of flares,  left in the US.  Esterline Defense Technologies,  also known as Armtec,  makes both chaff and flares.  It is now owned by Transdigm,  which is known among some sources for non-competitive price gouging.  Kilgore Flares company (a division of Chemring Countermeasures Company USA) also makes flares.  Chemring is in turn owned by a company in the UK,  thus being a foreign-owned defense item source.

These are definitely business areas that could use some competition.

Finally,  I would rather not share my towed decoy spreadsheet.  However,  I might consult,  using it.