Ballistic Coefficient Study for Earth Entry

It has been suggested that inflatable or extendible heat shields can be used to lower the entry ballistic coefficient,  and thereby lower entry heating,  perhaps to the point of not needing heat protection on a stage or other item returning from low Earth orbit. 

To that end,  I used my spreadsheet version of the old H. Julian Allen and A. J. Eggers 1950’s-vintage entry model,  at fixed entry speed and angle below horizontal,  with a constant entry interface altitude.  I kept the object mass and hypersonic drag coefficient constant,  and used a fixed nose radius to heat shield diameter ratio. 

All I varied was the diameter (and nose radius right with it).  This produced a set of ballistic coefficients β = M/(C_D*A) that decreased dramatically from a near-Apollo value of 300 kg/m²,  down to very low values at very large diameters.  See Figure 1 below for the scope investigated and inputs used (all figures are located at end of this article).

The trajectory model uses a simple scale-height type exponential model of density with altitude.  It presumes a constant angle below horizontal in a 2-D Cartesian modeling set up.  It presumes the drag coefficient (and thus the ballistic coefficient) is constant with speed.  It corresponds to a certain velocity-altitude trend that is doubly exponential.  This is only approximate,  but it really is in the ballpark!  End-of-hypersonics for a blunt object is usually local Mach 3,  which for Earth,  is just about 1 km/s,  but I arbitrarily took this down to 0.7 km/s (about Mach 2.1),  which is well into the range where ribbon chutes can be deployed.

The results I obtained for each of the four ballistic coefficient cases are given in Figures 2 through 5 below.  I expected to see the end of hypersonics altitudes increase,  and the peak stagnation heating rates decrease,  as the ballistic coefficients reduced,  and they did.  I also expected to see peak deceleration gees increase as ballistic coefficients decreased,  but that is not what I got:  peak gees stayed just about the same for all 4 cases.

I then ran stagnation surface temperatures at those peak heating rates,  for a low emissivity and a high-emissivity case.  I did the analysis in US Customary after converting the heating rates,  then converted the temperatures back to metric.  These show a strong decrease as ballistic coefficients get very low,  but are still problematic for anything but high-temperature steels and exotic alloys!   They are reported in Figure 6 below.

I also ran the average pressure exerted upon the heat shield at that observed constant 6.3 gee peak deceleration.  This is nothing but mass times gees times the acceleration of gravity,  then divided by the heat shield blockage area.  These are not as problematic as the stagnation point temperatures,  by far.  They are also reported in Figure 6.

Whether the inflatable or extendible heat shield concepts are survivable,  I leave to others. 

Figure 1 – Inputs Used for Entry Ballistic Coefficient Study

Figure 2 – Entry Trajectory Results for the Highest Ballistic Coefficient

Figure 3 – Entry Trajectory Results for a Lower Ballistic Coefficient

Figure 4 – Entry Trajectory Results for the Next-to-Lowest Ballistic Coefficient

Figure 5 – Entry Trajectory Results for the Lowest Ballistic Coefficient

Update 4-12-2025:  Oops,  found an error concerting to degrees C in my data.  Revised Figure 6 replaces the original.  

Figure 6 – Temperature and Pressure Results for the Ballistic Coefficient Study

Update 4-12-2025:

I went ahead and estimated the attached-flow heating rates as stagnation divided by 3,  and the wake zone heating rates as stagnation divided by 10.  This is only an educated guess,  but it is rough ballpark correct. 

From these I computed surface temperatures that equilibriate the convective heating with thermal re-radiation to surroundings at 300 K Earth temperatures.  There is no ablation,  no transpiration cooling,  and no conduction into an interior heat sink.  These temperatures are shown in Figure 7.  Bear in mind that they are very approximate! 

Figure 7 – Temperature Trends Around the Entering Structure

The pictures I’ve seen of inflatable and extendible heat shield concepts seem to fall in the range of 2 to 3 for shield/capsule diameter ratio.  2.5 diameter ratio is about an area ratio near 6.  Factor 6 below typical capsule ballistic coefficients (near 300 kg/m²) would be about 50 kg/m².  Bigger diameter ratio may be too fragile to serve,  since I have not seen any concept images with ratios any bigger than about 3.

At a rather low ballistic coefficient of about 50 kg/m²,  assuming a dark and emissive surface,  we are looking at surface temperatures near 1100 C at stagnation,  near 790 C for attached-flow regions near the rim of the shield,  and near 500 C for all the surfaces immersed on the wake zone behind the heat shield.  If the surfaces are not highly-emissive,  those temperatures will be significantly higher yet!  That is what the plot indicates.

The table just below gives some typical “max service temperatures” for a variety of possible materials of construction.  It would seem that there are no flexible materials one could use to construct inflatable or extendible heat shields for Earth entry from low orbit,  which would not be damaged or destroyed by only one use. 

Carbon cloth might work,  but would suffer both serious oxidation damage,  and heat-induced embrittlement,  preventing any re-use.  It might actually suffer burn-through holes,  if too thin or too-lightweight a weave.

TV Commercial Content Is Out of Control!

As of Wednesday 9 April 2025,  I just timed the commercial content of a local 5:00 PM news broadcast as just about 10.5 minutes out of a 30 minute slot.  And I just timed the commercial content of a national broadcast news program as 10 minutes out of a 30 minute slot starting at 5:30 PM.  That corresponds to 36.7% commercial local,  and 33.3% commercial nationally. 

In both cases,  the majority of the commercial content was in the second half of the 30 minute time slot,  which really means during that second half of the news program,  there was actually more commercial time than there was news time!

These stations are supposedly licensed by the FCC to broadcast “in the public interest”.  Commercials in a news program are not in the public interest,  they clearly are in the profit interest of the advertisers.  It is only the news content that is actually in the public interest!  That is obvious even to the casual observer,  no matter how the lawyers might spin it!

In the 1950’s and 1960’s,  a typical hour-long prime-time program had 51 or 52 minutes of content,  and 8 or 9 minutes of commercials.  That corresponds to 13-15% commercials.  (Most programs were only a half-hour long back then,  but at about that same percentage commercials.)  You can time the DVD’s of those old programs for yourself! 

In the 1980’s,  this had changed to around 42 to 44 minutes of program,  and 16-18 minutes of commercials in an hour time slot in prime time.  That is 27-30% commercials,  about double the commercial percentage of 2+ decades earlier! 

Now,  4 decades since the 80’s,  it is even higher at 33-37%,  right there in prime time news broadcasts!  Outside prime time,  it appears to be even higher commercial content!  When flipping channels,  it often seems like there’s more commercials than content.

As a case in point,  on Thursday 4-10-2025,  I scrolled through all 36 channels that I can pick up with a rabbit-ears antenna,  between 2:10 and 2:15 PM.  Two of those are shopping channels (all commercials),  and one is a weather update (no commercials).  Those 3 don’t count.  The rest all show content with commercials.  As I scrolled through,  I counted 13 out of that 33 as showing commercials,  not content.  That’s an empirical estimate of 39.4% commercials in non-prime time!

So,  how does so much commercial time actually qualify as “broadcasting in the public interest”? 

Is there no law or regulation limiting this commercial content?  If not,  there should be! 

And I suspect there once upon a time there was at least a regulation,  which was quietly done away with,  long ago.  It was eliminated simply so that the advertisers could make more money!  Probably at the behest of the politicians those advertisers bought. 

What Trump Has Brought

I know that the great majority of my neighbors here in McLennan county voted for Donald Trump,  and for the other candidates of the Republican party that he dominates utterly,  in all the federal and state races.  I must wonder if you actually like what you have been getting.  I’m pretty sure it is not what you thought you were voting for.

The Economy

He promised you lower prices and prosperity.  What he has done with his tariffs inducing trade wars,  is to push what was a good economy to the brink of recession,  and start high inflation,  in less than 80 days.  This from the “expert businessman” who actually has 6 bankruptcies of record.  Look it up yourself!

The first symptom is the recent huge drop in the stock market.  Wall Street is not the economy,  but it is an early indicator,  as are the recent job losses and layoffs (besides the fired government workers,  which also makes job hunting more difficult for you).  The actual effect on the full economy lags by months.  The sharp rises in prices for just about everything due to tariffs will happen much faster,  but will persist well into the coming recession,  because of the supply disruptions the trade wars also cause.

You did notice the drops in your 401(k) accounts and investment portfolios,  did you not?  That’s just the beginning of this! 

Border Security

Trump promised both a closed border and mass deportations,  and he has begun doing exactly that.  But how he is going about this,  is the problem!  Adding more wall doesn’t help,  because all you need to get over a wall is a taller ladder.  You fix the immigration system instead,  which is a job Congress has failed to do,  since not long after the end of World War 2. 

It is the mass deportations without any due process that are the big problem!  Mass deportations of anyone not white,  regardless of whether they are legally here or not (or even a bona fide citizen)!  That is entirely illegal!  Not to mention unethical and totally immoral!

This is based on the demonstrably-false belief (and propaganda) that all immigrants are evil.  Trump’s minions that are in charge of ICE and the related agencies,  are betting that you will let them get away with these crimes,  because too many of you believed the propaganda lie about immigrants,  and so don’t care what happens to the deported. 

They are even defying court orders to return some of those they deported in error,  rather than trying to correct those wrongs.  “Commit any evil not to admit being wrong” seems to be the order of the day.

Social Safety Nets

Trump and the Republicans promised they would cut government (which they are doing),  but also that they would not damage your Social Security or Medicare.  Given the disparities between promise and action described above,  there is absolutely no reason to think your Social Security and Medicare are safe! 

They are in fact the largest portion of the budget:  the biggest,  fattest target!  The government workers who run them are already being fired.  So,  what do you think the ultimate result will really be?  It will start with the chaos of payments erratically not made to you,  or on your behalf!  Then it will get worse!

Operation of Your Federal Government

Trump and his minions (especially Musk) have been firing government workers at the FAA during a spate of airline crashes and near-misses.   They have been firing government workers at the IRS during tax season.   Just how does that serve you? 

Trump put a vaccine denier in charge of Health and Human Services when we are threatened with two possible pandemics (bird flu and measles),  and he and Trump have been firing heads of agencies that see to the safety of your foods and drugs. 

Funding has been cut for all kinds of medical and other scientific research.  That last includes criminal extortion:  universities are being forced to implement Trump-desired policies (many based on propaganda lies,  not fact),  or else lose their research funding.

This extends to pressuring the mainstream media outlets to say only positive things about him,  lest they get taken to court,  or in the case of PBS and NPR,  lose their federal funding.

Trump and his minions control the Executive Branch,  and they also control the Legislative Branch of your government because they utterly dominate the majority party in both houses of Congress.  They have demonstrable friends on the Supreme Court,  and several minions appointed to federal judgeships that will do their bidding instead of properly following the law.  The courts that still oppose them are now being openly defied. 

If you remember your civics classes,  consolidating all federal power into the Executive branch would be the very definition of dictatorship!  Now do you understand the “ways” that Trump spoke of vaguely,  in order to stay in office for an illegal third term (or more)?

You are about to lose your democracy!

Foreign Policy and Our Allies

Trump and his minions have already angered our NATO allies by apparently switching sides in the Ukraine-Russia war.  He so very clearly wants to give Putin a victory there,  when the Ukraine was actually NATO’s proxy army against Putin’s ambitions of European conquest.

Trump’s tariffs and trade wars only make that anger worse.  Our allies around the world,  not just NATO,  now consider us an unreliable ally at best,  and likely not an ally at all.  Damaging our alliances when we face four threatening adversaries (Russia,  China,  North Korea,  and Iran),  three of which are nuclear armed,  is doing our adversaries jobs for them. 

Doing your enemy’s work for him is very clearly “providing aid and comfort” to that enemy.  That is one of only two definitions of treason written into our Constitution.  Go read it for yourself!  It’s written in plain English,  not legalese.  You need no lawyer or judge to interpret it for you.

Treason is most certainly impeachable,  and it lies far outside any “Presidential immunity” intended by a Trump-friendly Supreme Court.

Protests

Here in the last few days,  there have been mass protests around the country against the policies of Trump and his minions.  There has even been a protest right here in Waco,  Texas!  Given the magnitude and severity of the problems described above,  why is that surprising?  Especially since Trump’s majority in the popular vote was quite slim nationally?  I hope these protests continue and grow,  despite the attempts to shackle the mainstream news media. 

Recommendations

I have two:  (1) join the protests if they continue (and I think they will),  and (2) contact your federal Senators and your House Representative. 

If you do contact them,  point out the ongoing crimes,  and demand they take action against them,  lest they be complicit in them. 

I already have.  3 times now,  without any observable effect so far.  So,  I will continue.

Update 4-8-2025:  A slightly-edited version of this article ran as a board of contributors opinion piece in the Waco Tribune-Herald today.  

About Nuclear Pulse Propulsion

Depending upon the detail method chosen,  this kind of revolutionary propulsion could be in flight test within 5 years,  and flying in its initial form in 10 years.  That would be the 1950’s fission technology.  The other versions might perform better,  but lack the materials,  and the necessary detonation or containment technologies,  that are required even to build test devices.  They still might not be ready to fly in 50 to 100 years,  if fusion is involved,  according to some experts.

This article is based upon a NASA paper and two Wikipedia writeups about pulse propulsion,  plus George Dyson’s book “Project Orion” about his father’s work on the Orion project at General Atomics in San Diego,  CA,  in the 1950’s and early 1960’s.  That last begins with company R&D work leading up to their first government contract. 

Between those four sources,  a pretty good picture of the propulsion is available,  particularly the technologically-ready fission charge version originally pursued in the 1950’s and early 1960’s.  For readers wishing to pursue this further,  those references are:

AIAA paper 2000-3856 “Nuclear Pulse Propulsion - Orion and Beyond”,  by G. R. Schmidt,  J. A. Bonometti,  and P. J. Morton,  then from the NASA Marshall Space Flight Center,  Huntsville,  AL.

Wikipedia article “Nuclear Pulse Propulsion”,  as retrieved 2-26-2025,  and last edited January 2025. 

Wikipedia article “Project Orion (nuclear propulsion),  as retrieved 2-26-2025,  and last edited February 2025.

George Dyson,  “Project Orion – the True Story of the Atomic Spaceship”,  published 2002 by Henry Holt and Company,  New York City.  (A second edition is forthcoming very soon,  if not already available.)

The basic external detonation concept is depicted in the Figure 1 sketch below.  All figures are at the end of this article. 

The idea is to explode a fission bomb at a safe distance behind the vehicle,  which vaporizes a reaction mass,  and blows that reaction mass into the pusher plate at the rear of the vehicle.  This requires a sort of “shaped charge” technology for the fission device,  in order to increase the amount of reaction mass intercepted by the pusher plate.  There are shock absorbers between the pusher plate and the rest of the vehicle,  to smooth-out the high-gee “hits” into a nearly-continuous and almost-steady acceleration. 

Figure 2 gives some indication of the effects of vehicle size on this process.  Bigger mass is inherently a larger pusher plate dimension,  which then intercepts a larger fraction of the plasma blast created by vaporizing the reaction mass.  The bigger mass also reduces the high-gee “hit” from the explosion,  making the shock absorber design easier.

At the time this technique was pursued in the 1950’s and early 1960’s,  it was thought that the main environmental concern would be the radiation fallout in the atmosphere from a surface launch.  Being fractional-kiloton (KT) devices,  leading to low-KT devices once out of the atmosphere,  there is less fallout than one might otherwise suspect,  more or less comparable to one atmospheric test of a low-range megaton (MT) thermonuclear device.  See Figure 3.

The risk of electromagnetic pulse (EMP) effects was not really recognized until after the “Starfish Prime” megaton-range nuclear test,  that was conducted in space in 1962.  Some data about that are given in Figure 4.  This really restricts where and how one might surface-launch such a vehicle.  These vary inversely with the square of the distance,  and directly with yield.  Bear in mind that we simply do not have the necessary technological capabilities yet,  to build such vehicles out in space,  so surface launch is still the only means available in the short term.

Based on the data in the four references,  a rough approximation to the performance values one might expect are given in Figure 5.  These are quite remarkably high,  sufficient for sending crews pretty much anywhere within the solar system,  on relatively short trips.  Some of the fusion concepts,  if they can really be made to work,  might even be suitable for interstellar missions. 

It is this author’s opinion that we need to get over our fears about “nuclear things in near-Earth space”,  modify the Space Treaty to allow this kind of propulsion,  and simply “get on with the war”.  However,  finding massive new fissionable material resources is inherent to support the quantities of fissionable material that will be necessary.  If not on Earth,  then “out there” somewhere. 

As a conceptual example,  the one-way velocity requirement to go from low Earth orbit to rendezvous with asteroid 2024YR4 is about 5.9 km/s as depicted in Figure 6.  Back to low Earth orbit,  about 4 years later,  the same velocity requirement can decelerate one back to low orbit,  excluding all rendezvous and course correction requirements.  If one wanted to send a large expedition to explore mining this asteroid (to include bringing significant mass home),  using a pulse propulsion vehicle already based in low orbit,  the rough sizing of such a vehicle’s weight statement might look like the numbers given in Figure 7.  The contrast with a chemically-powered vehicle is quite stark.  But with pulse propulsion,  the basic message is to build it big!

Figure 1 – The Basic Concept of Nuclear Pulse Propulsion As It Was Originally Pursued

Figure 2 – “Bigger Is Better” For Nuclear Pulse Propulsion As Pursued in the !950’s and 1960's

Figure 3 – About the Risks From Surface-Launching a Nuclear Pulse Propulsion Vehicle

Figure 4 – About the “Starfish Prime” Nuclear Test That Revealed the Risks of EMP

Figure 5 – Assessment of Achievable Performance Vs. Size With Fission Pulse Propulsion

Figure 6 – Getting to Asteroid 2024YR4 At Its 2028 Close Approach

Figure 7 – How a Large Round-Trip 4-Year Mission Might Be Mounted to Asteroid 2024YR4