New calculations even more fatal to Hoagland's latest crackpot theory (Updated 8/29)

The following post to the "Dark Mission" blog was censored today. Bear in mind that, on his horrible web site, Hoagland seeks to prove that the 600 ft/sec velocity surplus at orbit insertion of Explorer 1 was too great to be explained by over-performance of the solid rocket stages. In the equations, g is the acceleration due to gravity in ft/sec², I_sp is the specific impulse of the stage in seconds, and W_i is the initial mass of the stage plus its fuel and whatever else it is carrying. dV is the increase in velocity provided by the stage.

Somebody with more skill at rocket-science than me has provided an even more ferocious condemnation of Richard Hoagland's faulty mathematics in attempting to calculate the velocity addition of Stages 2,3 and 4 of Explorer 1.

He points out that, using Hoagland's notation, Konstantin Tsiolkovsky's rocket equation is normally written as:

dV = g x I_sp x ln(W_i/W_f)

where W_f is the final mass at burnout (but before discarding the burnt-out stage)

He then points out that it's not permissible to aggregate the stages and evaluate the equation once. You are obliged to take it stage by stage, and this is his result:

STAGE 2
----------
W_i = 1020+280+80
        = 1380
W_f = 1380 - 530 (weight of the burned fuel)
        = 850

dV = 32.2 x 220 x ln(1380/850)
        = 7084 x 0.482
        = 3,414 ft/sec

STAGE 3
------------
W_i = 280+80
        = 360
W_f = 360 - 140 (weight of the burned fuel)
        = 220

dV = 32.2 x 235 x ln(360/220)
        = 7567 x 0.492
        = 3,723 ft/sec

STAGE 4
-----------
W_i = 80
W_f = 80 - 48.5 (weight of the burned fuel)
        = 31.5

dV = 32.2 x 235 x ln(80/31.5)
        = 7567 x 0.932
        = 7,052 ft/sec

TOTAL delta-V
---------------------
3414 + 3723 + 7052 = 14,189 ft/sec

An additional 600 ft/sec represents 4.2% over-performance.

There is no need to resort to an anti-gravity field to account for this. Hoagland's entire thesis is therefore falsified. Cheers.

There's another, possibly simpler, way of looking at this. Since the parameters of the elliptical orbit are precisely known, the orbit velocity can be calculated from a reliable equation. Deduct the burnout velocity of the first stage -- also known, but with less precision -- and what's left is the dV of the solid upper stages. Calculations done this way were offered to the "Dark Mission" blog, but blocked. Hoagland and Bara accept nothing that challenges their ridiculous and misguided ideas.

Richard Hoagland writes that the solid upper stages of the Juno 1 rocket that launched Explorer 1 only contributed 3,520 ft/sec of the total orbital injection velocity. Well, let's see now...

DATA:
Planned orbit 220 x 1,000 miles (352 x 1,600 kM)
Actual orbit 223 x 1,592 miles (357 x 2,547 kM)
Radius of Earth 6,375 kM
Gravitational constant, µ, of Earth 398,660 kM³/s²
Cut-off velocity of Jupiter-C rocket (Juno's liquid first stage) 9,020 mph = 13,229 ft/sec [1]

CALCULATION:
semi-major axis of actual orbit, L_smaj, (357+6375+6375+2547)/2 = 7827 kM
distance from center of Earth to orbit point, R, 6375+357 = 6732 kM

velocity at orbit injection, V_orb = √(µ(2/R - 1/L_smaj)) [2]
2/R - 1/L_smaj = 0.000169
V_orb = √67.493 = 8.215 kM/sec = 27,111 ft/sec (actually only 2.5% greater than planned)
less the velocity achieved by the first stage: 13,229 ft/sec

Ladies and gentlemen, get out your calculators! In about 3 seonds you will falsify Hoagland's entire theory.

[1] http://www.astronautix.com/lvs/jupiter.htm
[2] http://en.wikipedia.org/wiki/Orbital_velocity

There's a small discrepancy between the two calculations, to be sure -- due to uncertainty about the velocity at first-stage burnout, perhaps.

Other factors that would be considered in a really accurate calculation:
* Correction to the value of g as the rocket ascends away from Earth -- a small positive vertical increment
* Boost given by rotation of Earth -- separately calculated as 1100 ft/sec horizontal
* Gravity drag -- perhaps negative 1000 ft/sec vertical

However, the discrepancy is nothing to compare with the difference between 14,000 and 3,520.

Hoagland's new crackpot theory defeated by his lousy math

The latest buffoonery from Richard Hoagland is a treatise in three laborious parts on an anti-gravity field allegedly discovered at the launch of Explorer 1 fifty years ago, and then kept secret until now. Mike Bara posted on the topic recently, somewhat lamenting the fact that, in an error-filled four-hour marathon on "Coast to Coast AM", Hoagland had pre-empted their plan to reveal this deep-dark-secret in a future edition of "Dark Mission". My response was censored and not permitted to appear:

>>Oh well. It is truly amazing stuff. You guys' heads will explode.<<

Explode with laughter, possibly. Hardly for Hoagland's logic or for his mathematical skill.

Turning first to his logic, what he alleges happened to the Explorer and Vanguard series must obviously have also happened to any spin-stabilised satellite launch. Now, I don't exactly know how many spin-stabilised satellites have been launched in the last 50 years, but it's a lot. Hoagland wants us to believe that an important factor affecting the final orbit insertion velocity of these satellites remained unknown to the engineers whose responsibility it was to calculate rocket ascent profiles. Unknown because it was declared secret "at the highest levels of government".

I say.... Nonsense.

Now to the math.

The equation Hoagland presents for deriving dV, the velocity added to the rocket by stages 2,3,4, in ft/sec, is as follows:

dV = -g*ISP*ln(1- W_p/W_i)

where

g = accel. due to gravity (ft sec^-2)
ISP = specific impulse (sec)
W_p = weight of propellant burnt (lb)
W_i = initial weight of vehicle (lb)

He then inserts figures to get:

dV = -32.2 x 228 x (662lb/1380lb) = 3520 ft/sec

If I were his mathematics tutor, I'd give him an F for that.
By his own figures, from the Smithsonian, total weight of the three stages = 1020 + 280 + 80 = 1380, correct
Empty weight = 490 + 140 + 31.5 = 661.5
Therefore weight of propellant burnt = 1380 - 661.5 = 718.5, NOT 662.

If we accept his equation, the value of dV is 5389, not 3520. Hoagland appears to have forgotten to derive the natural logarithm.
[calculations re-done correctly in aug 25th post on this blog]

Maybe you guys should think again about using this garbage in a future edition of "Dark Mission".

If Hoagland/Bara do decide to publish this stuff, despite the elementary mathematical errors, it's a safe bet the publisher, Adam Parfrey, won't notice. He doesn't understand simple everyday logic, certainly not complicated stuff like arithmetic.

In his radio appearance Hoagland triumphantly declared victory over his critics, noting that none of them has e-mailed messages along the lines of "Hoagland Blows It Again". Richard, you may now eat them words.

Hoagland & Bara wrong as usual

The destruction, last February 21st, of the crippled military satellite USA193, was the occasion for more errors by H&B. Ever alert for the appearance of what they call the "ritual numbers" 19.5 and 33 in space affairs, Mike Bara posted on that day a totally erroneous claim that the navy ship that launched the fatal missile was at 19.5°N latitude, as was Sec. Def. Robert Gates when he made the announcement that the mission was going ahead. Similar erroneous material appeared on Hoagland's unreadable web site. As I pointed out at the time, the exact location of the ship was not known but it was announced as north of Hawaii, and therefore above 22°13'. Gates was in Honolulu, at 21°18'. Overall control of the operation was from Omaha, at 41°15' N.

A commenter on the official "Dark Mission" blog returned to this topic on August 10th, posting links to some new comments (also some not-so-new, like James Oberg's analysis in "Spectrum"). My additional comment was, of course, censored and not permitted to appear on the blog.

LEST WE FORGET:

Richard Hoagland, commenting on the destruction of USA193 on 'Coast to Coast AM' stated that he was sceptical, because the Columbia space shuttle contained more hydrazine than the spy satellite when it disintegrated, and no concern about toxicity was expressed at that time.

This, of course, was completely wrong on both counts. A typical performance from the program's so-called 'science advisor' who makes errors every time he appears on that wretched radio show. Its producers are evidently too clueless to know the difference between a scientist and a buffoon.

Another "stunning confirmation"?

        Undoubtedly Richard Hoagland's favorite adjective is "stunning", and one of his very favorite uses of it is in the phrase "In a stunning confirmation of [insert one of his crackpot theories], newly published results... bla bla bla".

        A classic example was the 25th June post on the darkmission blog, headed "New Study Confirms More Aspects of Mars Tidal Model". This referred to computer modelling at UC Santa Cruz, suggesting that historically Mars suffered a colossal impact with an asteroid about half the size of the moon. Mike Bara claimed confirmation of the so-called "tidal model" despite the fact that:

• The collision was in the opposite hemisphere
• It happened, according to the computer model, 4 billion years ago, cf. 65 million for the tidal theory
• It was a single object, whereas the tidal theory involves "splattering" of the southern hemisphere by the products of a planetary explosion.

        Mike Bara did, in fact, allow a blog-comment along those lines, responding with his usual substitute for rational argument -- "You're an idiot".

        Now comes the latest of these hilariously false claims: "New Research Reinforces Key Aspects of Hyperdimensional Physics", posted on 6th August. The peg was a paper in a journal of the Astronomical Society of Australia suggesting a spin-orbit coupling between the sun and the giant planets, accounting for some features of the sunspot cycle.

        Bara wrote that this is "a flat-out, indisputable confirmation of the Hoagland\Torun Hyperdimensional Physics model", although, of course, it is nothing of the kind. He also wrote that, at solar max, " sunspots, solar flares and coronal mass ejections, ... tend to cluster around the tetrahedral 19.5° latitude".

The following blog-comment was censored, and not allowed to appear:

From the wikipedia article on Spörer's Law: "At the start of a sunspot cycle, sunspots tend to appear around 30° to 45° latitude on the Sun's surface. As the cycle progresses, sunspots appear at lower and lower latitudes, until they average 15° at solar maximum. The average latitude of sunspots then continues to drift lower, down to about 7° and then while the old sunspot cycle fades, sunspots of the new cycle start appearing at high latitudes."

 19.5° is, as usual, in Hoagland's imagination only.