>>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- Wp/Wi)
g = accel. due to gravity (ft sec-2)
ISP = specific impulse (sec)
Wp = weight of propellant burnt (lb)
Wi = 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.