Hoagland and Bara still confused about Explorer 1

        There are signs of a slight rift between those terminally erratic writers Hoagland & Bara on the question of Explorer 1, America's first satellite. Not that either of them is right about the orbit, but they now appear to be wrong in significantly different ways.

        Hoagland, as some readers of this blog will remember, made an attempt to apply the Tsiolkovsky equation to the four-stage rocket Juno 1 that launched Explorer. He completely screwed up the calculation, admitted as much about nine months ago but so far has made no move to correct his web page.

        Hoagland's general thesis was that the rotation of the three solid upper stages induced an "anti-gravity effect" which added significantly to the velocity of the final orbit insertion. An additional reason to discount this claim, beyond Hoagland's appalling math, is that by the time the upper stages fired the rocket was traveling horizontally, so gravity is not really the point.

        Mike Bara had his own excruciatingly fallacious attempt at deriving the excess velocity of Explorer 1, but perhaps he somehow sensed that they need something more plausible than anti-gravity to explain their incorrect figures. Earlier this week he stated that perhaps "the spinning changed the burning properties of the fuel." This was in the course of an hour-long podcast interview hosted by Robert Bradbury (who had failed to read any part of The Choice prior to the recording, oops.)

        I'm having a hard time imagining anything less plausible than this attempt to explain what does not need explaining. If the upper stages had been liquid-fueled the idea might have had some superficial credibility, since liquid rocket fuel does indeed slosh around in flight and needs management to ensure a good burn. But we're talking here about military-grade solid fuel which does nothing other than burn enthusiastically when someone puts a match to it.

        Now for the good news. In the course of the podcast (00:45:00 approx) Mike said "Probably not everything in my book is correct." HOORAY. The first step toward redemption is recognition of ones failings.

Rocketry geeks read on...
        Juno 1 was, frankly, a bit of a lash-up—put together in an atmosphere of near-panic as the USSR twice demonstrated its superiority at getting to orbit, and other US rocketry crashed and burned on national TV several times. It was a Jupiter-C rocket with one additional stage.


        Von Braun had a special version of the Redstone missile made, with tankage stretched by eight feet. He fueled it with 60% unsymmetrical dimethyl hydrazine and 40% diethylene-triamine, instead of the alcohol fuel the Redstone was designed for, increasing thrust to 83,000 lb. Burn time was 155 sec, and specific impulse 235 sec. On top of that he added three upper stages, consisting of clusters of 11, 3, and 1 Baby Sergeant solids, with specific impulse 220, 235 and 235 sec. The trajectory of the Redstone first stage was guided by aerodynamic surfaces, but the upper stages had no terminal guidance whatever. For stability, the whole upper stack was therefore spun up to a rotation rate varying from 450 to 750 r.p.m. Thus, it was known in advance that the actual orbit parameters could not be predicted with great accuracy. The nation didn't care—it wanted to see something American in any orbit that could be contrived.



        To achieve orbit, a rocket has two separate tasks—get the payload high enough, then boost it horizontally to sufficient velocity to maintain the orbit. An altitude of 122 km and a velocity of 7 km/sec are approximately the minimum requirements. At cutoff of Juno's first stage, it had a velocity of just over 4 km/sec pitched over to 40° from horizontal. The upper stages were then allowed to follow a purely ballistic trajectory for over four minutes until the stack was horizontal, before sequential firing under direct ground command.

        The ideal theoretical orbit was 352 x 1600 km. In fact they achieved 357 x 2547 km. It was in noticing that rather big apogee excess that Hoagland & Bara made the elementary error of declaring that the whole thing had 60%[1] more energy than anticipated, not realizing that orbital velocities are calculated on the semi-major axis, NOT altitude above the Earth's surface. Mike Bara wrote "I won't bore you with the details, but the fact is a miscalculation of that type simply cannot happen." He should perhaps have bored himself with some details before writing such garbage.

        When you work out the math correctly, the velocity at orbit insertion turns out to have been 8.215 km/sec, cf. the planned 8.018 km/sec— an excess of 2.46% and well within known slop factors such as rocket fuel performance, pitch angle, and upper atmosphere wind speed.

Hogwash
        So Hoagland & Bara between them delivered four hours of overnight radio, one long web page and two book chapters of complete hogwash, based on a childish lack of understanding of rocketry. I wish I thought their fans cared, but alas those people are so gullible I swear they'd accept kool-aid if it was offered.

==========================================
[1] 60% was Bara's figure (The Choice, p. 144.) Hoagland said 30% on Coast-to-Coast AM, but the inaccurate calculations in his web page suggest 17%. All three figures are, of course, wrong.