Rocketry: The Gateway To Understanding Space Technology

Few people living today are aware the Space Age began on October 4, 1957 with the launch of the Russian Sputnik satellite. (See newspaper clipping). Sputnik was a resounding event, and had the impact of a train collision on the American educational system and citizens'  consciousness. As the attached graphic shows, Sputnik was a 184 lb. satellite that orbited the Earth every 96 minutes at an altitude of about 900 km (600 miles).

I was 11 at the time, and had much more interest earlier on that particular day (a Friday) in how my Milwaukee Braves would fare in Game 3 (the next day, Saturday) of the World Series against the New York Yankees - than in any space exploits.

Some days later, we heard the first radio 'beeps' from Sputnik. The signal had been picked up by an RCA receiving station at Riverhead, New York and relayed to the NBC studios in Manhattan, when most of us alive then in the U.S. heard it over the Huntley-Brinkley Report.

How did the nation, including  politicos, react? (This was during the Eisenhower administration which alas, for most of the population today constitutes ancient history!) According to Paul Dickson, author of Sputnik: The Shock of the Century, p. 23:

"Polls taken within days of the launch showed that Americans were concerned - so concerned that almost every person surveyed was willing to see the national debt limit raised and forgo a proposed tax cut in order to get the United States moving in space"

The Sputnik moment triggered a space competition that would ultimately see the United States reaching the Moon before the Russians. It disclosed a collective willingness to sacrifice financially, via raising the debt limit,  and rescinding a proposed tax cut to achieve it.  And with very good reasons. By the time of Sputnik's launch in October, 1957, the Russians were producing some 66,000 engineers a year compared to the United States' 22,000. In addition, the key subjects of higher math and physics were almost nowhere to be found in the U.S. secondary school curriculum - nor were there the teachers to teach them. All this had to be factored into the coming expense to get the U.S. on a competitive par with the Soviets. Teacher education and training alone came to over $1 billion by the time of the Apollo 11 lunar landing.

By the early 1960s, physics, astronomy, math as well as the hobby of model rocketry had become a part of many students' lives. Those who might have been mildly interested in psychology or medicine turned instead to mathematics, physics, and rocket engineering. And the memory of Sputnik became the driving impetus leading many of us to want to build our own rockets - with their own payloads.
Space phenomena such as auroras, asteroids, cosmic rays and solar flares - while important -  also often provoke the desire to learn more about space technology. After all, getting a space telescope in orbit above Earth is the optimum way to observe celestial objects, only surpassed by  sending space probes to actually land on asteroids to take samples, e.g.

http://www.esa.int/Our_Activities/Space_Engineering_Technology/Asteroid_Impact_Mission/The_art_of_landing_on_an_asteroid

Thus the study of space often itself begins for many with the study of space vehicles and also construction of rockets. If one then begins by building and launching simple rockets - he or she goes a long way to becoming informed about the physics of space flight overall, as well as energized to learn more about advanced space propulsion systems.

My own rocketry exploits ran in parallel to my astronomy devotion. At the same time I was building my own refracting telescopes to observe celestial phenomena from M13 (globular cluster)  in Hercules to M 8 (Lagoon Nebula) in Sagittarius, I was also constructing my own model rockets to launch publicly - e.g. at Mgsr. Edward Pace High (where the entire school would be let out to watch a launch).  Below is shown a typical 2- stage design I'd use, with dimensions.


My single stage rockets were up to 16-18" in length and generally contained a payload section with parachute, within which a lizard, frog or cricket was often placed - on a comfortable wad of cotton to withstand the g-forces. A tiny side panel was cut out with plastic glued over it to allow a kind of small window.

Rocketeering, of course, also required a thorough study of the related physics principles. What is it that causes that single stage rocket to be thrust upwards? And can one compute the altitude from certain basic parameters? The first question can be answered with respect to the diagram below, and a model rocket launched by Colorado high school rocketeers::

As indicated in the diagram, the rocket’s motion changes when a fraction of its mass (D m) is released in the form of ejected gases. Since the gases acquired their own momentum, the rocket receives a compensating momentum in the opposite direction.  Therefore, the rocket is accelerated as a result of a push from the gases. In free space, or a vacuum, the entire system works independent of the presence of any opposing medium.

Assume at some time t, the momentum of the rocket plus fuel is: (M + D m)v, then at some later time: (t + D t), the rocket ejects some fraction of mass D m, so the rocket’s velocity must increase to (v + D v). By appealing to Newton’s 3^rd law via an application of conservation of momentum,  we may write:

Total initial momentum of the rocket system = Total final momentum of the system

Then we get:

(M + D m)v = M(v + D v) + D m(v – v’)

Where v’ is the velocity with which the fuel is ejected relative to the rocket. The equation can then be simplified to yield:  Mdv = v dm, which may be integrated, viz.:

M ò_v1^v2  dv = v ò_m1^m2  dm

Or, letting m2 = M _f, m1 = M _i and v2 = v _f, v1 = v_i^:

v _f – v_i^:   = v’ ln [M _i / M _f]

Where the left side shows the difference between the final and initial velocities, M _i refers to the initial rocket mass (fuel plus rocket proper) and M _f refers to the final rocket mass with fuel expended.  (In general, for most rockets,    M _i  >> M _f ).

To see how this works, say a model rocket is launched by an amateur group in central Colorado (see image  at top)  of initial  total mass 1.0 kg. They used a Zn S (zinc sulfide) solid fuel engine for which the exhaust gases attained a velocity of 100 ms ^-1 relative to the rocket for 3 seconds.  After this interval, the rocket mass decreased to 0.05 kg.   We can then find the rocket’s acceleration and estimate the altitude assuming zero air drag and a near –vertical launch angle.

We have: M _i = 1.0 kg, M _f  = 0.05 kg

 Therefore, the difference between initial and final velocities is:

v _f – v_i^:    =  v’ ln [M _i  / M _f]

v _f – v_i^:     = (100 m/s) ln [1.0 kg/ 0.05kg]

v _f – v_i^:    = (100 m/s) ln(20) = (100 m/s) (3) = 300 m/s

The altitude can be estimated by using the kinematic eqn.

s = ½ at²

where s is the vertical displacement for an acceleration a, over time t.

s = ½ (300 ms^-2) (3)²  

s = 450 m  or  1 485 ft.

For the rocket itself, the key parameter is usually the thrust, on which the rocket's velocity will depend. The graphic below gives an idea how the average thrust of a given rocket engine is obtained:

Total Impulse, as indicated above, is extremely critical and a property of the solid rocket engine one uses - each of which has a specified value in model rocketry with units in Newton-seconds or pound -seconds. The 16 0z. in the factor on the extreme right is because this is generally regarded as the upper limit for the model rocket. Above this and there is too high a danger of instability - mainly that the design will not allow the center of gravity to be ahead of the center of pressure as it needs to

be.

Let's say the model rocketeer wishes to compute the velocity v2 from the equation above, using the units (feet-pounds) as indicated.  Let the total impulse of the engine be 10 pound-seconds, and the burn time of the engine be 2 seconds. Then the force F or thrust is:

(10 lb-sec)/ 2 sec  x (16 oz/ 1 lb) = 80 oz.

Then the velocity v2 = (80 oz/ 10 oz   - 1)  32 ft/ sec/sec (2 sec)

Assuming the average weight of the rocket at lift off is 10 oz.

v2 = (8 - 1) (64 ft/ sec)  =  7( 64 ft/ sec)=  448 ft/ sec or about 135 m/sec

Which is a reasonable value.

Many model rocket enthusiasts  of course, go on to full amateur rocketry which entails the construction of large metallic tube rockets capable of going thousands of feet in altitude. Different safety rules apply to these "full fledged" rockets, and their design and construction is also much more complex because now instead of buying a ready -made engine as in the case of the model rocket, you are designing your own. This means you need to get the design of the rocket engine nozzle very precise.  A typical design layout is shown below:

The computation for the effective thrust coefficient C_F shown at the bottom is related to the physical specs including the atmospheric pressure,  P_a    , the chamber pressure,  P_e  , the ratio of specific heats (C_p /C_v )  for combustion products k .

The combustion chamber cross-sectional area (A_e / A _t)  is the ratio of nozzle exhaust area to throat area) given by:


(A_e / A _t)   =  (M _t / M _c)  [(1 + M _c ² (k -1 )/2/ 1 + M _t ² (k -1 )/2] ^k+1/2(k+1) 


Where M _t is the Mach number of the gases in the throat, and M _c is the Mach number at the end of the cylindrical section.

Generally, the diameter of the nozzle throat needs to be about one third the diameter of the combustion chamber, while the angle of the converging section of the nozzle needs to be approximately 30 degrees, and the angle for the diverging section 15 degrees. The failure to properly design the nozzle is probably responsible for most amateur rocket misfires.


Of course, those of us doing any rocketry back in the early 60s didn't have access to computers or even scientific calculators like the spoiled students today. Nope, we used the one reliable instrument we had, the slide rule. For me, the good ol' Mannheim type as shown below:

Today, most of these instruments are relegated to mathematical displays in certain museums, but I still have mine and even check it out every now and then, computing a tangent, cube root or ...a rocket's thrust, velocity.

In more than a few ways, today's space exploits and technological developments - including many citizens' continued interest in space- was incepted by the launch of Sputnik - and more critically, the proactive response to it.

For those who'd like to learn a lot more, I provide the link to MIT's Astrodynamics course below:

https://ocw.mit.edu/courses/aeronautics-and-astronautics/16-346-astrodynamics-fall-2008/

Enjoy!

 

Should Down Syndrome Kids Be Going To College?

According to a front page Denver Post story from May 31 ('Bill Would Find A Path'), a bill is now awaiting Governor John Hickenlooper's signature to enable Down syndrome kids to attend college in Colorado. According to the Post:

"A bill that passed both chambers in May, awaiting Gov. John Hickenlooper's signature, would fund a pilot program in three state colleges for student's with intellectual disabilities such as Down syndrome or autism who still want a college education and experience."

Reference is then made to Colorado being a state "for 140 years"  and "all that time there has been one demographic excluded from getting a college education - people with intellectual disabilities"

But could there, in fact, be a sound reason for this? Indeed, a sound reason why most people - despite their illusions - are not really college qualified. As I noted in a prior post, e.g.

http://brane-space.blogspot.com/2016/05/what-is-purpose-of-university-education.html

"by the late 19th century the university would arrive in the U.S. as a center of inquiry wherein specialized published research set the modern educational institution apart from mere public opinion, religion and government, But even at this time, university students were mostly wealthy and white. A university education was viewed as the privilege of the few not the right of the multitudes.  The masses, indeed, were believed to be incapable of exercising the intellectual heft needed to pursue research of any kind."

This exclusion was done for several reasons: 1) Those in the unprivileged, mainly working classes, could not afford to learn philosophy, advanced math or literature (the extent of college offerings then) when they often had extended families to support, 2) the academic standards for admission were highly selective and demanded proof of intellectual attainment as well as achievement, and 3) the intensity and demands of the typical college curriculum militated against all but the most intellectually equipped students.

These stipulations and limitations began to alter with the dawn of the 20th century and especially after the launch of the Russian Sputnik on Oct. 4, 1957. See e.g.

http://brane-space.blogspot.com/2011/01/another-sputnik-moment-hardly.html

The Russian space feat sent shock waves through the American higher education establishment, as well as secondary education. Almost overnight much more emphasis was placed on physics, advanced algebra and other courses geared toward space science and engineering. At the same time the once careful academic gate keepers realized they had to open their doors to more students. However, this didn't mean a college "free for all". Most universities still demanded evidence to do college work based on either ACT or SAT test results - when both of those were valid aptitude tests, not achievement tests (as they are now).

Many kids were excited by the notion of space studies, or astronomy and being at the cutting edge of such learning. However, once they entered the relevant college courses - say for astronomy - they realized they were in over their heads. They were initially 'star struck' but then realized they were unable to do celestial mechanics or even introductory astrophysics. See e.g.

http://brane-space.blogspot.com/2013/11/math-drives-astronomy-pt-2.html

And:

http://brane-space.blogspot.com/2013/11/math-drives-universeand-astronomy-part-3.html

This is also applicable now, despite the fact many universities have watered their curricula down, as well as the quality of their courses via grade inflation, e.g.

http://brane-space.blogspot.com/2013/05/grade-inflation-continues-to-render.html

Despite this, millions of entering college students require remedial courses in math, English to become college ready - indicating the secondary schools aren't doing their jobs, or that the students are graduating without being held to account.  It stands to reason that a Down syndrome kid to even be ready for the most basic college course, would have even greater need of remedial courses at much greater cost than its promoters believe.

According to Mac Mascovits (ibid.):

"As a society we're OK saying everybody else but them"

But this glosses over the immense hurdles these kids will face. And why do they even want to attend college at all?   One of the prospective students, Connor Long (who graduated from Boulder's Fairview High in 2012) "hopes to get enrolled in one of the pilot programs so he can explore chemistry and theater arts."

Explore? What does that even mean? A college chemistry lab is definitely no place to "explore" - with all the dangerous chemicals around including nitric acid, HCl (hydrochloric acid) and other reagents.  When Connor has to do a titration with HCl will he be properly prepared? Will he know what he's doing? Or just want to "explore" around the lab? 

What about the actual coursework for the Chemistry classes? Balancing chemical equations, performing chemical computations, and even - lo and behold - getting into the basics of quantum mechanics as it pertains to the atom? Does Connor even have a faint clue what he's in for and how much will be demanded of him? I doubt it.

We are also informed (p. 8A):

"The bill's funding would give $75,000 a year for four years toward the pilot programs. The money will be used to hire mentors to help the students choose classes, acclimate to dormitory life and guide them through the ins and outs of academia......the initiative will raise an extra $25,000 a year to help get the program running. Students will be expected to pay standard tuition."

What about dorm life? From my own recollections (e.g. at Loyola, USF)  it was difficult enough for non-intellectually challenged students to deal with residents coming in all hours drunk and puking into trash cans. Will these Down syndrome kids handle that, or freak out?  It's one thing to say they will be helped to "acclimate" to dorm life, it's another for them to actually experience it first hand.

The Post article does add:

"The students will live in dorms with a 'typical' roommate and a dorm mentor will be around for extra supervision."

Well, he or she better be!  I also question the wisdom putting a Down student in with a "typical"  roommate.. Are these geniuses running the program even aware of what typical roommates are like these days?  Even if the Down syndrome kid is blessed to have a totally sympathetic, 'all in' roommate at his side, how long will it be before the latter grows impatient by the constant need for 'hand holding' to answer the Down syndrome kid's questions that his mentors didn't address?

The idea, obviously, is noble but it may not work out in practice unless the roomie is extraordinary as opposed to "typical".

At nearly the end of the Post piece we finally learn that:

"The students will audit two classes per semester with the hope of developing a certificate program they can take. The classes will be modified for the students by a volunteer or staff member so the instructor is not responsible for doing so."

One of the advocates for the Colorado Initiative for Inclusive Higher Education also adds (ibid.):

"Even though they are auditing we want them to be active participants in the class so they will participate in the discussions and do a lot of work so they can learn the content."

Still there will be a 'bail out' alternative available in case these kids find that they're out of their depth even in terms of course modification and auditing. This entails "coordinating with educators and parents at the K-12 level to let them know this is an option."

The motivation behind the whole initiative and pilot program?

"So when they get done they have a job so they can be financially on their own and get their own apartments".

But there are more practical methods than this to open employment doors for these kids. I already noted this in a previous post, e.g.

http://brane-space.blogspot.com/2014/12/four-year-colleges-arent-only-or-best.html

Wherein I pointed out:

""Is there an alternative that is rational and practical? Yes, and it requires people - students and parents- not to look at a four year college as the only solution for high school grads. As reported in the Denver Post, Colorado now needs 47 percent more  workers to fill "middle skill" jobs: RNs, airplane mechanics, auto mechanics, electricians, plumbers etc. Colorado, also, is not unique in such mid-level skill job needs - one can find them across the country."

This alternative would be a trade school or a community college that offers a trade certificate, e.g. in automotive repair.

Something to consider.

Another 'Sputnik moment'? Hardly!

Rocket design I used to launch lizards, crickets and roaches (inserted into a cotton-lined payload section) to be part of the Rocket Age that swept the USA in the wake of Sputnik.

In his State of the Union address last night, President Barack Obama was mostly very fuzzy with the speechifying, only becoming exact and precise in a couple of places- including the necessity to not grant any further extensions of the Bush tax cuts.

The part that caught my attention was when he invoked the Russian satellite Sputnik - launched on October 4, 1957, in asserting "This is our generation's Sputnik moment" - in terms of a revival of American competitiveness. In this respect, he outlined initiatives in five areas: innovation; education; infrastructure; deficit reduction; and a more efficient federal bureaucracy (vowing to freeze federal spending for five years). He also pledged to increase the nation’s spending on research and development, as a share of the total economy, to the highest levels since John F. Kennedy was president, and vowed to prepare an additional 100,000 science and math teachers over the next 10 years.

For those who weren't alive at the time, Sputnik was a resounding event, and had the impact of a train collision on the American consciousness. As the attached graphic shows, Sputnik was a 184 lb. satellite that orbited the Earth every 96 minutes at an altitude of about 900 km (600 miles).

I was 11 at the time, and had much more interest earlier on that particular day (a Friday) in how my Milwaukee Braves would fare in Game 3 (the next day, Saturday) of the World Series against the New York Yankees - than in any space exploits. So far the Series was tied 1-1, with the Yanks taking the first game at Yankee stadium 3-1 on Oct. 2nd, and the Braves coming back to tie it 4-2 on Oct. 3rd.

So Oct. 4th was a travel day with the Series to resume in Milwaukee (I was living in Miami at the time, and had been since January, 1956). Because of this, the evening news of the Sputnik I launch had even more impact on me than it otherwise might have (say if a game had been played). The entire news was dominated by the weird looking craft and its 4 long antennae.

Some days later, we got the first radio 'beeps' from the thing. The signal had been picked up by an RCA receiving station at Riverhead, New York and relayed to the NBC studios in Manhattan, when most of us alive then in the U.S. heard it over the Huntley-Brinkley Report.

How did the nation react, as well as politicos? (This was during the Eisenhower administration which alas, for most of the population today constitutes ancient history!) According to Paul Dickson, author of Sputnik: The Shock of the Century, p. 20:

"Ross Perot recalled in a 1997 interview: 'This is just like Kitty Hawk, the world is forever changed and I'm going to be part of that new world.' Ralph Nader, then a third year student at Harvard Law School, told Air & Space magazine, 'It hit the campus like a thunderbolt'.

Dickson notes three pages later:

"Polls taken within days of the launch showed that Americans were concerned - so concerned that almost every person surveyed was willing to see the national debt limit raised and forgo a proposed tax cut in order to get the United States moving in space".


THAT - specifically - encapsulated what was necessary to translate THAT rhetorical Sputnik moment into a space competition that would ultimately see the United States reaching the Moon before the Russians. It disclosed a collective willingness to sacrifice financially, via raising the debt limit and rescinding a proposed tax cut, to achieve it. Compare that to the current predominant meme that "we've already spent too much" and factor in Obama's implicit cooperation with it by announcing a 5-year federal spending freeze ....at the same time as a putative "Sputnik Moment". Cognitive dissonance, anyone?

By the time of Sputnik's launch in October, 1957, the Russians were producing some 66,000 engineers a year compared to the United States' 22,000. In addition, the key subjects of higher math and physics were almost nowhere to be found in the U.S. secondary school curriculum - nor were there the teachers to teach them. All this had to be factored into the coming expense to get the U.S. on a competitive par with the Soviets. Teacher education and training alone came to over $1 billion by the time of the Apollo 11 lunar landing.

Let us also quickly understand and acknowledge the marginal highest tax rate was then 91% compared to a measly 36.5% now and that not even allowed to rise to 39% by rescinding the Bush tax cuts. So again, how can anyone be serious about calling for a Sputnik moment when the money isn't there, and no one really wants to provide such funding - whether for training new teachers (100,000 according to Obama, but more realistically 250,000 is what we need), as well as repairing our crumbling infrastructure.

Hell, most Americans today are more focused on the DOW crossing 12,000 than that the American Society of Civil Engineers has awarded our infrastructure condition a 'D' and estimated its repair cost (merely to being rendered serviceable) at $1.7 trillion!

But this indicates how much further we've willingly divorced from reality since those Sputnik days back in October, 1957. We place more inherent value on a number in Maul Street's Casino than on the actual fiscal sacrifice required to ensure a "Sputnik moment" becomes reality!

And how mammoth would the JFK inspired Space Race project be? Dickson again (p. 217):

"On May 25, 1961, Kennedy addressed a joint session of Congress and asked for a joint commitment to 'landing a man on the Moon and returning him to Earth', within the decade. America's biggest, costliest and most ambitious effort ever was under way, rivaled only by the building of the Panama Canal and the Manhattan Project's building of an atomic bomb to end World War Two."

Dickson goes on to note that a $20-40 billion estimate of cost was provided, with $20 billion being the final tally. Or, about $100 billion in today's dollars. The problem here is that the cost to accommodate Obama's "Sputnik moment" could easily be $2 trillion, just to repair the existing infrastructure so all our roads and bridges don't collapse, and the training of 100,000 teachers. (Some independent news assessments have been around $500 billion for the whole thing, but this lowballs the total infrastructure expense dramatically.)

If you want to factor in an alternative energy project to attain the goals Obama mentioned last night, making us virtually oil-independent by 2020 (meaning more than 50% of energy would have to come from non-oil sources) you better toss in another trillion!

But WHERE is this going to come from? Well, a trillion of it might have been available had the Bush tax cut extension not been passed last month - but that train's left the station. As it is, the Repukes want more tax cuts, and vast spending cuts on the order of $500 billion or more. In this sort of climate - and with most of the population concerned over debt, there's little leeway to launch massive new projects on a par with what we did as a nation after Sputnik.

Back to the early 1960s, the American educational system was truly transformed as for the first time up to 50% of high school students actually took a physics, as well as advanced math classes (trig and algebra II). Many of us were on a "rocket high" as we followed each rocket launch in the race to beat the Russians.

I got into the design and construction of amateur (model) rockets, which I used to launch either lizards, or roaches up to altitudes of 1500' or more. Some of those launches actually filmed by Miami TV station, WTVJ. A design and computational graphic are shown above. Most of the calculations for the design could be done in under three hours, using my trusty Mannheim style slide rule. (There were no electronic calculators back then, folks!)

That was an era where an entire generation's imagination had been captured, and teachers of math and science could enter a classroom and fully expect 100 percent attention, because all of us wanted to learn. We wanted it so we could become rocket engineers, astronauts, or anything remotely allied to space and the distant planets.

Sadly, in the diminished age of Twitter, Facebook, i-pods, i-pads and X-box game stations most of that wonder has been lost, and I doubt it can be recovered, even if the funds could be found to fuel a "Sputnik Two".

It just isn't in the cards.

But hey, nice thought, Mr. President!