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Per GW Johnson's request, the post for lesson 8B has been corrected.
The pdf file is now available, to accompany the Slide Show.
(th)
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Work in progress today 2023/08/25:
Attached are the Powerpoint slideset, and the written document as a pdf, for lesson 5.5, teaching how to do fast transfer ellipses. 5.5B ois a separate email, and there are 3.
Attached are the Powerpoint slideset, and the written document as a pdf, for lesson 5.5B, the problem-solving session for fast transfer ellipses. 5.5 is a separate email, and there are 3.
I updated the "orbit basics.xlsx" spreadsheet, which had 4 worksheets in it, to handle what was needed for lessons 5.5 and 5.5B. The update is two additional worksheets, "sun centered" and "integrals". The original version I sent does not have the two new worksheets, and they are essential for the fast transfer calculations. Updated spreadsheet file attached.
That does make a total of 4 spreadsheet files associated with the entire course. There is "orbit basics.xlsx" (lessons 3, 5, and 5.5), "entry spreadsheet.xlsx" (lesson 7), "TSTO veh sizing.xlsx" (lesson 8), and "rocket nozzle.xlsx" (lesson 9).
Update at 17:16 local time ... all five files are not copied to DropBox. The next step is to install the links in NewMars.
Update at 19:28 local time ... all updates are completed. I'll ask Dr. Johnson to proof the work.
If there is anyone in the active membership willing to help by trying the course and providing feedback, that would be welcome.
If there is anyone NOT already a member who would like to help by trying the course and providing feedback, please see the Recruiting topic for procedure.
(th)
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All the links lead to the correct files. I tried downloading the orbit basics spreadsheet and it seemed to work. It looks like the entire course is there.
Lesson 0 describes scope and content.
Lessons 1-3 teach about elliptical orbits in two-body orbital mechanics, with lesson 3B a problem-working session using the orbit basics spreadsheet. Lesson 4 gives the empirical stuff you have to deal with for launch to low orbit, with 4B a problem-working session. Lesson 5 is about interplanetary transfers with min-energy Hohmann ellipses, and 5B a problem-working session. Lesson 5.5 is about faster transfer ellipses, with 5.5B a problem-working session. I added two worksheets to the orbit basics spreadsheet, specifically to handle these higher-energy ellipses.
Lesson 6 is about a lot of empirical stuff for entry descent and landing, with 6B a problem-working session. Lesson 7 teaches the user how to do the old 1953-vintage hypersonic entry estimates, using a spreadsheet version of the old H. Julian Allen analysis. 7B is a problem-working session. The entry spreadsheet is up there to download.
Lesson 8 is about using all of this to rough-out a rocket vehicle that might accomplish your mission, using a spreadsheet to automate the repetitive stuff. Lesson 8B is a problem-working session. This presumes you have "good" data for tour effective exhaust velocity in the rocket equation. It does the rocket equation, but it also looks at adequate thrust levels. The rocket vehicle spreadsheet is up there tp download. It is pretty much "tailored" to do TSTO for Earth launch to orbit.
Lesson 9 is a traceable way to generate the "good" data for exhaust velocity, by running the engine internal ballistics and compressible-flow nozzle calculations on a spreadsheet. Lesson 9B is a problem-working session. (The tables in the textbooks for Isp are uncorrected for real-world stuff, rather than try to correct them, it is actually just as easy, if not easier, and a whole lot more trustworthy do it "from scratch" with chamber c* velocity.) The engine ballistics spreadsheet is up there to download. It includes a data library for some propellant combinations.
GW
Last edited by GW Johnson (2023-08-26 09:15:57)
GW Johnson
McGregor, Texas
"There is nothing as expensive as a dead crew, especially one dead from a bad management decision"
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We (NewMars) have received word that our request to add a flyer about Dr. Johnson's class to the Literature Bags at the upcoming Mars Society Convention in October has been granted. GW provided content for the front and back of the flyer, and it is up to us now to hope/affirm that the flyers will be printed by the printer in a timely manner, and delivered to the Mars Society volunteers in time for the Stuffing Party!
If anyone NOT going to the Convention would like to see the flyer pdf files, please post a request in Housekeeping! They'll be uploaded to Dropbox immediately.
(th)
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Tahanson43206 has somehow posted a couple of orbit images I created, while looking at paths to launch a payload from Earth to a station in LEO. These images are located in post 184 of the "GW Johnson postings" thread in the "meta new Mars" topic of the "new Mars" section of these forums. My explanations of these figures are in the next posting, post 185.
Any of you can do exactly what I did and get it right, using the "orbit basics +" class materials posted here in this thread. This can be done for Earth, Mars, the moon, or anywhere else. I did this using the orbits spreadsheet that is part of the class materials. You can, too. Just download the pdf documents that are your textbook, and the spreadsheets associated with the classes. It's complete enough that you can teach yourself how to do this, if you don't already know how. (The powerpoint slides are more for teaching others how to do this.)
GW
PS/update:
The course has 9 lessons. The lesson by number is a sort of lecture session. That same lesson number with a B suffix is a problem-working session for that lesson's topic. The problems are for "learn-by-doing", but there are worked demo problems, followed by assigned-to-the-student problems, plus answers to the student problems for checking results.
There is a lesson 0 overview, and then lessons 1-3 cover the basics of 2-body orbital mechanics of elliptical orbits. To support this are some worked problems, problems for the student to solve as learn-by-doing, answers to the student problems, and the "orbit basics" spreadsheet to support actually doing all this stuff.
Lesson 4 is about launching to orbit, complete with demo problems and student problems. No spreadsheet, this stuff is very simple hand calculations, being based on the data coming from orbit basics out of lessons 1-3. The objective is empirically estimating the mass ratio-effective dV values that go into the rocket equation. These are corrected from the ideal values for gravity and drag losses.
Lesson 5 is about interplanetary transfers, mostly about min-energy Hohmann transfers. The "orbit basics" spreadsheet supports that, too. Demo and student problems in 5B.
Lesson 5.5 is about faster-than-Hohmann interplanetary transfers. The "orbit basics" spreadsheet supports that more advanced activity, too. Again, demo and student problems in 5.5B.
Lesson 6 is about the more general stuff related to entry, descent, and landing issues. This is very simple hand calculation stuff, there is no spreadsheet. There are demo and student problems in 6B.
Lesson 7 is about the specifics of hypersonic aerobraking entry, using a very simple 1953-vintage method originally used for ICBM warhead entry estimates. There is a spreadsheet to support doing this. Again, demo and student problems in 7B.
Lesson 8 is about how to use the rocket equation correctly to size rocket vehicles. The emphasis is on launch vehicles, but this applies directly to interplanetary vehicles, as well. There is a spreadsheet to support it. Demo and student problems in 8B.
Lesson 9 is about getting the right values for the Isp to support doing the vehicle sizing work that lesson 8 covers. There is a spreadsheet to support finding Isp from propellant fundamentals and realistic nozzles. It includes a database of several propellant combinations. Again, demo and student problems in 9B.
Last edited by GW Johnson (2023-10-31 13:50:45)
GW Johnson
McGregor, Texas
"There is nothing as expensive as a dead crew, especially one dead from a bad management decision"
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We may be visited by a Mom who may be interested in looking at Dr. Johnson's course on ellipses, which is offered in this topic.
I'm hoping everyone contributing to the forum in the near future will keep our visitor(s) in mind.
(th)
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Depends upon what they are interested in.
If it is only orbital mechanics, all they need is lessons 1-3 (the basics), plus lessons 5 and 5.5 for interplanetary transfers. The 3-body "cheat" with 2-body models is in lessons 5 & 5.5. That's OK for dV, not OK for navigation.
If they are interested in determining realistic dV requirements for actual missions, add in lessons 4 (launch) and 6 (entry descent, and landing).
You only need lesson 7 (the entry spreadsheet calculation) if you are interested in the details of entry dynamics and heating.
You only need lessons 8 (sizing vehicles) and 9 (estimating engine performance) if you are interested in how to actually size rocket vehicles.
-- GW
GW Johnson
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"There is nothing as expensive as a dead crew, especially one dead from a bad management decision"
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For GW Johnson re #32
Thank you for your thoughtful response!
Please imagine you are a 12 year old (I know, that was a long time ago) .... You are given an opportunity to learn how to pilot/navigate a space craft, as a career option. And that opportunity is available with a teacher who is still alive and able to answer (some) questions. You wouldn't know what to be interested in. It is the role of the education institution to try to help a new learner to master the basics, and to make the learning experience as interesting as possible, given the non-trivial subject matter.
I think the best path forward is a collaboration with a teacher who is interested in adding this content to an existing math/science program.
It's been so long, I don't remember what a 12 year old is expected to know ...
If anyone in the NewMars membership has a clue, please help out.
It there is someone reading this who would like to help out, please see the Recruiting topic for details.
(th)
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A 12 year old is most likely a 6th grader. That's still 3 years away from 9th grade Algebra-1, where the bulk of the effort is on linear and quadratic equation math. Algebra-1 is the first time students see equations with letters (variables) in them.
10th grade is the usual grade for teaching geometry, where the conics like ellipses are briefly introduced, but not much is done with them.
The Algebra-1 texts have the conics (like the ellipse) in them as advanced stuff, but with (illegal) teaching-to-the-test going on, only the basics get taught (it's a low-ball test). Most student never see real content about the conics, or about logarithms and exponentials, until Algebra-2, usually in the 11th grade.
It's college algebra and college trig that get heavy into conics, logarithms, and exponentials. Most college students are still having real troubles with simple linear and quadratic equations, because of the low-ball nature of the standardized tests, which dumbs-down what they are taught in high school.
Been there and done all of that.
As a result, I'm unsure that even a very bright 6th grader is ready to take on the algebra equations with variables in them, that are classic orbital mechanics, much less the logarithms and exponentials that are the forms of the rocket equation. There would need to be some heavy-duty math tutoring to get such a youngster from basic arithmetic to algebra. They spend all of the 7th and 8th grade doing that.
GW
GW Johnson
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"There is nothing as expensive as a dead crew, especially one dead from a bad management decision"
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For GW Johnson re #34
Thank you for the very helpful review of what a 12 year old is likely to have seen in math at this point!
The concept I am pursuing is capturing the imagination of 12 year olds around the world, to entice them to pour on the coal to learn as much as possible about everything related to the career goal.
The physical age of an individual is not (in itself) the determining factor for learning. There are some (not a lot, but some) examples of humans who have raced ahead due to a combination of ability, interest, family support and other factors.
The traditional pace of instruction (and learning) is understandably set by the community goal of developing productive citizens able to contribute to the ongoing maintenance of the civilization we have, and to contribute directly or indirectly to advancing the state of knowledge and practice.
We are once again approaching the summer break in the traditional (US and probably some other nations) education program. That summer break is an opportunity for an intensive learning experience for a 12 year old. In the US, the summer break was historically defined by the needs of the agricultural community, which at the time comprised the bulk of the population. It persists into the present day as a welcome break for teachers and students alike.
In the context of ** this ** topic, please think about how you might partner with teachers who might be interested in testing the capability of individual students to tackle intensive learning.
In the context of this forum .... most participants appear to be well past peak learning years, but there remains a lingering capability to learn new material or new skills. The major factor I observe in attempts at new learning is the combination of decreased energy and available time.
(th)
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Tom:
The only "trick" to this is getting youngsters to ditch their pre-conceptions, and understand a math equation at the Algebra level as nothing more than an "input-output box". The inputs are the values you insert where the letters (variables) appear on one side of the equation, then you carry out the indicated arithmetic operations once the numbers are inserted, getting the answer (the output) for the one remaining letter variable on the other side of the equation.
The notion of variables you cannot isolate to one side is quite foreign at that early age; that first shows up in Algebra-2 and College Algebra. Youngsters are too easily stymied by such roadblocks. Too mysterious for them. But it shows up all the time in compressible flow when trying to find Mach number from area ratio. Such as doing rocket nozzle calculations, along with some really-non-integer exponents.
Multiplication, division, addition, and subtraction are what they understand at the 6th grade level. Generally speaking, they don't yet know what exponents are, although integer exponents are rather easy to teach as the repeated multiplications that they really are.
It's the non-integer exponents that are really hard to teach, even to high-schoolers nearing graduation. That usually starts as fractional exponents (roots). The "trap" the students usually fall into, is using a calculator to get the answer, without actually understanding the meaning of what they are doing. It cripples them in later study, especially when the exponents become irrational numbers. And that pretty well prevents understanding logarithms. (Which in turn makes calculus a completely hopeless case.)
I think for 6th grade to 8th grade, it's the astronomy connection in science classes that might make the basic classical orbit mechanics in lessons 1-3 of interest to brighter students. It helps explain what they see in the sky at night. However, there's a lot of squares and square roots involved with the classical orbital mechanics equations describing positions and velocities, plus one cube or cube root in the period expression. Those will be the "long poles in the tent" for teaching this stuff to kids that young. The connection between astronomy and math instruction is quite strong.
I really do believe they need to do it by-hand, pencil-and-paper, before introducing any software (or calculator) that does it for them. Otherwise, the connection to advanced (for them) math instruction gets lost in the "monkey-see, monkey-do" trap, and your student product is then extremely vulnerable to garbage-in, garbage-out troubles. And those GIGO troubles can be more-than-discouraging enough to cause them to quit.
GW
Last edited by GW Johnson (2024-03-27 10:41:19)
GW Johnson
McGregor, Texas
"There is nothing as expensive as a dead crew, especially one dead from a bad management decision"
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