# How to learn some basic science/ mechanics?



## student123 (Sep 12, 2011)

Just back from holiday where I read 'The engines of our ingenuity' by John Lienhard and 'Victorian engineering' by L T C Rolt

in the 1st book:
'the modern propeller bladed windmill is 3 or 4 times more efficient than the advanced 18th century mills and 40 times more powerful'

I'm thinking ummm there's another factor of 10 in there somewhere but what is it?

in the 2nd book:
re water wheels: 'the buckets or floats on a water wheel have to revolve at half the speed of the water impinging on them''
I'm thinking ummmhow does that go then?


Thats a couple of examples. I can go find the answers to those , but generally there's a feeling I dont know enough fundamental science / mechanics.
I've looked up concepts like force, power, work in books & seen formulae but not really got a feel for it.
For example if you showed me 2 random projects of the month & asked which was more efficient / powerful I'd probably have to guess.

Also when I learned electricity I learned using the 'water pipe' example. Ok to a point but I want a deeper understanding.

This ring any bells with anyone in terms of learning the fundamentals? I could sign up for evening classes for a year or so, but I'm hoping to find a quicker way. Anyone got any suggestions / experiences for learning the basics?

Mike


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## kustomkb (Sep 12, 2011)

http://www.homemodelenginemachinist.com/index.php?topic=15591.0

The site mentioned here may be of some help.


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## mklotz (Sep 12, 2011)

Let's not confuse "knowing enough" with "getting a feel for". The former is an academic pursuit and the latter is mostly a matter of experience. Most experience isn't all that useful unless you have the academic framework in place so that you can relate the experience to its underlying principles.

Your best bet, of course, is to take some college level courses in physics and mathematics. The physics will give you the framework and the math is necessary to really understand the physics.

If you wish to study on your own, a good introductory physics text is "University Physics" by Sears and Zemansky. Do the problems - you'll never learn physics if you don't do the problems. (The recommended book has the answers to the odd-numbered problems in the back.)

You'll need some proficiency in analytic geometry, vector calculus, and differential and integral calculus. Get "Calculus and Analytic Geometry" by Thomas, which also has answers to some of the problems in the back.


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## JorgensenSteam (Sep 12, 2011)

Mike-

I struggled in a big way with math in school, and the reason was that math teachers don't teach applied math, but just pure theory.
Pure math theory without any connection to the real world has no meaning to me.

I learned electricity using the water flowing in pipes analogy.

If you are very lucky, you can find that rare individual who is good at both math and explaining how to apply math to practical everyday problems.

When I was in school, we had to take an EIT (engineering in training, now called engineering fundamentals) test, and this test covered a wide variety of topics across many branches of engineering, such and electrical, mechanical, thermodynamics, statics, dynamics, you name it.
I still have my EIT study guide because it has a summary of the major formulas used for each of these fields.

If you look at the forumulas used in engineering, they are pretty much the same for mechanical, electrical, thermodynamics, aerodynamics, etc., but just written in different ways, such as V=I*R and PV=MRT.

The formulas for any branch of engineering all have to adhere to the same constraints regarding the laws of physics, and the law of physics says there must always be a conservation of energy. Electrical equations are often used to model mechanical systems, since it all boils down to the flow of energy, and the electrical formulas can easily describe the flow of energy.

Think in terms of a black box, which may be an engine or motor of some type.
You have to input a certain amount of energy into this black box, and no matter what, you cannot get more energy back out of the box than you put in, and will always get less energy back out, since some mechanical energy will always be converted to heat energy via friction, etc.
Understanding a machine is like the expression used for understanding people, "follow the money", but instead use "follow the energy" and you will understand the machine.

Generally there are a few basic formulas that define each branch of engineering, and you really just need to understand those formulas. The formulas are basically the same, but just written using different variables, so they seem different, but they are really generally about the same.

Mathematics is basically a language, and if you can read the language, then you can understand a machine and how it will operate.
E=mC squared is a simple little formula, but the meaning behind it is that if you split an atom, you get two smaller particles, and a huge amount of energy released.
Bottom line is that matter contains a huge amount of energy.

Geometery defines planes and lines which are drawn on these planes.
Algebra defines the fundamentals of addition, subtraction, multiplication and division.
Algebra is very basic, and came from some farmer wanting to sell 10 bushels of corn, or figure out how to grow 100 bushels instead of 10, or sell 1/2 of his 10 bushels, etc.

Statics applies geometry to vector equations. Vectors are variables with have both a magnitude (force) and a direction.
If you can add up all the vectors in a truss bridge, you can find out where the forces are concentrating, and design the bridge to function safely.
Static equations are applied to things that are stationary and not moving.

Dynamics used vectors that are moving, such as an ice skater who controls their spinning speed by moving their arms closer or further away from their body.

Once you get into dynamics, you get into calculus.
Many of the old steam engine books from the 1,800's are full of calculus, and it was well understood in the 1,800's and before.
Calculus is a lot simplier than most people think, and basically deals with rates of change (such as the rate of change of velocity), and integration which is just addition.

The reason you need calculus to design a steam engine is because you have a situation where the piston starts with zero velocity, then accelerates (acceleration is just the rate of change of velocity) to some maximum value when the crank is near 90 degrees, and then begins to decelerate to a zero velocity at the end of the stroke.
If you plot out the acceleration, you can also figure out the maximum forces that are generated on the parts, and design the part and fastener accordingly.

Changing the velocity or direction of a mass always requires energy.
You transfer the energy from the burning fuel to the water, converting it to steam, then let the steam expand in the cylinder, transferring some energy to the piston, then store some of the energy in the flywheel. Other energy is lost due to friction of the parts that make contact, and some energy is wasted just accelerating and decelerating parts. Any unbalanced forces have are transmitted into the frame and then the base of the engine, and the base then has to absorb this energy.
A percentage of the energy from the burning fuel is converted into useful work (generally a pretty small percentage).

Math is like machining, if you use it a lot, you generally get better at it, and understand it better.
Engineering school is like math boot camp, where you are forced to learn the language of math and how to apply it.
Difficult at first, just like machining, and easier over time. Unlike machining, I can use an eraser on my equations if they are not correct.

There are some good fundamentals books out there.
Hope this helps.

Pat J


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## Troutsqueezer (Sep 12, 2011)

Just be glad that you can now use scientific calculators to speed up your math calculations. When I was in college, all we had were slide rules. The only calculators around then were "four bangers" - add, subtract, multiply and divide. Not even a square root function.


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## JorgensenSteam (Sep 12, 2011)

True story, when I started engineering in 1976, they had this giant slide rule hanging up in front of the classroom.
On the first day the instructor said "everybody needs to buy a GOOD slide rule".
I walked straight to the main office and withdrew from school.

Two years later, I signed up again, and this time the instructor said "everybody needs a GOOD calculator".
I thought to myself "now I can handle that", and I did.

Its not about how good you are at using a slide rule (or even a calculator).
It is about understanding and applying formulas efficiently.
A calculator is like going from hand washing clothes in a nearby stream to using a washing machine.

Pat J


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## Lakc (Sep 12, 2011)

While I remember the basic calculator taking the world by storm, it still only gives you an answer. The slide rule shows you the relationship getting to the answer.

One of the brightest guys I know has a habit of making slide rules out of napkins to explain concepts at Saturday morning breakfasts, taught me more then any plain answer does.


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## mklotz (Sep 12, 2011)

Pat

You wrote:

"If you look at the forumulas used in engineering, they are pretty much the same for mechanical, electrical, thermodynamics, aerodynamics, etc., but just written in different ways, such as V=I*R and PV=MRT."

I would really like you to show me how Ohm's Law and the Perfect Gas Law are "pretty much the same".

I have to take issue with some other things you said...

"Generally there are a few basic formulas that define each branch of engineering, and you really just need to understand those formulas. The formulas are basically the same, but just written using different variables, so they seem different, but they are really generally about the same."

Technical understanding is not about memorizing a bunch of formulae; it's about understanding the laws that govern nature and then using math to derive whatever expressions or results you need. No, I don't rederive the gas law every time I need it but the important thing is that I could derive it from Newton's laws applied to atoms presumed to behave like tiny billiard balls.

Trout,

You mentioned "not even a square root function".

I've been pondering this for a long time. Pick up any cheapo four banger - the kind that you can find at the dollar store or the kind your broker sends you for your birthday. Every damn one of them has a root key. My question is, "why?" The average American can't compute a 10% discount. He surely isn't doing any calculation involving roots. In fact, I'm sure he doesn't know what a root is. So why is that key on every four banger?

Don't tell me the function is already on the chip so they put it on the keyboard. These things are designed to be made as cheaply as possible. That extra key may represent 5% of the manufacturing cost. Leaving it off might lead to another penny profit in a world where a penny matters.


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## student123 (Sep 12, 2011)

Just want to say thanks to you all for your replies. Thanks in advance for any additional info.

Hmem is a great place to hang out.

And so to bed...


Mike


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## bearcar1 (Sep 12, 2011)

I have to take exception to some comments regarding the usage of calculators. What would/do the youngsters in our midst do if they were not allowed the use of one or one is not at hand for them to use but a 'big bamboo' was? I think that I already know the answer to that one.... they would most likely google the answer or use their smart phone. Sure, it may be a great deal easier to use a calculator but then nobody ever said that life was going to be easy. To be so flippant indifferent about using a slide rule to me showsn a lack of ambition in a twisted kind of way.


BC1
Jim


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## JorgensenSteam (Sep 12, 2011)

Hey Marv-

Good points.
I guess what I was trying to get at is that there are things that are very similar across engineering fields, such as voltage is analogous to pressure, and current is analogous to fluid flow, resistance in electricity is similar to resistance in a pipe, etc.

Perhaps not a perfect example of formulas that I stated, but hopefully some got the general idea.

We used analog computers in lab, and by dialing in various amounts of resistance, inductance, and capacitance, we could model any system, electrical, mechanical, or otherwise, and check on stability, natural frequency, etc., but without actually having to build some physical system. I guess that is what I am driving at when I say all systems follow the same laws of physics.

Some people are into going all the way back to derivations, but others really need to just know what the general formulas are and how to use them. I see forumulas as tools in the toolbox, and I don't really want to make my own tools from scratch, I just want to have them and know how to use them. Any knowledge of how the formulas are derived is gravy on top, but is not the meat and potatoes of the matter.

These are just my opinions with a few random thoughts and generalities added, so don't mistake any of this for anything scientific, proven or exactly correct.

The problem I have had is a lack of documentation about how to dig the formulas out of the old books and apply them to an engine design now.
I have been going back and finding the formulas which relate piston postion to valve position, and plotting displacement diagrams for valve gear design.

I have also resurrected formulas for port and passage sizing, and recently completed some dynamic balance calculations for counterweights on the crankshaft, using formulas from the old books.

This is the type stuff which is extremely difficult to find anywhere (how to apply old formulas to new engines, with complete "how-to" documentation and examples).

I have always admired pure math, but pure math without an application to engine design is of no use to me as an engine builder/designer.

Pat J


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## mklotz (Sep 12, 2011)

Sigh.


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## JorgensenSteam (Sep 12, 2011)

I think it all boils down to what you want to get out of modeling, and what approach you want to take.

Interests vary greatly, and does the level at which people want to get involved in the math.

Some love pure math for the love of math, others are applied people only.
Sort of like Chevy and Ford people.

To me, it is not so important if you are using an abacus, a slide rule, a calculator, or sticks and rocks to do math, what is really important is what you build/design, not what tool you used or how good you are at using a tool.

If math falls in a forest, and nobody is around, did math really happen?

Things to ponder.

 ;D ;D ;D

Pat J


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## ttrikalin (Sep 12, 2011)

mklotz  said:
			
		

> [...] Get "Calculus and Analytic Geometry" by Thomas, which also has answers to some of the problems in the back.



now that's a nice book. 

take care, 
tom in MA


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## dalem9 (Sep 12, 2011)

Hi I agree with what you are saying ,But the old saying is if you don't use it you lose it.You seem to know alot about this stuff. So I have a question for you.I do not want an answer but to know how to find my answer.I am building Kozo 0-4-0 switcher in 1/32 scale.This is a live steam engine.I would like to know how to figure out the size hole I need to put in my orvis for my burner.And how to construck my burner. I do know there is a lot to know on figuring this out like boiler size ,tube size ,fuel pressure, and so on and so on .I have brought several books , but have not found the information I need.Any help will be greatly appreciated .Thanks Dale


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## JorgensenSteam (Sep 12, 2011)

Dale-

I am not sure who you are referring to in your question, and I am sure no burner expert, but I have played with several of them of various fuel types.

What fuel are you using, liquid (white gas, alcohol, kerosene, etc.), propane, etc.?

Proane burners seem to be pretty easy to make and use, since you can easily regulate the fuel pressure and thus the flame size. You can use some of the MSR backpacking stoves such as the "pocket rocket" as a guide, or even use that valve and orfice and adapt if you use propane.
http://cascadedesigns.com/msr/stoves/rapid-cooking/pocketrocket/product

I have seen some of the alcohol burners use a wick inside of a tube with adjustable slots. Also pretty simple.

The white gas burners typically loop the liquid tube through the flame first to vaporized the fuel, and again, MSR makes some good examples of that, such as their "Wisperlite".
http://cascadedesigns.com/msr/stoves/simple-cooking/category

I think if you tell us what fuel, many will be able to tell you what you need to know.

Pat J


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## dalem9 (Sep 12, 2011)

my fuel will be butane .Thanks Dale


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## dalem9 (Sep 12, 2011)

My burner will slide inside a 3/4 inch copper tube like on the aristo-craft g guage live steamer Dale


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## JorgensenSteam (Sep 13, 2011)

My guess (those familiar with small locomotive boilers will have to weigh in on this and verify if this guess is in the ballpark) is to take a 1/8" piece of brass tube, and drill #60 holes in it 1/4" on center down both sides of the tube, but drill the holes angled up at 45 degrees and above the centerline of the tube, so as to make a "V" shaped row of flames. Mount the tube towards the bottom of the 3/4" copper tube.

Seal the end of the tube and feed propane in via the other end.
It would only take a tiny amount of propane pressure to run this.

My guess on this is based on observing the orfice size and flame size on my BBQ propane lighter, with the pressure set on the lowest setting.

Pat J


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## JorgensenSteam (Sep 13, 2011)

I made a quick burner out of 1/8" brass tube and some #55 holes drilled either side.

The flame is not uniform along the length of holes, and I think I need an air break between the orfice supplying the propane and the manifold with the rows of holes in it.

I used a standard propane tank/valve/orfice from a plumbing torch.

This is not a very good design, I don't recommend it.

Pat J


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## Ken I (Sep 13, 2011)

Someone just gave me a brand new slide rule as a curiosity - I looked it up and down and asked him "where do you put the batteries ?" (I did most of my initial academia with a slide rule.)

As far as scientific calculators go - if you know what all the function buttons do you are in very rarified territory - I would guess less than 0.1% of the world's population could answer yes to that.

I can't and I'm pretty numerate (scored in the top 1% in my GMAT)

That said working through them points to the deficiencies in your maths and what you might want to know more about. 

Ken


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## kvom (Sep 13, 2011)

I recall that when I took trig in HS we had to use a small book that listed the values of all the trig functions for each minute of angle, and that we had to learn to interpolate. In college we had to use sliderules in many engineering classes, and I lost 3-4 of them over my college career. In the thermodynamics class the first day the professor would show us how to use the rule to compute x**y, a feature needed very frequently.


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## dalem9 (Sep 13, 2011)

Thanks Guys I have a .0096 drill that I got to try for the orfic . i like the 45 degree ,I will try this Thanks again Dale


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## dalem9 (Sep 13, 2011)

I under stand that I ow you guys an apoligy. I am deeply sorry .Dale


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## BillH (Sep 13, 2011)

Gentleman, without spending ANY money, one can learn the basics on how to do things, even without a calculator. Just a pencil...
Let me introduce you to http://www.khanacademy.com

I highly suggest this page for anyone who has a thirst to learn the basics, and most certainly for anyone who needs to study for a placement exam before entering a new college.


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