Beam Axles - Front, Rear or both.

[Z]

... In my view the best references I have in my library are Mechanics by Den Hartog and Statics by J.L. Meriam...

Ralph,

Thanks for re-endorsing these "old-school" textbooks to the current generation of students. (FSAEers who have been around here for a while will know that I have recommended the old staple of Hartog several times. Even to the point that I recently splashed out ~$3.99 and ordered it off the web (+p&p)!)
~~~o0o~~~

Students,

Another book British students might try is "The Theory of Machines" by Thomas Bevan (I picked up a copy at one of my kid's school fetes for $0.50?). The preface to the first edition (1939) states that the book is "...based on lectures given at the Manchester College of Technology ... [and] ... I have chiefly had in mind the needs of the student who is preparing for a University degree in engineering ... but I hope that many of the sections will appeal to the draughtsman and designer."

So, although this is a textbook suitable for "trade school" students, IMO it explains Mechanics better than most modern University level books.

(FWIW, Bevan's ToM gives an account of a reciprocating engine's "inertia torque" that is infinitely better (yes!) than all my other modern textbooks on "Advanced Engine Technology..." (<- a hint here on a really bad book!). However, a downside of ToM is that it uses imperial units (albeit in a well explained way), and some of the examples may seem a little odd. For example, the "inertia torque" example has a horizontal single-cylinder engine of Bore = 9", Stroke = 24", Conrod-length-c/c = 5 ft, Piston-weight = 580 lbs, Conrod-weight = 500 lbs, RPM = 120, ... etc. But the torque calculations even include the effect of gravity acting on the Conrod... )

The IMPORTANT POINT I want to make is that, IMO, the above old-school Mechanics books can give you a much better understanding of the essentials of "Vehicle Dynamics" than all the currently fashionable, subject specific textbooks on VD, as well as the various Computer-Sims and seminars that are frequently advertised on these pages.

The big difference is this:

* The old-school textbooks teach Mechanics as a very general subject that has been proven to work over many hundreds of years, beyond any measurable accuracy, and in a huge range of different fields. It is based on very clearly explained foundations (the Definitions and Axioms), with everything else then deduced from these in a very rigorous way. Man went to the bottom of the oceans, and then to the top of the atmosphere, and then on to the Moon, and did a whole lot of other things, all using this stuff.

* Production car, or worse yet, racecar specific VD, is usually taught as if it is some sort of very specialised field that is unique to itself. It is full of its own specialist jargon, most of which is NEVER clearly defined! There is rarely any mention of foundational concepts, and instead there is much use of arbitrary simplifications, most of which, again, are NEVER explicitly stated. These thus leave error margins that are completely UNKNOWN. And with all its talk of "magic numbers" (go to the seminars) it is closer to voodoo and witchcraft, than to real engineering.
~~~o0o~~~

I'll have another, maybe longer, rant in the next post.

But in the meanwhile here is one of Ralph's pictures again.

Attachment 252

Keep this image in mind whenever people tell you that "BEAM-AXLE CARS WILL NOT WORK" on the bumpy FSAE tracks - "Hey, sometimes there are cracks in the pavement about..., like ..., you know..., a whole 1/2" high!!!"

Oh, and remember that the above cars lap at 140 mph (~220 kph = ~2 x fastest FSAE).

Z

[Z]

... Another good resource for a general review is MIT's Open Courseware 8.01 Classical Mechanics video lectures by physicist Walter Lewin...
Link: http://ocw.mit.edu/courses/physics/8...1999/index.htm

I have much to say about these lectures (mainly, they are undeniable proof that the education system is truly spiralling down the S-bend), but will try to keep it brief.

First, THE GOOD NEWS.
====================
* Lewin proves that a generous dose of showmanship can make apparently boring subjects (ie. maths, science, tech-stuff, etc.) quite entertaining. Lots of simple experiments, preferably all with the expectation of catastrophic results, certainly works well for the "Mythbusters", and IMO it works well in the classroom too. More please!

* Along with simple, but REAL experiments, the blackboard is a good means of communicating difficult concepts. The act of drawing (mainly spatial) problems allows each part to be explained as it is introduced. Then erasing a small part and redrawing it allows changes-over-time to be depicted. I reckon Lewin proves that modern, gee-whiz, Computer-Aided-Presentations are a backward step. Ie. they are a boring slide-show, with very little "theatre" (... and none of those dotted lines!).

* SHOUTING IS GOOD, to get IMPORTANT points across!!!

* VERY IMPORTANT - Lewin stresses in the early lectures that,
"... any measurement is MEANINGLESS, without an estimate of its uncertainty".
This is something that students here should note well, because it is perhaps even more important in Engineering than in Science. As noted elsewhere, bad error estimates in Science = dud experiment, but in Engineering they can = jumbo jet falls out of sky and kills many people. So, please, no more wishbone-pickup-points, etc., given to 5 decimal places (in millimetres!!!).
~~~o0o~~~

Now, THE BAD NEWS!
===================
(Here I should note that Lewin is teaching the "Establishment View of Science", so below is not exclusively his fault.)

* The whole subject is presented as a hotch-potch of seemingly unrelated factoids. IMO it should be taught, as it used to be, as a rigorous Axiomatic-Deductive system of enquiry. Namely, (and see Newton's "Principia", or better yet Euclid's "Elements", for good examples):
1. Start with clear DEFINITIONS of the important concepts.
2. Make very clear statements of what is NOT KNOWN, but must be ASSUMED so that progress can be made (eg. Euclid's "Postulates", or Newton's three "Axioms", or "Laws of Motion", all of which are UNPROVABLE). Fewer of these Unprovables is better (see N's "Rules for Reasoning...").
3. Deduce other useful stuff (ie. the "Propositions") in a rigorous way that can always take you back to the above foundations alone.

* FAR TOO MANY EQUATIONS. Certainly, too much time spent cranking the handles of these equations. The lectures are presented in a way that suggests that "equations" are the foundational constructs of the whole subject, when they most certainly are NOT! The true foundations are the above Axioms->Deductions approach, while equations are merely chimney pots on the roof. They are just one of the types of tools that can be used to calculate some of the answers. Frankly, all the time spent on the equations is boring, and detracts from the learning.

* An example of the above two points is the section on friction. The "Friction-Force = Mu x Normal-Force" equation is, more or less, presented as if it is on an equal level to Newton's Laws of Motion. It is nothing like them! The "friction equation" is nothing more than an empirical "best-fit" approximation. It is based on the observation that in a lot of experiments (but NOT ALL) the area of the contacting surfaces does not make much difference. Based on this very limited approximation, FSAE cars should corner just as fast when they are on skinny little pram tyres. In fact, many Physicists today still insist that wide tyres are of no help in motorsports!

* Another example of the sloppy, ad-hoc approach is the introduction of "Statics" near the end of the series, when it should be much closer to the beginning. This is made even worse by the very sloppy usage of the concept of "Torque". There are occasional vague mentions of Torque being DEFINED as the Vector-Cross-Product of one (!) Radius and one (!) Force vector. This is very wrong, and very misleading, because this same "Torque" is then used (correctly) as the net "Couple" acting on the body, after ALL the forces have been moved to the CG. (For a brief explanation of this, see Figure 3 a few posts up, and extrapolate to all forces acting on the body.)

* Another example of sloppiness is Lecture 11 where Lewin claims Newton "postulated" the Universal Law of Gravitation. Rubbish! Near the front of "Principia" Newton POSTULATES his three (unprovable) Axioms, and towards the end he DEDUCES that an "inverse-square..." relationship best fits the available empirical data. Regarding any deep and meaningful explanation of gravity, he famously says "hypotheses non fingo" (= "I frame no hypotheses").

* And now for the most DISGRACEFUL, SLANDEROUS, REVISIONIST NONSENSE of the lot! In Lecture 6 Lewin (as with too many other Scientists today) claims that Newton's Second Law is "F = mA". He then claims that as the speed of the body approaches the speed of light "... Newtonian Mechanics no longer works, and we must use Einstein's Special Relativity...". Utter codswallop!!! So wrong, on so many levels... The least bit of research shows that NII is, essentially, "Force is proportional to rate of change of Momentum" (ie. F = P-dot, as appears buried in the middle of a list of equations late in the series, as if it is "just another equation"). Bottom line, all evidence available today suggests Newton's version of NII is correct all the way up to the speed of light!
~~~o0o~~~

I am not sure which of the above points is most troubling.

Regarding the last point, I have heard or read this clearly explained several times over the years. (In fact, adding one more Postulate to Newton's three allows E = mc^2 to be deduced.) And I am NOT in the business of teaching this stuff. Professor Lewin should know better! I can only assume this is Modern Science's attempt to feel better about itself, by claiming (falsely!) that "We are a lot smarter now, and our modern theories are so much better than that olden-day stuff...".

But I think that the whole modern approach to teaching this subject is the bigger problem. It should not be treated as if it is a glossy, coffee-table-book, that can be randomly dipped into at any page, while still claiming to give a deep understanding of Nature. Without a deep appreciation of the foundations of the subject, and how the rest is then rigorously built on top of those foundations, there is really NO UNDERSTANDING AT ALL.

As always, comments and criticisms most welcome.

Z

[Jay Lawrence]

Z,

I was thinking about this 'everything from 1st principles' point of view and wonder if we as humans skip steps so that we may progress? I don't need to know how an engine works to put one on a cart and therefore make it 'better'. I don't need to know how radio waves work in order to control an R/C car. I don't need to know a great deal about aerodynamics to play golf. I learn about things such as these because they are of interest. If everyone had to learn all there is to know from the very basic principles upwards, we'd run out of life before we made any progress! Something about giants and their shoulders...

Just a thought.

[rrobb]

The examples mentioned aren't attempts to approach the limit dictated by the underlying principles like motorsports and engineering competitions.

[rwstevens59]

Z,

1. Old texts:

Yes, I too seem to find many of the older texts more 'readable' and understandable. Newer texts (physics, mechanics, machine design etc.) are very flashy, lots of useless graphics, colors, etc. but totally disjointed and frustrating, to me anyway.

2. Professor Walter Lewin:

I will not defend him or his teaching methods. I will just say I personally learned something from his video lectures and that his showmanship helps make the basic points stick in some way for me.

His is the perspective of a physicist not an engineer. And as you say there is a pretty big difference.

Lastly from the course outline:

"8.01 is a first-semester freshman physics class in Newtonian Mechanics, Fluid Mechanics, and Kinetic Gas Theory. In addition to the basic concepts of Newtonian Mechanics, Fluid Mechanics, and Kinetic Gas Theory, a variety of interesting topics are covered in this course: Binary Stars, Neutron Stars, Black Holes, Resonance Phenomena, Musical Instruments, Stellar Collapse, Supernovae, Astronomical observations from very high flying balloons (lecture 35), and you will be allowed a peek into the intriguing Quantum World."

Quite a bit of ground to cover for a fall semester freshman course on classical mechanics. And also quite an advertising pitch for a basic freshman physics course.

Hmm...I guess I did wind up defending him in a way despite what I said above.

Oh, and for those interested and who did not come up with an answer for the ball and track demonstration problem, the answer can be found in lecture 29.

3. Too many equations:

Try a few of these videos on for size from one of MIT's basic dynamics courses:

http://ocw.mit.edu/courses/mechanica...2011/index.htm

Now there is an alphabet soup course designed to be 'specific' after a freshman gets past Lewin. Makes Lewin's course seem absolutely devoid of the maths.

I fundamentally agree with your insistence for a grounding in the very bedrock of the logic and deductive reasoning used by the creators of this subject. However, I also know that we have created an engineering profession so heavily reliant on technology, computing power in particular, that there just isn't time in four or five years to even scratch the surface for a student.

That is what makes FSAE important in my opinion. If for no other reason than there will at least be a very few engineering students who have truly attempted to build something, anything, and found out for themselves how difficult the process can be. What they build is immaterial to me, personally. Think of all the rest...

As far as the false profits of engineering science are concerned, they have always been there and will continue to be, most likely even in vastly greater numbers with the availability of the internet to pedal their wares.

And... Back to Beam Axles!

Ralph

[rwstevens59]

Z,

One last point on all the confusion concerning the terms moment, couple and torque. Look for torque in the Hartog index, none. In index of Statics by J.L. Meriam 'Torque, see Moment of Force'. In any physics text I have torque is defined as r X F.

Couples in Hartog are designated as C in Meriam as M (same as moment).

Point, physicists use torque, no moment or couple and engineers use moment, couple and torque with only one source of clear distinction I could find on Wikipedia under Torque of all places. Did you write that entry?

No wonder students get all turned around and confused.

Ralph

[Jonny Rochester]

Z,

I was thinking about this 'everything from 1st principles' point of view and wonder if we as humans skip steps so that we may progress? I don't need to know how an engine works to put one on a cart and therefore make it 'better'. I don't need to know how radio waves work in order to control an R/C car. I don't need to know a great deal about aerodynamics to play golf. I learn about things such as these because they are of interest. If everyone had to learn all there is to know from the very basic principles upwards, we'd run out of life before we made any progress! Something about giants and their shoulders...

Just a thought.

hear hear..

[rrobb]

Z,

I was thinking about this 'everything from 1st principles' point of view and wonder if we as humans skip steps so that we may progress? I don't need to know how an engine works to put one on a cart and therefore make it 'better'. I don't need to know how radio waves work in order to control an R/C car. I don't need to know a great deal about aerodynamics to play golf. I learn about things such as these because they are of interest. If everyone had to learn all there is to know from the very basic principles upwards, we'd run out of life before we made any progress! Something about giants and their shoulders...

Just a thought.

My post in response to this was not clear.

If I may, I'd like to restate my point;


I don't believe that Z is advocating reducing every task to first principles. As you state, that would be inefficient.

However, there is a fundamental difference between pursuits like motorsports and the examples given in the above quote.

Take the case of controlling an RC car. The underlying physics of signal transfer through electromagnetism are not an area where you can get much of a performance boost. Radio waves are, in this case, a commodity. If one were to devote years of study to devising a more efficient manner of sending control inputs to the car, the improvement over standard off the shelf items would be minimal.

A similar situation applies to the golf example. No amount of study into aerodynamics will net you the same performance improvement that learning how to swing a club consistently will.


Contrast those with the design of vehicles whose primary purpose is to operate at the very edge of their performance envelope. Motor racing vehicles spend almost there entire life at or near design limits. With the exception of maybe single use space launch vehicles, nothing else even comes close.

This performance envelope is defined by the laws of physics. Understanding these laws has a massive impact on our ability to develop a vehicle able to test these limits.




Cory

[Jay Lawrence]

Yes, but like learning how to swing a golf club consistently, I can learn how to apply magic numbers and simple 'roll centre' approximations without having to go down into first principles of mechanics (or aerodynamics/projectile motion in the golf example). Maybe I will lose a tiny amount of initial performance (i.e. my more learned competitor might get to the track with perfect spring rates and no need for dampers and have a car that is immediately at its design limit) but it is likely that I would have a vehicle ready quite earlier than he/she because I have stood on some shoulders, applied a top down approach, and not spent the time to get to the very basic fundamentals. The extra time is what I use to tune the car in the real world and bridge my theory gap.

Perhaps my examples were a bit off, and I'm not necessarily advocating to forget the classical side of things, it was just a thought.

[Tim.Wright]

I agree more or elss to the last few posts. The problem with many óf these short cuts (e.g. roll centres...), is that it is often taught as though they ARE the first principles.

I'm pretty resentful of the fact that the first few years of my professional life as an automotive engineer were spent unlearning stuff that I was "taught" in various books and seminars