Beam Axles - Front, Rear or both.

[Ahmad Rezq]

Erik,
Well Said. I must say that i haven't read the "Principia" before. Now I have a copy and I'am reading it in my free time (Tough English).

In DEFINITION III
" Upon which account, this vis insita, may, by a most significant name, be called vis inertice, or force of inactivity.But a body exerts this force only, when another force, impressed upon it, endeavours to change its condition ; and the exercise of this force may be
considered both as resistance and impulse ; "

The reason for the above corruption of Newton's version of Mechanics is that early 20th century science had no good explanation for how "Inertial" forces work, so they simply got rid of them at the "axiomatic" stage (ie. at the ~10:15 quote from video).

I didn't go on reading Principia, Had Sir Newton explained how a body exerts the inertia force.

How does a body exert inertia force, Erik ?
How can we classify the inertia force ?
What's meant by (Force) ?

[BillCobb]

A Higgs boson goes into a church and the priest says "Hey, you can't come in here".
"Oh, yeah?", says the Higgs. "Well without me, you can't have Mass."

[Z]

Ahmad,

Had Sir Newton explained how a body exerts the inertia force ... ?
How can we classify the inertia force ?
What's meant by (Force) ?

Those are very difficult questions to answer, indeed.

Many thousands of years, and many clever people have tried, but still no clear-cut answers.

Important to note that Newton made no attempt to explain the "how" or "why" of Inertial forces. Instead he simply took them as "a given" and included them as such in the Definitions section of "... Principia...".

As I have noted before, Newton's book (which in English is "The MATHEMATICAL Principles of Natural Philosophy") was written in the same "Definitions + Axioms => Deductions" style as Euclid's Elements. As such, neither of these books belongs in "science", nor do they claim to be explanations of "how/why" the real world works. Rather, they are an idealised, though rigorous, mathematical model, which may be, within limitations, used to solve real world problems. (Eg. Euclid - How do you evenly subdivide your circular farm for your five children? Newton - How do you build a winning FS/FSAE car?)

Also worth noting here that Newton never gave any sort of "how it works" explanation for gravity, as is often claimed these days (eg. the much repeated phrase "...Newton's Universal Law of Gravitation"). In fact, he did just the opposite by very clearly and publicly stating "I frame no hypotheses!". Instead, Newton calculated the motions of bodies, or orbits of planets, as they would be under numerous different types of attractive force. For example, a force that is constant, or a force that varies inversely with distance, or a force that varies inversely with the square of distance, or the cube, or higher order..., and so on. He then simply noted that the observed motions of bodies and planets, of which there was much empirical data available at the time, best fits the "inverse square" model. But to restress the important point, he never claimed to explain the detailed "how" of gravity.

Not much has changed since. There is no really good, "deep and meaningful", explanation today for "how" gravity works. The General Relativity explanation is circular gibberish. Namely, "... mass bends space-time, and curved space-time tells mass how to move...". Err..., yes..., but which did the "bending" or "telling" first? And, more importantly, HOW do they do it???

Similarly, all the other "real forces" are today explained in terms of "field theories". (Edit: Indeed, the property of "Mass/Inertia" is lately being explained as due to the Higgs-Field, as Bill so succinctly put it! ). But there is never any deep explanation of "how" these fields themselves work, namely what they are made of, or where they came from, and so on. The "explanation via fields" is really just a convenient calculating device, and quite similar to the approach used in the Elements and Principia. They are very useful in helping you figure out what will happen in certain real-world situations, but they give no deeper explanation than their "assumptive" base.

Furthermore, with these "aether"-like field theories taking over on the explanation front (...ah, yes, the aether is back! ... Newton's Absolute Space is reborn!), the old fashioned notion of "force" has pretty much been eliminated from modern Science teaching. Nowadays it is more fashionable to talk only of the "Symmetries of Natural Laws", which in turn generate "Conservation Laws". For example, we assume Nature behaves the same "now" as "then", ... so Energy is conserved. We assume stuff happens the same "here" as "there", ... so Linear Momentum is conserved. Assume stuff happens the same in "this-direction" as "that-direction", ... so Angular Momentum is conserved. (Or something like that...)

The Conservation Laws then lead to a slightly different approach to solving Mechanical problems. Here you can google Lagrangian and Hamiltonian Mechanics, vs Newtonian Mechanics. Same fundamentals, but different approaches to finding the solution. In short, L&H deal with the "energy" in the system. Since this energy is a directionless "scalar", it can sometimes be easier to keep track of it than those damned difficult force and momentum "vectors" in N-Mechanics, which keep changing their directions. On the other hand, L&H-M requires you to know (or assume you know?) the values of some things at ALL times (ie. the amount of energy), whereas N-M deals only with the "right now" and how it will change in the next infinitesimal time-step.

The big disadvantage of L&H-M is that they have difficulty dealing with "NON-conservative" forces (although sometimes there are work-arounds). Typically, non-conservative forces come out of engines (which turn "heat-energy" into mechanical-energy) and friction (which, in a mechanical sense, destroys energy). But (!!!) these non-conservative forces are almost the majority of what you deal with in Vehicle Dynamics. So, IMO, while L&H-M can be useful as a short-cut when dealing with some problems that are relatively "frictionless", for most of VD it is better to stick with the old fashioned Newtonian "forces".

Newton gave a reasonably good "practical" description of these forces in the commentary just after "Axiom/LoM III - To every action there is always opposed an equal reaction...". Namely;
"Whatever draws or presses...
If you press a stone with your finger...
If a horse draws a stone tied to a rope, the horse ... will be equally drawn back towards the stone...".

So, in everyday language, forces are just the "pushing" or "pulling" of one thing against another. This notion of "what is a force" was commonly understood, and widely used, for at least a century prior to Principia, with the many developments in the field of Statics in 1500-1600s (... google Simon Stevin/Stevinus...). Hence, I guess, Newton did not think it necessary to give a more detailed definition of such.
~~~o0o~~~

Summary 1. - You are hurtling down that long straight towards the sharpest hairpin on the FS/FSAE track. Wouldn't it be wonderful if you could just spin the steering-wheel and have your car zip around the hairpin, with NO FORCE AT ALL required from the tyres? That would indeed be the case if there was NO such thing as "Inertia", or its damned annoying forces. Sadly, it is because of those damned Inertia-forces that your tyres have to work so hard to get the car around the corner. And the greater the "quantity of motion" of your car (ie. "momentum" = Mass x Velocity), the harder your tyres have to work. In fact, too much M x V and your tyres say "We give up... You win Inertia!!!"

Conclusion 1 - You score more points by having high V, so try to reduce your M as much as possible. And increase your aero-DF...
~o0o~

Summary 2 - In the above battle between Tyre-forces and Gravity/Aero-DF+Inertial-forces, your suspension is the meat-in-the-sandwich. If you want to have a good understanding of what happens to your suspension during said battle, then it is easiest to picture it getting squashed between the upward-and-centripetal Tyre-forces, and the downward-and-centrifugal Gravity/Aero-DF+Inertial-forces.

Conclusion 2.1 - From above picture, you should clearly see that high Roll-Centres are BAD on independent-suspensions (see "Jacking force..." thread), but high RCs are acceptable on beam-axle-suspensions (draw the FBDs, which show NO similar jacking effect...).

Conclusion 2.2 - Picturing Inertial-forces as being VERY REAL makes Mechanics much easier to understand!
~o0o~

Hope above helps in some way... Back to enforced holidaying...

Z

[Ahmad Rezq]

Erik,
"I like to read what you write. Your writings are very structured."
Some search keys which I will look at them after the exams.
-----

An example from the Egyptian street
11903887_1138435082836605_8873595556890789679_n.jpg

Turning over a swing is a normal thing in Egypt specially in festivals.
This person may not be an Engineer or a physicist but he trusts the Centrifugal Force.

[Ahmad Rezq]

- I was thinking about the steering with the front beam axle, i know that there are some ideas posted by Z and others about the steering and how to reduce bump/roll steer.
but i was wondering has any team run a front beam axle with the traditional rack and pinion/or any other steering system mounted on the sprung mass. i didn't design any beam axle before but i can make rough calculations to calculate the steer in case of bumps and rolling.
IMO this can save alot of pain in the steering design for front beam axles.

[BillCobb]

Regardless of what kinematics you arrive at, the compliance(s) are the most difficult to minimize for your body mounted gear. There WILL be relative motion between them because that's what the unsprung mass's job is. The steering shaft can no longer be a fixed length, so the sliding element is the usual culprit in wear, durability, flexure, lash and compliance. Then there is the issue of resolving the steering effort reaction torques from SWA inputs, braking and cornering.

[Z]

... has any team run a front beam axle with the traditional rack and pinion/or any other steering system mounted on the sprung mass.

Ahmad,

The most common arrangement for the steering of front-beam-axles is, indeed, to mount a steering-box on the "sprung-mass", namely on the "body" or "chassis". Bump-steer and roll-steer are then minimised by having the steering-tie-rods run close and parallel to the beam-axle-constraining-links that go from chassis to beam. See countless trucks/buses/tractors today, and most every passenger car prior to WWII, for examples of such. This is essentially the same problem as with independent suspensions, where the steering-tie-rods should be parallel to their upright's "n-lines" in that area of space (ie. ~parallel to the wishbone or other control-arm links).

Mounting the steering-box or R&P on the beam itself can also work (and has been done...), but now you just change the problem to one of providing a flexibly jointed shaft going from body-mounted-steering-handwheel to beam-mounted-R&P, as mentioned by Bill.

But all things considered, bump/roll-steer of the front-wheels is NOT A BIG PROBLEM in FS/FSAE, because:
1. There are NO bumps in FS/FSAE (at least none big enough to cause big problems)!
2. There is very little body-roll, because of the small +/- 25 mm mandated suspension travel, and the typically very stiff springing that often results in NO body-roll at all (other than from tyre-squash).
3. The driver can easily correct for small steer-changes of the front-wheels.

Note that any unexpected steering of the rear-wheels, either from bump, roll, or compliance-steer (= slop + flex!), is much worse than at the front, because the driver only senses rear-steer after the whole car has changed direction significantly, by which time it may be too late for correction. By comparison, small bump-steers at the front during hard cornering are no different to crossing some lower or higher grip sections of track, which the driver constantly corrects for anyway (if they are anywhere near "the limit").

More important things to get right with your steering-linkage are:
1. Minimise slop (ie. "backlash"). You can live with some flex, but too much slop is downright annoying.
2. Minimise stiction. A smooth, low-friction steering makes fast driving much easier (see Pete Marsh's post somewhere...). A steering system with high levels of stiction + slop is near impossible to drive fast.
3. Get Ackermann right. To get good lateral forces (Fy) from BOTH front-tyres when going through tight corners, the two front-wheels need quite a few degrees of "dynamic toe-out". More than 10 degrees for the tightest hairpin. Typical worst-case levels of bump/roll-steer should be much less than this, perhaps ~1 degree, so they can be 10 x lower down your priority list.

Fix the big problems first!

Minimise slop (=compliance) and stiction, and get Ackermann (over full range) and RELIABILITY right first... (I recall one potentially fast Team that only just managed to finish Enduro after their R&P decided to become "fully-floating"!!!)

Z