Polar moment of inertia

[Petrus]

also written as MR2   

We all ´know´ that a mid engined car turns direction quicker.

It gets a bit more tricky when trying to get the nitty gritty.

I have managed to confuse myself about the yaw axis; the center around which a car rotates.
If the car would be on a frictionless turntable, thén I get it but it is not: A car has the front wheels steering with the rear wheels being a moving pivot point.
So... How does thát translate to car dynamics?
Anyone know or can point me into a direction?

[scm2004red]

Simples

http://www.formula1-dictionary.net/motions_of_f1_car.html

[scm2004red]

Or- courtesy of Wiki



https://en.wikipedia.org/wiki/Yaw_(rotation)#:~:text=other%20rotation%20systems-,Measurement,sense%20a%20car's%20turning%20visually.

[Petrus]

Thank you and it exactly points out my confusion.
Moving around the Z-axis is NOT how a car changes direction and the caption also states this.

Have a look at the illustration:
Although the forces on a frictionless surface may act around this virtual center, there ís a surface on which the front wheels steer ´around´the rear wheels moving forward, apart from their slip angle of the rear tyres.
Imagine the front and rear wheels on tarmac, turn the front wheels and push the car sideways. It does not rotate around the z-axis.
Push it forward and again it does not rotate around that axis.

The Z-axis itself MUST move sideways because of this and it does, otherwise the car would not corner.
Therefore the theoreticical yaw axis cannot be the real world axis around which the car rotates.

Now, take into account that the rear wheels take a tighter turn than the rear wheels and it gets more confusing still, with the Z-axis moving sideways even more and the car turning léss.

So yes, I get the vírtual Z-axis and virtual yaw moment like in an airplane. BUT a car is not like that because of the friction of the tyres and steered front wheels.

In your wiki link it is more like the door than like the airplane.
Look at that door.
Take it on itself and the Z-axis is the heart line, the center line.  Just like represented in the F1 car. But add the hinges and the hinges are the Z-axis. So what about the tyres??
Thís is EXACTLY my confusion.

I am currently reading articles ´under´  https://en.wikipedia.org/wiki/Bundorf_analysis

Imo it all underlines the folly of the 50/50 weight distribution myth.


p.s. note the MR2 as illustration in the load transfer article

[Petrus]

Found a source to study which will keep me from mischief for a while...

https://books.google.es/books?id=wHlkbBnu9FEC&pg=PP1&dq=Tyre+and+vehicle+dynamics&redir_esc=y#v=onepage&q=Tyre%20and%20vehicle%20dynamics&f=false

[scm2004red]

Too much brain activity for me after an over indulgent Christmas. I work on the principle of "if I go backwards into a hedge, it's because the engine is behind me, or forwards, it's because the engine is in front"! The dynamics of it all makes my head hurt.

[Petrus]

Ok, so a simple one:

Angular inertia determines the rotational inertia of an object for a given rate of rotation. The yaw angular inertia tends to keep the direction the car is pointing changing at a constant rate. This makes it slower to swerve or go into a tight curve, and it also makes it slower to turn straight again.

Angular inertia is an integral over the square of the distance from the center of gravity.
Mass near the ends of a car can be avoided, without re-designing it to be shorter, by the use of light materials for bumpers and fenders or by deleting them entirely.

If most of the weight is in the middle of the car then the vehicle will be easier to spin, and therefore will react quicker to a turn.

Much adoo about what we know to be the case anwyay ;-)
Next is figuring the science of dynamics out. I still want to understánd.
But.. regardess, will try do away with the front crash bar. Already lightened the rear one.

[MRSwede]

Ok, so a simple one:

Angular inertia determines the rotational inertia of an object for a given rate of rotation. The yaw angular inertia tends to keep the direction the car is pointing changing at a constant rate. This makes it slower to swerve or go into a tight curve, and it also makes it slower to turn straight again.

Angular inertia is an integral over the square of the distance from the center of gravity.
Mass near the ends of a car can be avoided, without re-designing it to be shorter, by the use of light materials for bumpers and fenders or by deleting them entirely.

If most of the weight is in the middle of the car then the vehicle will be easier to spin, and therefore will react quicker to a turn.

Much adoo about what we know to be the case anwyay ;-)
Next is figuring the science of dynamics out. I still want to understánd.
But.. regardess, will try do away with the front crash bar. Already lightened the rear one.

Aren't the crash bars helping with the rigidity of the chassis ?

[Petrus]

Aren't the crash bars helping with the rigidity of the chassis ?

I used to think so but when I took the rear off found that the bolts do not really provide a sturdy connection. It is pretty thin steel box section with the bolts bearing on a minimal surface on the inner plane only.
Also, these bars do not feature in the scematics for the frame structure. The only drawings where they are shown is in the distribution of impact forces.
If you have a look through @Adam28´s Munter build you will find them deleted too.
I will find out soon enough. If I don´t like it when I have the apron off, then only the washer bottle will go.

Anyway, the ´bumper´ phrase applies to the bucket and contents at the front too. It explains that the spare wheel & toolbag make the care both more understeered and more stable at speed; more rotational inertia.
As the centre should be about behind your seat, you can understand that the effect of that mass times the square of the distance is significant.
The crash bar is only 4 kg but still... 4 kg both as weight ánd as the furthest away from the rotational axis as possible. Make that distance 2 meters for ease of calculation and you can see that the polar moment is considerable. Worth a try imo.

[MRSwede]

In the under body picture the are still there ?

[Petrus]

In the under body picture the are still there ?

In ´ghost´ yes; not part of the high tensile structure.

The bars dó have a function just not to add rigidity to the structure.

Would have taken the apron off today but the weather is dreadful. Will try tomorrow.

[Petrus]

Back to the polar moment of inertia.

If I understand it correctly, deleting the front crash bar and washer (half full) bottle will reduce the resistance to turning by 36 kg/m or 24 lbs/ft.

Here is a link with an article between popular and scientific: http://www.auto-ware.com/beckman/phors13.htm with even a bit of humor!

[Ardent]

Slightly more the Belle thread than here. But whilst it's fresh in my mind.
Surely you will need the washer bottle come Test time. For how strict the are, I struggle to believe they  wouldn't test to see you can wipe your screen.

Could you just run with no water in it, from a weight point of view. Then bung a litre in for testing.

At a KG/L of screen wash. The majority of the weight must be the fluid.

[Petrus]

Slightly more the Belle thread than here. But whilst it's fresh in my mind.
Surely you will need the washer bottle come Test time. For how strict the are, I struggle to believe they  wouldn't test to see you can wipe your screen.

Could you just run with no water in it, from a weight point of view. Then bung a litre in for testing.

At a KG/L of screen wash. The majority of the weight must be the fluid.

Yes, they test it but apart from that it does come in handy even when it rarely rains over here. Coúld but do not want to go without.

The bottle itself is silly large and surprisingly hefty. Also as far forward as it gets. I am a bit surprised that this gets just about nó mention in  threads about adding lightness.
I am replacing it with a 1l. plastic bag closer to the bulkhead and fill that half up.

[Joesson]

The bag type reservoir I believe was on an early car, maybe my '60's Imp. But that was in the UK and insufficient to meet the needs, whatever was OE I replaced it with a 5L plastic container. Adding weight to the front of my unmodified Imp seemed to improve things generally.

[Petrus]

The bag type reservoir I believe was on an early car, maybe my '60's Imp.

Just about any car from that era had something akin.

I coúld do with a smaller bag still, one extra one way valve and a rubber ball, but as the wiring & switch are there anyway the pump is actually lighter than that.

[Petrus]

Now back to the PMI.

Moving heavy parts the engine even a couple of inches closer to the CM can dramatically decrease the PMI because it varies as the square of the distance of parts from the CM. This is thé crux of a mid engined car!
Same goes for deleting parts at the extremities. Hence the notable effect of a lightweight muffler on our MR2 as it taking the spare out (or adding a bag of sand slowing it down considerable).
Obvously an overall light car has less inertia in any direction, rotational too.
Ergo;
- adding lightness reduces the PMI
- and the reduction increases with the square of the distance to the CM

For me the surprise was the square of the distance.
It does PÍNG!! explain the appearantly too large effect on stability of removing/adding weight in the front bucket whereas a full versus empty tank, which is a larger weight difference, has nó effect.

Cóól 

[Ardent]

That now makes sense.
Unless I missed it elsewhere. I thought you were going to go without altogether, that caused me to raise an eyebrow.

Moving on nothing to see. Back to inertia and a few KG less of it up front.

Edit
cross post

[Petrus]

Back to inertia and a few KG less of it up front.

The polar moment of inertia of the few kilos less is times the square of the distance adding up to surprising torque more/less needed to change direction; 36 kg/m or 24 lbs/ft less from taking off the crash bar and fitting a lighter washer bottle is WÁY beyond what I expected.

Nów I also understand the confusion about the effect of lighter wheels!
It is not just the unsprung weight ´weighing´ more than sprung weight, not even the gyroscopic effect, it is also TWÍCE a PMI: One of the wheel itself and the other as part of the car and both at double the speed.
Ok, I cannot (yet) quantify the effect but I dó now understand the basis of the appearantly wild claims about the effect.

[Ardent]

- and the reduction increases with the square of the distance to the CM

For me the surprise was the square of the distance.
It does PÍNG!! explain the appearantly too large effect on stability of removing/adding weight in the front bucket whereas a full versus empty tank, which is a larger weight difference, has nó effect.

I promise I am on topic here. Despite the comparison about to follow.
The square bit is indeed significant.
The correlation for me, is in terms of photography.

If I am using flash and I stand 1m away from you to take your portrait. The exposure is what it is.
But if the distance between you and me changes to 2m. Twice the distance. I don't need twice as much flash power, I need FOUR times the flash power. For the same exposure.

Flash power or weight. If the inverse square rule is in play. Then that makes a much bigger difference than one naturally imagines.
Which brings me back to me, to you, referring back me regards the sense of weight reduction going to the Malian zorst.
So having reduced weight out the back. I might whip the spare out the front. Just to see. Obviously I'll have to put it back as that would not be vanilla.

Edit
cross post again

[Petrus]

I promise I am on topic here. Despite the comparison about to follow.
The square bit is indeed significant.
The correlation for me, is in terms of photography.

If I am using flash and I stand 1m away from you to take your portrait. The exposure is what it is.
But if the distance between you and me changes to 2m. Twice the distance. I don't need twice as much flash power, I need FOUR times the flash power. For the same exposure.

Flash power or weight. If the inverse square rule is in play. Then that makes a much bigger difference than one naturally imagines.
Which brings me back to me, to you, referring back me regards the sense of weight reduction going to the Malian zorst.
So having reduced weight out the back. I might whip the spare out the front. Just to see. Obviously I'll have to put it back as that would not be vanilla.

Good comparison imo.
Even when you knów, it is simply not instinctive.

I´d say replace the spare by a foam can.

Rather relieved about the wheels btw. Although not actually bugging me it was in an ´unresolved´ drawer at the back of mind.

[Petrus]

How did you get on with the de-spare-wheel trial Jason?

I have taken off the crash bar and reservoir.
Not taken it out for a spin. The job was slowed down by four frenchies under the car, on top of me, nicking tools. Too much fun to lock them up though.
Will be going for a longish ride tomorrow so not much sense in a hurried too short trial.

[Ardent]

Back in the office (bedroom) today.
Might be a new years day or weekend job.

agree. Better to wait and do a proper test than half a job.

[Petrus]

Back in Antequera.
Ok, so itdoes not a different car make; it is 8 kg only after all but for being less than 1% of the crar weight it makes an absurdly large difference.
Mind, althouh it makes the same difference going through a long constant radius corner as when changing from a lefthander to a righthander (or vv.), as a human being you do not féél the force needed to keep deflecting a car through a constant radius corner because the G force is constant. Flicking the car from on direction to another you dó feel because the G forces change direction.
Right; it flicks notably bquicker. Marginally but the charming passenger volunteered it so it is not me feeling it because I knów I changed something.

Now the ´difficult´ bit. For the týres, the constant radius corner ís a constant change in direction and any decrease in PMI makes their life lighte, meaning that the same effort results in more cornering speed.
Lees PMI = less force needed to change direction = using the same force, the same change of direction can be done at higher speed.

@Ardent  To easily experience that using the frump bucket:
- have the spare wheel and tool roll plus something heavy more in
- drive through a looooooong corner
- do some left/right vv. and on/off roundabouts
- íf traffic non-density permits try ´slalom´ the dotted line on the highway with the driver side front wheel, speed at your discretion (the important bit is repeat at some speed)
- repeat same with the lot out of the bucket

[Ardent]

@Petrus
From your post 18.
Nów I also understand the confusion about the effect of lighter wheels!

The other side of the same coin.
Nów I understand why the effect of heavier wheels (17s) felt so wrong.

From your post 23.
@Ardent  To easily experience that using the frump bucket:
- have the spare wheel and tool roll plus something heavy more in
- drive through a looooooong corner
- do some left/right vv. and on/off roundabouts
- íf traffic non-density permits try ´slalom´ the dotted line on the highway with the driver side front wheel, speed at your discretion (the important bit is repeat at some speed)
- repeat same with the lot out of the bucket

I will.
Still dialing into the fresh tyres. But yes, will give that a go.