zero polar moment of inertia

[pompelmo]

what is zero polar moment of inertia!!!!!!

[Scuderia_Russ]

There was talk of this in Racecar Engineering recently.

[Ciro Pabón]

what is zero polar moment of inertia!!!!!!

If you think as the mass as "something" opposing force when you try to move an object, you could think of moment of inertia as "something" opposing forces (torques) when you try to rotate or bend the same object.

The point where the weight of the object is equally distributed around, is what we call center of gravity. To calculate the moment of inertia, you should multiply the area of the object times the distance to the axis of rotation or center of gravity.

The further are the mass of the object away from the center of gravity or axis of rotation, the bigger is its moment of inertia.

You can read whatever you want, or you can try to experiment with a strip of paper and some light coins or clips. I guarantee that in 5 minutes and 4 easy steps, you will "get it":

1. Cut a strip of ordinary printer paper across, maybe 5 or 6 centimeters width (two or three fingers). Divide it in two, or fold it. You should end with a strip of paper of maybe 5 cm x 10 cm (2x4 inches).

2. Make a "bridge" with the strip of paper, between two supports of equal height. I am using two erasers here, but do not worry, just put the strip horizontal between two "somethings".

3. "Load the bridge" with something light. I have ordinary clips. My "beam" can take one or two clips before bending too much and slipping out of the supports. If you have coins, you may find it cannot take even one without failing.

4. Fold the strip lengthwise at each edge, so you end with a bridge that has the shape of an U and the same length as before. You now have an "U" beam (actually, a "C" beam, but let's continue). Put the strip of paper between the supports again and load it. You will find that you do not have enough paper clips to bend it. The humble paper strip can take easily several coins. Push it with your finger. See?

What you have done is changing the moment of inertia of the paper, moving the material away from its axis of rotation. This axis goes across the "deck" of the bridge.

When the strip is flat, and you look at it from the "end of the bridge", the paper is a thin line. The distance to the axis of rotation is zero, so it has zero MOI. When you make the "U" beam folding the paper, you have separated the paper from the axis of rotation, and now you have a "real beam".

The new "U beam" will have a lot more of resistance to bending. It will also have a lot more of resistance to rotation around (I know I am confusing some people here) the axis perpendicular to the axis of rotation we considered when analyzing its resistance.

This is what I meant when I said that a car with zero MOI would have zero stiffness. It can only be a point or a massless object.

[pompelmo]

tnx... i've got it in the first sentence..i'm a senior in physics..tnx anyway

[Ciro Pabón]

tnx... i've got it in the first sentence..i'm a senior in physics..tnx anyway

I see. Anyway, you should try the paper strip and clips experiment. You know, physics can "see it", but engineers can "feel it".

[West]

Another easy way to feel a difference in polar moment is to take a 10 lb dumbell and rotate it w/ ur wrist; then take a 10 lb barbell and try the same

[ginsu]

It is not an spherical car, only the wheels. You can keep the car pointed in any direction while the wheels push it sideways. You do not have to rotate the car.

BTW, I have seen, maybe a year ago, a radical car (Peugeot?) that has a giant wheel that goes round the cockpit. It is beautiful, but I have not been able to find it on the web again.

Actually, I wasn't referring to your spherical wheel car, I was referring to an object with a near zero-polar moment, a sphere. If you wanted to make a car with near zero-polar moment then it would have to be shaped like a sphere. Obviously, the sphere would have to be very light weight and have most of it's mass near the center of the sphere, and it still would not have zero-polar moment.

I forgot to mention that a car with zero moment of inertia would have zero resistance to bending. It would be the worst chassis in the world. When you design a bridge (or a chassis, I imagine) the torsional and bending moment resistance depends on the third moment of inertia, wich is the integral of the area, when you "turn" it around an axis perpendicular to the load. No inertia, no resistance.

I don't think this is true for a spherical car because the line of action of all contact forces would be through the Center of Mass, causing no bending forces.

[MrT]

As pointed out it's impossible to achieve.

The amount of polar inertia has a massive effect on vehicle stability as also stated. For events such as Formula SAE and student, one tries to have a low POI as you need the vehicle to change direction quickly and be very responsive. Events such as F1 and circuit racing have highe POIs when compared to formula SAE cars as they require stability and would be undrivable otherwise!

Its all a balance of compromises as is most of vehicle dynamics.

[kilcoo316]

Are F1 cars at the stage where engineers can choose to enlarge the PMoI for handling reasons as part of the design?


Surely considering the mass centralisation concept behind the hugely successful Honda RC211V would mean that F1 cars are a long way from that point?

[DaveKillens]

Are F1 cars at the stage where engineers can choose to enlarge the PMoI for handling reasons as part of the design?


Surely considering the mass centralisation concept behind the hugely successful Honda RC211V would mean that F1 cars are a long way from that point?

The laws of physicis have a limit, with suspension, engine, transmission locations, the moment of inertia will be there. But it can be changed slightly, such as when Ferari sdded weights to the nose. That adds weight to the nose for increased front tire grip, but obviously adds a lot of inertia.
The fuel tank is placed very close to the center of gravity so that adding or diminishing fuel has little change in inertia, just added mass. Relocating heavy components closer tot he center of gravity is a common practice in F1.
But the latest Toyota has a spacer between the chassis and engine, and thus allows them moving the mass of the engine fore and aft to change the weight distribution and moment of inertia.

[kilcoo316]

But it can be changed slightly, such as when Ferrari added weights to the nose. That adds weight to the nose for increased front tire grip, but obviously adds a lot of inertia.

Hmm, I suppose it would depend on what the change is for:

1. Less oversteer in middle of corner - weight distribution (inertia)
2. Less initial turn-in sensitivity (MoI)


But I think as a general rule, the car cannot react quick enough on initial turn in, and oversteer towards the apex is more caused by inertial moments from the rear (i.e. gearbox) trying to overtake the c of g.

Therefore reducing PMoI is always the goal.


Note, there is a distinction between inertia and moment of inertia.

[NickT]

Ok you will need some space for this. Try sitting on a swivel chair and spinning. When spinning put your legs out straight infront of you and hold them for a few seconds, then pull them in tight again. Its a very basic pratical demonstration of what happens when you move the PMI around and its fun to

You can do it on a childrens round about in a park, get it spinning and then hang as far out as you can, then move quick in as close to the centre axle as you can.

Have fun, I did