Hope that clears it up for you.
Bob
Michael.
> "Polar moment" deals with weight distribution relative to distance from the
> center of mass. A car with a low polar moment will have more of the total mass
> closer to the center. In such a configuration, it may be less likely to begin
> spinning, but like a skater with arms pulled in tight to the body, once it
> does, the rate of spin will be higher.
> Hope that clears it up for you.
> Bob
> Cheers.
> __________________________________________________
> "That's not car control, that's crisis management"
> __________________________________________________
Polar moment of inertia could also be rephrased as " Inertia at the
poles". Or, the amount of inertia at the extremities, i.e. the front
and back ends of the car in our case.
Remember that mass has inertia. i.e. all mass wants to maintain is
current state of movement. If its station it wants to stay stationery.
If its moving in a certain direction at a certain speed then it wants
to carry on without alteration. The tendency to maintain a current
motion state is called inertia or momentum. Whatever term you like.
Consider this...
Say you had two different spheres of equal diameter and overall
weight ( mass ). Sphere A has a foam center and a solid steel shell.
Sphere B has a solid steel center and a foam shell. The overall size
and weight of each is identical. Each will also have an identical
center of gravity. Overall straight line acceleration and deceleration
etc of the spheres as a whole will be the same in each case. But the
properties of how the spheres rotate about their own respective
centers will be very different.
Sphere A - Foam center with steel shell.
The mass of this sphere is concentrated towards the outer rim. There
is relatively little mass near its center. When rotated through a
given amount of degrees the outer rim moves faster and further than
the center, simply due to the larger diameters as you move out from
the center. Lets pick two positions from the center. A near center
point might move only say 2cm for the exercise while an outer rim
point moves 20cm for the same degree of rotation. With a heavy outer
rim, there's a lot of mass and therefore inertia to start moving. It
take more than usual force to move the heavy outer rim from a static
status. Also once it is moving, it takes more than usual force to stop
the heavy outer rim from continuing to move ( rotate ).
Sphere B - Solid steel center with a foam shell.
In this case the heavy steel mass of the center is the part that is
only moved the relatively short distance of 2cm for the given
rotational degrees of movement, The faster moving, more distance
covered, outer part of the sphere in this case has much less mass.
Because the outer diameters have little mass in this case changes in
their speed and direction incur much less inertia forces than if they
were heavy.
You see ...
The heavy-outer-rim sphere is harder to rotate a given amount
requiring more force, or more time for a given force. Once rotating it
takes more force/more time to stop it rotating. It could be described
as sluggish and slow to react to rotational influences, but had better
stability. By contrast the lighter-outer-rim sphere is easier and
faster to rotate. It might be described and more nibble and lively,
more responsive, to rotate, but less stable.
If you apply these points to car design you can see that the more you
concentrate the cars' weight away from the ends and towards the center
the less polar inertia there will be and the car will rotate easier
requiring less force to change direction in overcoming its own
rotational momentum. and less force/time to slow its rotation, just
like the spheres. The more weight towards the ends the more sluggish
it will be influenced by rotational forces but the more stable it will
be also. The less mass in the extremities the more lively or
responsive it will be to rotational influences but the less stable it
will be.
As a point of interest there are a number of vehicles that try to
minimize the mass at the ends of their structure. Sailing boats for
instance, especial racing ones where comfort is not a consideration,
try to concentrate their mass towards their center so that the bow and
stern can bob up and down freely with the minimum of inertia
resistance. Airplanes do the same to some extent so that that can
change attitude to the airstream with a minimum of force required to
overcome the planes own rotational inertia, although in that case some
amount of longitudinal rotational stability is also desirable.
In short, ( and I am not know for saying anything in short ), the more
weight towards the ends the greater will be the resistance to a change
in an objects rotational velocity state, as explained above.
Hope this makes sense.
Regards
Phillip McNelley
> Can anyone explain
[a lot of enlightening stuff]
So, if you want a car that turns easily, you will try and place the
heavier components like engine and driver (in my case, that is :) near
the center of the vehicle?
Perfectly.
--
Wolfgang Preiss \ E-mail copies of replies to this posting are welcome.
> Isn't "polar moment of inertia" that time of the year when the pengins
> hibernate?
> Thank you for this explanation. Very clear.
> Paul
Nicely explained..
LB
BSPN Motorsports..
> >> Cheers.
> Polar moment of inertia could also be rephrased as " Inertia at the
> poles". Or, the amount of inertia at the extremities, i.e. the front
> and back ends of the car in our case.
> Remember that mass has inertia. i.e. all mass wants to maintain is
> current state of movement. If its station it wants to stay stationery.
> If its moving in a certain direction at a certain speed then it wants
> to carry on without alteration. The tendency to maintain a current
> motion state is called inertia or momentum. Whatever term you like.
> Consider this...
> Say you had two different spheres of equal diameter and overall
> weight ( mass ). Sphere A has a foam center and a solid steel shell.
> Sphere B has a solid steel center and a foam shell. The overall size
> and weight of each is identical. Each will also have an identical
> center of gravity. Overall straight line acceleration and deceleration
> etc of the spheres as a whole will be the same in each case. But the
> properties of how the spheres rotate about their own respective
> centers will be very different.
> Sphere A - Foam center with steel shell.
> The mass of this sphere is concentrated towards the outer rim. There
> is relatively little mass near its center. When rotated through a
> given amount of degrees the outer rim moves faster and further than
> the center, simply due to the larger diameters as you move out from
> the center. Lets pick two positions from the center. A near center
> point might move only say 2cm for the exercise while an outer rim
> point moves 20cm for the same degree of rotation. With a heavy outer
> rim, there's a lot of mass and therefore inertia to start moving. It
> take more than usual force to move the heavy outer rim from a static
> status. Also once it is moving, it takes more than usual force to stop
> the heavy outer rim from continuing to move ( rotate ).
> Sphere B - Solid steel center with a foam shell.
> In this case the heavy steel mass of the center is the part that is
> only moved the relatively short distance of 2cm for the given
> rotational degrees of movement, The faster moving, more distance
> covered, outer part of the sphere in this case has much less mass.
> Because the outer diameters have little mass in this case changes in
> their speed and direction incur much less inertia forces than if they
> were heavy.
> You see ...
> The heavy-outer-rim sphere is harder to rotate a given amount
> requiring more force, or more time for a given force. Once rotating it
> takes more force/more time to stop it rotating. It could be described
> as sluggish and slow to react to rotational influences, but had better
> stability. By contrast the lighter-outer-rim sphere is easier and
> faster to rotate. It might be described and more nibble and lively,
> more responsive, to rotate, but less stable.
> If you apply these points to car design you can see that the more you
> concentrate the cars' weight away from the ends and towards the center
> the less polar inertia there will be and the car will rotate easier
> requiring less force to change direction in overcoming its own
> rotational momentum. and less force/time to slow its rotation, just
> like the spheres. The more weight towards the ends the more sluggish
> it will be influenced by rotational forces but the more stable it will
> be also. The less mass in the extremities the more lively or
> responsive it will be to rotational influences but the less stable it
> will be.
> As a point of interest there are a number of vehicles that try to
> minimize the mass at the ends of their structure. Sailing boats for
> instance, especial racing ones where comfort is not a consideration,
> try to concentrate their mass towards their center so that the bow and
> stern can bob up and down freely with the minimum of inertia
> resistance. Airplanes do the same to some extent so that that can
> change attitude to the airstream with a minimum of force required to
> overcome the planes own rotational inertia, although in that case some
> amount of longitudinal rotational stability is also desirable.
> In short, ( and I am not know for saying anything in short ), the more
> weight towards the ends the greater will be the resistance to a change
> in an objects rotational velocity state, as explained above.
> Hope this makes sense.
> Regards
> Phillip McNelley
