# I Mechanics of a car turning left

#### Ranger Mike

Gold Member
You covered a lot of ground there...(bad pun)..off roaders set up their chassis with zero offset as they must turn right and left. races running on left turn only tracks have a lot of offset on the chassis to assist the turning process. In both cases there is some degree of " drift" but the results sought is to be able to corner better than the other driver. it is not so much the tires cornering characteristics as th chassis set up to deal with momentum and track resistance.

#### A.T.

You covered a lot of ground there...
The next logical step is turning dynamics while driving on water...

#### Chestermiller

Mentor
I have some practical experience modeling the structural mechanics of automobile tires under various modes of loading. Our interest was in the inter-laminar shear stresses that develop between the various anisotropic tire cord layers comprising the structure under load, and the tension variations along the tire cords in the layers. It was a very difficult mechanical system to model for several reasons. First, the layers are anisotropic (and begin and end at various locations along the contour), second, contact problems with surfaces are always difficult, and third, there are large changes in tire contour curvature which result in numerical problems involving prediction of unrealistic wiggles in the surface. Even the problem of tire contact with the ground (without rotational inertia, or cornering loads) was very difficult. We finally got it done, but it was a bear of a problem.

#### sophiecentaur

Gold Member
Bouncing requires elastic deformation, while turning doesn't.
I can't quite get a grasp of that idea - if you really mean it in an extreme way. Bouncing is 'easy' and can often be described in terms of coefficient of restitution (the schoolboy's friend) which can be anything from 0 to 1. In the case of a cornering tyre, there must be some restoring force from the tyre foot in order for the tyre to return to its original shape. You seem to be suggesting that the coefficient of restitution (or some sort of equivalent) has to be near zero. Why would that be necessary?
I can see your remark could apply to racing slick tyres which are taken almost to melting to achieve good stiction.
a train negotiates a curve using a completely different principle, namely the conic profile of its wheels
Isn't the conic profile there to give a suitable differential action on corners when the axel is necessarily rigid?

#### A.T.

Bouncing requires elastic deformation, while turning doesn't.
You seem to be suggesting that the coefficient of restitution (or some sort of equivalent) has to be near zero.
Saying that something is not required doesn't imply that it must be zero.

#### vr-marco

Isn't the conic profile there to give a suitable differential action on corners when the axel is necessarily rigid?
The conic profile of the wheels is what makes the train go around a curve without the need for lateral friction (the inner flange is just a safety mechanism). The fact that the axle is rigid is just a mechanical simplification made possible by the mentioned cornering dynamics. A train would work as well with independent wheels (in fact there are some designs without rigid axle) or with a differential (which is in fact not needed and would therefore be a waste of weight and money).

#### A.T.

The fact that the axle is rigid is just a mechanical simplification made possible by the mentioned cornering dynamics.
Explained nicely here:

#### sophiecentaur

Gold Member
Saying that something is not required doesn't imply that it must be zero.
I was interested if you had any idea about the order of magnitude involved. Plus, bouncing doesn't actually require elastic collision. Perhaps you could have expanded on your original statement.
The conic profile of the wheels is what makes the train go around a curve
Is that enough of a description, I wonder? The cones are in opposite senses for the inner and outer wheels. I can't picture what's actually going on to provide a centripetal force.

#### FactChecker

Gold Member
2018 Award
The conic profile of the wheels is what makes the train go around a curve without the need for lateral friction (the inner flange is just a safety mechanism). The fact that the axle is rigid is just a mechanical simplification made possible by the mentioned cornering dynamics. A train would work as well with independent wheels (in fact there are some designs without rigid axle) or with a differential (which is in fact not needed and would therefore be a waste of weight and money).
I don't understand how it would work without a rigid axle. Wouldn't the outer, larger-diameter wheel just rotate slower if the axle is not rigid?

#### Ranger Mike

Gold Member
Please see APTA PR-M-S-015-06 Standard for Wheel Flange Angle for Passenger Equipment. This is a the standard for railroad wheel contact angle to prevent low speed climb. Similar specs on the actual rail profile. Summary - there is a detailed profile of the wheel and the rail to provide maximum safety and most durability considering the mass of the train and horizontal land vertical forces applied to both as the train moves at speed. So the wheel is not a cone shape as such under high magnification as it may appear. The flange shape of the wheel has certain profiles at certain points to provide maximum contact minimum wear.

#### sophiecentaur

Gold Member
A train would work as well with independent wheels
That sounds right but the above video implies that the axle needs to be rigid for directional stability. To work with a rigid axle, the rotation rate must be proportional to 1/radius of curvature for both wheels, if slipping is to be avoided so the slopes on the cones need to be appropriate. The video doesn't actually say how the optimum cone angles are calculated; they will depend on the gauge of the rails, I guess.

"Mechanics of a car turning left"

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