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Question - I am curious about what factors are involved in
automotive engineers/designers choices of wheel sizes. What are the
effects of increasing or decreasing wheel size in relationship to
engine power and vehicle performance?

As far as power transmission is concerned, you can regard the wheel
as just another gear. Among other considerations, enlarging the wheel
would necessarily raise the axle and, thus, the car's center of mass.
Also, changing the wheel size would change the angle of the force
delivered by a bump in the road. If wheel sizes change a lot, curbs
and speed bumps must also change correspondingly, or they would not
have the same effect on a car.

Lengthy discussions about wheel size effect on automobiles can be found on
the Internet. Basically, automotive designers balance wheel cost,
performance, comfort, and appearance so as to make vehicles that customers
want to buy. Large wheels with high performance tires are more expensive,
but generally give better "handling,"

The main effect of changing the wheel diameter on a car is the need to
change the gears which change the ratio of engine speed to wheel rotation
speed; larger wheels clearly rotate more slowly for a given car speed.
However, the acceleration and top speed of a car does not depend on the
wheel diameter if the gear ratio is optimized for that diameter.

Larger diameter wheels have the advantage that they average the road surface
over a larger area so small bumps are not so noticeable.

More important is the weight of the wheel. The lighter the wheel, the less
is the kinetic energy of the wheel at a given speed and so the more of the
work of the engine is used to drive the car forward. It is also easier to
design suspensions which are more comfortable if the wheel is lighter. A
lighter wheel can go up and down more rapidly when subjected to the forces
of the bumps in the road and the spring connecting it to the body of the
car.

The ideal design is, I am sure, a complicated problem.

Performance in which use?
There's off-roading, track racing, load carrying, efficient
transportation, safe transportation, cheap transportation, posh
transportation...
Designers cannot win for everybody, so they are to some extent casting
about for the best point in their market...

A larger, heavier tire and wheel assembly will gain more kinetic energy
from each short bump it encounters,
which the suspension then tries to absorb without passing on to the
passenger cabin.
So smaller tires give a smoother ride.
When tires bounce, a given amount of suspension hardware can put them back
in contact with the road quicker if they have low mass.
So smaller tires should give better handling.

The ground-contact footprint of the tire will grow or shrink until air
pressure bears almost exactly the weight of the car.
[ inflation_pressure x footprint_area x number_of_tires =
vehicle_weight ]
For a given weight you could use small tires inflated to high pressure,
or small tires at low pressure with a long, soggy footprint,
or larger tires with either pressure.
Flexing and smacking heavy rubber on the pavement every revolution uses
some energy, makes some rolling friction,
so I think that small tires at high pressure are known to be the most
fuel-efficient choice.
Large flexing of rubber at high speeds also makes heat, which makes tires
wear out or blow out sooner.

It is not always engines pushing tires. Often tires push engines back.
Smaller wheels have less angular inertia, and less torque when skidding,
so they present less threat of damaging the power-train metal parts.
This is most evident in off-roading, where huge tires sometimes break
drive shafts or axles when a tire suddenly lurches into a rock.
The axle is caught between the sudden torque on the tire, and the angular
inertia of the geared-down engine.
(The fluid clutch in an automatic transmission is a partial safety-relief
for this stress.)
But I am becoming very aware lately that when you apply gears to an
angular inertia (say of an engine),
the apparent rotary inertia goes as the _square_ of the gear ratio. That
figures in somewhere.

On the other hand, small high-pressure tires have more load per square
inch and should wear down faster,
and large low-pressure tires often have better traction in various
circumstances.

Large diameter wheels and tires effectively put the car in a slightly
higher gear,
which in principle could be compensated for by having a different set of
gears in the power train,
but in the real world that change isn't usually cost-free.
If your engine is overpowered or "torquey" with its given gear set, a
larger tire diameter helps you use that for speed.
Conversely many small engines will need small tires to do their (very
modest) best acceleration.

The rotary inertia of huge tires can reduce a vehicle's acceleration,
but that's only a factor when the wheels and tires are a substantial
fraction of the vehicle's mass.
Other than monster trucks or beginner-designed RC or robot vehicles, it
usually does not matter much.

Choosing an aspect ratio is a more current issue for engineers.
A tire can protrude for beyond the rim to a distance larger than it is width,
or be "thin and wide" with less sidewall.
Thin and wide can have less lateral flexure during extreme cornering,
and I think there is some technical reason why it is a more viable option
than it used to be.
Certainly wide tires must have radial-ply rather than bias-ply reinforcement,
so the wide outer face can remain "flat".

US Department of Energy.

 
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Great, thats the FAQ in different words

 
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lol useful, so thanks, but alot of that is in th faq.

 
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It sure helped me understand more on thee impact Wheel and tires have on cars overall.