tire vs power and weight
Your contact patch will remain the same if you run a 175mm wide tire or a 235mm wide tire IF, and this is a big if, you use the same make and model tire and same tire pressure in this comparison.
Now if you would run a wider tire with lower tire pressure, your contact patch would increase also increasing your static traction.
Now before all of you either start arguing with me or go out and buy super wide rubbers and stuff them under your cars, hear me out further.
Narrow tires will not roll as well as wider tires. Wider tires will distribute your vehicles weight across the wider contact patch, deforming the tire less. The more tire deformation will result in more rolling resistance of the tire. But, wider tires are less aerodynamically efficient at high speeds and add extra drag to the overall vehicle.
Taller tires have more affect on tire traction than wider tires in pure lateral movement (i.e. drag racing). But as a result of running taller tires, you increase the torque on your entire suspension and drive train systems, causing potential for component failure.
In the case of tires, although traction increases with load, it increases less than linearly, and coefficient of friction decreases with load. A larger contact area reduces the load per unit area, resulting in more grip. There is a point of diminishing returns, such as weight and aerodynamic drag. It's also true that a larger tire dissipates heat and with a lighter load involved, it wears less. Another reason for a larger contact area is to compensate for debris or track imperfections interfering with the tire and pavement contact.
Note that load sensitivity is commonly used to adjust the understeer or oversteer of car. When a car turns, the down-force on the outside tires is increased and the down-force on the inside tires is decreased. The body of a car also rolls a bit, and the suspension can be used to unequally distribute the load between the front and rear tires. If the front end is relatively stiffer, then more of the down-force is exerted on the outside front tire, and the relative grip is reduced because of tire load sensitive. A stiffer front end causes the front end to lose some grip in turns, resulting in understeer. A relatively stiffer rear ends results in oversteer. Street cars are generally setup with understeer, while race cars are setup with a small amount of oversteer.
For a variety of reasons, such as deformations, molecular bonding type reactions as well as surface roughness, real world friction isn't the simple thing described in physics books.
Now to sum up everything rather than starting an endless rant…
Going wider will not always give better traction.
If you want an all sweeping statement that is roughly true. Wider contact patch sacrifices linear traction for lateral, narrow tires sacrifices lateral for longitudinal traction. And the most important thing about tires is not contact patch area but that they are at correct working temperature.
Wider tires are not always better. They don't always give better traction. It depends on the car, the situation, the conditions.
Eg. Rally cars use wider tires when on tarmac rallys, and use (surprisingly) very thin tires on ice rallys.
F1 cars used to use narrow tires until aero began to be used in the 60's.
Drag racers actually want tall tires, width is there to stop the tire being destroyed.
An example I can think of is formula student cars, they used to use 8 inch tires but couldn't get them up to temperature. They switched to 6.5 inch and got more grip because they can get them up to temp.
So before you go out and buy some super wide meats and cut the crap out of your fenders to stuff them in there…. Sit back and consider some factors.
What temperatures are you going to be driving in? Are you only accelerating in straight lines like drag racing or are you autocross racing and need more lateral stability? How long do you want your tires to last? Obviously sticky tires don’t last as long as hard compound tires, but have a much higher coefficient of friction. And running tires with lower tire pressure can put too much heat into the tire.
Lastly, if you are using your car as a DD, running 235mm wide tires when the stock size is 195mm, probably isn't helping you at all. Instead of modifying your car to fit these tires and paying higher prices for these wide tires, really isn't worth anything to you unless you plan on whipping it through your local neighbor hoods like a rally driver on a daily basis (which I will never encourage or think is “cool” to drive like an idiot on public roads)the point is though the mentality that wider always = better is wrong. There is an optimum limit even on drag racers.
Basically though, there are just so many factors to consider when choosing a tire that one post cannot cover all of them. Gearing, suspension setup, driver preference, car classing rules, car style/power-train layout, car weight, wheelbase, wheel width/diameter, compound, heat generated, tire aspect size, power of car, overall width of setup, ...the list goes on.
The theory all summed up sometimes a narrower tire will be faster than a wider tire for a variety of reasons.
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