Whilst on a advanced driving course a police accident investigator told me that tyre width does not increase grip. So they always use a stopping distance that is the same for prosecuting people. I can see his point - more width less downward force per area but I also race cars and know wider tyres of the same compound give better lap times. So who is right and and does dry/wet affect this?

I don't think you can nail it down to a single factor like width.
Racing cars are very carefully set up for individual track conditions and tire width, pressure, compound, and so on must be figured into the equation along with the car's weight, gearing, engine characteristics, and so forth.

Some lad slapping a pair of "racing" tires on his ride because they look cool is not likely to be accomplishing much.

I quite agree about the some lad comment. But my track car and indeed F1 cars go quicker with greater tyre area for a given set up. Tyre pressure for width is an issue in my comparisons as it has to change to keep the tyre in a reasonable shape.

saying wider tires increase grip is like saying taping the ring finger to the pinky improves a quarterback's passing.

there are many other factors to consider. a car's stopping distance involves many other variables that traction does not affect. I have found that using wider tires, with properly selected profile, tread, etc, improved my traction over narrow tires, but I also improved the tread when I changed tires, so my results are not valid.

the blanket statement that larger tires do not make a larger contact patch is not univwersal, though.

When looking at the equations for friction on a rolling object the equation that is used is F = u (w/r) Where u is the coefficient of friction, w is the weight expressed a a force and r is the radius of the rolling cylinder.

Looking at the equations you may assume that since width of the cylinder is not a variable you would assume that it is not a factor. The coefficient of friction between two surfaces is not a simple calculation it is usually a measured value that depends on many factors. When dealing with surfaces that deform or there is molecular adhesion, the coefficient of friction is not independent of the areas in contact. So width, inflation, diameter and material of the tire will effect the coefficient of friction.

The physics in the formula are sound. Assuming same material/compond - dunlop in my tests, rolling diameter is the same (with my previous reservations on inflation) I am still quicker on wider tyres. Could I be getting in to stiction and sliding resistance vs rolling resistance confusing my basic degree level physics ideas. And are the police wrong just assuming compound/road surface for stopping distance. Thanks you for the educated reply hawkmage.

The police are wrong. The width, inflation, diameter and material of a tire as well as the amount of weight on it will determine the amount of friction and the possible stopping distance.

A rubber tire on concrete will have a lower coefficient of friction than on asphalt also water or oil on the road will decrease the coefficient of friction. Also does the car have anti-lock breaks or did to wheels lock-up, the sliding friction is lower than the rolling friction.

In theory, there is no difference. Ignoring all minor physical effects and just considering the main physical law of friction, the surface the tires touch the ground with doesn't matter at all.

On a "dirty" road, the tire width can make a HUGE difference!
Wider tires have more cuts and can displace much more water. This reduces the chance of aquaplaning and gives you much more grip to steer and brake.
On ice and snow, the tire can grab the snow/ice better and in case of braking they push much more snow away "wasting" energy which helps stopping sooner.

On mud, wider tires can't bit the mud as well. Narrower tires sink in and find stones and chunks in the mud to grab. If the mud is too liquid, the tires sink in up to the axle.

Choosing the correct kind of tire, width and air pressure is serious science. You can't say that wider is always better. Each tire width has advantages and disadvantages.

bikerwookie, here's one article out of a series that explains tires quite well:

http://buildafastercar.com/node/9

I advise reading all the associated articles as well, good info there.

Hawkmage brings up what is likely the most important point, that the idealized formula doesn't apply all that well to tires. People who are taught the basics without getting into the specifics tend to go for the simplified case rather than delving further.

I suspect your police investigator may have been expressing his personal opinion and/or summarizing what he was taught. Hard to say without further discussion with him. I do know that braking distances from forty years ago are still taught in many beginner and advanced driver training courses. Things have changed dramatically in that time!

To sum up quickly, wider tires use essentially the same amount of rubber on the road (given the same car weight and tire pressures) to provide more grip by controlling the tread face better, yielding a higher average coefficient of friction. However, if that wide tire is not provided with the means of staying relatively flat to the road in dynamic situations (wide rims and proper suspension geometry and set-up), they won't perform their task properly and can cause issues of their own.

For a given tire pressure (ignoring the sidewalls) the same amount of tire will be in contact with the road regardless of the width.