Originally Posted by
Krio
Sorry to disagree, but that's not so straight forward. I assume the example here was for a defined set of parameters and most likely not for off road?
The bigger issue in determining the coefficient of friction of rubber on a rough surface hinges highly on 2 things: the tires ability to maintain contact with the ground (the suspension) and the contact patch. The contact patch is very straight forward in on-road scenarios, but on a surface that isn't level means there needs to be enough force behind the tire to conform it to the surface of the track. Tires are designed to deform the right amount for a given weight. Any more and you run into the situation you presented where the mass of the car is increasing faster than the frictional force generated, but any lighter and the coefficient of friction starts falling off faster than the mass of the car. The result is a bell curve-esque graph with an ideal mass.
Now, keeping the tires in contact with the ground is the second part. There is a big reason why most people say a heavier car is better on a rougher track. It's because the suspension can act more efficiently with a heavier car. Let's say 'X' is the mass of the car (just the sprung mass) and look at what happens as X approaches 0 and as X approaches infinity:
As X approaches 0, you are eliminating the mass that the shocks 'push against' to keep the tires in contact with the ground. If you hit a bump and the tires move up the bump, there is nothing for the shocks to push against once the tire is over the bump. The tire will continue upwards in a state of free fall. Picture rolling a tire over a garden hose at a decent speed. The tire would bounce off the hose a couple feet in the air before returning to the ground.
Now, as X approaches infinity you are providing an immovable object for the shocks to push against in their effort to keep the tires on the ground. You could go for an infinitely stiff spring to match and the tires would follow the grounds imperfections perfectly. What it comes down to is the ratio of unsprung mass to sprung mass. The higher the ratio, the better the suspension will be able to keep the tires on the ground.
As an example, 8th scale buggy tires are designed with a 7 to 7.5 lb car in mind, as this is a typical weight for nitro buggies in this current crop of cars. When electric 8th scale first hit the scene, they were tipping the scales at 8 or more lbs. On rougher tracks, many people found their electric buggies to handle better as their suspensions worked more efficiently through naturally whooped out sections. However this extra mass is beyond what the tires were designed for, so losing some weight would benefit the handling of the car on smoother tracks. Some people took it to the extreme, getting their 8th scale buggies down to 6.5 lbs and have found their cars more skittish as the tires can't properly conform to the track surface. It's all a balancing act.
Disclaimer: I've left out the possibility of redesigning tires as the average consumer can't do such a thing. Plus, minimum weights on each class mean that most tires are designed to work their best close to that weight.
Let's dissect what's happening here. I still stand by my statement about less weight increases tire efficiency. The problem with tires is they are never consist and and are always changing. From surface to contact patch to weight transfer humidity, ambient air pressure, tire air pressure, sidewall flex, ect. And will change with each tire, so the constant we have to tune for is how grip is effected by weight, and I still stand by the fact that a tire with less weight will be more efficient than a tire with more vertical load. Now let's not confuse grip with driveability. A light car with too much grip will change directions quickly, so now let's look into the heavier buggy in your example was easier to drive and thus quicker. For now let's assume I'm wrong and that tire grip vs weight is linear (the function might be t=w or maybe t=w/2 or possibly t=w*2 where t=traction and w=vertical load or weight. Or better yet let's just ignore traction for a minute). Now what we want to focus on is the variables that have changed and how they have effected the buggy. Let's take three identical buggies and name them A, B, and C. Buggy a is a buggy that was built with now weight added and has a perfect l/r and f/r balance and weighs 7lbs. Buggy B is one that is identical to buggy A except for one thing, buggy B added 1lb of weight directly on the center balance point of the chassis. Now buggy C is the same as buggy B except for the .25lbs was added to each corner for a total of 1lbs. Now let's apply newtons law of motion to these buggies and compare how they act in a turn. Newtons law of motion summarized is that an object in motion stays in motion and an object at rest stays at rest unless acted upon by an outside source. So from the we can see that buggy A is the lightest buggy and will be the twitchiest of the 3 buggies, well buggy B and C weigh the same so they should act the same right? Actually no, now if we look at how the car rotates buggy C will have more body roll in the corners regardless of the weight, and it will also be the numbest car of the 3. The reason being is that the further out the weight is from the center balance point, the further the weight has to travel and more speed is required to make it change angles (think of swinging a bat with a ten pound bag on the tip of it vs a ten pound bag on the handle of the bat) what's going on in your example (more so than how tire traction is effected by the extra vertical weight) is the effects of weight transfer on these buggies, buggy C is going to push on entry more than buggy B and buggy B will do the opposite in comparison. When you change one aspect if the suspension many things are effected and that's where people get lost. Now when I said more traction does not make a car easier to drive, the best example I can think of is with onroad touring cars. If you are running a rubber tire and change to a rubber based foam tire without changing anything else, the car will be many times harder to drive with the higher traction of the foam vs the rubber. This is my take on things I'll leave it up to you to take it or leave it.
Edit: the reason suspension wasn't added into the tire grip equation is that no suspension is perfect and varies from car to car (including chassis from the same manufacturer, the traction numbers listed above should NEVER be used to tune you suspension rather they are there to show the relationship of grip to weight and that's what we use to tune our suspension. If you have a 4000lbs car it will never pull 1g of mechanical grip. At best you might be able to reach .75g's but again that will vary from car to car)