It's true that F1 cars are basically reverse-airplanes and generate an enormous amount of downforce (within regulations). But the huge amount of stress/wear that places on the tires, and the very soft rubber compound of racing tires themselves for maximum-grip, means that the tires are usually recycled or disposed of after each race. That, of course, wouldn't work with production cars and tires that are expected to last for at least a reasonable amount of time. As it is, some high-performance and ultra-high-performance, summer-only, dry-weather tires already have disclaimers on them warning of potential rapid wear and typically about 10-15,000 miles of tread-life.

 

OK, so this is where your theory gets into a circular argument. You can't have more grip (coefficient of friction) due to weight and then cancel that weight out in the resulting acceleration. You need to keep all variables equal, and then look at the effect of weight on the coefficient of friction.

As Gengar said, at the theoritical maximum, when traction gives off, adding more weight will increase traction to provide more acceleration.

 

Here's a thought experiment:

A box that weighs twice as much that is pushed twice as hard (so twice the force) will move the same distance.

No matter the weight of the box, the amount of acceleration that "occurs" when static friction is overcome is the same.

As gengar said, cars are not idealized rigid bodies, so there's a bit more complexity to their acceleration than that, but for your specific question, I think the above is a good example.

 

I'm sorry that I can't reply to all of you right now (partly since I should probably be working right now ), so I'll focus on gengar for now.


But the thing is that none of those things -- weight distribution, the variable value of μ, etc -- matter while the car is not traction limited. At that point, the only limitation is the the mass of the car and the amount of torque that the wheels are producing. If the tires are gripping the road as well as they need to, then it really should be a much simpler discussion. It makes sense, too, since 99% of the design effort in terms of performance is focused on how to get the tires to stick to the road as well as possible.



I suppose I wasn't clear in my original post (my mind was all over the place). I understand that I'm over-simplifying things, but that was kind of the point. I know there is far more in play than just these two basic physics formulas, however, I believe that they still give us a good high level view of the overall story.

I guess my thought here (at least after combining what you have said with my original thinking) is that, yes, extra weight with all else being equal will cause some problems in cornering by affecting μ, weight transfer, etc. But my point is that all else doesn't need to be equal. It seems like in most cases, the effects of the extra weight can likely be overcome with proper tires, lowering the center of gravity, stiffening the chassis, etc.

Obviously these things can likely only be adjusted within certain limits, so weight does still matter, but my main point here is that if these equations are even *remotely* correct, then it seems to me that we as car enthusiasts frequently overstate the effect of weight on a car's performance. And now that I think of it, history seems to kind of confirm that, too, since cars are getting heavier and heavier every generation, yet also getting faster and faster in just about every way.



EDIT: Going back to the original topic, though, can we safely agree on one thing? Can we agree that, with all else being equal, increasing the weight of a car cannot possibly increase its ability to accelerate? Whether the weight be on the front wheels, rear wheels, or wherever?

 

With ALL other variables being and remaining equal, that would be a true statement.

 

Not quite. The total weight of the car is dfferent from the weight on each axle.

In a truck, for example, especially a light duty 4x2 not intended for towing, there will be a very poor weight distribution and little weight over the rear axle relative to the front. A Ford Ranger, for example, is 60/40, meaning there is 50% more weight over the front than the rear. (1720 lbs front / 1180 lbs rear)

In this example, adding some ballast (bags of sand) in the bed can increase it's traction, and therefore ability to accelerate. 350 lbs, for example, changes the distribution to 53/47. (How much exactly for the right amount of trade off between traction and acceleration, I don't know.)

This is due to the inquality between the value of mass used for F=m * a and the value of mass used for Ff = Fn * m; in this case the mass attributing to normal force (that is, the mass attributed to the rear axle) increases by a greater percentage than the mass of the entire vehicle.

I think the only scenario this would apply is like the one I describe. For pretty much any non-truck, the inequality between gain in mass attributing to normal force versus gain in total mass is likely not large enough.

 

The logic is that for the given weight of the car, it will accelerate faster if that weight was on top of the rear wheels (the powered wheels).
So what your friend means is that during acceleration, it is helpful to TRANSFER the weight from up front to the rear wheels. Once you are in stable speed, the transfer should be completed and balanced 50/50 for neutral handling.

 

this is getting way to complex guys. I think were spinning our wheels right now. LOL ( sorry it was too easy)

 

^^ see my explanation above. Too easy.

 

Well sure, this is basically the same thing you said in your last post. To reiterate, the difference is that previously, you were assuming that the car was traction-limited all the time. Now we are assuming that the car may or may not be traction-limited at any given moment, and this is a pretty realistic assumption. It becomes unrealistic again (for most cars in most situations, anyway) if you go all the way to the other end and assume that the car is not traction-limited all the time.

First off, if you don't add the extra weight and make all those performance improvements to the tires and chassis and weight balance, then your car will still be faster. I'm not sure the "weight can be overcome so it's not that important" argument is compelling.

Performance car enthusiasts and trackday guys battle against weight because it affects every performance characteristic of the car. More mass means worse acceleration, worse cornering, worse braking. It's the easiest way to improve all-around performance. That's why weight is considered the enemy.

And surely no one is saying that weight can't be overcome. How else would an X5M get around a racetrack faster than a Cayman or a Lotus Evora, then? Car manufacturers know that it is cheaper to get more performance out of a heavy, low-stress, low-rpm gigantic literage engine than it is to improve performance by doing things like cutting weight, having a better-balanced chassis, or a tuned suspension. (And as we can see by so many of the current offerings on the market, it's clearly cheaper just to put a gigantic engine in something than to develop a car that is fun to drive.)



Infra pretty much answered this above: The important issue is how much weight is on the driven wheels. The only thing I would add is that there could be situations when μ is so low that the available friction is so low that ballasting could make a difference (although again, as you yourself alluded to in your OP, this is unlikely under dry conditions).

I remember once when I was out at a small drift track after a rainy weekend and one guy spun out and put his rear wheels into a muddy ditch and couldn't do anything but spin them. So we all piled into the trunk until he was finally able to get moving.

 

The unfortunate news is, the real world isn't theoretical, and simple physics equations don't take into account all the issues. Weight and mass are not interchangeable terms. Tires don't generate constant grip. Suspensions don't always keep tires in perfect contact with the surface they need to generate grip. So simple physics can't take into account all the issues. If it were this simple, racing would be completely boring.

 

Hmm... that's a fair point... I didn't think of that for some reason. When you increase the weight strictly over the driven wheels, you are increasing the frictional force by a a disproportionate amount. I don't think it'd be hard to work out the math for that, either.

Let's say p is the percentage of weight on the driven wheels (though obviously this will vary quite a bit under acceleration/deceleration), and k is the amount of mass added over the driven wheels, then I guess the equation after adding the mass would be something like:

(m + k) * a = (p*m + k) * u * g
a = (p*m + k) * u * g / (m + k)

And the m's no longer cancel out... And the smaller p is, the more helpful k will be. I guess as p reachess 0, you have:

a = k*u*g/(m+k)

Meaning increasing k increases acceleration (if u*g > 1, which it will be). If I remember my calculus properly, though, the limit of the acceleration as k approaches infinity brings us back to the original equation:

a = u * g

Oversimplification again, I know, but it does shed some light on things I suppose... I guess I'm kinda rambling to myself/thinking aloud now, though.

 

I still dont see how all else being equal, a car acceleration theriotically is independant of weight.

Maximum friction allowed by tires, and maximum applied force to move a car with those tires. Sure, the car acceleration is independant of it weight. Because whenever u change weight, the tires max friction changed, and your max applied forces changes to comply. Then the weight is irrelevant.
.

In reality, everything affect friction, and friction affect the car. In reality, the same car, same tires, same condition, heavier = slower acceleration.

 

You're both right, and I understand that. I just would have thought that even basic, simplified physics would have shown more clearly why weight is so important. Because as someone who is pretty passionate about cars, technology, math, and science, I was kind of blown away when I actually worked this out since the whole "weight is evil" axiom is something I've taken for granted for so long. I thought the reasoning behind weight being bad for performance was very simple, but it's actually quite a bit more complex than I realized.


I don't think anyone ever said this. If I said it somewhere, then I misspoke.

In a traction-limited scenario under acceleration (or deceleration), then weight doesn't matter very much, but you are not usually traction limited when accelerating, even on a track. You are when braking, but the problem with extra weight when braking is that it will heat up your brakes more quickly, even if it doesn't necessarily affect stopping distance at first.

 

Isnt this all common sense Lol