Scale, or "Big heavy cars V small light cars".

[Chris Wilson]

Hopefully some of you will find this interesting:

 

 

SCALE EFFECTS

 

In searching for a simple physical explanation for the inherent manoeuvrability/agility advantage smaller cars seem to have – they always seem more responsive, nimble and communicative than larger cars – a simple physics model was used. In this model yaw acceleration was taken as the index of agility, the car taken as a rigid body, and then the torques and inertia scaling investigated. The inertia of a rigid body about a vertical axis through the C.G. scales as the mass multiplied by the square of the dimension. Since mass scales as the cube of the dimension, the MOI scales as the

fifth power of the dimension. The torques about the C.G. have two components: The distance of the tires from the C.G. scale as the dimension, while the loads on the tires that determine the tire frictional forces scale as the mass or the cube of the dimension. Thus the torques scale as the fourth power of the dimension. Hence the yaw acceleration, T/I, scales as the fourth power/fifth power, or as the inverse of the dimension, i.e., as the size increases the inherent yaw acceleration capability decreases. (Alternatively, since mass appears in both the numerator and denominator of this quotient, the effects cancel, and the dimensional scaling alone remains and determines the scaling result given.) That seems reasonable, and tire load sensitivity would add some additional scale effect in the same direction. Diminutive athletes now dominate gymnastics and diving sports for similar physical reasons, probably. Conversely, large cars should be inherently more stable than small cars. Excellent engineering can camouflage these inherent characteristics, of course. I still rate a 1,500 pound 1965 Lotus Elan as the most responsive car ever, but after 50 years it may only be in relative terms, then versus now.

 

Are these conclusions from this simple physical model qualitatively correct? If so, it suggests that of the various car types rear engine cars (rearward C.G.) are inherently more nimble than other types because they have the longest lever arm to the front tires that provide turning torques about the C.G. It then follows that mid-engine cars (central C.G.) are next most nimble and front engine cars (forward C.G.) the least nimble. This all seems qualitatively consistent, but excellent engineering etc. Again, is this qualitatively correct?

 

 

 

At the other extreme of the handling spectrum, spin or oversteer skid recovery, or control, these rankings would be reversed. Here the rear tires would be key in regaining traction. Front engine cars with the longest lever arm to the rear wheels would seem to be quickest/easiest to control or recover from spin/oversteer conditions. This ease of control perhaps explains why drifters and sprint cars are typically front engine/forward C.G. machines – they are inherently easier to control. Then mid-engine cars next in terms of recovery/control and rear engine cars last – they have the least leverage from the rear tires. And, yes, that was indeed a snap spin in the 911 RS America! Again, this seems consistent with experience and common understanding. If so, why do scribes commonly state regarding mid-engine cars that “they are very difficult to spin, but once initiated they are GONE quickly and can’t be recovered”. Perhaps since many mid-engine cars handle very well the tendency may be to overdrive and when the spin occurs it indeed is very difficult to detect or control.

 

So, is this simple physical model a reasonable basis for making the conclusions reached? Are the conclusions reasonable? Couldn’t find any such macro summary of vehicle design characteristics on handling in my modest library. The answers are undoubtedly contained in Milliken, for example, in all the math, but a concise summary is not offered. Your views would be highly valuable. If not this model and conclusions, then what simple basis is appropriate?

 

Actual designs are more complicated than the simple model proposed. One never can simply scale anything up or down. However, that said, the simple model proposed is not unreasonable, and the questioner has correctly understood its physics.

 

If:

 

• We have a mass that we are angularly accelerating about a centre of rotation with a known force;
  
• The mass’s radius of gyration and the force’s moment arm are in a constant ratio to each other;
  
• The magnitudes of the force and the mass are in a constant ratio to each other;
  
• We vary the radius of gyration and the moment arm, maintaining the above conditions,
  

 

Then:

 

• The linear acceleration of the mass will be constant.
  
• The angular acceleration of the mass will be inversely proportional to the radius of gyration.
  

 

If we double the size of the car, and the coefficient of friction at the contact patches doesn’t change, then the car will have half the yaw acceleration at the limit of tire adhesion.

 

With real cars, there are a number of other considerations.

 

Sheer bulk makes a car harder to manage in the confines of real-world road situations, and requires us to slow down to avoid hitting things. The wider the vehicle is, the less we are able to straighten out the turns. One of the big advantages of motorcycles is their ability to take much straighter lines through turns, especially tight ones, than cars can.

 

As we lengthen the wheelbase, we get more off-tracking. In tight turns and at low speeds, the rear wheels track further inside the fronts. In sweepers, the rear wheels track further outside the fronts. This increases understeer in tight turns and oversteer in fast ones.

 

As the wheelbase gets longer, we need to steer the front wheels more to make a given turn. As the car gets heavier, we need to use slower steering to maintain a given level of steering effort, or we need to add power assist, or use stronger power assist. Good power steering can be pretty nice, but it’s hard to beat the feel of well designed unassisted steering in a small, light car. In any case, for a given steering ratio (hand wheel degrees to road wheel degrees), a smaller car will need less steering wheel movement to negotiate a given turn, at any speed.

 

Are cars with low yaw inertia are more or less inclined to spin, and are they harder or easier to catch? Well, they accelerate in yaw faster. That means it takes less to destabilize them but also takes less to catch them. The car will do a bigger wiggle when it hits a slick spot while cornering. It will oversteer less on exit in a chicane or lane change. It takes a smaller correction to catch a slide, but you have to be quicker with it.

[bignum]

Interesting stuff and spot on i think, explains why GTR`s aren`t great on tight circuits, just their physical size and mass is against them.

[mellonman]

I guess thats why rc cars can do amazing things

[j_jza80]

It also explains why the best driving Japanese sports car didn't have GTR in its name, nor NSX or Supra.

 

 

Small, short wheelbase, light weight, perfect weight distribution. It would have been perfect if it weren't for that engine, and questionable build quality.

[naybad]

Can totally agree with this I have a nice but supra but on alot of roads my clio 172 feels so much fast and defo.more fun

[Digsy]

I think the physics model is too over-simplified to be useful. I don't believe that cars have anything near a third power relationship between size and mass. I would guess that cars vary quite widely in height and length but in % terms not very much in width. I would also guess that a car's moment of inertia is almost totally not coupled to its size nor its mass as (is discussed later on) the mass distribution has a much more significant effect.

 

So as they say themselves, I more or less agree that the results are qualitatively correct, but more by coincidence than anything else.

[goldenvtr]

My starlet and mx5 turbo piss all over many super cars on track and I the real world. But the overall drive of a big engine and big car are diffrent. I would take my mx5 out everyday if it wasnt so in practical. It ticks all thw right boxes for driving pleasure performance and wow factor. My starlet does require more concentration to drive so its good on track but as a road car it becomes tiering around town... this maybe of some contribution to the thread beibg as I've had alot of big and small powerful cars. Light cara are more fun but big cars have practical mediocre fun