Re: [cpk] The Garage (v1.4, updated 17.10.16 - 73 cars)

I’ve seen some requests for explanation of my physics model (calculator) that was introduced with The Garage, so I finally decided to put it all together into a step-by-step instruction along with some insights.

**1. Power and mass**It quickly became quite apparent to me that linear transformations (scaling by some constant) of car’s power and mass in real life is a very inflexible solution, which could yield satisfying results only for certain classes of vehicles. For example, formulas that would work nicely for, let’s say, race cars that have 500+ horsepower and <1000kg, would not function well for “normal” cars with much less power and weight of more than 1500kg - and conversely, linear formulas calibrated to road cars would make and sports car totally overpowered or even undriveable.

Therefore I use a formula that limits the leverage of high power and low mass and boost the performance of heavier, less powerful vehicles.

*Power = 15*([Power in hp]+16)^(4/7)-75*

Mass = 12*([Mass in kg])^(1/2)These formulas are quite arbitrary indeed, and were obtained basically by trial and error until I came up with curves which I liked. After some testing I decided to stick to them and up to this moment I’m quite satisfied with the results.

**2. Aero**Basically it is calculated as drag coefficient (cd) times frontal area, but both for many cars these parameters tend to be uncertain or even publicly unavailable. I use real drag coefficients whenever it is possible, and if it is not, I estimate it (sometimes simply by taking a random, but believable value), but in order to compensate the uncertainty, I use corrected frontal area calculated on the basis of 3D model which depends also on the car’s aerodynamic profile, precisely on the width of the car (W) and height of 3 points:

A: height of the front of the car

B: height of the bottom of the windshield (if it’s sufficiently far from the front, otherwise 0 (eg For trucks and buses))

C: height of the roof

*CFA = 1.5*W*(0.75A-B+1.25C)*The idea behind the formula is that the most important factor is the height of the car, but the aerodynamic drag also depends on how “quickly” the car “emerges” from the ground (low profile -> small A -> smaller resistance, for example for C Class cars). In the end, high B value indicates the low slope of the windshield which gives an aerodynamic advantage.

Then there is the final formula:

*Air resistance = cd*CFA***3. Key assumptions regarding the steering**The model assumes that due to the technological progress, performance of cars in terms of grip and maneuverability increases over time – 1 year difference causes an increase of:

- grip by 0.005
- balance by 0.002
- downforce by 0.5

In the following chapters the model year is denoted by MY.

The second underlying assumption is about the relationship between the wheelbase-to-length ratio (denoted as WtL) and car’s balance. The idea is that cars with high WtL ratio are more stable (slide less), but at the same time suffer from worse agility (less balance).

The third idea is the subdivision of vehicles into performance classes: So far I’ve been using the following classes:

7+: prototypes

6: GT cars

5: Supersports cars

4: Sports cars

3: Sedans/saloons, muscle cars, hatchbacks

2: City cars, family cars, SUVs

It is not set in stone though, and I frequently use fractions and assign cars to classes arbitrarily, to my liking. For example, Mazda 787B is 7, Ferrari LaFerrari is 5.5, Lexus LFA is 5.25, Aston Martin Vanquish is 4.25, Nissan 370Z is 3.5, Dodge Challenger R/T is 3, Land Rover Evoque is 2.5. Class should be assigned independently from the model year, so for example Ferrari 166MM is class 5 as well, even though it is not supercar by today’s standards – but this is compensated by the first assumption regarding the technological progress over time.

The fourth and last construct is the impact of car’s layout (engine position and drivetrain) on the steering. In a nutshell:

AWD cars have superior grip, balance and sliding

RWD cars have good grip and balance, but tend to slide more, while FWD cars have worse steering, but better stability.

RM is the “optimal” position and provides best balance between stability and steering. Engine too far to the front will disrupt the car’s steering ability.

As sketched above, layout will determine the “bonus” grip, balance and sliding of the car which will be added on top of the formula. The detailed parameters are presented in the tables below.

Attachment:

bonus.png [ 12.87 KiB | Viewed 644 times ]
**4. Grip**Grip is calculated using the following formula:

*Grip = 0.75 + 0.005*(MY-1950) + 1.5*(WtL-0.58) + 0.75 + 0.15*Class + Grip_bonus* **5. Balance**Balance is calculated using the following formula:

*Balance = 0.3 + 0.002*(MY-1950) + 0.66*(0.58-WtL) + 0.02*Class + Balance_bonus***6. Sliding**Sliding is calculated using the following formula:

*Sliding = 0.05 + 0.5*(0.58-WtL) + Sliding_bonus***7. Downforce/wings**Downforce is calculated using the following formula:

*Downforce = 0.5*(MY-1950)+1.5*(0.75+Class)^2 + Downforce_bonus*Where Downforce_bonus is a value allocated on the basis of car’s special qualities and features such as advanced bodywork or rear/fron wing (and their sizes). Usually it varies from 5 to 20, maybe 30 for prototypes.

That’s it – it may feel overly complicated, but in fact it uses the minimal amount of information (year, power, mass, layout, dimensions, drag coefficient) which are easily available, a bit of creator’s judgment and nothing more. Hope you'll find it useful.