Drag Coefficient

[Tonka Crash]

I ran across a web page that got me thinking about this again.  It had some equations useful to extract drag coefficients from data we can get from telemetry.  I took a Lotus 135 and the VW Golf to the Nissan speedway for testing. 

From that website:


You can solve the equations for CdA using terminal velocity HP and speed.  Then you can  calculate drag at any speed or the horsepower required for a given speed.  To get CdA you just need the HP required to hold any single speed.  This needs to be a constant speed, so terminal velocity is probably easiest.  You also need to use a flat track.  Hills will throw this off, so the straight on the Nurburgring is out.  The FM1 test oval would be perfect for this kind of data collection.  The front straight on the Nissan speedway seems to work, at least I got the same answers going either direction. 

In pseudo excel syntax:
CdA(sq. ft) = HP*550/(Speed*5280/3600)^3/(density/32.174)*2 where acceleration is zero
drag(lbf)  = 0.5*(density/32.174)*(Speed*5280/3600)^2*CdA at any speed

where:
density is in lbm/cu. ft., if you find slugs/cu. ft. drop the /32.174 from the above equations
speed is in mph  the 5280/3600 is to get to ft/sec for the units to work out
HP is horsepower multiplying by 550 gets to ft-lb/sec for the units to work out.

I played around with trying to get constant speed points and found it's really tough to hold zero acceleration.  When I did get really constant speeds the HP required matched the drag predicted from the CdA obtained at terminal velocity.  Just .01g off acceleration can throw off the HP reading by about 5-10% 

Since HP and drag matched without being offset that tells me rolling resistance is either non-existent or rolled up in the CdA value.  Rolling resistance should be relatively constant.  The way the car launches from a dead stop also feels like there is no rolling resistance, just a breakaway force that has to be overcome to unglue the car from it's parking spot and then only enough power to balance drag.  One of the steady points I got was 9mph down the front straight. It took .07 HP which works out to only taking 2.88lbs of force to push a car at 9mph where my predicted drag was 2.59lbs.  Considering that the telemetry doesn't give very many decimal places I considered this pretty solid evidence that rolling resistance is part of drag or not modeled.

I also determined in game air temperature to be 70F by parking the car for 20 minutes and letting the tires cool.  They settled on 70 at the speedway and Laguna Seca.  It wouldn't surprise me to find that Turn 10 was lazy and its a constant across all tracks. Tuning could get pretty interesting if they just added atmospheric effects.  Temperature and density changes should affect engine performance, tire grip, and aero.   I also assumed sea level conditions air pressure.  This changes the air density in the equation to 0.074887 lbm/cu ft

For the Lotus Elise 135

CdA   Aero Config
9.3    stock
10.3   add splitter@85
10.6   add wing@100
11.0   add splitter@45 & wing@50
12.0   add splitter@85 & wing@100
12.8   add splitter@125 & wing@150
12.8   add splitter@125 & wing@150 motor swap+30HP

For the VW Golf

CdA   Aero Config
10.5   stock
10.3   add diffuser
11.8   add diffuser & splitter@85
12.2   add diffuser & wing@100
12.5   add diffuser & splitter@45& wing@50
14.0   add diffuser & splitter@85& wing@100
15.2   add diffuser & splitter@125 & wing@150
14.0   add splitter@85 & wing@100 no diffuser
13.6   add diffuser & splitter@85 & wing@100 & Sideskirts

What is this good for?  You got me. I'm just offering this up as more information that can be extracted from the telemetry.  Maybe someone can find a way to use it for tuning.  It would be interesting to see values for a wide range of cars.

[Blooze]

There's a lot of good work here Tonka; thanks for sharing!

re Rolling Resistance: I think this is rolled up within a value that is stored in association with the track.  A friction coefficient.  Perhaps density is included here as well.  At any rate, I have noticed that different tracks seem to require different alignment settings (i.e.; Road Atlanta needs an extra tenth to keep tire temperature warmer on the inside when compared with Tsukuba or Sebring Short).

I agree.  Without the data being published before hand, finding it seems to hold little value.

However, your labors are not without value.  You seem to have proved that whenever they are available, the purchase of the diffuser and side skirts would be an automatic no-brainer...

$

[Hoplee]

First, for Tonka:

BRAVO.
(*applause)

And second, for everybody:

I disagree that there is(are) no obvious and immediate application(s) for the data provided by such exercises as Tonka's CdA extractions above.

There are often interminable arguments over why certain cars exhibit certain behaviors, such as the Charger. These arguments stem from the fact that we're not given all of the in-game variables that determine one car's behavior, performance index etc. versus all the others. Determining the in game equivalent of the CdA moves us one very large step towards defining these critical variables that are not revealed by the game or previous research. I propose that a CdA database could be a very useful addition to our tuning tool-box, especially on longer tracks, or tracks with significant straight sections.

Now what can we plebeians do to get more data for y'all 'Spreadsheet Wizards'?

[Tonka Crash]

The more data collected the better, but after reading Blooze's comment some other variables may affect the CdA.  I did a motor swap in the Lotus, bumping HP up by 30 and confirmed that the terminal velocity was where the drag equation predicted.  So this means a value determined on a stock engine will accurately show top speed changes for added HP, as it should. 

If rolling resistance is built into the CdA value tire pressure, compound, rim width and diameter need to be looked at to see if they change the CdA value.  It may be that there are too many variables to isolate effects of any one.  I did the aero changes on the VW to see if the drag from adding a wing was consistent with the Lotus.  I was hoping to find a simple relationship, like a rear wing capable of 150lbs always changed CdA the same amount regardless of the car.  It may be that you have to configure your car and then get a CdA for later use.

I'm just theorizing here, but the one use I've tried is that by plotting the drag against engine force available in your final gear you can be see how gearing changes affect terminal velocity.  I was able to tweak 6th  in the VW to get a 2mph higher top speed from what it was set at before I started.  Conventional wisdom has been to set gearing so that you hit redline at the end of the longest straight in your final gear.  That's probably still fine for short tracks that don't approach maximum speeds, but on longer tracks I don't know if this is optimal.  Since most engines have the peak HP before redline, power is already falling while drag is climbing and the terminal velocity will then be gearing limited to a lower velocity than what the engine is capable if the gearing were moved to make more power available at higher speeds. 

One other thing.  Acceleration in gear can be calculated in each gear. Using Blooze's transmission calculator.  Force in a gear at any speed is just the taking the HP column divided by speed in gear column and multiplied by 375.  F_engine=(HP/V)*375

Then, provided there is no wheel spin:

Acceleration (g) =(F_engine-F_drag)/weight

[Blooze]

There is another variable that probably affect's the CdA as well, at least Turn 10 alludes to it when they state that providing a front rake (suspension lower in front) can increase the DF.

Once collected, this data could be used to set up transmissions, and perhaps evaluate engine components.  But consider that we have devices in place can accomplish the task already using the Trans sheet as stated, and the work gathering the data would not be trivial.

You would have to do the CdA calc for every car n^n-1+1 (I think that is the equation) where n is the number of body parts that affect Frontal Area.  And then a set of 3 formulas to alter those values linearly by rake, front, and rear DF ranges.

That is what I think would need to be done to get the database that you are talking about.  Judging by what Tonca said was required to get the 0 accel speed for each instance, the task is a lot more work than I would care to get in to.

I have a hard time just talking myself into building the Torque sheet on a per-application basis.

$

[BarbecuePete]

I noticed when running the PT Cruiser in the hot hatch challange that it felt like the car was trying to push a huge weight down the road in front of it...
This was especially noticeable when trying to get off the line, I ended up with a very long first gear that basiclly bogs the engine down so it gets grip and pulls away, but you can hear the tyres spinning slightly as the revs rise... it has full WR so its not like there is much weight holding it back and although the tyres are 'only' 235 width, thats not exactly skinny.. but it certainly feels like there is something stopping it moving forward off the line...

[Spiny Anteater]

To complement Pete's comments, I noticed a similar thing when I've run the R-Class cars. They launch much better with full aero than with minimum d/f. For those cars with that mcuh power, weight seems to be an advantage in gaining traction when moving off the line. Your results with the Cruiser suggests to me that they have modelled the drag co-efficient in such a way as to affect the weight of the car, even at standstill. But I can't think what advantages there could be in modelling it in that way.

[bimmerlovere39]

I'd imagine that a constant resistance would be slightly easier to model than a dynamic resistance (increasing with speed).

Another thing I wonder about is drafting and how this effects this.  Hm.  If the forza aero model was cracked, it could offer huge advantages with Aero setup.

I wonder - if Turn 10 knew how far people were testing the sim, would they try and improve on it, or just say that they/us were a vast minority and not care?

I'll be watching this intently... might try and get some numbers of my own... (I get enough math in school lol)