Some restrictor research

I did some research into using restrictor and ballast as a BoP measure. Ballast has the disadvantages of changing the handling and feel of the car, as well as impacting tyre wear badly. Using the restrictor to slow cars down is more appealing. But is the restrictor as linear as ballast (i.e. does double the restrictor double the slowing)? The answer is no.

I did some experiments letting an AI drive the Ferrari 599XX EVO around Red Bull Ring, at different levels of restrictor, and ballast (using a custom championship). I then plotted average lap times at different levels of handicap. As expected, the ballast is pretty linear - i.e. more ballast has a linear effect on lap times.

But here's the graph of restrictor versus the percentage lap time slow down.



You can see that it's non-linear - more restrictor slows the car down even more. Using a trendline in Google Sheets, the graph is best approximated by a power equation:

% increase in lap time = 0.0327 x Restrictor ^ 1.98​

If you want to go the other way - i.e. figure out how much restrictor to add to slow a car down by x% - you can solve with:

Restrictor = exp((ln(%Increase) - ln(0.0327))/1.98)*10​

E.g. if a lap time is 1:40, but you want to slow it down to 1:41.5 for BoP - this is a lap time increase of 1.5%

Using the restrictor equation above, you get Restrictor = 69%.

Now, this is all based on one car at one track. In future, I'd do some more experiments with different cars (turbo vs normally aspirated etc) and different tracks, to see if a power equation is still the best fit to the data points in general.

UPDATE
Here's the restrictor graph for the Ferrari 458 GT2. For this car, the restrictor is linear. So the effect of restrictor on laptimes can be very different from car to car.
Although for this car in particular, the effect of the restrictor might be different because

And here's the Pagani Zonda R. Back to a more exponential looking increase, but interestingly now not really affected up to 25% restrictor.



McLaren P1 GTR
Has a weird dropoff with the rate of slowing decreasing at 100% restrictor. Maybe closer to linear?



Here are the restrictor curves alongside the torque/power curves (as calculated by CM):

Ferrari 599XX EVO


Ferrari 458 GT2


Pagani Zonda R


McLaren P1 GTR


What does it all mean? I don't know. Just that increasing restrictor affects every car differently!

 

One thing with restrictor testing with AI is they shift at the same rpm so adding restrictor if they shifted up a bit sooner would likely lose less time. A human can generally figure this out but AI are unlikely to be coded by this, the data with AI will be a good baseline but as with most forms of BOP a good driver may find better ways to lose less with these. Either by setup changes or altering basic driving adjustments, it would be nice to have a list of BOP effects on certain cars using your method however. As it should still be a relatively good indicator of performance impact for the majority of human drivers that tend not to look for alternative ways to deal with BOP effects.

 

There are some very clever buggers out there. Happy New Year to all you Genius types.

 

Huh, I didn't know the restrictor was modeled that way. I guess cars with existing restrictors (458 GT2, '13 F1 car?) won't feel any extra restriction until it's set pretty high as a result since you don't drive them to redline.

 

Do not confuse the rev limiter of the engine with the air restriction value for BoP; they are not the same.

Even with maximum air restriction the engine still revs to the same rpm, it just has less air to use to combust the fuel so the top of the power graph should have a lower plateau rather than a higher single peak.

(*afaik )

 

Right, but if how it works is "10% restrictor = 10% less throttle possible at max rpm (90-100% of pedal just opening the engine up 90%), dropping to 0% at 90% of max rpm" then if a car shifts at 80% of redline you won't notice it at all until 30-40% restricted.

 

Nope, read my post above, you are still confusing rev limiter with air restriction. They are not the same.

 

Here is an example of what happens when reducing the diameter of the air intake (i.e. reducing the amount of air the engine can take in at once).

This is basically what the AC Air Restrictor BoP value does, it lowers the maximum amount of air the engine can take in. This doesn't make a difference low down, but at the top end it reduces power developed. IT DOES NOT reduce the max RPM of the engine.

See this graph for a general idea:
As the diameter of the air intake decreases, the power graph plateaus at the top end.




Source: https://www.hks-power.co.jp/en/product/supercharger/universal_kit/restrictor.html
(yeah its from a supercharged engine but the effect remains the same).


Edit @Minolin - ah fair enough, that is a little bit of a corner case that I wasn't aware of, but in general I believe my point stands

 

I'm not confusing them, if you think I am then my post is not as clear as it should be. Your graph is exactly the same as what I'm describing.

 

Fair enough I may have misinterpreted you, no hard feelings sir

 

I’m using a BOP system in a league, with both ballast and restrictor plate. We quickly learned that penalizing with 100% restrictor and downwards 90%, 80% etc, was the wrong way to go. As of now, pole gets 25%, 2nd 24% etc.
Ballast is used in conjuction with laptimes vs average grid, so if you’re very fast, but crash out and therefore avoid a high restrictor penalty, you get ballast anyway so you won’t fly past everyone easily next race. It works, but took a few races to balance out the grid. The good thing is that it makes the league exiting to the end, no one knows who certainly will win the season. The downside has been that not everyone enjoys driving with even slight restriction and starts complaining.

Nice work Willy, makes good sense

 

Nice one Wally! (For a moment you had me thinking that the restrictor was a waste of time, since a 0.04% increase in laptime isn't really worth bothering with, but then I realised it was the fractional increase, not percentage increase )

The question about how the optimal upshift timing should vary (i.e. torque curve shape) with restrictor has me interested as well - has anyone actually made any telemetry measurements to prove how the restrictor is implemented in AC? If not I might have a go for the sake of curiosity. (And if nobody has a better suggestion I might as well choose the same car as Wally for the first attempt.)

 

I only assumed it was done in the same way as the cars ingame that already have some restriction built in by either fuel flow like some of the modern f1 cars, or air like some gt cars. I havent really tested much with the ingame restrictor but if you would test and show the telemetry to see how its implemented it would be useful to many.

 

Yes, a human may well adjust differently, but the AI has the advantage of being much more consistent, for testing. Plus, the AI is happily driving around and around right now while I type

 

Will have a go at generating some curves.
I think I already learned the answer to my main question though - i.e. "is the shape of the torque curve affected?": the answer seems to be yes, as you guys were assuming.
It's not exactly a definitive result yet though - all I've done so far is to run some single-player practice sessions on the test pad. I discovered that there's a console command "set restrictor" which I'm assming for the time being does the same thing as the multiplayer server restrictor. You can apparently set it to any value you like, including values way in excess of 100 (and negative values!). When I set it to something very large (I think it was 100000) I discovered that the terminal velocity in 4th gear was much lower than that in 6th, so the power peak had moved to a much lower engine speed.
Will do some "proper" tests with 0 and 100 though...

 

My experiences too. I've been using restrictor recently more than ballast, but as I'm finding out, restrictor is not as linear as ballast. People also complain too with restrictor that they are as fast as everyone else in the corners, but then get blown away on the straights. I think too that a mix of ballast and restrictor would be the best overall approach.

 

I have my system on Google sheet, if interested.
Here's the thread where it's shared to the league:
http://precisionracingleague.com/forum/viewtopic.php?f=111&t=1182

 

I added a bunch of other cars and power/torque curves in the 1st post.