Speed and accuracy improvements

First off, let me tell ya... you can make just about anything into a delicious Mexican-tasting dish with liberal application of ranchera sauce. Seriously, this stuff is good. Threw some remnants of rotini, farfalle, and chicken together with some shredded rice and half a bottle of sauce. Tasty as all get out. My all time favorite dish with this type of sauce is of course 'arroz con pollo' - particularly of the style available at Tequila's. If you're passing through any of those locations in Colorado I suggest you stop in and get it. You can tell them Jersey Tom sent you if you'd like, but they'll probably reply with, "¿Que? ¿Quien es este pendejo?"

Anyway, just as I was getting to the point of saying, "Well shit... anything more to this sim thing is going to be a real pain in the ass," I had a couple pretty good ideas to improve the realism and accuracy as well as solution speed.

1. Replace integration scheme.
I considered explaining the concept of numerical integration here, but instead I'm gonna direct you to Wikipedia if you're a non-engineer and really that interested about it. As I was mentioning in the earlier post on the topic, for the moment I'm using a dumb rectangular-method integration method. Generally the least accurate of any method I know, unless you're using a random number generator. Think I'll upgrade to the trapezoidal method for now, which is plenty sufficient given that the accuracy limitation will now lay in the engine torque function which is doing linear interpolation anyway.

Another viable option is to replaced the fixed time step method with a variable step method... but I'm not too excited about that at the moment.

2. New way to solve straightaways.
Currently my sim finds the braking point on a straight by stepping the initial application point backward 1 foot at a time, starting at 0. If you have a long braking zone, that takes a long damn time. At first I had been thinking of implementing an adaptive algorithm that increments the braking length in large steps if it's way too fast for the following corner. Better method is to do a single forward integration of acceleration from Turn X, and a single "backward" integration of braking starting from Turn X+1. The brake application point is their intersection. Bam! This alone should make the damn thing run literally 100x faster.

3. Add trail-braking and throttle modulation into and out of the corners
Whoa, now. Think I'm going to have to make a separate entry about this, because it's serious stuff. So serious that it precludes the inclusion of Mexican sauces.

Weekly news - Australia beats UK!

Turns out blogger.com gives me the option of looking up traffic stats for this site in a variety of ways. Giving an engineer data is always a bad decision as invariably they will waste way too much time looking at it in every way imaginable, and then ultimately present it in such a manner that suits their own ulterior motives, hidden agenda, or mood.

Not only do I get to see this, but also where people came from that clicked links to this blog, as well as Google search terms that brought them here as well! Some of the search strings were pretty interesting. In any event, this week saw a boost in views from Australia, mainly on account of a couple forum posts from Race Magazine. Welcome Aussies. Also had a few referrals from a 'Formula SENA' forum which I believe originates in Columbia. From what Spanish I recall, the post title was basically, "This blog has interesting pictures." ¡Bienvendio!

...e io sono un po triste che ci sono poche persone dall'Italia. Spiegate la parola, miei amici italiani!

For anyone else casually reading the blog, feel free to click the 'follow' button over on the right. It's interesting for me to see how many people check this out on a regular basis. 83 and counting!

Road America!!

While the actual project lap time is way off, for the most part this matches some real F1000 data at this track - surprisingly well considering I'm taking blind guesses at most of the car parameters. There are a few reasons for the time being off, but I'm not too worried about the absolute values as much as the relative change. Still have plenty to tweak for drag, downforce, and tire grip... but this is a pretty promising result.

Even in its rough state, I played a bit with it over 3 sim runs.

1. Baseline
2. Base lateral grip + 5%, longitudinal grip -5%
3. Base lateral grip -5%, longitudinal grip +5%

Not going to give away which did what... but one of them results in about 1.2% better lap time compared to the base, the other is 1.3% slower. On a 2+ minute lap at Road America, I'll let you figure out what time differential that is. Of course since this model has no combined mode operation, it's tough to say if it's directionally correct.

A lap around Martinsville

Ladies and gentlemen - holy fuck, we've done it. Some upbeat tunes are in order. If you're not a fan of my tunes, well, that's why this is my blog and not yours.

Allow me to show you a 30.1 second lap around Martinsville:

 

Right about now you may be saying to yourself, "Daaaang homie, that shit is fly." Alternatively you might be saying, "Well that looks fuckin' dumb." You'd be correct either way. It's a dinky little short track, it's not gonna look very cool. Also, admittedly, a 30 second lap at Martinsville is pretty damn slow! Cup cars (NASCAR) get around in under 20 seconds. However, my numbers for drag, downforce, tire grip level, and gearing, are all arbitrary. Also, my "driver" doesn't trail brake nor ease into the throttle, so again - absolute numbers are BS.

Believe it or not, for weighing literally over one ton more than a F1000, Cup cars also have a better power to weight ratio. A 358 ci (5.9L) V8 turning over 9000 RPM will do that!

Still got some stuff to check out to make sure everything looks legit, and then I can start breaking down a road course and seeing what it comes up with. Will have to see if I can dig up some actual F1000 DAQ at some racetrack to back-calculate appropriate numbers for drag, downforce, and mechanical grip. But for now... I'm catching up on Mad Men.

Baby steps - can put a straightaway together!

Nothing too thrilling tonight. First, credit to Liz C for turning me on to People Under the Stairs.

Good tune to sit back and have a vodka on the rocks.

Anyway. Pretty much got the straightaway stuff squared away. Making the ghetto solver was definitely a blessing in disguise with being able to set a distance limit for integration, rather than time. I'm sure that excites you - in many ways.

So for example we can come out of a 30 mph corner down a 1000' straight and back the braking point up in 50' increments:

 

Not super thrilling to look at, but important. There is time data that goes along with the velocity and distance outputs, not shown here. All the numbers for drag, downforce, and longitudinal tire grip are just made up at the moment so don't heed too much attention to it. If I wanted to be really fancy I could probably put a segment in the acceleration solver that puts a delay between gear shifts. I'll screw around with that a bit down the road.

So next up I need to make a quick and dirty corner solver (find max speed a corner of given radius can be taken, when including both tire and aero effects) and then the actual full lap solver. To actually run my first sim I'll need to define a track. Road America, Mid Ohio, or even Nelson Ledges will take some time to break down segment by segment. Therefore, as a first pass to make sure the damn thing works at all, I'm going to start with the most simple track I can think of...

Martinsville!

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Should really be able to wrap most of this crap up by this weekend, which is good given that I can potentially get out and be social. You would be amazed at the look of raw animal lust in a woman's eyes when I strike up a bar conversation about racecar vehicle dynamics.

Gearbox added to engine model - more or less

Positive - Added a transmission to my engine model.
Negative - Canned ODE solver no longer produces a believable result. To be honest, I'm not sure what the hell it's doing at all!

Solution: Ghetto-fy it. As in, my integration scheme is as follows:

y(i+1) = y(i) + yprime(i) * timestep;

Yeah, I know. Not exactly Runge-Kutta. But hey, whatever. Wanted something quick and dirty to make a result. It's an easy problem to solve (linear interpolation of the torque curve), and I have plenty of CPU power to just muscle it. I'm sure my other solver is failing out because of some accuracy or tolerance setting that I'm too lazy to fuck with at the moment.

To a degree this might be nice, in that instead of setting a time span for integration I can go one more step and calculate distance, and have the solver cut off after a certain amount of travel. Ultimately that's what I'm interested in for doing straightaway sims.

Here's the result though, with the following parameters. It's a little goofy under 3000 crank RPM since I have no dyno data, so I filled in some BS numbers (engine is pretty much stalled at that point!). By "Engine Thrust" it's thrust at the tires, coming from the engine. Obviously with the data below 3000 RPM being crap anyway, the 0-60 time isn't even worth looking at.

• Car weight: 1000 lb
• Drag model: Tuned to generate 400 lbf at 120 mph (arbitrary numbers)
• Final chain sprocket reduction: 3.250
• Rear tire OD: 22.6"
• Shift point: 11,000 RPM

Next up.. I'll have to clean up this solver and add the distance output and solution limit, then do the same for a braking sim, then start building the actual lap solver.

More success!

Giants beat the Redskins 31-7, I picked up some decent Chinese food, and I got more shit to work. Made a dinky little simulation run with a rough CBR1000 torque curve, a single gear, an arbitrary number for inertia, and a drag model tuned for a drag-limited top speed of 100 'units'.

 

You pumped? I'm pumped. I texted Brandon and Justin about it and they got pumped too, see below:

Next step will be to add some logic to the thrust model that flips between gears based on velocity. Shouldn't be too difficult. That will have to wait till tomorrow. I'm sure I'll be in a stellar mood tomorrow when I wake up early, see god forsaken snow outside, and then have to drag my ass outta bed to get ready for another week at work. Woo!