Math boffins, pit time question:

Discussion in 'F1' started by Bas Jaski, Apr 23, 2012.

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  1. Bas Jaski

    Bas Jaski Two Time F1 World Champ
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    Something has been bothered me for a while now. What if car A has a pitstop at 3.0 seconds. Car B, fighting closely with car A, makes his stop in 3.5.

    Some say, car B lost .5 of a second to car A. I say, car B lost a full second to car A, because in the time he was waiting for .5 of a second, car A was .5 of a second under way already.
     
  2. Qvb

    Qvb Formula 3
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    It is the same .5 of a second. Imagine if they both stopped at exactly the same time, then the fast one would leave and the second one would leave .5 seconds behind, and, had they been pitted side by side, the first car would be .5 seconds ahead.
     
  3. werewolf

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    two cars, each going flat-out full speed, equally, over the exact same distance. Each car stops, immediately, at the exact same time (and same point in space).

    car A stops for 3.0 sec and immediately resumes full speed.

    car B stops for 3.5 sec and immediately resumes full speed.

    How much time elapses between the cars arrival at the finish line?
     
  4. PCA Hack

    PCA Hack Formula Junior

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    You just blew my mind!

    Here are the pit times from yesterday http://www.f1fanatic.co.uk/2012/04/22/2012-bahrain-grand-prix-tyre-strategies-pit-stops/

    It's got to be .5 advantage, not 1.0.

    For example: Car #1 = 21.00 second total stop including 3.0 seconds while the car is in the air.

    The time on the pit lane limiter was 18.00 seconds - assuming no driver error, each car spends 18.00 seconds on the limiter from pit-in to pit-out. If Car #2 spends 3.5 seconds in the air it still only takes 18:00 seconds to enter & exit the pits. Thus the difference remains .5 sec.

    Maybe...:)
     
  5. 410SA

    410SA F1 Veteran

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    The laws of math are not suspended in F1. If a car takes and extra .5 of a second in the pits, that's all that happened - an extra .5. Whether the first car was moving or not at the time of the extra .5 makes no difference. The only addiotinal time taken is .5 of a second
     
  6. Ney

    Ney F1 Rookie
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    As long as the rate of accelleration from 0 to the mandated pit lane speed limit is equal, the .5 sec remains .5 sec. If the rate of acceleration is different, you would see it in the time on limiter value. In terms of distance on the race track, .5 at the Start finish is much greater than .5 at the slowest hairpin, but it is all still .5 sec. In laps and especially out laps are where time is often gained or lost.
     
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  8. Bas Jaski

    Bas Jaski Two Time F1 World Champ
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    Yes, but in the time the one driver is standing still for an extra .5 of a second, doesn't the gap grow bigger compared to the other driver since he is on his way already?
     
  9. Bas Jaski

    Bas Jaski Two Time F1 World Champ
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    Makes sense...:)
     
  10. Fast_ian

    Fast_ian Two Time F1 World Champ

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    An interesting conundrum indeed..... As with all things in F1, it isn't as simple as it first appears and is the reason some of 'em (all?) now have dedicated mathematicians / statisticians in the garage.

    My 02c; an additional 0.5 second in the air is indeed just a half second lost. However, Bas' point I think is that if I exit the pit lane that much ahead and get back to speed the gap is "stretched" in that period - It may still be half a second timewise, but I've gained "hundreds" of yards over you.

    I think..... ;)

    Anyway, I found an interesting article on the topic by Dennis Simanaitis of R&T back in 2003 - Back then, stops were refueling time limited of course so he factors in the dis/advantage of more/less weight in addition to tire degradation and/or the advantage of being on fresh tires. There's some basic algebra involved, so if thats not your thing "beware".....

    http://www.roadandtrack.com/auto-news/tech/modeling-formula-1-pitstop-strategy

    The intro has a link to another interesting DS story on "The gaming of F1". Enjoy!

    Cheers,
    Ian
     
  11. VIZSLA

    VIZSLA Four Time F1 World Champ
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    Gee zuss.
    On a Monday.
    Gimmee a break my head still hurts.
    :)
     
  12. Fast_ian

    Fast_ian Two Time F1 World Champ

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    :D

    I did warn you! :p ;)

    He also postulates that fuzzy logic could be a field for further "improvement" - Now there's a headache inducing area of study......

    Cheers,
    Ian
     
  13. VIZSLA

    VIZSLA Four Time F1 World Champ
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    All logic is fuzzy on Mondays.
    Most everything else is as well.
     
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  15. werewolf

    werewolf F1 Veteran
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    think of this :

    Two cars on the "starting line". All accelerations, and top speeds, are equal. One car starts 0.5 seconds after the other.

    What's the time difference at the "finish line"?

    EVERYTHING the first car does, the second will also do ... including crossing the finish line ... just 0.5 seconds later.
     
  16. Far Out

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    That's the point. You have to remember that you're talking about a distance in time, while you visually process a spatial distance. The latter may vary tremendously while the former stays constant.
     
  17. Fast_ian

    Fast_ian Two Time F1 World Champ

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    That's what I was trying to say! :) Thanks Florian ;)
     
  18. Far Out

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    An interesting talking point - in reality, fuzzy logic is dead. The only ones who still apply it are those who learned it during the fuzzy hype in the early 90s.
    That hype only came up because the thought behind fuzzy logic - to create mathematical methods which 'translate' fuzzy terms that humans can understand (like 'big' or 'small') into numbers - was pitched with the slogans that computers could now 'think like humans'.
    This was picked up by the mass media, and 'think like humans' (in a sense of 'process human terms') became 'computers are now conscious". And there was the hype.

    Compared to the expectations, fuzzy logic has found very few actual applications.
     
  19. Fast_ian

    Fast_ian Two Time F1 World Champ

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    +1

    I never said his postulation was correct though..... :) [This is from 2003 btw - Maybe there was still "hope", even then.....]

    Cheers,
    Ian
     
  20. Far Out

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    I of course never wanted to imply that you're a fuzzy fanboy! :D

    And while I'm ranting...


    ... game theory is another solution looking for a problem. At least in the technical area, I have yet to see an actual application that is not part of some purely academic construct.
     
  21. Fast_ian

    Fast_ian Two Time F1 World Champ

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    Damn, I'm beginning to regret digging it up! :D

    ;)

    Cheers,
    Ian
     
  22. Far Out

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    I hoped you'd come up with chaos theory now that I'm already in a rage! :( :D
     
  23. 410SA

    410SA F1 Veteran

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    As has been pointed out by others you are confusing linear distance (the gap between the cars) with linear time. Half a second in the overall sequence of events is half a second, no more, no less.
    You are talking about the first car moving away while the second car is stationary. What you forget is that for a period of time the first car was stationary while the second car was still moving toward the pit stop (effectively narrowing the gap), so whatever additional time the first car gained when it moved away, was initially lost when it came in for its stop. The net effect is that the first car gained only .5 of a second after both cars had come into the pits, stopped and then moved again.
     
  24. VIZSLA

    VIZSLA Four Time F1 World Champ
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    Much like two cars following one another around a circuit. As they brake and accelerate into and out of corners the gap in distance stretches while the gap in average speed remains constant.
     
  25. Far Out

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    If there is a gap in average speed, neither the distance in space nor the distance in time remain constant!
     
  26. VIZSLA

    VIZSLA Four Time F1 World Champ
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    Over the course of a lap there are increasing and decreasing gaps.
    The cars are hitting different (faster and slower) parts of the track at any given point in time but over a lap may equal one another in average pace ie; lap time.
     
  27. 410SA

    410SA F1 Veteran

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    Wow, you would be an interesting student in math class. Average is quite a simple definition. If both cars averaged the same speed over a lap, time and again, their average speed, and therefore the gap between them, would be constant

    The gist of it all is that if two cars in a race were lapping at the identical average speed per lap and the time gap between them at a particular point of the track, say the start/finish line, was 5 seconds, and then they both took a pit stop, where one took 3 seconds and the other took 3.5 seconds, then they resumed racing at the identical average lap speed, the gap between them, when they next crossed the start finish line, (after they both completed their pit stops), would be 5.5 seconds.
    It's really that simple.
     
  28. Far Out

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    Not average speed - a gap in average speed. If the average speed (integral( v*dt) / T with the lap time T) of car A is 150km/h and the one of car B is 160km/h, their temporal distance increases.

    Edit: Or is it possible that I'm nearing the limits of my language skills in terms of what 'gap' means? ;)
     
  29. 410SA

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    The initial poster did not refer to a gap in average speed, meaning a difference between the average speed of one car relative to another. The question assumed identical average speeds, therefore a constant time gap between the two cars at a particular point on the circuit where that gap was measured, and how that gap would change when another event occurred, a difference in pit stop times for both cars.
    Clearly, unless the cars were circulating at a constant speed, both the time and distance gaps would alter at different points of the circuit as the cars slowed and then accelerated to negotiate corners.
     
  30. Far Out

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    Yes, but I was quoting David, who was talking about... *drum roll*... a constant gap in average speed! ;)

     
  31. VIZSLA

    VIZSLA Four Time F1 World Champ
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    My English is worse than yours.
    By saying that the gap in average speed remained constant I was meaning to say that the average speeds (lap times) were the same.
    The point being that the physical gap between cars would vary as one sped up or slowed down for corners even if the total elapsed lap times were identical.
     
  32. Far Out

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    By our previous discussion I already supposed you wanted to say that, but the academic in me just couldn't let an imprecise statement left uncommented *sternly looking over the rim of my glasses* ;) :D
     
  33. kraftwerk

    kraftwerk Two Time F1 World Champ

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    Show some respect for your elders.......:D
     
  34. VIZSLA

    VIZSLA Four Time F1 World Champ
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    It's been a while since I've been taken to the wood shed.
    ;)
     
  35. Far Out

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    I thought you'd go there regularly with Steve... (cue Jane Birkin & Serge Gainsbourg!)
     
  36. VIZSLA

    VIZSLA Four Time F1 World Champ
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    I think that you're unfamiliar with the idiom.
     
  37. kraftwerk

    kraftwerk Two Time F1 World Champ

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  38. Far Out

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    Your chance to return the evil stare now! In a duet with Steve! ;)


    Back to topic, I find the idea of the article that Ian linked - the calculation of an optimal pit stop strategy - quite interesting, although I wouldn't do a Fuzzy approach. Is there any interest in discussing the topic in a more detailed matter? If yes, I'd dig out some lap time data tomorrow and sit down and think of how we could model it...
     
  39. VIZSLA

    VIZSLA Four Time F1 World Champ
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    Interesting turn that a "scientific" thread has taken.


    One of the first questions I have when watching a GP is what the pit delta is.
    That races are won and lost there is an old story but holds true.
     
  40. Far Out

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    Absolutely. And what I find rather problematic too is the importance of the order the pits are arranged in when it comes to the (necessary!) penalties for "unsafe release".
     
  41. VIZSLA

    VIZSLA Four Time F1 World Champ
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    Unsafe release?
    Is that code?
    :)

    This is a variation on the original question.
    Pit spaces are allocated by championship rankings.
    One end considered to hold an advantage over the other.
    But the total distance a pit stop covers is identical
    given the pit speed limit average speed (time in motion) should be the same as well.
    So what is the placement advantage?
     
  42. Far Out

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    The advantage - which I perceive, maybe it doesn't exist! - is when the team closer to the pit entrance is slightly faster. Not fast enough for their driver to 'regularly' overtake the other one, but enough for him to be already in the lane and thus forcing the others to hold their guy back if they don't want to risk the unsafe release.

    Edit: And I'm scared by the potential multiple meanings of "unsafe release" which you imply :eek:
     
  43. VIZSLA

    VIZSLA Four Time F1 World Champ
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    As the man taking the Rorschact test said. "but Doc, they're your dirty pictures!".

    ;)
     
  44. wax

    wax Three Time F1 World Champ
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    Simplify . . .

    1 car, not 2 cars.

    1 car, 2 pit stops.
    ________________

    Car pits for 3 seconds.

    Lap speed, momentum, inertia, gravity is maintained, etc.

    Car pits for 3.5 seconds.

    Lap speed, momentum, inertia, gravity is maintained equal to previous stop, etc.

    .5 second difference.
    _________

    Same thing if there were 2 cars.

    .5 second difference.
     
  45. VIZSLA

    VIZSLA Four Time F1 World Champ
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    Must be the variable gravity that threw us off :)
     
  46. Peloton25

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    If there is a treadmill in the pitlane can the cars still take off? :D

    >8^)
    ER
     
  47. VIZSLA

    VIZSLA Four Time F1 World Champ
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    Speaking of taking off.
    Given their level of grip why not run a race on a suspended track shaped as a möbius strip?
     
  48. Fast_ian

    Fast_ian Two Time F1 World Champ

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    A duet, or duel? :eek: ;)

    Sign me up! - It's a fascinating area for the geeks I guess! FWIW, my handy-dandy, super expensive timing app has all the data downloaded from the race. I'd need a lap chart to easily zoom in onto in laps etc, but reckon we've got a good starting place.

    I believe you're correct - Cars 1&2 always get the first box and it goes down from there. If I'm, say, #1 and you're right up my chuff on entry I stop before you, and hence get going again before you and can thence block your exit. [All else being equal of course.]

    Cheers,
    Ian
     
  49. 410SA

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    I think it depends on the track regarding the most advantageous spot. I believe the current championship team get to choose if they the want the first or last pit spot and everyone else goes from there in order of LY points
     
  50. Fast_ian

    Fast_ian Two Time F1 World Champ

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    For reasons I can't now remember, I do believe you're correct - IIRC, at least Silverstone (& Indy?) were set up that way.

    So, the question becomes, what's the advantage of doing it 'the other way'? If I'm at the far end, *and* I spend less time in the air than you, I can get out ahead. But, empirically, I still think I want to stop first and hence start first...... Does that change depending on the delta? ( I can't think why, but am going all Yoda on it now......)

    ..... Wheres Florian ;)

    Cheers,
    Ian
     
  51. TifosiUSA

    TifosiUSA F1 Veteran

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    This thread makes my head hurt ;)
     
  52. mousecatcher

    mousecatcher Formula 3

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    Yup, giving us the so-called (by SPEED anyway) concertina effect, where cars get spatially closer in braking, but not temporally (ie, time-wise, not a typo for temporarily) closer.

    This is a good time to mention the illusion of a car "pulling away" from another out of a corner. At 1m/s, a gap of 1s = 1m. At 20m/s, a gap of 1s = 20m. If 2 equally driven cars accelerate out of a corner at these speeds, the lead car appears to be pulling away but even though he is strictly maintaining a 1s gap, he extends the linear distance by 20 times! It's the reverse of the concertina effect and often gives a false impression to the viewer.

    As to the 0.5s thing, it's important to remember it's not just the time "in the box", it's the entire time in the pit lane that matters.
     

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