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Initial Velocity before impact

  1. Dec 29, 2013 #1
    HI gurus

    I have found helped on this forum, that I am trying again.

    I would like to know the steps I should follow in other to find the following

    I would like to find out how fast a car was going before impact, if after a T collision one of the car steer right and stop at 8 Meters from the initial impact

    1) there is no skid mark as car A did not apply breaks
    2) Car A steer right and stops 8 meters from the initials impact.

    is it possible to find out the speed of car A before the impact by having only the weight of the two cars and the distance that a car kept going after stopping.

    I know is asking a lot but I have been reading and reading and it seems like conservation of momentum is one way but I dont know for sure

    1) I would like to know the method you guru would follow to determinate this problem
    2) I would like to know the steps you would follow
    3) I would like to know the physics equation you would use.

    so would you please take the time to walk me through this steps.

    Thanks a bunch
  2. jcsd
  3. Dec 29, 2013 #2

    Simon Bridge

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    We can figure out how fast car A was going after the impact assuming a constant breaking and knowing something about the state of the road.

    Crash investigators use ballpark statistics for the road surfaces and the types of cars, tires etc.

    Depends on how much I was being paid ;)

    I wouldn't just use one - but it would basically be conservation of momentum - taking into consideration details of the crash site and conditions. It's not a simple process.

    Anyway - what you seem to have described is car A collides with the side of car B, and then steers to one side and parks. Presumably the impact pushed car B to one side? I'm guessing car B was also rotated by the collision... was car B stationary before the collision? Was car A stationary after the collision or was the deflection due to the collision rather than to deliberate steering?
    Last edited: Dec 29, 2013
  4. Dec 30, 2013 #3

    Thanks for jumping in and happy holidays
    car A was moving straight line , car B was moving perpendicular , car A hit car B on the driver side -|, car B rollover once and stop on its side car A steer right and stopped 8 meters and I take the deflection was due to the collision from the initial impact but hard to tell if steer accurred on car A trying to avoid the collision. can you tell from this what was the speed of car A.

    how would you go on finding this
    1) conservation of momentum
    2) next step like find the impulse
    3) next find the Kinetic energy.

    I know is a lot of work, but I was hoping to get the steps you would take to resolve this issue
    like I mentioned above.

    I am not a physic as you can tell,just looking for some help.

    Thanks a bunch chief
  5. Dec 30, 2013 #4

    Simon Bridge

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    After the collision, unless the driver was unconscious, it is certain that the brakes were applied and that steering happened. These are reflex actions and make it difficult to work out what comes from the crash and what doesn't.

    If I assume the driver braked from the instant of the crash, ignore the deflection, coming to rest in 8m on dry bitumen suggests a speed after the crash of 40kmph. But I suspect that some of that distance was actually on the verge of a road - grass or gravel?

    Car B rolling over twice is good - I can get a lower-level from that
    Did this happen on level ground? Did it flip twice in the air or roll over the ground?
    Did car B also rotate horizontally due to the collision - or did car A strike through the center of mass?

    The energy to roll the car over slowly is that needed to lift it onto each corner in turn ... there will also be energy losses from the collisions with the surface as it rolls which would need to be estimated. The exact calculation depends on the shape of the car.

    But you may just need to know if car A was travelling at a legal speed?
    In which case, you just need to see if the legal speed limit minus 40kmph has enough kinetice energy to flip the car once.

    Now there is an issue that comes up - if this is related to legal claims of any kind - I cannot help you.
    You need a certified expert on crashes. These guys also have a lot of data to throw at the problem.
  6. Dec 30, 2013 #5


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    Also, note that just because there isn't a skid mark, it doesn't mean the car didn't apply brakes. It just means the wheels weren't skidding. You can be braking quite hard, and still not be skidding the tires.
  7. Dec 30, 2013 #6

    That is the part I would lke to learn, what did you use to get to 40kmph( formula)
    car B rollover once on ground
    scenario down slope not to stip
    car A strike on driver side between doors

    I would like to know car A velocity at impact to cause a car B to rollover once and for car A to stop at 8 meters with almost to none data. well I see it that way, is like too much information is missing

    No claim of any kinds, just trying to learn about collision and how this aftermath event can be resolved by physics, this experts has to use the same methology and formulas used by physics.

    Thanks a bunch shimon and cjl for battling with me here. I know is time comsuming

    Happy new year anyways gurus
  8. Dec 31, 2013 #7


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    as Simon said above .... that's the real problem

    this topic comes up in the forums every couple of months or so. And the final answer is always the same.

    There's just too many variables for some one not directly involved with the particular incident, and skilled in dealing with such situations, that real answers just cannot be given.

  9. Dec 31, 2013 #8

    As stated , I have no claim pending at all but my own curiosity on how this expert get to their conclusion using physics, I have learned that there is a methodology in physics, and that is the part that I am trying to understand. for every event , there is a series of first,second and third phases that contribute to the end result, that is what I am looking for help with, just a ball park.

    for collision( a physics event), you should look for this variables and a set of methodology should be follow. but I could be wrong all together.

    Thanks again gurus
  10. Dec 31, 2013 #9

    Simon Bridge

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    You can model the car as a sliding block - in general:

    tldr: initial speed v from slid-to-stop distance d is given by ##v^2=2\mu g d##.

    The CI calcs look like this:

    Notice - this assumes sliding - very common in an accident, but the vehicle may, for instance, be fitted with anti-lock brakes so the wheels may not have locked up.

    good - you can try modelling the car as a rigid box to get a first approximation.

    "not too steep" is not scientific - give an approximate grade. We are not doing this for a court now, just demonstrating the process.

    That's right - it is very common that we start out with too little information. CIs usually visit the location and examine photographs so they can collect data.

    I'd always start out with some oversimplification and a bunch of statistics for similar circumstance crashes... the result of the resulting ball-park (called "back of envelope") calculation tells me what sort of information to look for first.

    Mostly what I do is look for reasons not to believe the initial calculation.
    So I assumed a dry bitumen road ... if it was wet, then the speed was lower, if it was gravel then the speed was higher. When I find them - notice that is "when" not "if" - I have to modify the calculation. Sometimes that means doing an experiment.

    The simple model for rolling a car goes like this:
    Model as a block ##w## wide and ##h## tall, length does not matter, the center of mass starts ##h/2## above the ground ... to roll it on it's side you have to lift it $$\Delta y_1 =\frac{1}{2}\sqrt{h^2+w^2}-\frac{h}{2}$$ ... it falls the rest of the way by itself so the next time rolling it takes energy away is from the side to the roof which is ... $$\Delta y_2 = \frac{1}{2}\sqrt{h^2+w^2}-\frac{w}{2}$$ ... rolling from the roof to the other side is the same as Δy1 and back to the wheels is the same as Δy2 ... so the minimum incoming kinetic energy to do that is 2mg(Δy1 + Δy2 ) ... so if ##u## is the speed after the crash and ##v## is the speed before the crash:

    ##mv^2 = 2Mg(2\sqrt{h^2+w^2}-h-w)+mu^2## ... for a very rough figure.

    m is the mass of car A and M is the mass of car B.

    It helps to be asking/answering a specific question. i.e. is the data consistent with car A travelling less than 100kmph (maybe that's the posted speed limit and it's a X intersection?)

    I did not notice information about what sort of cars they were ... so, until I know I'll pick a representative car:

    A 1998 Ford Fairlane has about 1700kgs and is about 1.4m tall and 1.6m wide.

    Plugging in the numbers for the described collision between two of them gives me about 46kmph ... so I can answer the question with a "yes" even if I am too slow by 100%.

    "The data provided is consistent with a solid T-impact between two similar cars at 50kmph."
    ... would be a preliminary, tentative, conclusion.

    Though I'd note that I'd really expect that the cars just slide and rotate a bit, and there are a lot of wand-wavey things going on. See? I can't stop thinking up ways I could be wrong.

    Disclaimer: this calculation is for demonstration purposes only - do not take this result as definitive or accurate or etc etc you get the idea. Actual crash investigations would use more information.
  11. Jan 2, 2014 #10
    Thanks a bunch and happy new year , you guys are INSANEEEE in the good sense of the word.

    Thanks again guys
  12. Jan 2, 2014 #11

    Simon Bridge

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    No worries.

    One of the caveats is that in order to roll a car like that, there needs to be some upwards directing nature to the collision i.e. if the rolled vehicle has a high center of mass.... in general: if you just push a car from the side with another car, it will slide, not roll.

    I don't have data to figure that.
  13. Jan 2, 2014 #12
    car A was a jeep grand Cherokee and the car B a jeep liberty.

    after reading all help here, I take car A by going 45-47 MPH had enough mass and energy to make car B to rollover at initial impact.

    Thanks a bunch shimon for your time , help and patience.
  14. Jan 2, 2014 #13

    Simon Bridge

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    Yah - it's just a matter of how the energy was directed.
    Jeeps have a high-ish center of mass don't they?

    A: JL 1.8m wide, 1.8m high 1800kg
    B: JGC , 2.2m wide, 1.8m high, 1700kg

    It looks like the front bumper of A would hit slightly under half-way u, and the JGC is quite wide...
    If the wheels do not sideways - the the angle to the road tells us something about how much of the impact energy got channelled into the road and how much went into turning it over.

    E=p^2/2m ... where p is the momentum delivered to car B.
    0.8m off the ground, pivoting about the far wheels ... 2.2m away ... that makes an angle arctan(0.8/2.2)~20deg
    so p.sin(20) is how much momentum goes into the rotation.
    We'd call this the specific impulse for the collision and assumes that all the energy to roll over was delivered within the first second or so. Certainly these vehicles have the power and torque to shove each other around at quite low speeds.

    sin(20) is about 1/3 ... so the value may be underestimated as much as three times!

    See what new data does?
    You'd have to go back and crunch the numbers - but if you witnessed the crash, you should be able to tell what feels right ... did it look like the GL was going very fast?

    Looks like the bumper would hit slightly below the com.
  15. Jan 3, 2014 #14
    I know my man, but you all are the gurus, this is just INSANEEE to me that you gurus can get to this observation and use physics to estimate what could happened. after reading all this I will get my a@# in gear and learn a little bit more now that I know , a little more than yesterday.

    Momentum/kinetic energy all that good stuff

    Thanks again shimon for taking the time to an eye opener experience.

    I saw it all, after making sure all passengers, where ok, I thought it was cool and then I started this journey, to understand what happened and how a JGC which was car A and hit the JL that turned left on car A's ways could have rollover a car just by going 45-48 max, hard to tell because I have no training in speed estimation, but for sure was not doing 50-60 miles an hour,so this is why I took upon myself to learn a little bit more about this scenario that you gurus handle so well.

    TO me an ordinary human being is hard to see how a car (car A) can rollover another car (car B) by just doing 45-48 MPH, it seems like too slow for that scenario

    Last edited: Jan 3, 2014
  16. Jan 3, 2014 #15

    Simon Bridge

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    Well car A can certainly push car B sideways ... rolling it over requires something stop the tires from sliding: say it hits the curb.
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