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Help calculating the G-Force in a corner

  1. Dec 10, 2013 #1
    Hi, I recently got a red light ticket for supposedly running a left turn and I wanted to try to fight the ticket. The officer told me I took the turn at 40-45 mph and then immediately wrote down 45-50 mph on the ticket. In one of my arguments, I want to try to prove that my car can't execute a left turn at 47.5 mph.

    I am an econ major so I thought I could use the help from you physics guys. If I know my speed
    (47.5mph) and radius of the turn, is it possible to show the amount of g-force experienced in the turn and then compare it again skidpad tests from lets say, road and track?

    Or is it possible to show the load on my tires from taking the turn at that given speed?

    I appreciate all input.

    Thanks again for reading my post!
  2. jcsd
  3. Dec 10, 2013 #2


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    $$a=\frac{v^2}{r}$$ where a is the acceleration, v is your velocity and r is the radius. Divide a by g to get the value as multiple of g.

    r could be tricky to evaluate, but at least a minimal r could be possible.

    The units are much easier to handle in metric units...

    That could be more tricky, as forces are distributed over 4 wheels.
  4. Dec 11, 2013 #3


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    Very few intersections are large enough to allow a left turn to be taken at 45 mph to 50 mph, even in a sports car with sticky tires. You didn't mention how large the intersection is though. An estimate of the radius would be from a bit inside the curb on the left (the intersection of crosswalks if there are crosswalks on that corner) to the center of the lane you started your left turn from.

    Although some cars can pull 1 g in turns under good circumstances, a street car is probably pulling between .6 to .8 g's in a turn. As mentioned acceleration is v^2 / r. To convert this into "g's" of acceleration (can someone check this math please?):

    g acceleration = ( (v mile / hour ) (5280 feet/mile) (1 hour / 3600 secs) )^2 / ( (radius (feet)) * (32.174 feet / sec^2)

    g acceleration ~ = speed^2 * 0.067 / radius

    Example, 30 mph with a 75 foot radius turn would be about .8 g's.
  5. Dec 11, 2013 #4
    Thanks, I really appreciate you guys getting back to me so quickly.

    I went on google maps and measured the distance and it looks like the distance is rougly 68 feet to the inside of the crosswalk on the left and from that point its about 55 feet to where I completed the turn.

    Since the radius is not the same from where I started the turn and where I ended the turn, would it be okay to take the average of the two distances?

    Thanks again guys for taking the time to help me out!
  6. Dec 11, 2013 #5


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    You could take somewhat of a "racing" line to increase the radius, but 65 feet would be a conservative estimate. With that radius, 30 mph would be almost .93 g's, possible in a sports car.

    45 mph to 50 mph is way too fast, but it wouldn't be the first time that a cop's estimate of speed was way off. It would be possible to be approaching the turn at 45 mph or so and then braking hard to 30 mph or so to make the turn, but a street car could not take a 65 foot radius turn at 45 mph.
  7. Dec 11, 2013 #6
    And did you?

    This thread screams 'got busted, help me weasel my way out of my ticket on a technicality'.
  8. Dec 11, 2013 #7
    It appears that the ticket is for running a red light, not speeding, as xxChrisxx said. The judge will not care how fast you were going, only that you didn't stop for the red light...which may only be the officers opinion, but their opinion will carry far more weight than yours. The officer is likely to state that you entered the corner at 45 mph and made the turn while braking...which totally changes your equation and is easily within the realm of possibility. Your best hope is probably that the officer doesn't show for court. 'He said - she said' will likely not end up in your favor without visual evidence. Sorry....been there and just paid the ticket; it was yellow! 8)
  9. Dec 11, 2013 #8
    Yeah I understand where you are coming from but the other part of my arguement is that the road was just freshly repaved and they had not yet painted on any road markers so we'll see if its enough to sway the judge.

    Anyways, I appreciate everyones input. It's tomorrow morning so wish me luck! haha
  10. Dec 11, 2013 #9


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    That is true so far as passing physics exams is concerned, but a bit of practical experience (and/or watching some TV or videos) of fast cornering shows at least two limitations so far as the OP is concerned.

    The angular velocity of the car around its own center of mass is not necessarily the same as its angular velocity around the curve; and the front and rear wheels are not necessarily pointing in the same direction, and sometimes not even close to the same direction.

    But if the basic offense was jumping the red light, the actual speed is fairly irrelevant anyway.
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