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Math Help - exponential acceleration factor in a model

  1. #1
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    exponential acceleration factor in a model

    I'm not sure this is in the correct area of the forum, so if not then please inform and I'll repost there.

    As you can tell i'm not really a Maths person, so any help gratefully received.

    I have attempted to model the curve of the relationship between v1 and v2, please see attached.

    The bold cells refer to the inputs of the model.

    We know that the optimal relationship between v2 and vavg is 1.05, as well as the values for d and t. We also know that v2 decays exponentially from a absolute maximum value of 21.496 as v1 increases.

    So you will see that in order for the curve of v2 to start at 21.496 and decay to the point where v2/v1=1.0625, I have used what I have called an "acceleration factor", which starts at v1=1 at a value of 1.0000000001 and exponentially increases the prior integer value of v1 by ^ acceleration factor.

    So, I am wondering how I can improve this to more acutely describe the relationship?

    I appreciate that I probably haven't described my goals or some of the constraints very well so please ask me if anything isn't clear.

    Thanks for any help!

    v1v2 model.xls
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  2. #2
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    Re: exponential acceleration factor in a model

    More acutely describing the relationship I mean there must be a better mathematical way of increasing the acceleration factor than by using the prior integer value ^ acceleration factor?
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  3. #3
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    Re: exponential acceleration factor in a model

    Probably someone brighter than I will find this comprehensible, but I am lost.

    You say that you "know" there is an exponential relationship between $v_1$ and $v_2.$ How do you know that, empirically or theoretically? If theoretically, what is the theoretical relationship? You say the bolded figures are the input. Does this mean that you have an empirical observation, but only one? If you have a valid and complete theoretical relationship, why bother with empirical data at all? If you have a theoretically valid relationship dependent on some parameters that must be determined empirically, how many such parameters are there and how do they fit into the theoretical relationship? Why do you restrict $v_1$ to integer values? Are you trying to find the optimum value for $v_1$ or a relatively exact numerical relationship between $v_1$ and $v_2$ over all feasible values of $v_1$?
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