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Math Help - Building the ideal snowboard jump/landing ramp

  1. #1
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    Building the ideal snowboard jump/landing ramp

    I'm anticipating a good winter this year, one with lots of snow. My yard is sloped quite a bit and it would be the ideal place for a huge snowboard jump, only problem is I need to calculate how fast I will be traveling when I hit the jump, how high and what angle the jump should be, and the distance and angle of the landing ramp to optimize my range. Here's what i've got so far:

    From objects near my house and yard I calculate that from the top of the hill to the point where the jump would be is a distance of 103ft with an angle of elevation of 6.7 degrees and a height of 12.2ft, it doesn't sound like much so I want to solve the general form of my equations to be able to adjust the figures, like adding a launching ramp at the start to get more speed, adjusting where on the hill the jump is, etc.

    I believe that the major forces acting on me and the board are weight, drag between my board and the snow and possibly aerodynamic drag when I'm in the air. I found an approximation for a coefficient of drag to be 0.04. I am going to start by creating general equations for the final speed I will be traveling at the start of the jump and possibly make a computer model to do the aerodynamic forces etc.

    Does anybody see any forces that I am missing because it would be crucial not to under-calculate drag?

    I'm looking at my diagram and it seems just like a box sliding down a ramp. Any suggestions?
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  2. #2
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    Jan 2010
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    Quote Originally Posted by gtozoom View Post
    I'm anticipating a good winter this year, one with lots of snow. My yard is sloped quite a bit and it would be the ideal place for a huge snowboard jump, only problem is I need to calculate how fast I will be traveling when I hit the jump, how high and what angle the jump should be, and the distance and angle of the landing ramp to optimize my range. Here's what i've got so far:

    From objects near my house and yard I calculate that from the top of the hill to the point where the jump would be is a distance of 103ft with an angle of elevation of 6.7 degrees and a height of 12.2ft, it doesn't sound like much so I want to solve the general form of my equations to be able to adjust the figures, like adding a launching ramp at the start to get more speed, adjusting where on the hill the jump is, etc.

    I believe that the major forces acting on me and the board are weight, drag between my board and the snow and possibly aerodynamic drag when I'm in the air. I found an approximation for a coefficient of drag to be 0.04. I am going to start by creating general equations for the final speed I will be traveling at the start of the jump and possibly make a computer model to do the aerodynamic forces etc.

    Does anybody see any forces that I am missing because it would be crucial not to under-calculate drag?

    I'm looking at my diagram and it seems just like a box sliding down a ramp. Any suggestions?
    Hi gotozoom, did you ever get any responses to this? I haven't yet found any other resource on the internet that helps.

    I'm currently working out the same problem for my son. I've done the basic math for a simple slope with ramp ignoring any resistances.

    Basically I used a quadratic equation to solve T, the time between leaving the jump and impacting (!) the slope, staring from three relationships - between height 'fallen' and time, between distance jumped and time and between height 'fallen' and distance. I still need to calculate the length of run up and adapt the computation to allow for an upward take-off... (including any deceleration from the ramp).

    Later I'll be looking to add some models of different jump layouts and to start taking in wind and snow resistance.

    = M =
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