Brit1275
Active member
reposting again, because I am JUST that cool...
terrain park physics? that'd be a pretty weak senior project rowen.
everything follows a parabolic trajectory, with an initial given angle. Foward horizontal velocity is a constant, while vertical velocity follows the equation V=Vo+At where Vo is the initial vertical velocity, and A is the acceleration (-9.8 meters/second squared in this case). Those two velocities, can easily be calculated from the angle of trajectory. The vertical initial velocity is equal to the total initial velocity, say Vt, multiplied by the cosine of the angle, and logically, the horizontal velocity is just Vt times the sine of that angle.
Distance travelled can be calculated, by finding how long it will take for the skier to go up then down using the integral of the above equation for the vertical velocity, the integral will of course give you the position. You solve that for zero, to get the time in the air. Multiply that by the intergral of the horizontal velocity, and you get distance travelled.
As far as tricks go, all rotation takes place around the skiers center of gravity, and that is the point that follows the parabolic path. For all considerations, you can assume that all of the skiers weight acts at that single point (somewhere in your belly). By twisted your body above your CG before taking of, but having your feet on the ground, you incure a moment about your center of gravity, and once in the air, you continue to rotate until you land, in which the opposite happens, and your feet incure in effect a negative moment opposing your rotation.
Bam, your senior project is done.
-------------------
be aware, ski with care
terrain park physics? that'd be a pretty weak senior project rowen.
everything follows a parabolic trajectory, with an initial given angle. Foward horizontal velocity is a constant, while vertical velocity follows the equation V=Vo+At where Vo is the initial vertical velocity, and A is the acceleration (-9.8 meters/second squared in this case). Those two velocities, can easily be calculated from the angle of trajectory. The vertical initial velocity is equal to the total initial velocity, say Vt, multiplied by the cosine of the angle, and logically, the horizontal velocity is just Vt times the sine of that angle.
Distance travelled can be calculated, by finding how long it will take for the skier to go up then down using the integral of the above equation for the vertical velocity, the integral will of course give you the position. You solve that for zero, to get the time in the air. Multiply that by the intergral of the horizontal velocity, and you get distance travelled.
As far as tricks go, all rotation takes place around the skiers center of gravity, and that is the point that follows the parabolic path. For all considerations, you can assume that all of the skiers weight acts at that single point (somewhere in your belly). By twisted your body above your CG before taking of, but having your feet on the ground, you incure a moment about your center of gravity, and once in the air, you continue to rotate until you land, in which the opposite happens, and your feet incure in effect a negative moment opposing your rotation.
Bam, your senior project is done.
-------------------
be aware, ski with care