hillbomber said:
Ok, tired of looking thru google and not finding what I'm after. I'm looking for the formula/s that would be relevant for downhill skateboarding. I know the basic of speed=distance divide by time and the formula for finding grade, but what I'm trying to find out is what would be one's average speed on an hill. Example:distance of road, ft. drop between elevations, weight of rider. (1.5mile, 555ft btwn elev,200#) I would like to have this one handy, so I can find out what speeds one could achieve on various roads. I'm also putting a graphics package together and would like to include formulas that are relevant to downhill skateboarding.
Any help would be very much apperciated!
Thank you
ok so the important quantities here are:
distance: 1.5 miles
change in height(y): 555ft
weight: 200lbs
im going to assume you want to take the hill to be a perfect triangle. to solve for the angle of the hill, you need a relation between the change in altitude and distance.
in this case: y=555ft and the hypotenuse is 1.5mile
note: convert to one distance measurement before computing
now we can find the angle through sin(\theta)= \frac{y}{hypotenuse}
from the same properties of the triangle, the effective force and acceleration can be deduced. being on an incline, there is a component parallel and perpindicular to the hypotenuse of the acceleration. we are concerned with the parallel acceleration. first, find the force down the incline:
ma_{parallel}=m a_{g}sin(\theta)
where the quantity ma_{g} is the force of gravity, or the weight
now that you have the acceleration, you can find the time it took to go down the hill:
d= v_{i}t + \frac{a_{parallel}t^{2}}{2} where d is the hypotenuse distance(1.5mi), and vi is youre initial velocity(0 if starting at rest)
and then its just a simple v=d/t to find average velocity
MAKE SURE ALL YOUR UNITS ARE IN THE SAME SYSTEM AND MAGNITUDE.
i can't stress that enough or your values will come out very differently