# Formula's relevant for Downhill Skateboarding

1. Jan 13, 2009

### hillbomber

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 acheive 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

2. Jan 13, 2009

### SmashtheVan

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 cant stress that enough or your values will come out very differently

3. Jan 14, 2009

### rcgldr

The forward force is your weight (gravity) times sin(angle of road from horizontal). The opposing backwards force is aerodyanmic drag and rolling related resitance and friction in the skate board. The two extremes are zero mph on a level hill, and about 125 mph straight down (assuming zero rolling resistance here - as in sky diving).

4. Jan 15, 2009

### Chuck St. Lou

What Jeff said about wind resistance and friction is going to affect your findings a great deal. And that will change a bit from person to person.
What your going to find out is that at an incline of 4 degrees for example, you'll accelerate and it's going to take you so much time to hit top speed (terminal velocity) and after that you'll just maintain velocity. To get a close approximation calculate the slope of different hills and time yourself or use a hand held speed indicator as you go down and measure how far you have to go to hit terminal velocity. With the results you could plot a graph.