OK, vertical velocity appears to be calculated using the same sine function on the angle of the incline, which is logical!
Vvert = velocity * sin(8)
so at, say 50.4 kph velocity is 14 m/s and vertical velocity on a 14% slope (8 degrees) is 14 m/s * 0.139 so Vvert = 1.946 m/s
On a 8 degree (14%) slope, an initial velocity of 50 kph (14 m/s), or 1.946 m/s vertically, would decelerate at 1.365 m/s/s and come to a halt in 1.387 meters or about 4.5 feet!
Even at 80 kph it would only take 3.3 meters, or about 10.8 feet!
A brick wall!
Sounds like bkool have decided to go for a much more realistic model...
Geoff
Your right Geoff, I have go my % and degrees mixed up.
14% is 14 up for 100 along therefore 14/100 Tan slope
= 0.14
therefore slope = 8% as stated
Sin 8 degrees is 0.139 also as stated multiplied by 9.81 is 1.36359 (m/s/s) pretty much as stated
50 kph (30 mph ish) is 13.88 m/s (close enough to 14)
But think this is either the acceleration or deceleration of an item along the slope not in the vertical
i.e. as you approach the vertical your acceleration/deceleration approaches 9.81 m/s/s in the vertical
Using this simple rule and object dropped would reach 13.88 m/s in about 1.5 seconds, on an 8 degrees slope it will take considerably longer as would the opposite deceleration going up.
So at a deceleration of 1.36369 m/s/s with an entry velocity of 13.88 m/s you would come to a halt in 10.18 seconds
Some 4 seconds more than I calculated for a 14 degree slope which is pretty much in proportion
Coming to a halt in 4.5 feet is less than a bike length which would throw you over your handlebars.
Also I think if this was the case skate-borders would never get up the other side of the ramp/tube whatever they are called.
The distance traveled in this time is = v1t+1/2at squared
=13.88x10.18+(1/2x-1.36369x10.18x10.18) meters
=141.3 - 70.66
=70.5 meters roughly
Probably didn't need to do all that because it was always going to be half of the area of the entry speed x time assuming a straight line deceleration to zero
Now if I go 70.5 meters along and 8% climb, how much have I climbed vertically = sin 8 degrees (= 0.139) x hypotenuse (= 70.5) = 9 .8 meters vertical
The general stopping distance for a car using brakes from 30 mph, not including thinking distance is 14m