Ke = ½M x V² From Newton's laws of motion.
f = Frictional Resistance
F = Force to pull
W = weight of object pulled
So f = F ÷ W
(Expressed as work)
Ke is also = Weight · frictional resistance · distance or W f d
M (mass) = W (weight) ÷ g (gravity)
1) Ke = ½M x V² = W f d
2) Ke = ½ · (W ÷ g) · V² = W f d
3) Cancel weight (W) by dividing both sides of the equation by (W)
½ (W ÷ g) · V² ÷ W = W f d ÷W
After doing the math leaves
V² ÷ 2g = f d
This is the reason Weight has no effect on the Skidding distance of a vehicle.
4) Isolate V² multiply both sides by 2g
V² ÷ 2g · 2g = 2g · f d
After doing the math leaves
V² = 2g · f d
5) Substitute the value of g (g = 32.2)
V² = 2 · 32.2 · f d
Do the math.
V² = 64.4 · f d
6) There are 5280 feet in a mile and 3600 seconds in an hour. So 5280 ÷ 3600 = 1.466
Convert V (velocity) to Speed (S). V = S · 1.466
(S · 1.466)² = 64.4 · f d
S² · 2.149 = 64.4 · f d
7) Isolate S² and divide both sides by 2.149
S² · 2.149 ÷ 2.149 = 64.4 f d ÷ 2.149
After the math leaves
S² = 29.96 f d
8) Square root both sides
Since sq. root is the inverse operation of sq. you're left with
This is rounded to
(N) For braking factor is added to compensate for tires that my not have received full braking.
Which leaves
G.Nations 09/97