Calculating Stopping Distance

**uptpilot** · 01-14-2009, 11:36 PM

Hey guys. I have a bit of a research project I need help on.

I need to find a way to calculate the stopping distance required by my 2000 Toyota Celica from a particular speed. The closest thing I could find is this:

http://www.copradar.com/preview/redlight/index.html

My car doesn't have anti-lock brakes so that would need to be another variable in the equation. Here's some of the various factors that I can think of...

1) car's weight
2) braking pressure/force (how does one measure this?)
3) tire condition (how do you measure this?)
4) street coefficient of friction (how do you measure this?)
5) amount of reverted rubber on the road
6) car's hydroplaning speed
7) all above factors corrected for anti-lock brakes available or not
8) slope of road
9) ambient temperature
10) car's starting speed

I'd appreciate any inputs.

-UPTpilot

**bigscot** · 01-15-2009, 03:58 PM

Braking distance is one of those very interesting but a simple traffic flow and transportation engineering calculations. I am still digging around for my note from that class but as soon as i can find them i will help you with your calculation.

You also need to add reaction time to that list: usually assumed to be 2.5 sec (comes into to play with stopping distance do to object in the road)

**Machinehead** · 01-15-2009, 04:09 PM

Originally Posted by bigscot

Braking distance is one of those very interesting but a simple traffic flow and transportation engineering calculations. I am still digging around for my note from that class but as soon as i can find them i will help you with your calculation.

You also need to add reaction time to that list: usually assumed to be 2.5 sec (comes into to play with stopping distance do to object in the road)

Those calculations are based on certain assumptions, and are not vehicle specific, as they are based on a design vehicle.

**bigscot** · 01-15-2009, 04:24 PM

These kind of equation are one of the best ways to calculate breaking distance. These calculation are what determine how long yellow lights are and how fast a speed limit is set to. And the link he provide is the same equations i am looking at.

uptpilot what speed are you wanting to calculate for ?

**judoGTI** · 01-15-2009, 11:48 PM

Just go out and do it. It will take less time

**bigscot** · 01-16-2009, 01:34 AM

Ok to save time here is the equation and a pair of exsamples:

Braking distance:

D = U^2 / (30 ((a/g) +/- G)

Min distance to stop after seeing an object in the road:

SSD = 1.47 (u) t + D

u = Speed when you applied brakes in mi/h
g = acceleration of gravity = 32.2 ft/sec^2
a = assumed deceleration = 11.2 ft/sec^2
t = reaction time = 2.5 assumed
G = % grade / 100 (+ uphill /- downhill)

Say 55 mph on a level surface:

D = 55^2 / (30 (.35) ) = 288.09 FEET

SSD = 1.47 (55) 2.5 + 55^2 / (30 (.35) ) = 490.215 FEET

Say 90 mph uphill at 10% grade

D = 90^2 / (30 (.35 + .1 ) = 600 FEET

SSD = 1.47 (90) 2.5 + 90^2 / (30 (.35 + .1 ) = 930.75 FEET

**84RegalRider** · 01-16-2009, 01:35 AM

we assuming an even road?
flat or normal road?
holding the steering wheel or not?

and i hate red light cameras so much.
im always more worried about the light then watching the rest of the road.

**bigscot** · 01-16-2009, 03:08 AM

All this is based on AASHTO skid resistance pavement design.

the levelness of the road is taken into consideration in the equation. G = % grade / 100 (+ uphill /- downhill)

yes we are assuming a normal not perfectly flat road. If you look at a cross section of a road the middle is almost always high to force water off the roadway.

Do you really remove your hands from the wheel every time you break? If so what state do you live in so i can stay out of it.

**84RegalRider** · 01-20-2009, 02:18 AM

what about condition of the pads and rotors? any warpage?
what about luggage too?

**Machinehead** · 01-20-2009, 12:06 PM

The calculations that bigscot is using make a number of assumptions to come up with a value. That value tends to be very conservative. Considering what's being calculated (stopping sight distance, or the distance required to come to a stop before reaching a stationary object suddenly appearing in the roadway) and the assumptions being made (friction, vehicle weight, driver reaction time, etc.), I'm certain there's a decent factor of safety associated with that calculation.

For a baseline average number, the AASHTO calculation is a quick and easy starting point. If you want an actual vehicle specific analysis, it's a lot more involved.