Wednesday, September 16

Caution - Science Content

Mostly, overtaking traffic makes a lane change to pass me long before the motorists get close. However, I’ve noticed that there seem to be a lot of distracted drivers out there. What does it mean if, despite a cyclist being right out front and center, a zoned-out driver doesn’t react until the last possible moment, and then just slams on the brakes? How close is “almost too late?”
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Assuming a panic deceleration of 0.7g in dry conditions (not today) for a competent, but not trained, motorist (my Jaguar does better), here are the results:

Derivation of the Table
Let’s assume, for the sake of simplicity, the cyclist keeps riding at a steady speed, (ChipSeal School of Italian Riding; described here). On the other hand, the texting motorist reflexively jams on the brakes of his/her Cadillac Escalade at the very last moment, and makes a “near maximum” deceleration.

The cyclist travels a distance:

VC*t = DC

where

.......................VC stands for the velocity of the cyclist
.......................t is the duration of the incident
.......................DC is the distance the cyclist travels during the incident
.......................* is a multiplication symbol

For a collision to be avoided, the motorist must travel no more than DC plus the following distance (FD) when the stop was initiated before the auto’s speed drops below the VC.

Assuming a constant deceleration, the motorist travels a distance of:

VM* t – ½ a* t*t = FD + DC

where
.......................VM is the initial velocity of the motorist
.......................FD + DC is the distance travelled by the motorist before a collision nearly occurs
.......................a is the braking deceleration slowing the Escalade down

and finally, as things progress to a conclusion, the motorist’s speed is given by:

VM – at = VC

The last possible moment to decelerate occurs when the motorist travels FD + DC with a final speed exactly equal to VC, all as shown in the three equations above. And that, my friends, after substituting everything in and solving, is what leads to the table.

Run Your Own Combinations
You can replicate the results in the table, as well as try other combinations yourself via the calculator, shown here. Just enter the amount of speed the car has to slow down rather than the total speed to see just how close that bugger can get and still not actually run the cyclist over. For example, if the cyclist is going 12mph and the motorist is going 39, enter 27 into the calculator. Or use the formulae above and create a little Excel spreadsheet.

2 comments:

Chandra said...

Nice Math! I haven't seen equations like these ever since Physics class in High School.

I am curious why you t square as t*t instead of t**2.

Peace :)

Steve A said...

I'd already defined "*" but not "**"

^ would also have worked. Superscipts are hard in html.

I was a little surprised to see just how close a motorist can be before applying the brakes. It explains why cyclists mainly only get hit from behind if they escape notice entirely. It also says; if you are going to be a salmon, be a SLOW salmon!

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