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The Math Is Simple After reading the TIP entitled You Only Hit The Car If You Don't Quite Stop In Time a person sent me a gentle critique of it as follows: The general points you make are fine but I think you might want to check your math.. Traffic Engineers have some rules-of-thumb they developed over time. They, for example, have found that if the street surface is dry, the average person can safely decelerate an automobile at the rate of 15 feet per second (fps). That is, an average person can slow down at this rate without any real likelyhood that they will loose control in the process. The measure of velocity is distance divided by time (fps). The measure of acceleration (or deceleration in this case) is feet/sec/sec in the units you chose. I believe he was trying to be helpful and was not just taking shots. As to the measure of deceleration being fpsps rather than fps, I take no issue with that. My article said that you could '... decelerate .. at the rate of 15 fps' , but I think it is clear from the context that what I was saying was that regardless of the velocity, say it starts at 88 fps, you could scrub off 15 fps every second. ie, after 1 second your velocity would be 73 fps, after 2 seconds it would be 58 fps, etc. For the mathematically inclined it would have been more accurate to say 'fpsps' rather than 'fps', but possibly more confusing to some. He went on to say: It would mean that you could stop your motorcycle in a total of 5.4 seconds (including the 1 second delay.) and your total stopping distance would be only 281.5 feet! If you'll look at any road test of a current production motorcycle you'll see that stopping distances from 60 mph are typically 120 - 140 feet. Cages are frequently in the 150 - 180 foot range. As to his suggestion that I recheck my math, I did, and obtained the same results. So that there is no confusion, my message argued the point that by increasing your braking skills you could significantly reduce both the time it takes to stop and the distance taken to stop your motorcycle. Further, though I acknowledged that a motorcycle racer could get 1g deceleration (32 fpsps), or more, a reasonably skilled rider could easily get deceleration rates in excess of 20 fpsps. And, by contrast, showed what Traffic Engineers use as an assumption of safely attainable deceleration rates by the average person (15 fpsps). So, I was not saying that you should (or can) try to get 1g deceleration rates, but that you can and should get much better braking (safely) than 'average' with just a little practice. As to the numbers: To determine how long it will take you to stop assuming a constant rate of deceleration, you need only divide your starting velocity (in fps) by your rate of deceleration.
Assuming a deceleration rate of 32 fpsps (1g), we calculate a braking stop time of 2.75 seconds (88/32). Distance traveled now is calculated to be 121 feet. (Ignoring the additional 88 feet you traveled before applying your brakes.) This is consistent with published reports, as he presented them. The math is easy, the message is too - Skillful braking can save your life. For those of you that are into math, I full well realize that I used an approximation for distance traveled when I simplified my formula and assumed an 'average speed'. Since the correct formula which would take the deceleration rate into account is beyond some of the readers, I chose to make it simple - because the message is also simple. (Besides, it yields the same answer.) If you are interested, to calculate the distance using deceleration rates you would use: x = x0
+ (v0 * t) - (1/2 * a * tē) Return |
