2WheelR wrote:
> Dr Engelbert Buxbaum wrote:
>
> We've already calculated that I came to a stop to turn a solid 11
> seconds before he even _arrived_ at the intersection. Let's visualize 11
> seconds.in that time, someone travelling 25 mph (which I'm guesstimating
> based on what I saw and what I know about that stretch of road, which i
> ride every day) would have about 400 feet to slow down for my already
> stopped car. thast's not cutting someone off, unless they are a
> freighter, or perhaps a barge.he was neither, though he mave have been
> dingy.
Let's do a little physics here.
You were going at, say, 50 km/h (about 30 miles/h, 13.89 m/s) and
decelerating to a stop over 400 m (about 0.25 miles).
Assuming a constant deceleration, s(t) = s(0) + v(0)*t + 1/2*a*t^2 (eqn
1) and v(t) = v(0) + a*t (eqn 2).
With s(0) = 0 m, s(t) = 400 m, v(0) = 13.89 m/s, v(t) = 0 m/s we can
calculate t = 57.6 s for you to reach the crossing and a = -0.241
m/s^2.
The cyclist was doing, say, 30 km/h (19 miles/h, 8.33 m/s).
The law requires a safety distance of half the speed in m, so you needed
to start passing before you approached the cyclist to 25 m, and you
needed 15 m distance after passing him. With 2 m length of the cycle,
that makes a distance of 42 m covered during passing, _relative to the
bike_ (that is in a moving coordinate system with the bike at the
origin). In this coordinate system you had an initial speed of 20 km/h
(50-30), or 5.56 m/s.
With s(0) = 0 m, s(t) = 42 m, v(0) = 5.56 m/s and a = -0.241 m/s^2 we
can calculate from (eqn 1) the time required for passing. Since this is
a quadratic equation, we get two possible solutions, 9.57 s and 36.6 s,
respectively.
Returning to a geostationary coordinate system we can calculate what
distance you covered in the real world during that time, using eqn 1
again. The results are 122 m and 347 m, respectively.
As you can see, in the worst case scenario you needed 347 m out of the
available 400 m to legally pass the cyclist. This left the cyclist 53 m
to brake from full speed (8.33 m/s). This requires an acceleration of
-0.654 m/s^2 and takes 12.7 s. Thus the cyclist would have had to brake
almost 3 times as hard as you, despite having worse brakes.
Now lets check how much time it would have required you to stay behind
the cycle instead of passing. You were going at 13.89 m/s, with an
acceleration of -0.241 m/s^2. When would your speed have dropped below
that of the cyclist (8.33 m/s)? Eqn 2 yields 23.1 s. During that time
you have covered 384.6 m. Going that distance at the speed of the
cyclist (8.33 m/s) would take 46.2 s, so the difference is 23.1 s, less
than half a minute.
Given this little "back of the brown envelope" calculation, you may now
understand why said cyclist was not amused. Note also that we used some
rather crude guestimates about distances and speeds. Putting in only
slightly different numbers would turn your behaviour from "barely legal
but rude" to "illegal". The difference between 400 and 347 m is only 13
%, after all.
It has been my experience that car drivers tend to underestimate the
space required for passing a cycle, and I vividly remember some sticky
situations resulting from that, hence my rather strong feelings.
