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Comment by mlyle | Hacker News Reader

> But if there are a bunch of children milling about an elementary school in a chaotic situation with lots of double parking, 17 mph is too fast

Hey, I'd agree with this-- and it's worth noting that 17^2 - 5^2 > 16^2, so even 1MPH slower would likely have resulted in no contact in this scenario.

But, I'd say the majority of the time it's OK to pass an elementary school at 20-25MPH. Anything carries a certain level of risk, of course. So we really need to know more about the situation to judge the Waymo's speed. I will say that generally Waymo seems to be on the conservative end in the scenarios I've seen.

(My back of napkin math says an attentive human driver going at 12MPH would hit the pedestrian at the same speed if what we've been told is accurate).

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Swedish schools still have students who walk there. I live near one and there are very few cars that exceed 20km/h during rush hours. Anything faster is reckless even if the max over here is 30 km/h (19 mph).

The schools I'm thinking of have sidewalks with some degree of protection/offset from street, and the crossings are protected by human crossing guards during times when students are going to schools. The posted limits are "25 (MPH) When Children Are Present" and traffic generally moves at 20MPH during most of those times.

There are definitely times and situation where the right speed is 7MPH and even that feels "fast", though, too.

> Hey, I'd agree with this-- and it's worth noting that 17^2 - 5^2 > 16^2, so even 1MPH slower would likely have resulted in no contact in this scenario.

Only with instant reaction time and linear deceleration.

Neither of those are the case. It takes time for even a Waymo to recognize a dangerous situation and apply the brake and deceleration of vehicles is not actually linear.

> It takes time for even a Waymo to recognize a dangerous situation

Reaction time makes the math even better here. You travel v1 * reaction_time no matter what, before entering the deceleration regime. So if v1 gets smaller, you get to spend a greater proportion of time in the deceleration regime.

> linear deceleration.

After reaction time, stopping distance is pretty close to n^2. There's weird effects at high speed (contribution from drag) and at very low speed, but they have pretty modest contributions.

I was thinking more that how hard the brakes are applied likely varies based on uncertainty of a collision.

Without that these vehicles could only start braking when certainty crossed some arbitrary threshold.

I think the strategy is a lot more nuanced than that.

In any case, with zero reaction time, linear deceleration time to stop is proportional to velocity squared. With reaction time, the linear deceleration time is that plus the velocity times the reaction time.

so the two cases we're comparing are 17 * r + (17^2 - 5^2) vs. 16 * r + (16^2), or 17 * r + 264 vs 16 * r + 256. As long as reaction time isn't negative, a vehicle that could slow to 5MPH starting at 17MPH could slow to 0MPH starting at 16MPH.

(There are weird things that happen at <2.5MPH reducing deceleration to sublinear, but the car moves only a few inches at these speeds during a panic stop).

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