Assume a spherical deer...
January 17, 2019 6:54 AM   Subscribe

Say there are two drivers, each with distinct reaction times, in two identical vehicles, on a straight two-lane country road. Each is heading the same direction at the same speed. Give a number of variables (e.g. probability of a deer crossing, reaction times, braking time), what configuration—you in the front or back, space between the cars, and speed—would minimize the chance of you striking a deer, while maximizing your speed?

I feel like I'm missing some constraint, since the deer can appear at any distance in front of either car, including between the cars. Other things I'm pondering are:
  • Does it actually matter how frequently a deer crosses?
  • Does the optimal speed change if there is only one car?
  • Does the problem reduce to the same a one-car version, if the drivers have identical reaction times?
  • Does maximizing speed preclude an "infinite space" configuration?
I’m looking for speculative answers, exact answers, or what information might be missing to get an exact answer.

This is my own thought experiment and not like, me cheating on a homework problem. I happen to often be one of those drivers because of my route to work, and I feel like restricting the number of variables could lead to an interesting and exact optimal configuration.
posted by Pig Tail Orchestra to Grab Bag (9 answers total) 1 user marked this as a favorite
*what configuration would minimize the chance of you striking anything, while maximizing your speed?
posted by Pig Tail Orchestra at 7:05 AM on January 17, 2019

since the deer can appear at any distance in front of either car

This is not a good assumption. While deer may sometimes jump out of nowhere in front of vehicles, in my experience, living in extremely deer-ridden parts of the world, this is rare. (Probably far more rare than people claim that it is, since it's a good excuse for hitting a deer out of inattention or excess speed.)

Generally, deer will stand in or just off to the side of the road (often because there's grass and greenery there for them to eat) and freeze when they see a car, until they suddenly decide what direction to run in, and run that way.

The faster you're going, the less time you have to react to the presence of the deer at all, and also the less time there is between when the deer spots you and when it does its flight-response thing.
posted by Kadin2048 at 7:10 AM on January 17, 2019 [4 favorites]

Deer are most active from dusk to dawn, so you have the best odds by only driving during the daylight. This also improves visibility.

FWIW, my mom worked 3rd shift growing up and she was struck by deer twice coming home from work at 3 am, once in the driver's side wheel well and once in the passenger side front door. She had a coworker with a convertible who had a deer jump into her back seat and out again. I have a coworker who was hit by a deer (passenger side door) while driving home from work just after dusk.

I don't know anyone who's hit/been hit by a deer during the day.
posted by DoubleLune at 7:21 AM on January 17, 2019 [3 favorites]

Kadin2048, I think that 'deer jumping out in front of you' very much depends on the amount of visibility you have. Also having lived in deer-ridden areas (UK), it's all well and good when you've got good enough visibility to see that there is a herd of deer ten feet off the road. But add rain, snow, fog, woodland, and deer can indeed suddenly appear. Especially woodland - a straight-ish road through the woods and you wouldn't think to slow down, but deer blend in and you may not notice them.

That said, in my years of driving on deer-infested country roads I had many more near-misses with logging lorries than I did with deer.
posted by Vortisaur at 7:23 AM on January 17, 2019 [1 favorite]

Before I take a stab at answering your question, I should note that I actually study the perceptual elements of this problem, and, as a consequence, know the literature here (on hazard detection, not just deer avoidance) fairly well.

My intuition is that most of your variables can't be easily predicted without a lot of data that we really don't have, but I'll see if I can shed some light on them and at least get you closer to an answer you can use to avoid a collision with a deer.

To start with your reaction time question; I'd break that out into how quickly can you respond and how long will it take you to slow down, either to a stop (longer) or enough that damage is minimized. The first part of this - reaction time to an unexpected hazard on the road - we actually have a good answer for. Green, 2000 is a meta-analysis of brake reaction time, and reports an average reaction time of ~1.3 seconds from event onset (when you can see the hazard and know it's a hazard) to brake activation (when you stomp). I've run an experiment pretty much looking at exactly this in the lab, and get an answer that's within 0.1-0.2 seconds of Green's. So, that's pretty easy. However, the next question is how long does it take you to slow down or stop. That's a direct function of braking force and speed of travel. Other people have done the calculations so I don't have to, and this is a good chart of the relationship and how far you'd travel.

From what you're describing (and the videos I use as stimuli that show exactly this circumstance!), let's assume a two-lane, non-divided roadway moving through a lightly built up or wooded area. Say your prevailing speed is 45 mph, to take a reasonable value from that table. It's listing about 97 ft of travel at maximum braking to stop dead. That's about a second and a half at 45 mph. It's also listing about 100 ft (again, about a second and a half) which is on par with what we know about reaction time to unanticipated events. So, if you want to be maximally safe, you need 2.5 seconds or more to notice the deer and stop.

However, this isn't a perfect answer. You can have other vehicles (both in your lane and in the opposite lane of travel). The deer isn't likely to oblige you by appearing far enough away that you can stop in time. The deer might even, as you suggest, appear between the cars if you're being careful and maintaining a significant following distance between you and a vehicle ahead of you.

My advice? Maintain as much following distance as you can, because distance on the road is time, and time is what you need to stop. You also really want to keep your eyes on the road when you're on a road where deer are a concern, because if you're, say, looking down at your smartphone mounted to the dash and using peripheral vision to keep an eye out for deer (another experiment I've run), it'll take you at least a third of a second longer (or, a couple of car lengths!) just to detect the deer, and then you need to brake.
posted by Making You Bored For Science at 7:26 AM on January 17, 2019 [12 favorites]

For the math problem, you want the two cars to be following each other with minimum (0) distance. While you talk about minimizing the odds of hitting the deer, I suspect you don't want to hit the other car either so the car with the slower reaction time should be in front.

Consider any configuration of the two vehicles at the time the deer (in an arbitrary position) crosses the road. This will lead to a collision if he is within the reaction space of car 1 or car 2. By following the slower reacting car arbitrary close, the faster reacting car makes their reaction space overlap and effectively not exist (since the deer is already going to be hit by the slower reacting car). As a result, with identical reaction times, infinitely short cars and the ability to drive arbitrarily close to one another, the two car case reduces to the one car case.

As for speed, let's split up the space in front of you into reaction space (the space you travel before you react) and breaking space (the space you travel after reacting but before breaking stops). Assuming that deer show up at a regular rate, your odds of hitting the deer within your reaction space is independent of your speed: the faster you travel, the larger the reaction space but the shorter the time that you risk encountering the deer; the two cancel out exactly as both relationships are proportional to speed. The breaking space, however, grows faster than linear (the space needed to break from 60mph is more than twice that for 30mph, indeed the simplified formula is quadratic) so to minimize the odds of hitting a deer within your breaking space, you should travel infinitely slowly.

As a note, I answered the thought experiment, not anything to do with real deer and there are a lot of unreasonable assumptions for real-world applicability.
posted by bsdfish at 7:42 AM on January 17, 2019 [2 favorites]

You want to be the driver with the faster reaction time, and you want to be in the rear car, sitting as close to it as you can while still being able to pull up safely if it does a very sudden stop in front of you.

By lowering the time between cars to its safe minimum, you maximize the chance that any deer that does get struck will be struck by the the front car.

Does the optimal speed change if there is only one car?

Yes, because you're forced to make a choice about what "optimal" means. If you're the only driver, your chance of hitting a deer rises with your speed; therefore, the goal of minimizing the likelihood of striking a deer is in direct conflict with the goal of maximizing your speed. In a single car, your chance of hitting a deer is minimal when your speed is zero.
posted by flabdablet at 7:44 AM on January 17, 2019

Me in front.

Why: 40 years of driving in Montana at high speeds in all kids of weather and roads and times of day and night. There are deer everywhere and you learn to look fo them a long ways off.

I've hit one deer in 500,000 miles. I would have missed it but my 6 foot 7 inch tall buddy was pouring himself a cup of coffee out of a thermos over his lap. I figured hitting the deer would cause me less damage than making Ken pour a thermos of coffee into his lap.
posted by ITravelMontana at 12:03 PM on January 17, 2019 [3 favorites]

Thanks for all the thoughtful answers!
posted by Pig Tail Orchestra at 7:30 AM on January 19, 2019

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