Physics Blogging Round-Up: Fast Cars and Spherical Cows

It's been a while since the last Forbes links dump, but since it's the last day of the month, I figure I might as well sum up a bit. Only two posts, but they have a connection that I'll expound on a bit to make up for the lack of material...

-- Can A Tesla Model S Really Accelerate Faster Than Gravity?: I got pointed to a story about the 0-60mph time for a Tesla, and said "That seems fishy..." After climbing back out of the Google rabbit hole, I tried to explain why that seemed unlikely to me, and the funny timing thing that might explain the result.

-- The Hardest Thing To Grasp In Physics? Thinking Like A Physicist: Some musings about how the trickiest part of learning to be a physicist is getting the mindset, particularly the highly reductionist use of "spherical cow" sorts of approximations.

So, the first of these really pissed off a lot of Car Guys, who left tons of comments, and some angry emails and tweets, pointing to a variety of other cars that supposedly accelerate at large multiples of the acceleration of gravity. I wasn't especially moved by most of this, in part because they're not particularly relevant to the question of whether the Tesla result is surprising. It's true that I didn't discuss the possibility of aerodynamic down forces that would allow for a larger frictional force, but those aren't actually important for a normal-ish car like a Tesla. A top fuel dragster is a completely different animal, and I'm not especially surprised that they work differently than an ordinary car.

The other issue I have with the angry reaction is that it really misses the point of the post (which, admittedly, I probably should've made more explicit). That is, I don't actually care whether the Tesla accelerates at 0.98g or 1.1g. My purpose in writing that piece, like most of what I write, really had more to do with the physics mindset than the specific numerical values. I was explaining my reaction and reasoning: when I read the original piece, I was immediately skeptical for reasons that have to do with physics, which sent me off looking for more information that might explain the faster-than-expected time in a way that didn't require surprising physics, and learned about a timing thing that's in the right ballpark to account for the apparent discrepancy.

I thought that was an interesting process (obviously, or I wouldn't've been sucked into Googling stuff about car testing), and worth laying out. I'm really not remotely invested in the specific numerical results-- if the tires they use turn out to be much stickier than the usual run of things so the acceleration is a little higher than I would expect, well, that's a nice bit of trivia. It doesn't really change my thinking about why that was a piece worth writing, which is largely that it illustrates the toy-model-building described in the second post. Thinking like a physicist means that the 0-60mph time isn't just a random factoid that could take on absolutely any value, it's something with a physical origin that you can model in a simple way, which leads to an expectation about what the time should be for a relatively ordinary car. And thinking "that's funny..." does, in fact, lead to something that's a little funny in the timing, which is also interesting.

But, yeah, I should've made that clearer, because, wow, are there people who are deeply invested in the accuracy of those numbers...

Anyway, that's the story of my recent blogging. Which may become sparse for the next several months, as I've gotten myself stuck on a grand jury that sits two days a week, and classes start next Wednesday, so my time is going to be very tight for the immediate future.

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The YouTube channel "Engineering Explained" also recently tackled the 0-60 time claims. He modeled it by looking at the best reported braking distances, computed the acceleration needed for that and assumed that was the best the tires could do, then used that to compute best possible 0-60 times.

His conclusion was that for the 5-6 street cars he looked at, the reported 0-60 times were reasonable, and that he feels the limit for 0-60 times in a street car is about 2s. A CoF greater than 1 was not unusual for high performance street tires, but not too much greater.

He did go over the results for a few racecars, including F1 and top fuel dragsters, but pointed out that they are using incredibly sticky tires and other features to get the high accelerations.

He didn't talk about the rollout, which is a feature I wouldn't have considered. I think perhaps an easy way to deal with it without too much change to the existing track setup is to use a double-gate: two light beams maybe a centimeter apart. The car rolls up until the first one is broken, timing starts when the second one is broken.

By Buddha Buck (not verified) on 31 Aug 2016 #permalink

Yeah, I was going to comment about the acceleration, it's not necessarily a pure friction effect. The tires deform significantly where they make contact with the road, which is a rough surface. I would expect that you'd get some non-friction "engagement" force (I'm struggling for a term here, essentially something like gear tooth engagement on an intermediate scale) which would help, and the vehicle's traction control system would presumably be able to keep that very close to the edge of slipping. It's also possible that aerodynamics are providing some downforce that would increase the available friction force, but I assume that's pretty small.

For comparison, a top fuel dragster is goes 1000 ft in under 4 s. Assuming a constant acceleration, that's about 4g's. Presumably almost all of that force is applied through the tires (maybe some thrust from the exhaust, but I assume that is minor). Again, aerodynamics are probably providing some down force to increase the available friction, but the dragsters seem to experience peak acceleration at the start, so I don't think we're losing much by ignoring that.

So, what's going on there? Combination of that mechanical engagement, bonding of the tire to the ground, I dunno. But given that they're hitting 4g's, it's not wholly unreasonable to expect that a car like the Tesla is able to exceed 1g. You will occasionally see skidpad numbers (measuring lateral acceleration) that exceed 1g, as well.

There's also a great xkcd comic about physicist annoying people when we talk about other fields.

You missed two things.

1) The data table for friction coefficients listed rubber on rubber as 1.16. That is probably natural rubber, but it tells you the important effect of "rubbering in" a race track. That black surface used for drag racing is concrete that has been systematically and professionally impregnated with the same synthetic racing rubber used in drag tires. A test track may have similar characteristics. (see below for more)

2) Electric motors have loads of torque. To oversimplify, torque is acceleration while power is top speed. The car may also have a CVT that, in sport mode, optimizes for acceleration. Conventional exotics are designed to go from 0 to 62 mph (100 kph) in first gear so there is no time lost during the shift. Gearing is set so you red line at 100 kph, which is what they test in Europe.

More on tires. (I did not read the comments so this could be repetive.)

Max friction is actually when there is a slight slip, particularly when turning. Friction increases up to a slip angle of around 10 deg IIRC, then drops off. For conventional tires, this is the "squeal" point and happens gradually. For race rubber, the peak is bigger and the drop off quite abrupt. It is not all about static friction.

Friction only costs money. You pay a lot more for "street" tires that have more friction, and you pay more often. Some have a treadwear rating of 050 or even 000. Since cars are tested as delivered, sports cars might come with tires that give good test times but wear out in 5000 miles. They are not the 40,000 mile rocks that have 0.8 to 0.9 friction coefficients. It is not uncommon to see 1.00 g skidpad results.

Top Fuel data would require a fast camera and tracker analysis, but 4 g is the average. I'll say that again. Average. They reportedly launch at close to 8 g and drop off to 2 g when they are going 300 mph. They get close to 60 mph in one revolution of the rear tires. This is possible because the tire is bonded to the rubber from the burnout (you can sometimes see the tire pick up the rubber from the track, like it was a tank tread) and they get downforce from lifting the rear of the car as the tires increase in diameter right after launch.. Aero effects kick in at 60-100 mph.

By CCPhysicist (not verified) on 08 Sep 2016 #permalink