Quantified Ramblings
Quantified Ramblings
Illustration for article titled Why 0-60 Times Should Be Replaced

Horsepower figures are meaningless (thus making power to weight ratios null as well), ring times are inconsistent, and 0-60 times are incomplete.

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So I admit some 0-60 times are impressive, some 0-100 times are cool, some 0-200 times are insane, and finally one 0-248 time is ludicrous. But I’m sure we have the technology to do so much better than this. I mean not me personally, but someone should.

Specifically, automakers definitely should. Automakers that make sports cars, super cars, and hyper cars are committing an egregious disservice to us, either because they’re lazy or scared of the of the consequences. Realistically, they probably already collect all the data I’d need. I’ll even go so far as they might even interpret it in the same way. A lazy google search (read: wrong keywords with top ten links actually read) however, leads me to believe that they do not publish this data. The reason for which may be obvious, but I’ll get into that later.

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The Proposal

Track the speed (or position as first semester calculus or common sense can explain their relation) over a period of time under hard acceleration. This should be done from a stand still to either legal, practical, or true top speed. We’ll define legal top speed as the highest speed limit in the target market for the vehicle, practical as the speed which the vehicle can reach on the longest strait available, and true top speed as just as it sounds. The first could be used as a standardized, marketable metric by manufacturers for everyday vehicles similar to mpg (though I have my qualms with that metric as well). The latter two could be used as a way to compare performance cars, either within a class or between classes, by auto journalists *cough* Jalopnik/Oppo *cough*. This is my proposal for how this could be cheaply implemented.

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The general idea is to track vehicle speed in a straight line from zero to a desired maximum speed at the smallest feasible time intervals to get the smoothest curve possible. I chose to show the most widely written about super car of my generation, the Bugatti Veyron (yes, at 21 I’m one of those millennials or whatever they’re calling us these days). This came as the obvious choice even before I found the limited data I used here, because of the completeness of all the testing that had been done and let’s be honest a car that weighs two tons and has a thousand horsepower is already a complete nerdfest.

Gathering the Data

So yet another quick google search revealed what may be the cheapest option in this OBDII data recorder. Though the logging rate is only 1 entry per second and I would prefer at least one entry every tenth of a second, for the everyday cars I could potentially have access to it should be sufficient.

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The logging is as simple as it gets; just plug it in and put the go pedal to the floor. Afterwards, find the first index where the speed is greater than zero and have this represent s(t) where t=1. s(0)=0 for obvious reasons and remove the readings after s(t) reaches the predetermined speed. Perform this test in a straight line on flat ground several times to ensure quality results and for later statistical analysis.

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Graphing Velocity

With the limited data I had for the Veyron, I quickly put together an excel sheet and graphed the data. For my own implementation I’d much rather present this in a cleaner format, but that will hopefully come at a later date.

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Illustration for article titled Why 0-60 Times Should Be Replaced

How simple is that?

Well okay there is a major flaw in this, because the time intervals aren’t evenly spaced in the graph but you get the point.

Edit: Some comments have brought up the issue of its the time to cover a distance that a lot of people care about. To answer that all we have to is take in integral of the curve and start it at whatever the beginning speed is (S[t]=?) and find the time where the area under the curve is equal to the distance desired. The delta t will be the time it takes to cover that distance.

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Graphing Acceleration

Some basic math can get us to average acceleration over the time intervals by graphing the slope between points. The mean value theorem tells us that the acceleration between these points has to be equal to the true acceleration for at least one point for some t between the points where data was recorded. We can graph s’(t)=a(t) like so:

Illustration for article titled Why 0-60 Times Should Be Replaced
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As expected, after the initial rise in acceleration from a stand still, the acceleration is converging towards zero as the Veyron approaches its top speed. Both Speed and Acceleration are interesting graphics that could be used to compare vehicles in a more visual manner. I’ll get to work coding a more efficient method of representing this for whoever wants to join me in a practical proof of concept.

Further Statistical Analysis

So as I previously mentioned, this should be done several times so an average speed at each time t can be found as well as statistical variance (a.k.a. sigma^2) to show the consistency of a cars performance.

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Interpreting the Results

So now in this (hopefully ephemeral) theoretical world we have a few solid samples from a variety of cars, how can we interpret this?

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  • Compare two or more cars you are considering purchasing and focus your attention on the acceleration within a range of speed that you can picture yourself achieving. No sense in touting the Veyron’s acceleration on the top end if you live in the US and never plan on seeing a track (I have not, nor will I ever, condone street racing).
  • Use the graphs to visually assess the performance of various transmission options, whether you are a row-your-own diehard, the proud owner of a DCT, complacent slushbox user, unfortunate CVT owner, electric car fanboy, or the first lunatic to test out Koenigsegg’s hybrid/final drive system.
  • Apply the same ideas to braking performance. I’d expect this to be more linear, but I’m not an experienced enough driver or engineer to speculate.
  • Use this data to optimize the gearing in a track car. I have no idea about how to go about this, but if there’s any place on the internet where someone has documented this, it’s probably somewhere in the Jalopnik sub blogs.
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Who’s In?

So I’m looking for one or more partners in the southern NH or northern MA area to help me. Ideally they have the following things:

  1. A car they’re willing to test (we can use mine as well, but I currently drive a 2008 automatic golf and something a little faster might be more fun).
  2. A valid license and some experience driving at faster speeds.
  3. Access to a runway, drag strip, or track with a long straight (I refuse to be a part of this on anything but a closed course).
  4. Weekends or nights free (assuming access to the venue could be had at the same time).
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Drop a line in the comments if you’re interested and I’ll give you an email you can contact me at. I also have a few ideas about cornering to be assessed at a later date and so much more. If you have any questions about the blog or authorship privileges take a look here.

About the Author: Patrick Nichols is a graduate of Saint Anselm College, where he received his BA in Mathematics. Other than numbers, he enjoys sports (especially hockey), beer, cars, outdoor activities in general, and plants (despite a very mediocre high school level knowledge in biology).

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[Photo Cred: HD Wallpapers Fit]

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