Kind of complicated math/physics/biology question about cars

[Traab]

Ok, here I am, driving my Bugatti Veyron Super Sport. I am having a freaking blast maxing out its speed at 267 mph. Suddenly, I notice something off in the distance. GOOD LORD! There is a cliff face in front of me! The question is, with is the average reaction time of a driver, and the deceleration rate I could get at best through braking, how much distance would I cover before being able to bring this monster vehicle to a complete stop?

[Aedilred]

I believe the average reaction time is around 1.5 seconds. At 267mph you'd travel 193.6 yards (roughly) or about 580 feet before you hit the brake. After that it depends how good the Veyron's brakes are. The Bugatti website indicates the car can decelerate from 400-0 km/h (about 250-0mph) in "under ten seconds").

Of course the calculation here isn't as simple as the first because you're constantly decelerating, and you'd need additional information about the power of the brakes. But fortunately Wikipedia has the answer anyway - it's about half a kilometre (1760 feet; 586.7 yards). In total you'd travel about 0.44 miles.

[Traab]

I believe the average reaction time is around 1.5 seconds. At 267mph you'd travel 193.6 yards (roughly) or about 580 feet before you hit the brake. After that it depends how good the Veyron's brakes are. The Bugatti website indicates the car can decelerate from 400-0 km/h (about 250-0mph) in "under ten seconds").

Of course the calculation here isn't as simple as the first because you're constantly decelerating, and you'd need additional information about the power of the brakes. But fortunately Wikipedia has the answer anyway - it's about half a kilometre (1760 feet; 586.7 yards). In total you'd travel about 0.44 miles.

Whew, thats one heck of a thing there. Heh, sorry for the odd question, I was just reading a random news article about the latest super cars and they brought up the insane power and potential top speeds and such so I was curious about how ludicrously far away you would have to be from a potential accident before you could stop. A virtual half mile is just a mind boggling distance when you think about it. I mean, think how that would look. You would have to train yourself to react to something a half mile away instantly and realize its a crash waiting to happen to have any hope of avoiding it. Anything less and your 2.5 million dollar car is scrap.

It just honestly doesnt make sense to me. I can understand wanting to drive fast, wanting to show off, things like that, but the kind of speed and power these new cars have is so over the top that only the most experienced race car drivers could ever hope to control them at their top speeds without causing a horrible fiery crash.

[Aedilred]

It just honestly doesnt make sense to me. I can understand wanting to drive fast, wanting to show off, things like that, but the kind of speed and power these new cars have is so over the top that only the most experienced race car drivers could ever hope to control them at their top speeds without causing a horrible fiery crash.
Realistically, these cars aren't designed for road use. They can't handle speed bumps, they're really wide and struggle with parking spaces and are set too low for good visibility in traffic. Not to mention speed limits, which will stop you getting anything like the car's full potential out of it, and fuel economy. On British roads, I think you'd struggle to approach anything more than about 120mph anyway for traffic ahead of you, unless the road was completely empty.

Once you get them off the roads and into controlled track environments you have a bit more freedom, but even then you probably wouldn't expect to hit top speed in a Veyron or the like on a regular circuit, only a straight-line drag race. Looking at an F1 car on one of their circuits, which have better acceleration and braking than the Veyron and are driven by (give or take) the best drivers in the world, they only really attain top speed for a couple of seconds on the long straights. Top speed is rather less important in a racing environment than acceleration, downforce and braking. Nevertheless, under the right circumstances you could fairly safely hit 250mph+ and that must be a serious rush.

Realistically, the top end sports cars aren't even designed for racing per se - they're status symbols. The Veyron was pretty much explicitly designed as a stunt/vanity project, because VW wanted to produce a car with 1000hp. That they went on to produce a car that was also really good is probably down to German tenacity, where Lamborghini or TVR would just have gone "meh, it'll do" and watched the first generation of cars explode into fireballs. The cost alone means the majority of owners (and there aren't many!) will never get anything like their potential out of them. People buy these sorts of cars for their looks, for the badge, for the theoretical numbers, and because they can. Some people do race them, of course, but that makes the whole thing even more expensive.

None of which is to say that if I won the lottery tomorrow I wouldn't have acquired a Lamborghini by Friday, of course.

[Traab]

Arent they on a several year waiting list of back orders? :smallwink: I think I would buy one used just for the sheer "wtf?!" factor. "Yep, picked it up for a song! Only driven a few hundred miles by a little old lady who only took it to church on sunday!"

[factotum]

Not to mention speed limits, which will stop you getting anything like the car's full potential out of it, and fuel economy.

Fuel economy would definitely be an issue--I recall seeing somewhere that a Veyron running flat out at 267mph will drain its fuel tank in around 12 minutes. OK, you'll travel more than 50 miles in that time at that speed, but even so, not something you'd do for a trip down the shops!

(It's amazing to think that you can buy a car capable of those speeds, though--the specially-built "Bluebird" that Malcolm Campbell used to set speed records back in the 1930s wasn't much faster than that, and you definitely couldn't have done a shopping trip in that car!).

[Kato]

267mph (about 430 km/h)really is a mind boggling speed for a car.. Quick google suggests it's even above the record for Formula One cars and I have no idea where you would actually go that fast... even at night on a German highway (which still has no speed limit and at night might actually be empty enough to allow for such speeds) but it's just totally unreasonable.. In driving school I think I recall we got taught a formula which was squared speed divided by 100 (I always wondered how they came up with that one but never asked). According to this you would even require 1.8km or a bit more than a mile to halt when driving 267mph which... is pretty crazy. Though I have no idea how reasonable.

[factotum]

Quick google suggests it's even above the record for Formula One cars

F1 cars are not actually the fastest racing cars in the world in a straight line--that title would probably go to Indycar, where I believe they can hit 250mph. Where F1 cars really *are* incredibly fast is going round corners--I know of a motorway slip road which does a 270 degree turn, and you're holding on for grim death going round that at more than about 50mph in a normal car; yet an F1 car would probably barely slow down for that corner.

[Kato]

F1 cars are not actually the fastest racing cars in the world in a straight line--that title would probably go to Indycar, where I believe they can hit 250mph. Where F1 cars really *are* incredibly fast is going round corners--I know of a motorway slip road which does a 270 degree turn, and you're holding on for grim death going round that at more than about 50mph in a normal car; yet an F1 car would probably barely slow down for that corner.

Huh, I didn't know that. Thanks :smallbiggrin:

[Aedilred]

In driving school I think I recall we got taught a formula which was squared speed divided by 100 (I always wondered how they came up with that one but never asked). According to this you would even require 1.8km or a bit more than a mile to halt when driving 267mph which... is pretty crazy. Though I have no idea how reasonable.
A lot depends on the quality of the brakes. The braking distances taught as part of driving tuition are based on theoretically sound calculations, but they're not necessarily up-to-date in terms of the input, i.e. the actual effectiveness of the brakes at slowing the car (they may not take into account developments like ABS, for instance, which shorten the distance considerably). Racing cars - and sports cars by extension - tend to have more formidable brakes than normal road cars, disproportionate to their increased weight and speed. Economising isn't really an issue when you're dealing with cars costing tens/hundreds of thousands of pounds, so you can afford to put (relatively) better brakes in a 911 GT than a Ford Focus.

[Mrc.]

They applied lots of limits to the power of the engines in F1, partly as a result of some fatalities (only two in the nineties, IIRC but many, many more in previous decades) and partly to give more of a tactical approach. Of course, this just meant that instead of whoever had the fastest car won, it came down to whoever had the lightest and most aerodynamic car won, but that could just be me being cynical.

In F1, they have a couple of systems to augment these things. Firstly the DRS or Drag Reduction System, a button which can be pressed to open up part of the rear spoiler and help reduce drag. During qualifying, they can use it whenever but in the race you must have passed a certain line within one second of another car to be allowed to use it, and only during an 'overtaking' straight. The clue's in the name: not enough overtaking was going on so they tried to force the issue.

The second thing they use is called 'kers' and is a boost of up to 50 bhp if I remember rightly. This can be applied at any point but you get a certain amount per lap. Any unused is wasted, so it tends to be used in conjunction with DRS to enable or prevent an overtake.

Regarding human reaction times, 1.5 seconds seems a lot. In A level Physics we get told to use 0.1 seconds as the fastest realistic time for human error, but 1.5 seconds is quite a long time. Certainly, the time taken to register, and the time for the neurons to send the message will be far shorter.

[warty goblin]

IIRC for most people reaction time is on the order of .5 seconds, less with good reflexes or training.

[dehro]

clearly you must accellerate and jump the cliff

[Traab]

clearly you must accellerate and jump the cliff

Considering how many laws of man that speed violates, it almost HAS to violate a few laws of physics as well, so that could work! So here I am, cruising at a nice steady 260+ mph and I see a cliff. I hit the nos, hold on tight, and jump that sucker like I grew wings baby!

[dehro]

according to the ACME rule of gravity, as long as you don't look down, you should be fine

[erikun]

First, I'd like to point out that 267 mph is absurdly fast. The speed limit on U.S. highways is only 65 mph to 70 mph, depending on state. That's four times the speed that most vehicles ever travel! Even some of the worst speeders generally only reach 120 mph, and they tend to take (understandably) long times to stop from that speed.

I should also note that slamming on your breaks at 267 mph is probably a bad idea. After all, running a stationary rubber object against the ground at those speeds would be highly destructive. I'd recommend a stopping distance of several miles, and given the speeds we're talking about, you should be driving in an area clear enough and flat enough where that sort of visibility is easy enough.

Secondly, I have it on somewhat believable authority (http://what-if.xkcd.com/61/) that, driving at those speeds, you'd have trouble just staying on the ground. Apparently, aerodynamics tend to work against most cars once they get over 150 mph - rather than being pushed into the ground and increasing traction, the air pressure passing under the vehicle increases enough to lift the car completely off the ground. Other cars have apparently seen problems as well over 200 mph. Taking a look at the Veyron, I'm not seeing anything that would change the aerodynamics from a traditional car, which makes me very hesitant to try driving one around at 200+ mph speeds.

I'll let someone else take it for a testride at that level first.

[tomandtish]

Those kinds of speeds also cause all sorts of perception problems as well. I suggest watching the Top Gear episode of the first time James May drove the Veyron. He comments that as he was just about stopped, he started to open the door (like many people do), then looked down and realized he was still doing 40 mph.

There are only a few places in the world where you can get a Veyron up to absolute max speed, and most of those are test tracks built for speed runs. Or as I like to put it: "What's the point of owning a car that you can't legally take out of second gear?".

It's designed to generate tremendous downforce at speed. That and its weight (it is very heavy for its size) is why it stays on the road at high speed. But it doesn't do great in corners. And (of course) any production road car that hits a significant bump, dip, or gust of wind at 200 mph is in serious trouble.

[Jimorian]

Here's in-car footage (http://www.youtube.com/watch?v=gWAavCjVQvM) of the Hennessey Venom GT hitting 270 mph last month. It took 45 seconds to reach top speed, and 20 seconds to slow down to normal driving speed again (around 40 mph). Even for non-emergency braking it was pulling half a G! They used the Space Shuttle runway at Kennedy Space Center, which is 3.2 miles long compared to most international airport runways which are typically 2 miles long.

[factotum]

I should also note that slamming on your breaks at 267 mph is probably a bad idea. After all, running a stationary rubber object against the ground at those speeds would be highly destructive.

Good thing that a Veyron has ABS, then--you can brake as hard as you like and the wheels won't lock (unless you're in snow or other slippery conditions, but I definitely recommend not attempting 267mph if it's like that where you are :smallwink:).

Re: that Venom GT video--what I found amazing was that it was still accelerating at around half a gee when travelling at 200mph! Now that's some power...

[dehro]

this here (http://www.youtube.com/watch?v=LO0PgyPWE3o) video is relevant

[erikun]

Good thing that a Veyron has ABS, then--you can brake as hard as you like and the wheels won't lock (unless you're in snow or other slippery conditions, but I definitely recommend not attempting 267mph if it's like that where you are :smallwink:).

Re: that Venom GT video--what I found amazing was that it was still accelerating at around half a gee when travelling at 200mph! Now that's some power...
Well, I will admit that I'm not too familiar with ABS systems. Rather thankfully, I haven't found a need to slam on my breaks with any sort of frequency while driving. :smalltongue:

Looking at the videos, it looks like most of the speed is lost simply by taking the foot off the gas - which certainly makes sense. It's actually kind of interesting to see what they did to actually make the car work and viable (for some sense of the word) at those speeds, rather than just stucking an engine that could do 250mph into just a standard car body.

[dehro]

if they hadn't put a lot of thought about windforce, downward force and all manners of tricks to keep the thing where it belongs, simply sticking a powerful engine in there would have transformed it in a sure accident.

that said, any car, when you take her to top speed will decrease speed rapidly once you lift your foot off the pedal, well before you start braking. simply put, the engine is straining to achieve top speed, and doing so only because of your foot on that pedal. take it off and it will stop straining, decellerating rapidly.
but then, it will still go at quite a pace, as James May demonstrates with the Veyron at the end of the video I linked. You WILL have to brake, eventually :P

[tomandtish]

this here (http://www.youtube.com/watch?v=LO0PgyPWE3o) video is relevant

I stand corrected. I had been working from memory and remembered 40 MPH, which was 30 mph too low! "Gee, I can open the door at 70!"

[erikun]

I stand corrected. I had been working from memory and remembered 40 MPH, which was 30 mph too low! "Gee, I can open the door at 70!"
That's a british show, with british metrics. 70 kph is just over 43 mph.

[Asta Kask]

When did Britain go metric?

[FinnLassie]

I have to note that in the UK, roadsigns and cars still use miles and mph.

[Aedilred]

Yup, mph is still the standard over here. I've never quite understood where the American stereotype about us using metric came from. Most of our weights and measures are now metric, as a result of a long-lasting campaign to convert us, but probably the majority of colloquial uses are still imperial, and overall the system is a hybrid. I think attempts at trying to metricate us further have been officially abandoned, because our stubbornness proved too much.

[erikun]

Huh. The fact that they were using kph throughout the video made me think that it was what they use typically.

[dehro]

tipically they use miles.. but in this case they were in Germany, driving a german produced car. No idea whether May was talking miles or kilometres.. he may have reported what he read on the dashboard or may have first made the conversion in his head.

[Jimorian]

Yup, mph is still the standard over here. I've never quite understood where the American stereotype about us using metric came from. Most of our weights and measures are now metric, as a result of a long-lasting campaign to convert us, but probably the majority of colloquial uses are still imperial, and overall the system is a hybrid. I think attempts at trying to metricate us further have been officially abandoned, because our stubbornness proved too much.

To be fair, on the other side, the U.S. is functionally metric under the hood, it's just that we talk about everything in imperial for pretty much the same reason.

[Aedilred]

Huh. The fact that they were using kph throughout the video made me think that it was what they use typically.
The video dehro posted? That uses mph consistently, until he starts referring to the (German) telemetry box, at which point May makes the point that it's in kph, and from then on gives the output figures before converting them into mph for the viewer (until he's going too fast to do that).

[Knaight]

To be fair, on the other side, the U.S. is functionally metric under the hood, it's just that we talk about everything in imperial for pretty much the same reason.

There's a lot of imperial used in engineering (e.g. machines built to work in increments of 1/10,000 inches, wrenches, bolts, screws, etc. built to imperial diameters, etc.). Actual research is generally done using metric, and you won't see something like a paper on chemical synthesis listing quantities of reagents in cups or ounces, but the U.S. is imperial in most ways.

[dehro]

There's a lot of imperial used in engineering (e.g. machines built to work in increments of 1/10,000 inches, wrenches, bolts, screws, etc. built to imperial diameters, etc.). Actual research is generally done using metric, and you won't see something like a paper on chemical synthesis listing quantities of reagents in cups or ounces, but the U.S. is imperial in most ways.

I think the only thing that is still using imperial pretty much all over the world is the definition of size of TV screens.

[Tyndmyr]

I believe the average reaction time is around 1.5 seconds. At 267mph you'd travel 193.6 yards (roughly) or about 580 feet before you hit the brake. After that it depends how good the Veyron's brakes are. The Bugatti website indicates the car can decelerate from 400-0 km/h (about 250-0mph) in "under ten seconds").

Of course the calculation here isn't as simple as the first because you're constantly decelerating, and you'd need additional information about the power of the brakes. But fortunately Wikipedia has the answer anyway - it's about half a kilometre (1760 feet; 586.7 yards). In total you'd travel about 0.44 miles.

Average human reaction time is 215 milliseconds when alert(because being actively tested for it). The usual numbers you will see is a result of people extrapolating in drivers being bored, not paying attention, etc. These are not normally factors at 267, because if you are not paying attention at that speed, you're already dead.

So, actual stopping time is MUCH shorter.

Full disclosure: I used to street race. Sadly, nothing I drove ever went that fast. However, quoted stopping times ARE entirely BS when applied to a competitive or otherwise unusual environment.

[sktarq]

One factor to consider is the training of the driver. I mention this because stomping on the breaks can lead to trouble controlling a car that is traveling quickly. "Mild" swerving is not uncommon for people pushing the car or personal limits. With something like a Venom or Veron I'm going to speculate that reaching personal limits would be much more common. Now general, when the car begins to get squirrely the driver lifts off the brake a bit. Now ABS helps with this but doesn't eliminate it. So your drivers ability to hold the car strait and steady (and thus to floor the brake pedal) would be a relevant factor.

[Brother Oni]

To be fair, on the other side, the U.S. is functionally metric under the hood, it's just that we talk about everything in imperial for pretty much the same reason.

Well your version of Imperial. If I said I weighed 'fourteen stone'*, I'm sure they'd be a number of blank looks from across the Pond. :smallbiggrin:

As Aedilred said, we mostly use a hybrid system. I can't do science in imperial measurements (working in foot pounds per second drives me nuts when watts is so much easier), but I'd have to think about how heavy/tall I was in metric measurements.

*For international readers: 1 stone = 14 lbs = 6.4 kg

[Karoht]

Something also forgotten, the Veyron has an air brake system as well, demonstrated in the James May video (if you watch the full program that is, assuming that video is just the run up to 250 mph). It's not just brake pads and computer controlled ABS at play here.

Defensive Driving course 14 years ago said reaction time was .75 to 1.5 seconds for non-race car drivers.

[Knaight]

Defensive Driving course 14 years ago said reaction time was .75 to 1.5 seconds for non-race car drivers.

This doesn't take into account how anyone driving at really high speed is going to be paying much closer attention than the average driver in normal conditions.

[Karoht]

This doesn't take into account how anyone driving at really high speed is going to be paying much closer attention than the average driver in normal conditions.Agreed. I failed to mention, it was in reference to conditions of normal traffic, including trying to navigate in busy traffic.

[Bluemir]

493m braking assuming a typical day of 20 degrees celsius with a pressure of 101kPa. Due to weather this figure could vary between 489m and 497m.

Add reaction time of 0.4 to 0.6 seconds and the answer is between 540m and 570m.

\begin{document}
$\\*
\textrm{Force is given by, where F is force, p is momentum and t is time (d essentially means change)}
\\*
\stackrel{\to}{F}=\frac{d\stackrel{\to }{p}}{dt}
\\*
\textrm{Momentum is mass multiplied by velocity, mass is constant so can be brought outside the change giving, where m is mass}
\\*
\stackrel{\to}{F}=m\frac{d\stackrel{\to}{v}}{dt}
\bigskip
\\*
\textrm{Only forces when braking are the brakes and air resistance}
\bigskip
\\*
\stackrel{\to}{B}_{F}=\textrm{Braking Force }
\stackrel{\to}{A}_{F}=\textrm{Air Resitance}
\\*
\stackrel{\to}{F}=\stackrel{\to}{B}_{F}+\stackrel{ \to}{A}_{F}=m\frac{d\stackrel{\to}{v}}{dt}
\\*
\frac{\stackrel{\to}{B}_{F}+\stackrel{\to}{A}_{F}} {m}=\frac{d\stackrel{\to}{v}}{dt}
\\*
\textrm{A formula for air resistance valid at speed's cars travel at is given by}
\stackrel{\to}{A}_{F}=\frac{1}{2}{C}_{d}A\rho{v}^{ 2}
\\*
\textrm{Where ${C}_{d}A$=Drag area, a constant determined by the shape and material, which is $0.74{m}^{2}$ for a Veyron.}
\\*
\textrm{$\rho$ is the density of air, approximately 1.2kg${m}^{-3}$ on Earth's surface, v is velocity, therefore }
\\*
\stackrel{\to}{A}_{F}=0.444{v}^{2}
\\*
\textrm{Braking force of a Veyron is 1.3mg, which is 13m m${s}^{-2}$ therefore}
\\*
\stackrel{\to}{B}_{F}=13m
\\*
\textrm{Putting the two forces back together, with the mass of the Veyron being 1888kg}
\\*
13+0.00023517{v}^{2}=\frac{d\stackrel{\to}{v}}{dt}
\\*
(13+0.00023517{v}^{2})dt=d\stackrel{\to}{v}
\\*
\textrm{$\stackrel{\to}{v}+d\stackrel{\to}{v}=$ New $\stackrel{\to}{v}$}
\\*
\textrm{Velocity is distance travelled over change in time, therefore, where D is distance}
\\*
\stackrel{\to}{v}dt=d\stackrel{\to}{D}
\\*
\textrm{Therefore, we can simply iterate to numerically arrive at the answer, with smaller dt arriving closer to the true result}
\\*
\textrm{V=119}
\\*
\textrm{while V greater than 0}
\\*
\textrm{dt=0.001}
\\*
\textrm{v=(13+0.00023517${V}^{2}$)dt}
\\*
\textrm{V=V-v}
\\*
\textrm{d=V*dt}
\\*
\textrm{D=D+d}
\\*
\textrm{/end}

$
\end{document}

[ace rooster]

First, I'd like to point out that 267 mph is absurdly fast. The speed limit on U.S. highways is only 65 mph to 70 mph, depending on state. That's four times the speed that most vehicles ever travel! Even some of the worst speeders generally only reach 120 mph, and they tend to take (understandably) long times to stop from that speed.

I should also note that slamming on your breaks at 267 mph is probably a bad idea. After all, running a stationary rubber object against the ground at those speeds would be highly destructive. I'd recommend a stopping distance of several miles, and given the speeds we're talking about, you should be driving in an area clear enough and flat enough where that sort of visibility is easy enough.

Secondly, I have it on somewhat believable authority (http://what-if.xkcd.com/61/) that, driving at those speeds, you'd have trouble just staying on the ground. Apparently, aerodynamics tend to work against most cars once they get over 150 mph - rather than being pushed into the ground and increasing traction, the air pressure passing under the vehicle increases enough to lift the car completely off the ground. Other cars have apparently seen problems as well over 200 mph. Taking a look at the Veyron, I'm not seeing anything that would change the aerodynamics from a traditional car, which makes me very hesitant to try driving one around at 200+ mph speeds.

I'll let someone else take it for a testride at that level first.

Yeah, it is seriously fast: a mile every 13.5 seconds. Locking the breaks at that speed would be bad, which is why it has ABS. Break cooling airflow is preportional to speed, so the breaks will not overheat at any speed. May as well use them to the full.

The Veyron is not most cars. There is a huge amount of aero work done on it, particularly on the floor. The airflow under the vehicle is accelerated to reduce pressure under the car, holding it down. As most of the work is under the car, and at the base of the back of the car, it is not obvious to the untrained eye. The issues with cars doing backflips are mostly because of bumps lifting the nose of the car, which increases the pressure under the car. Avoiding bumps should be fine.


As for fastest cars about, top fuel dragsters seem the best bet. 330mph in a quarter mile! If you want somthing that can turn corners, you would probably be best looking at the modern sports prototypes rather than the open wheel cars. Much lower downforce, but hugely lower drag (Those open wheels are not much more aerodynamic than a brick). The group C cars of the 80s were running 250mph speeds, and the modern ones are significantly better aerodynamically, with more power. The FIA doesn't permit the straights to get up to those speeds anymore though, so hard to know how fast they are.