JohnnyBahamas

I've got a theory about this situation: More people are more stupid than ever.

Can't fix their own lawn sprinklers, can't run their own TiVo, and can't stop their cars because they're stupid, stupid, stupid.

But the putz who can't stop his Prius is a GENIUS compared to the freakin' stupid loons who babble about these events being part of a government conspiracy to help GM. NOW THOSE PEOPLE ARE IDIOTS... and stupid, too.

I see stupid people.

simsgw

During one of those "Well, you never know what's out there" episodes concerning UFO's back in the 70's, I found out one of my friends, a highly respected programmer who invented JOVIAL, had been asked to validate a film claiming to show UFO's in flight. He had been convinced and came back an advocate. (Programming talent does not equal engineering talent, let alone an intuitve grasp of physics. Or even reality apparently.) Since I was in range engineering for the Western Test Range at Vandenberg, he was eager to show me. I think he felt a real rocket scientist would certainly see the implications of his new religion.

He played a copy of the film, and I gently pointed out that the movement of the unresolved bright objects, his UFO's, correlated with the movement of the lens' axis. They were almost certainly artifacts of the lens used on the camera, the most likely being an effect of the sun striking a multi-element lens from an angle outside the image angle. He poo-pooed this plain jane answer: "The guy with the camera says he wasn't anywhere near the sun and he's never seen anything like this with his camera." Oh. Well, fair enough. I suppose. Could we doubt an eyewitness? Then he went on to explain that he had computed the 'position' of the unknown flying objects. "The data are consistent!"

Well, okay, I said. Show me your answers. "See, they were here when we see them first. Then at frame XXX, they are at this altitude and position. Finally, at frame YYY we see them at this altitude and position before the film runs out." I pointed out that given the frame rate of the camera, that required a speed of (Rough numbers here. It's been forty years) 4,000 miles an hour in the atmosphere from the first position to the second. Then they decelerated to an angular rate of zero and back to a speed of (let's say) 7,000 mph in the opposite direction. Thus requiring an imposed acceleration of (I don't remember, but it was about a thousand g. Not numerically incredible since we work at levels of 25 thousand g for some applications. But not with aircraft of course. Neither manned or unmanned. Gold leads on IC's run like melted wax at those loads.). His response: "I thought so! I thought so! You see! They've got artificial gravity on board! No earth aircraft could have done that. That proves it!" I was beginning to see the trend, but I was young and patient, so I stuck with it.

"Hmmm. How wide an area reported the sonic booms? They would have been intense with that sort of hypersonic flight at such a low altitude." (These days, we hear the shuttle's peculiar sonic boom when it returns to Earth over an area of many hundreds of square miles. I have as a witness that is. Only NASA's incident reporting line knows how big an area it is overall.)

"Sonic booms?" he said. "There were none reported. My God, they've got a way to control the formation of sonic booms! What do you think? A force field moving the air around the vessel? Could they..." What I thought... well, I think I remembered we had a launch in three days and I would have to get back to work.

Some arguments can't be won. Each impossibility demonstrated becomes evidence of greater fictional conspiracies, or corporate incompetence, or simply voodoo-like behavior from physical systems ill-understood by most people.

Notwithstanding that truism...

I have a little more time tonight, so I can take a few minutes to treat this as a puzzle. How to illustrate an interesting engineering problem. Only for those who believe in physics of course. Absent that, anything is possible.

Let's picture one of the front stub axles of that Prius or the rear stub axle of my P-car. Also known as the half-shaft in each case. (Well, I assume a Prius has independent suspension. It changes nothing but the language we use, so stick with me in any case.) Now picture one of those stub axles. It is a metal shaft with a wheel and some rubber bits we can ignore bolted onto one end. On the other end, we have a complex differential nobody ever understands anyway, so we'll ignore it and look at the other end of the drive train. There we have a viscous connection to a source of torque. (I actually have looked up the torque of that electric motor and it's pretty feeble, but we have bigger fish to fry, so we'll move on.)

For our thought experiment, let's picture a straight shaft with a fluid connection to a source of torque on one end, and on the other a source of torque acting to slow the shaft: the disk brake.

Can we assess the strength of those sources? Well, getting actual torque figures at the shaft is pretty messy calculating. Whether you're trying to go from the engine performance down to the wheel or from wheel torque back to the engine. Just listen to guys arguing about dynamometer results some time. So let's keep this simple. We only care about change of motion. About acceleration and deceleration of the vehicle. We know there is a direct linear relationship between the torque delivered to that end, the one down there with the wheel, and the thrust that results where the tire's contact patch lies on the road. And we know that absent violent wheel spin and axle hopping the achieved acceleration in feet per second per second has a linear relationship with that thrust. I think we can ignore wheel spin and axle hop with a Prius and we'll choose to ignore it for the Porsche since I'm just keeping it around to have a fun comparison. (Since I drive that particular Porsche and this essay, I am entitled to grab my fun where I find it. So there.)

A Prius will accelerate from zero to sixty in 9.8 seconds according to Toyota. In an interesting symmetry, my Porsche will reach 100 mph in slightly less than that according to Car and Driver: 9.4 seconds. In fact, we all know the Prius won't keep that up. Somewhere between ninety and a hundred the thrust resulting from the torque that can be delivered by the IC engine and the electric motor declines until it is matched by the combination of drive train friction and atmospheric drag. We will skip an interesting sidebar about the relationship between the torque characteristics of electric motors and internal combustion engines, and the efficiency of disk brakes. Let's soldier on. (i.e. It didn't entertain me. I'm still driving. The bottom line was that we are being very optimistic about the engine/motor here and pessimistic about the brake performance.)

Giving the news accounts and that hyper Prius the benefit of the doubt, we'll use 94 mph. Up to sixty, that Toyota value is enough torque to create 9 fps squared on average or about 0.3g. The Porsche manages 15.6 fpss or 0.5g. Mind you, the Prius is being averaged over its best case starting region. We're averaging the P-car clear up to a hundred. That is misleading, albeit fun. Mostly I did it because the first thirty mph in a Porsche is a region of great wheel spin, so the data are highly variable. Time to 100 makes a more reliable indicator. At any given speed the P-car actually will deliver more than twice the acceleration of the Prius.

So without converting to footpounds, there we have a number for the torque that the engine/motor combination can deliver: Enough to produce 0.3g.

How about the brakes? Well, the Prius manages 0.89g according to Car and Driver. That will vary of course, but it is very likely tire limited, as are almost all cars, so any representative number will do for our purposes. If it were otherwise, C&D would have been howling about the terrible brakes on this car. "We can't get the ABS to engage!" they would scream. Those brakes aren't great, but neither are they terrible for its performance class. What all this means is that the capacity of the disk brake has not been reached in a normal road test stopping exercise. The anti-lock system watches for incipient lock-up of the tire and backs off on the pressure. If we increase the tire's traction somehow, then the disk brake will provide more torque, but we have no data from a single road test that tells us how much more. Conversely, suppose some source of opposing torque were put on the shaft, that would keep the disk from delivering the torque to the tire that it normally would at that same hydraulic pressure. In such a case, the ABS would let the pressure increase until eventually tire lock-up was approached or the hydraulic capability of the system was reached. Again, we have no data.

So we'll use this value of 0.89g knowing that it understates the performance of the brake itself. The Porsche manages 1.06g. Same caveats. And we as enthusiasts obviously look for other traits in our brakes, but they don't affect this problem either so we'll ignore them too.

So, here we are. Let's suppose that shaft in our problem has to do some work by decelerating that rubber thingie on one end while the inertia of a 3000 lb car is trying to keep it rotating. At 94 mph, the tire is rotating at roughly 1250 rpm. Actually, 1265 for the Prius and 1217 for the Porsche, but we aren't counting. How long will it take to bring that down to zero rpm? Several people have pointed out that getting it down to around 150 rpm would be fine. That's a road speed at which even a Prius could make a u-turn, so stuck throttles become just an interesting story. Lots of options. Point it into a big Oleander bush and call a tow truck. But we'll go all the way to zero rpm for neatness.

In normal operations, the Prius needs 334 feet to do that from 94 mph. It is wildly optimistic to say it can reach that speed, but if one did, the brakes would slow it down even better than they do at the speeds C&D tested, so it would be a shorter stopping distance, but we'll stack the odds against the brakes to make sure we get a correct answer. Leave it at 0.89 g. The P-car needs 280 feet or a short wedge shot from 94 mph.


Now let's go to a stuck throttle. The Prius engine/motor combination produced enough torque to achieve 0.3 g. That shaft is in fact one type of analog computer. (Yeah. I'm that old. [sigh] We used them for spacecraft simulators at one time.) And this is a simple subtraction problem. If we can produce .89 g in one direction, and we apply a force generating 0.30 g in the opposite direction, the answer is simple arithmetic. Our shaft now produces a net torque equivalent to 0.59 g in the original direction. So the net braking thrust is that value, and it gives the Prius a 94 to zero stopping time of 7.07 seconds for a distance of 488 feet.

It should shock no one that the greater horsepower of my Porsche will hinder braking even more if the throttle sticks and I do nothing sensible about it. It takes the P-car 7.53 seconds and 519 feet this time. Ah well, you win some and you lose some.

All this is a simplified engineering problem of course. It isn't one shaft, but four on a car. And comparing a Prius and a C2S, only two of those shafts will be driven shafts. (I decline to discuss a C4S. Too tired already.) How does all that affect our conclusion?

The front brakes get most of the pressure as someone observed. I've seen very high estimates for the split on a heavily front loaded car like Prius, but let's use a conservative number. Assume a 60/40 pressure split. Remember we're using torque equivalent values, so we're saying the deceleration thrust required of the tires is distributed 30% to each front tire, and 20% to each rear tire. The power is delivered only to the fronts however. So 30% of braking thrust able to produce 0.89 g deceleration is enough thrust at that wheel to achieve 0.27 g of the braking. Since the engine/motor combination is able to produce 0.30 g total, it can only deliver a counter-thrust good enough for 0.15 g to each front wheel. That means each front wheel will continue to deliver braking thrust enough for 0.12 g. (Simple analog computer still. I don't care how many logos you hang on it. 0.27 minus 0.15 is 0.12.) Twice that for the front wheels together.

The front wheel brakes combined will overpower the engine/motor by a net braking thrust sufficient for 0.24 g. Meanwhile the rear tires will produce at least the same decelerating thrust, so they'll provide their 40% of 0.89 as before, or 0.36 g. Adding the contribution of all four wheels, the net deceleration will be 0.6 g. With a slight rounding error, that provides a check because it matches the overall numbers 0.89 g braking reduced by 0.30 g of acceleration thrust.

I said at least the same decelerating thrust because with the net deceleration reduced to 0.6 the weight transfer will be less and the rears will have more effective load pressing them to the ground. With a four-channel ABS, or a two-channel system split front/rear, they will receive more brake pressure to their calipers and therefore provide more retarding force. But again, I don't know the Prius system design so we will be conservative and ignore that possible improvement in brake performance.

Before we leave the Prius, let me note in passing that this answers another question someone asked: "But will there be time?" Yes. There will. 488 feet is less than half the length of a California off ramp. Much less. That gives you time to enter the off-ramp like a Porsche driver without backing off early (at 94 mph for all love), notice the car doesn't slow when you do back off, and panic for a full six seconds before finally stomping the brakes. Which is what is taught these days I hear: "Stomp and steer." Very inelegant, but effective in this case. How six seconds? Well, an off ramp is 1320 feet. Deduct stopping distance and you have 832 feet beforehand to think. 94 mph is 138 feet per second, ergo you have six seconds. Even a Prius driver should manage to find the left pedal in that length of time. If he wants to.

And another question that was asked: "Will it be too much time?" That is, will it take long enough to stop the car that brake fade makes it impossible to finish stopping? Without actual testing I will not assert that Prius brakes are good enough to make that stop without some fade, but 7.07 seconds is not very long to apply a modern disk brake. They certainly will heat, as they must to reach their full braking force, but applied properly they should not heat beyond that range in a single stop of this type. There is a relevant standard for U.S. cars that would tell us, but I can't remember the values it specifies as minimum performance. Maybe someone else does.

I mentioned once before how easy it is to fake disk failure by simply applying light pressure. This causes the pad to drag on the disk and heat until it glazes. Along the way it may well catch fire as volatiles boil out of the pad material. I managed that once in a demonstration. None of that has anything to do with stopping cars, just abusing brakes for the entertainment value or for purposes of fraud. Flaming brakes may be relevant to some news stories, but not our engineering puzzle.

My Porsche is more interesting. Or at least a hypothetical Porsche like mine. I decline to even picture treating mine this way. Since the rear axles only receive an assumed 40% of the braking pressure, they can be overwhelmed by an S engine if it is near its torque peak. I don't propose to investigate the driveline in more detail tonight, but basically you might well be spinning the rear tires while in full ABS braking mode on the fronts. You would of course stop, since there will still be a net 0.56 g of braking thrust, but you might end up rotating as you do, unless PSM manages to balance things.

I seriously doubt the dynamics work out that way, but I grant it's an interesting idea and it would be fun to watch someone demonstrate what happens. Maybe someone can sell The Mythbusters on trying it. With their Carrera, not mine.

Gary

richc

This Toyota mess is going to make a few Congressmen a lot of money.

wwest

Analog computers....Applied Dynamics AD-4 or AD-5, or their NJ competition...?

Now add ABS and the lack of regenerative braking to the equation...

Doesn't the Prius use ELECTRIC for power brake boost...??

"....You would of course stop,..."

How can you be certain of that...??

With the rear wheels spinning, "driving" furiously, what limit might ABS put on the declining rotation rate of the front wheels....??

Meanwhile I'll go out and disconnect the brake light switch on our 1st gen Prius.

Fahrer

I could not help but notice that the guy who reported his problem with his Prius was wearing a Corvette Club jacket in one of the news interviews. Hmmmm......I wonder if he knows how to control a car at high speeds?

Mike in CA

Factors contributing to Toyota unintended acceleration/braking problems:

Genuine mechanical/design issues 30%
User stupidity 60%
Media hype and political opportunism 10%
Government/GM conspiracy (really?) 0%

alexb76

LOL!!!!

Priceless... exactly what I wanted to tell the runaway driver!

Silver lining of all this for Toyota, they will lose all the idiot drivers to Kia and Hyundai, and get more smarter buyer/drivers, which means they lose a lot of sales in the US!

Da Hapa

My guess is that it's actually more like :
Genuine mechanical/design issues 1%
User stupidity 70%
Media hype and political opportunism 29%
Government/GM conspiracy (really?) 0%

Parts fail.. Designs aren't perfect. Big companies get arrogant and try and hide their mistakes. So I don't for one second think it's impossible that a very small % of these folks actually encountered some issue. But I think those issues were very, very, very few and far between.

swajames

+1, I absolutely agree on all points and also your percentage estimates.

wwest

Puzzling...in a way...

How many people died in that airplane crash in upstate NY last winter, 50..??

Just because the idiot pilot reacted the wrong way, pulled back on the "stick", when the stall warning went off. Why not have a system that PREVENTS an idiot pilot from taking the wrong action in a PANIC situation.

How many times must you put a pilot through this scenario in a flight simulator before his natural survival instincts have been retrained to react more properly..??

Clearly not enough in that case.

alexb76

Are you seriously continuing to argue your point??? that is absolutely flawed in so many ways I don't even wanna take the time to respond to!

How in the world a guy who couldn't stop the car with regular service brakes, did it with e-brake?!?! Like in FWD cars, the e-brake on the rear works better than service brakes?!

Sometimes you gotto admit your THEORY is just wrong and learn from some people who know what they're talking about based on pure engineering and physics.

This guy was either absolutely the most stupid driver in the states, or is totally lying about the whole runaway sitation, there's absolutely no question about it at all after looking at all the facts!

Mike in CA

We can quibble over details but I think we agree on the main points; user stupidity...big factor
conspiracy.......no factor

wwest

"..based on pure engineering and physics.."

And what I have been saying that is somehow adverse to those tenants...?

The front brakes were unquestionally compromised because they had to not only overcome the normal inertial effects of >3000lbs moving at 70MPH but had to work against the HSD system DRIVE torque. And the rear braking effects may have been compromised by ABS.

So how long before the brake pads are so heated that they have no frictional coefficient against the rotors...?? Or even BOIL the brake fluid..??

In my opinion there is no way to know the truth of this matter unless someone disables the "BTO" (disconnect the brake light switch and the brake fluid pressure sensor), puts the gas pedal at WOT, accelerates to >70 and then tries to see how well the brakes work to stop the car.

alexb76

Everything! Just as Gary said, it's like arguing against gravity

Which has been tested and proven in much more powerful cars as Kevin posted with brakes having a lot more torque than engine.

utkinpol

Well, I always wondered - in those 'runaway' cars, cannot those people just turn ignition key off? Or does it get stuck in 'on' position together with gas pedal?

But, who knows. May be it is an alien conspiracy after all.