Physics/math in car commercial

[aktep]

@fiddlesticks

I noticed when I saw this commercial during the football games yesterday (the single commercial that wasn’t the rock-em-sock-em robots commercial) that there was fine print at the bottom of the ad saying something to the effect that the “falling car is simulated”. So, no, they did not.

It says “Aerial sequence simulated” which could plausibly mean that just the shots of the call falling, shown from above, are fake.

[zut]

@Sapo

I think the important thing is that it is plausible. That the time it would take for the car to run that distance at top speed is less than what it would take it to free fall that same distance.

I scrounged up my spreadsheet. Assuming this Lexus is the vehicle, I’m using a weight of 3748 pounds, an area of 79 square feet (60 by 190 inches), and a drag coefficient of 1.1, which is just my best guess.

With that, the terminal velocity is about 193 ft/sec (132 mph) and the time to fall 4000 feet is about 24.7 sec. That’s an average speed of 161 ft/sec, or 110 mph. The shape of the curve:

**Time    Vel. Height**
0.0     0mph 4000ft
1.0    22mph 3983ft
2.0    42mph 3933ft
3.0    61mph 3855ft
4.0    77mph 3753ft
5.0    90mph 3629ft
6.0   101mph 3487ft
7.0   109mph 3333ft
8.0   115mph 3168ft
9.0   120mph 2995ft
10.0  123mph 2817ft
11.0  126mph 2653ft
12.0  127mph 2448ft
13.0  129mph 2261ft
14.0  130mph 2071ft
15.0  130mph 1881ft
16.0  131mph 1689ft
17.0  131mph 1497ft
18.0  131mph 1305ft
19.0  131mph 1112ft
20.0  132mph  919ft
21.0  132mph  726ft
22.0  132mph  533ft
23.0  132mph  340ft
24.0  132mph  146ft
24.7  132mph    0ft

Note terminal velocity is approached rather quickly.

(To head off certain objections: this is not to say the vehicle drop was actually performed. But examining the underlying plausibility is still worthwhile.)

[JeffB]

So this commercial demonstrates that this Lexus can go 110 mph? Not very impressive.

[Chronos]

So this commercial demonstrates that this Lexus can go 110 mph? Not very impressive.

It’s even worse than that, I think. Why did they pick 4000 feet, specifically? They would have gotten more impressive results with a higher drop. And if they could have gotten more impressive results, they would have. Therefore, I think we can actually conclude that this Lexus can only go 110 mph.

[Ludovic]

@robby

You’d need a coefficient of friction between the tires and the road of greater than one. One of those rocket or jet engine cars should be able to do it, though.

I wonder what the coefficient of friction on airplane wheels is…

[Chronos]

I wonder what the coefficient of friction on airplane wheels is…

Irrelevant. And that’s all I’ll say, and all anyone should say, on that topic.

[DSYoungEsq]

@Chronos

Irrelevant. And that’s all I’ll say, and all anyone should say, on that topic.

Come now, we know that they built the runway to be able to go backward as fast as … <ducking and running>

[iamthewalrus_3]

@robby

I wonder if a car that can accelerate at greater than g is even possible. I don’t believe that it is. You’d need a coefficient of friction between the tires and the road of greater than one. One of those rocket or jet engine cars should be able to do it, though.

As has been pointed out, it’s quite possible. Not only is it possible to get a coefficient of friction greater than one, it’s also not necessary. Those really fast cars have serious wings on the top to push them into the ground, which makes the normal force much more than g.

[Sapo]

what’s the acceleration (in g’s) of a top fuel dragster? anyone?

[MrFloppy]

yabob in post #9 says 3g and points to a wiki article that suggests 5g.

According to this semi-infamous posting, it is closer to 8g.

[MrFloppy]

Upon further review…That link seems to have incorrect info as notes at the bottom of the page indicate.

Apparently though, pulling the chutes causes a deceleration of 5gs.

[yabob]

@MrFloppy

yabob in post #9 says 3g and points to a wiki article that suggests 5g.

According to this semi-infamous posting, it is closer to 8g.

The 3 g was averaged for the entire 1/4 mile run. The wiki article suggests 5 g during the initial part of the run, which I can believe.

Here’s a picture of one with a few stats underneath, including “4.5 G’s”:

http://www.toddpaton.com/2004car.htm

[yabob]

And the wiki article figure of 0 to 100 in 0.8 seconds is actually closer to six (5.7).

[Rick]

@MrFloppy

Upon further review…That link seems to have incorrect info as notes at the bottom of the page indicate.

Apparently though, pulling the chutes causes a deceleration of 5gs.

From the bottom of your link

I’ve seen the data from a fueler that is a perennial championship
contender and can say that their launch g’s are between 4.5-5 g’s and do
not diminish to less than 2 g’s throughout the run. The highest
g-loading on the driver, however, is not on the launch. It is when they
pull the chutes. They were traveling at 2 g’s forward and then see 5 g’
s backward so their body sees a 7 g jolt that persists for a few
seconds. This helps to explain why Kenny Bernstein always seems to be
barely able to breath when they interview him after a run… Quite a
few funny car guys have found out the hard way that the belts weren’t
done up tight enough, including Ron Capps who almost went through his
windshield after pulling the chutes on a run. Other racers have had
detached retinas from a harsh parachute opening.

To go 250 MPH at half track (660 feet) from a standing start you would
need to pull a constant 3.16 g’s. No where near 8 g’s… If you
accelerated at a constant 4 g’s (88 MPH/sec) you would be doing 396 MPH
in 4.5 seconds (at the finish line) which would give a trap speed well
over the 330 MPH region that is currently measured.

By the way, at the launch of the car, there is no downforce other than
the vehicle weight. Plant all of it on the back tires and have a
coefficient of friction between the tires and the road of 1.0 and it
will accelerate at up to 1.0 g before breaking the tires loose if the
engine power, etc, is there. (It was the belief that you could not have
a coefficient of friction greater than 1.0 that had physicists claiming
that you could not exceed 200 MPH in the quarter mile. How wrong they
were…) By the same corollary, you can figure out the coefficient of
friction of the start line by the amount of g’s you pull… (Top Fuel
slicks and traction enhancer are good for a coefficient of friction of
4.5-5. The stuff left at the starting line almost pulls your shoes off
you feet when you walk on it…)

So yes, you can pull 1G+ at the start line.

[Chronos]

(It was the belief that you could not have
a coefficient of friction greater than 1.0 that had physicists claiming
that you could not exceed 200 MPH in the quarter mile. How wrong they
were…)

Certainly, mu > 1.0 is uncommon and remarkable, but was it ever actually considered impossible? I’ve a hunch you could even find some pair of ancient materials which would do better than that.

[Sapo]

I am thinking of a rack and pinion and see no reason why they couldn’t accelerate at any insane rate you could mechanically create. Once you consider that the rubber is actually bonding with the pavement, well, the sky is the limit, I guess.

Are there any “real” cars that can put 1g at a traffic light? I think I remember a friend bragging that his Susuki GSX-750R could do just that (and this was a few years ago).