Competition Math can be fun.

[Rebel Ram]

I have a question for the racing number crunchers. With one G (the force of gravity) = 32 feet per second, per second. You were to pull exactly one G for the distance of a quarter mile, what would your speed be at the trap?

 

[drury]

If I did the math right, you would be going about 198. 2mph, and your ET would be 9. 08 seconds.



The basic formulas are:

distance = 1/2 * acceleration * time^2

1/4mile = 1320 feet = 1/2 * 32 ft/sec^2 * ET^2

ET = square root(1320 feet * 2 / 32) = 9. 08 seconds



velocity = acceleration * time = 32 ft/sec^2 * 9. 08 sec = 290. 65 ft/sec = 198. 2 mph

 

[Rebel Ram]

You see there? Wasn't that fun? Anyway,,, I was watching TV and this cheesy Lexus commercial shows a new xyz/q (whatever) model out accelerating another car dropped from a hight equal to the distance driven to the same spot and beating it in the nick of time and avoiding getting squashed. So who believes that a luxury sedan can do a 9 second quarter mile?

 

[Dockboy]

Download and save this little application



http://home.comcast.net/~gdapron/draguess.exe



It will estimate your 60' G-force



here is mine:



You Input: 1/8 mile = 7. 588 1/4 mile = 11. 889



Here are my ESTIMATES:





-----------------------------------------------------

: Distance : Calc Time : Instant MPH : Trap MPH :

-----------------------------------------------------

: 60 ft : 1. 74 : 39. 1 : :

: 330 ft : 4. 89 : 73. 1 : :

: 1/8 mi : 7. 59 : 92. 2 : 90. 7 :

: 1000 ft : 9. 92 : 105. 6 : :

: 1/4 mi : 11. 89 : 115. 5 : 114. 6 :

------------------------------------------------------



---------------------------------------------------------------------------

: 0-15 : 0-30 : 0-45 : 0-60 : 0-75 : 0-90 : 0-100 : 0-110 : 0-125 : 0-140 :

---------------------------------------------------------------------------

: 0. 49 : 1. 19 : 2. 15 : 3. 44 : 5. 1 : 7. 2 : 8. 9 : 10. 8 : 0. 0 : 0. 0 :

---------------------------------------------------------------------------



G-Force at 60 MPH = 0. 47 1/4 to 1/8 Ratio = 1. 57



Again (Y/N)?

 

[GFritsch]

Doesn't the car in the commercial have a running start?



130 mph / 60 minutes = 2. 17 miles a minute

2. 17 miles a minute / 60 seconds = . 036 miles a second.

. 25 miles / . 036 miles a second = 6. 94 sec quarter mile.



Even at 100 mph that's around a 9 second quarter mile. With a running start the car would have to be traveling at 100mph or better to beat the falling car covering the same distance if Drury is correct with his 9 second figure. (My math is not good enough to check him :-laf )

 

[E7mack96]

I came up with less than 7 secs to travel 1320 feet. 1320 feet = 402. 33 meters. Force of gravity is 9. 8 Meters/sec/sec. To maintain a constant 1 g of acceleration, it would equate to a 6. 41 sec quarter mile.



9. 8 * 6. 41 * 6. 41 = 402. 66 meters



This is going to mean your speed is much higher

 

[GFritsch]

I came up with less than 7 secs to travel 1320 feet. 1320 feet = 402. 33 meters. Force of gravity is 9. 8 Meters/sec/sec. To maintain a constant 1 g of acceleration, it would equate to a 6. 41 sec quarter mile.



9. 8 * 6. 41 * 6. 41 = 402. 66 meters



This is going to mean your speed is much higher

Roughly 140mph to achieve 6. 41 sec quarter mile with a flying start. Can't remeber what car is in the commercial, but if it is a high powered car with a high governed limit, 140 is not out of the question. (of course one would have to read the fine print on the commercial that only appears for a second and is too small to read) :-laf As I will be in a vegitative state watching football all day, I will keep my eye out for the car, flying start, etc. .

 

[E7mack96]

My post was meant as a reply to the first post only. The flying start stuff is a whole different animal.

 

[E7mack96]

Also, the ET of 6. 41 sec and the speed of approx 140 mph, is from a standing start.



In that commercial, the car falling from 1/4 mile in the sky does hit "terminal velocity" due to wind resistance and probably did not hit the ground at 140 mph.



The car on the ground launching from a standing start is not gonna run a 6. 21 sec 1/4 mile. a 12 sec 1/4 is unlikely too.



As a side note, has anyone seen the program the showed you can beat a red-light camera by doing 170 MPH (like thats gonna happen) It didn't even detect the car. at lesser speeds (140ish) the red-light camera detected you, and you were still close enough for the 2nd flash to get your plate #

 

[drury]

I'm sure Lexus doesn't make a car that can do a 9 second quarter mile, but acceleration in the quarter mile is not constant. It drops off drastically as you shift gears and as your speed picks up and wind resistance becomes a factor. Dockboy pulled 1. 57 G running an 11. 9 sec quarter mile, and it is quite easy to believe that Lexus can make a stock car that could pull a little over 1 G for this distance shown in the commercial. We have a Lexus RX330, and it's one of my alltime favorite cars. It's just the right mix of zippy, luxury, easy to maneuver in traffic, easy to park, & affordable. When I bought it, the only SUV's that came close were the BMW X5 (20-30K more $$$), the Nissan FX45 (poor ergonomics & build quality), and Porsche Cayenne (ridiculous $$$). It won't keep up with my MegaCab though