Help with car maths

I'm trying to solve a question for autocross (when you should downshift into 1st if there is a real slow corner using a basic spreadsheet.

The situation, you come out of a slow corner at 20 mph either in 1st or second gear, and accelerate for a given length, lets say 500 feet. I'd like to run the calcs once for starting in 1st gear then shifting, and once for just doing the whole thing in 2nd.

At one time I considered myself good at math, heck I'm a professional engineer. however there is something I'm missing because my numbers don't make any sense. Someone smarter than me help me out.

I'm trying to do this with my dad's s2000, and ignoring aero and wheel slip.

the force to the ground = (engine torque X gear ratio X rear end ratio)/tire radius

for the s2000, torque is right at 120 ft lbs up to 6000, then jumps to about 140 first gear is 3.133 and the combined rear end and secondary reduction is 4.95 with a 26 inch diameter tire

so force = 120 ft/lbs X 3.133 X 4.95 / 13/12 = 1718 lbs

F = MA so A = F/M so 1718/2800 = .614 ft/sec^2

Isn't this really low? an s2000 should hit 60 in around 5 seconds. that's 88.2 feet per second. accelerating at less than 1 ft/sec.

What the heck am I doing wrong here?

What is the radius of the tire in feet?

Have you read this from the Megasquirt guy: http://www.bgsoflex.com/shifter.html

radius is 13 inches. 26 inch tire. so 13/12 = 1.0833

Nope, but I'll read it now.

I think you forgot gravity. Weight of car is lbm which is 32.2*lbf. Need to multiply torque by 32.2 to get same units? Gives 20ft-s^2 which would give theoretical 4.5 sec 0-60. But this may be way off. Been a while since I played with acceleration but remember this biting me constantly on PE to KE problems.

the biggest reason for NOT downshifting is A) the time involved (downshifting isn't the problem here, as you're braking anyway) but you do lose time/forward G's when you upshift … and B) if you're not accustomed to shifting (i.e. road racing) then you can easily have timing issues with the shift, and C) if you don't have a LSD you lose a lot of forward G's while your unloaded tire is spinning uselessly and the loaded tire is not doing much

I get all of that, but at some point it would make sense to downshift. If you come out of the corner at 10, 5 mph? at some point you would need to, I just need to figure out when

It always FEELs faster to grab 1st gear coming out of a tight turn. The timer rarely confirms this.

wbjones wrote: the biggest reason for NOT downshifting is A) the time involved (downshifting isn't the problem here, as you're braking anyway) but you do lose time/forward G's when you upshift … and B) if you're not accustomed to shifting (i.e. road racing) then you can easily have timing issues with the shift, and C) if you don't have a LSD you lose a lot of forward G's while your unloaded tire is spinning uselessly and the loaded tire is not doing much

icaneat50eggs wrote: I get all of that, but at some point it would make sense to downshift. If you come out of the corner at 10, 5 mph? at some point you would need to, I just need to figure out when

trucke wrote: It always FEELs faster to grab 1st gear coming out of a tight turn. The timer rarely confirms this.

what trucke said … by all means try it … let the stop watch dictate what you do … we used to have an autoX on the city streets here, and of course it always had a pin cone (basically a 5 lane steer) but even there I'm betting I wasn't going as slow as 5 mph

but like I said, try it and let the stop watch be your guide

icaneat50eggs wrote: I'm trying to do this with my dad's s2000, and ignoring aero and wheel slip. the force to the ground = (engine torque X gear ratio X rear end ratio)/tire radius for the s2000, torque is right at 120 ft lbs up to 6000, then jumps to about 140 first gear is 3.133 and the combined rear end and secondary reduction is 4.95 with a 26 inch diameter tire so force = 120 ft/lbs X 3.133 X 4.95 / 13/12 = 1718 lbs F = MA so A = F/M so 1718/2800 = .614 ft/sec^2 Isn't this really low? an s2000 should hit 60 in around 5 seconds. that's 88.2 feet per second. accelerating at less than 1 ft/sec. What the heck am I doing wrong here?

6k seems like a really short shift for an S2k, no? I would think you would need to account for going all the way to redline. That, and you would have to shift before you got to 60, so you'd have to do two sets of those calcs, one for first up to redline and one for the time you spend in second, and then add in the dead time for the shift.

The above would then need to be compared with the acceleration you get by leaving it in second for the entire length of the straight coming out of the corner, to see where your breakeven is in terms of length of the straight after corner exit.

nocones wrote: I think you forgot gravity. Weight of car is lbm which is 32.2*lbf. Need to multiply torque by 32.2 to get same units? Gives 20ft-s^2 which would give theoretical 4.5 sec 0-60. But this may be way off. Been a while since I played with acceleration but remember this biting me constantly on PE to KE problems.

This. Do a units analysis, your 0.614 came out in units of lbf / lbm, which doesn't jive. Need to use mass in slugs for English unit equations.

Frankly all of this is easier in metric units.

MattGent wrote: Frankly all of this is easier in metric units.

This. Also its easier if you use power instead of torque.

Accel = [net power]/(mass * velocity)