Car Engine Problem: Acceleration Function of RPMs

[krab]

My car has 82 ft-lbs torque at 7000 rpm. Let's trace that through:
At the crank:

torque= 82 ft-lbs, rotation speed= 7000 rpm, power= 109 hp

Gear ratio reduction in first gear = 3.166, so

After the transmission:

torque= 260 ft-lbs, rotation speed = 2211 rpm, power= 109 hp

Gear reduction through differential to wheel axle = 4.313, so

At axle:

torque= 1120 ft-lbs, rotation speed = 512 rpm, power= 109 hp

Notice the torque is not conserved? It is 82, then 260, then 1120. Notice the power is the same throughout? Of course there are frictional losses, so a few % of the power is lost. Maybe there is only 100hp at the rear wheel. But then there is a similar 8% reduction in torque at the rear wheel to 1027 ft-lbs.

 

[shyboy]

That's right, but some crude equations could be helpful
Let's assume that the energy is conserving, so power on the gears is conserving.
Let's imagine gears as ideal cyliders. Then power at any given moment

$$P=F\times v=F\times \omega \times r=T \times \omega$$

here F is a force and T is a torque. Now, if we increase the rotational frequency, we lose torque and vise versa.

 

[whozum]

Ok, can we fit this thread into the data on this one: https://www.physicsforums.com/showthread.php?t=71727 ?

 

[whozum]

I have more detailed numbers if you wish
Times at
60'
330'
1/8mi
1000'
1/4mi
final speed, speed at 1/8mi

 

[krab]

Does 3560 lbs include driver?

I find for avg. of 100hp: 1/4mile time=17.66s, trap speed=78.5mph, top speed=107.6mph, 0-60time=9.9s, 60ft time=3.1s, 1/8mile time=11.4s, speed=64.4mph.

 

[whozum]

Sorry, the actual car weight is 2500 lbs, and I weigh 160lbs, plus an ambient 10-15 lbs for other stuff. These calculations, can you elaborate/

 

[krab]

Sorry, the actual car weight is 2500 lbs, and I weigh 160lbs, plus an ambient 10-15 lbs for other stuff. These calculations, can you elaborate/

That changes things a lot. I'm sorry to have to tell you you are only getting an average of about 80hp to the ground. The formula I use is in a previous post in this thread. Do you know your top speed? If you do, I can make the calculations more accurate. Right now I'm just guessing on air resistance.

 

[whozum]

My trapspeed was 77mph, the highest I've ever gotten it to was 115.

I know my car sucks, but can you show the method used to get to that answer?

 

[krab]

Here is the code, written for a Matlab-like program. To understand it, you need to know that variables like x and v (in feet and feet/sec) are vectors. The formula for v comes from a straight-forward integration of the differential equation in post #28. Then the time vector t is found from a numerical integration of dx/v.

! b is the air resistance coefficient; it is about 0.013
! for cars, about 0.0055 for motorcycles
b=?4
! ?1 is power in hp. p is power in ft.-lbs./sec.
p=?1*550
vinf=(p/b)^(1/3)
! ?2 is weight in pounds of vehicle (don't forget the fat driver)
m=?2/32
! ?3 is initial acceleration g's. This may be limited by traction or
! in any other case is given by first gear ratio.
v1=p/?2/?3
x1=v1^2/64/?3
t1=v1/32/?3
x=[(x1+.5):1319.5]
v=vinf*(1-(1-(v1/vinf)^3)*exp(-3*b*(x-x1)/m))^(1/3)
iv=1/v
ttt=t1+integral(x,iv)
generate tf 0 ,, t1 100
xf=16*?3*tf^2
display `1/4 mile:'
=ttt[#] !seconds
=v[#]*30/44 !mph
display `top speed:'
=vinf*30/44 !mph
vout[1]=88
display `0-60:'
=interp(v,ttt,vout)
display `60 ft time:'
=sqrt(120/?3/32)

 

[whozum]

I meant from a physics perspective, rather than a computational. Sorry, that just looks like a bunch of garbage to me, because I don't know MATLAB syntax.